A METHOD OF SELECTING OPTICAL MATERIALS

Abstract: A method is described for selecting optical materials to use in designing color-corrected optical systems. Various dioptric, catadioptric and anamorphic optical systems are described, which use only two different types of optical materials to obtain precise axial color correction at three, four or five wavelengths (depending upon the particular optical materials), with only very small chromatic aberration ocurring at wavelengths between the precisely color-­ corrected wavelengths. Examples of color-corrected lens systems comprising more than two glasses are also de­ scribed.

Description: COLOR-CORRECTED OPTICAL SYSTEMS TECHNICAL FIELD This invention relates generally to color-corrected optical systems. More particularly, this invention pertains to the selection of optical materials for designing optical systems that are color-corrected at more than two wavelengths. BACKGROUND ART The optical region of the electromagnetic spectrum is generally understood to extend from the far ultraviolet wavelengths (about 0.36 um) to the near infrared wavelengths (about 1.10 vim). The selection of optical glasses for designing lens systems that are color-corrected at more than two wavelengths in the optical reaion has been discussed by a number of investigators, including: (a) N.v.d.W. Leasing, J. Opt. Soc. Am. 47, 955 (1957) (b) N.v.d.W. Lessing, J. Opt. Soc. Am. 48, 269 (1958) (c) N.v.d.W. Leasing, Appl. Opt. 9, 1665 (1970) (d) R. E. Stephens, J. Opt. Soc. Am. 49, 398 (1959) (e) R. E. Stephens, J. Opt. Soc. Am. 50, 1016 (1960) (f) M. Herzberaer, Optica Acta 6, 197 (1959) (9) M. Herzberger and N. R. McClure, Appl. Opt. 2, 553 (1963) (h) M. Herzberaer, Optik 35, 1 (1972) (i) H. Drucks, Optik 23, 523 (1966) (j) H. Schulz, Optik 25, 203 (1967) (k) H. Schulz, Optik 25, 208 (1967) (1) H. Pulvermacher, Optik 30, 297 (1969) (m) H. Pulvermacher, Optik 30, 396 (1970) (n) M. Herzberaer and H. Pulvermacher, Optica Acta 17, 349 (1970) (o) B. L. Nefedov, Sov. J. Opt. Technol. 40, 46 (1973) (p) A. B. Agurok, Sov. J. Opt. Technol. 44, 114 (1977) (q) M. G. Shpyakin, Sov. J. Opt. Technol. 45, 81 (1978) (r) M. G. Shpyakin, Sov. 0. Ont. Technol. 45, 219 (1978) (s) G. A. Mozharov, Sov. J. ODt. Technol. 44, 146 (1977) (t) G. A. Mozharav, Sov. J. ODt. Technol. 47, 398 (1980). An optical "multiplet" is an optical system comprising a number (designated generally herein by k) of refracting elements made of a number (desiqnated generally herein by q) of different optical materials, where each refractina element is made entirely of a particular optical material, with the various refracting elements in combination providina color correction at a number (designated generally herein by n) of wavelengths. The refracting elements could be configured as lens elements, prism elements, or anamorphic elements, depending upon the nature of the optical system. The term "color correction" as used herein with respect to dioptric and catadioptric systems means correction of axial chromatic aberration. Thus, to say that a lens system or a Manain mirror system is color-corrected at n wavelengths means that n wavelenaths are brouaht to a common focus on the optic axis of the system. For a prism system, "color correction" means correction of chromatic dispersion -from the total deviation angle of the system. Various combinations of optical alasses were discovered in the prior art for desianina lens systems that brina more than two wavelengths to a common focus. Previous lens systems, which were color-corrected at more than two wavelenaths, generally required three or more different types of optical glasses for making three or more lens elements. There was little success in the prior art in identifying suitable pairs of optical glasses for designina lens doublets (i.e., lens systems comprising only two lens elements) capable of brinaing more than two wavelengths to a common focus. U.S. Patent 3,395,962 to Herzhereer, et al. described a photographic objective comprisina three lens triplets, with each triplet beina individually color-corrected at four wavelengths. M. Herzberaer, in reference (f) on the above list, suanested that color correction of an optical lens system at four wavelenoths is substantially equivalent to color correction for the entire spectrum bounded by the most widely separated of those four wavelengths. A lens system comprising only two lens elements, i.e., a doublet, is inherently simpler than a lens system comprising a triplet or higher-number multiplet of lens elements. In terms of fabrication cost and compatibility with constraints imposed by the practical considerations involved in designina optical instruments, a lens doublet that is color-corrected at three or more wavelenaths would ordinarily be preferable to a higher-number lens multiplet color-corrected at the same number of wavelengths. A computer-aided search to identify pairs of optical glasses suitable for desianioa lens doublets that are color-corrected at four wavelengths was made without success by R. R. Widely, Jr., as reported in Appl. Opt. 1, 368 (1962). However, WiLley did report that certain pairs of alasses can be used for designina lens doublets color-corrected at three wavelengths. An article by M. Gaj and J. Nowak in Optik 29, 321 (1969) stated that lens triplets color-corrected at three wavelengths could be designed using various pairs of glasses listed in the optical glass catalog published by GlaswerleSchott of Mainz, West Germany. However, two of the pairs of glasses identified by Gaj and Nowak were said to require an additional fluorite lens element to produce the desired color correction at three wavelengths. Gaj and Nowak did not report any design data necessary for versifying the design and for constructing lens elements made from the optical materials identified in their article. U.S. Patent 3,674,330 disclosed particular pairs of alkali halide crystals from which lens doublets that are substantially achromatic over a broad spectrum of wavelengths in the far infrared region, i.e., at wavelengths longer than 1.5 um can he designed. However, there have been no reports in the literature of any crystal pairs that can be used for desianina lens systems color-corrected at more than two wavelengths in the optical region. The 1977 article by A. B. haurok, which is reference (p) on the above list, reported on an investiaation of the glasses listed in the Russian optical glass cataloa GOST (All Union State Standard) to identify pairs of optical glasses suitable for designing lens doublets color-corrected at more than three wavelengths. The search indicated that no two alasses in the GOST catalog can be combined to make a lens doublet that is color-corrected at four wavelengths. Agurok also reported that no two glasses in the Schott catalog had been found, which in combination make a lens doublet that is color-corrected at four wavelengths. The various alaorithms that were developed in the prior art for selecting optical alasses for designing color-corrected lens systems made use of conventional glass parameters (i.e., Abbe numbers and relative partial dispersion ratios) to characterize the dispersive properties of the available types of optical glasses. The approaches taken in the prior art, however, never led to an algorithm of general validity for identifyina compatible combinations of optical materials for designing lens multiplets that bring more than two wavelengths to a common focus. Until the present invention, the problem of correcting optical systems for chromatic aberration has been one of the most difficult problems facing optical designers. A theoretically rigorous procedure for selecting compatible pairs of optical alasses for designing lens doublets that are color-corrected at more than two wavelengths has eluded previous researchers. Non-riaorous "cut-and-try" methods have failed to identify compatible pairs of optical glasses for designing lens doublets color-corrected at more than three wavelengths. C. G. Wynne, in an article entitled "Secondary Spectrum Correction with Normal Glasses", Optics Communications 21, 419 (1977), noted: "It has been generally accepted that the correction of secondary spectrum aberrations, in optical imaginq systems, neressarily requires the use of glasses having abnormal relative partial disnersions. This is . . . an error, arising from defects in the accepted theory of first order chromatic aberrations." The inability of the prior art to develop a unified theory for selecting optical materials to use in designing optical systems that are color-corrected at more than two wavelengths can be attributed to the unavailability, until now, of a tractable mathematical model for representing optical materials in terms of their dispersion characteristics. DISCLOSURE OF THE INVENTION Buchdahl's Dispersion Equation: The index of refraction (also called the refractive index) of an isotropic homogeneous optical material such as a glass, a crystal or a plastic is a function of the wavelength X of the optical energy passing through the material. Thus, when an optical material is cut and polished to make a lens element, each wavelenath (i.e., each color) is brought to a focus at a different focal position. Manufacturers of optical classes conventionally characterize each type of glass in terms of the refractive index of the class at certain specified wavelencths, viz., the wavelengths of the solar emission lines. In the cataloas published by the leadinq glass manufacturers, measured values of the refractive index of each glass are listed for the specified wavelengths. In optical design work, however, it is often necessary to know the value of the refractive index of a class at some wavelength other than those wavelengths specified in the manufacturer's catalog. The refractive index of a glass at any particular wavelength is determined by interpolation from the values given in the catalog by using a called dispersion formula. A great variety of dispersion formulae have been developed over the years to express refractive index as a function of wavelength. A collection of well-known dispersion formulae is given by W. J. Smith In Modern Optical Enaineerina, McGra--Hill Book Company, Inc., New York (1966), PP. 147-1tR. In recent Years, a power series dispersion formula derived from a quantum model has come into practically universal use among optical glass manufacturers throughout the world. This power series dispersion formula, which expresses refractive index N in terms of wavelength A measured in micrometers, is: Nê = An + A1#ê + A2#-2 + A#-4 + A#-6 + A#-8, (1) 3 4 5 where the so-called dispersion coefficients A. (j = 0, 1, 2, 3, 4, 5), 3 which are provided for each alass bv the manufacturer, are obtained by a method of numerical analysis based upon a least squares fit for measured values of the refractive index averaged over several glass melts. All major optical glass manufacturers provide these dispersion coefficients A. for each glass, so that optical designers can compute 3 the refractive index of any,optical class for any desired wavelength. A formidable obstacle to the development of a tractable mathematical model for representina any optical material in terms of its dispersion characteristics has been the lack of a dispersion formula in the form N = z anxn for predicting the refractive index N, where the coefficients an are characteristic of the particular optical material and are independent of the wavelength #, and where the variable x is a function of the wavelength, i.e., x = x(x). None of the dispersion formulae collected by Smith, op. cit., expresses refractive index in this mathematically suitable z a nx n form; and neither does the quantum model dispersion formula of equation (1). An expression for refractive index, which provided the starting point for a mathematical model that made the present invention possible, was first introduced by H. A. Buchdahl in a monograph published by Oxford University Press in 1954. This monograph was subsequently reprinted as Optical Abberration Coefficients, Dover Publications, Inc., New York (1968). Buchdahl's analysis becan with an expression for refractive index in the form N = N* + c/(s -A*), which is known as the Hartmann dispersion formula, where N*, c and x* are constants that are characteristic of the particular optical material. Buchdahl introduced a change of variable from wavelenath x to a so-called color coordinate, or chromatic coordinata, #, which allowed the refractive index to be expressed in the form N = N0 + #1# + #2#ê + #3# + ... + #n#n, (2) where No is the value of the refractive index at a selected base wavelength #0, and where the color coordinate # is defined as = $##/(1 + &alpha; ##). (3) The quantity DA is defined as the change in wavelength relative to the base wavelength, i.e., = # - # 0, (4) and the term a is a "universal'" constant that is substantially independent of the dispersion characteristics of the particular optical material. The coefficients 9s, called the dispersion coefficients, are constants characteristic of the particular optical material, and in general vary from one type of optical material to another. P. J. Sands in J. Opt. Soc. Am. 61, 777 (1971), in which he developed the theory of homogeneous lenses, discussed the accuracy of Buchdahl's dispersion formula as given in equation (2). The color coordinate w introduced in equation (2) is a function of wavelength x, and is "universal" in the sense that it does not involve characteristics of the particular optical material. Upon computing values of a for six common optical classes, Buchdahl found that the values of a lie within rather narrow bounds for wavelengths in the visible spectrum when the base wavelength #0 is chosen to be that of the sodium-D line, i.e., 0.5893 m; This suggested to Buchdahl that a could be reaarded as a "universal" constant for all glasses for wavelengths in the visible spectrum. The value of a calculated by Buchdahl was a = 2.5. Ordinarily, the optical materials used for desianin lens systems are optical glasses. For this reason, the analysis presented hereinafter usually refers to optical glasses. However, the analysis is valid for optical materials generally, and is, therefore, applicable reaardless of whether the particular optical material under consideration is a glass or some other material such as, e.a., a crystal (e.g., fluorite or quartz), or a viscous liquid (e.a., immersion oil). The change in refractive index sum as a function of change in wavelenath sx relative to the selected base wavelength AO, i.e., SN(X) = N(A) - NO, iS defined as the dispersion of the optical material at the wavelength A relative to the base wavelength A0. From equation (2), the dispersion N of an optical material can be expressed by an equation in the form cN(l 9 Y (5) i=l which will be referred to hereinafter as Buchdahl's dispersion equation. A detailed analysis of Buchdahl's dispersion equation (5) for all the various types of optical glasses listed in the latest catalogs published by five leading optical class manufacturers was undertaken by P. N. Robb and R. I. Mercado, applicants herein. The optical glass manufacturers whose cataloas were used were Schott Optical Glass, Inc., Duryea, Pennsylvania; Ohara Optical Glass Mfa. Co., Ltd., Sagamihara, Japan; Hoya Corporation, Tokyo, Japan; Cornina-France, Avon, France; and Chance Pilkington Ltd., St. Asaph, Clwyd, U.K. A total of 813 different types of optical passes were included in the analysis. An announcement of this analysis was published in an abstract in J. Opt. Soc. Am.71 (12), 1638 (1981). The power series in equation (5) converses very rapidly. The converoence was found to be so rapid that all 813 glasses studied could be mathematically modelled usina only the first three terms of the power series, with a resulting maximum absolute error of only 0.0001 in the visible spectral ranee from 0.4 vm to 0.7 um. It is noted that precision alass melts, on the other hand, can be made to a tolerance of only 40.0002. Thus, a quadratic dispersion model based upon Buchdahl's dispersion equation, i.e., a dispersion model wherein the degree of the polynomial in equation (5) is given by n - 2, can predict the refractive index of an optical glass twice as accurately as the glass can be made. It was also found that a cubic dispersion model based upon Buchdahl's dispersion'equation, i.e., a dispersion model wherein the degree of the polynomial in equation (5) is given by n = 3, can predict the refractive index of an optical qlass over an extended spectral range from 0.365 u to 1.014 um with an accuracy that is approximately equal to the accuracy that can be maintained in making precision glass melts. It is remarkable that the value of a, for which Buchdahl adopted the "universal" value of 2.5 on the basis of an analysis of only six glasses, was found to vary within the narrow range from 2.299 to 2.960, with an average value of 2.577, for a population of 813 classes. Buchdahl's value of a = 2.5 used in defining the color coordinate w in equation (3) was therefore virtually exact. Buchdahl calculated the dispersion coefficients 9j of equation (5) using refractive indices for n wavelengths in an nth-deqree Dolynomial and using a base wavelenqth of = = 0.5893 um, which is the wavelength of the yellow sodium-D line. Since equation (5) is linear in the dispersion coefficients v;, Buchdahl's procedure yields a system of n simultaneous linear equations in n unknowns. Buchdahl's procedure can be readily implemented with the aid of a computer. Values for the dispersion coefficients Vi obtained using Buchdahl's procedure were compared with a least-squares solution usinq seven wavelengths in the visible ranqe (from 0.4 um to 0.7 um) and ten wavelengths in the extended spectral range (from 0.365 um in the ultraviolet to 1.014 urn in the near infrared). It was found that the maximum error could be reduced by a factor of three or more using the least squares method. Adjustment of the least-squares weiqhts and selection of a base wavelength so as to reduce the maximum error further gave a total error reduction factor of five. R.I. Mercado and P.N. Robb announced in an abstract published in J. Opt. Soc. Am. 71 (12), 1639 (1981) that they had developed a method for selecting optical glasses for two-element lens systems whereby Daraxial color correction could be obtained for three, four and five wavelengths. The glass selection method was indicated to be based on use of Buchdahl's coler coordinate w rather than on the use of Abbe numbers and relative partial dispersion ratios. Meanwhile, the method has been generalized to enable selection of glasses for designing multiplet optical systems comprisina two or more different types of glasses. Theoretical Basis for the Invention: In the mathematical model leadina to the present invention, the dispersive properties of a particular type of optical alass are described in terms of the dispersive power D of the glass. The dispersive power D is a function of wavelength A according to the relationship D(x) = - 1 , (6) NO 1 where No is the value of the refractive index N of the glass at the base wavelength AO. The base waveleneth X0 may be arbitrarily selected, but is preferably the wavelength at which monochromatic aberrations are calculated for the optical system that is to be designed using the glass. In developing the theoretical basis for the present invention, the dispersion term dN in equation (6) is replaced by an nth-degree polynomial in the color coordinate # in accordance with Buchdahl's dispersion equation (5). Thus, equation (6) is rewritten as EMI11.1 where the coefficients nj, called the n-dispersion coefficients, are given by nj = ';i/.(N0 - 1). Like the v-dispersion coefficients of equation (5), the n-dispersion coefficients of equation (7) are constants of the particular type of glass and in general vary from one type of glasto another. The difference in the dispersive power of a particular type of optical glass over a walvelength range #1 < # < #2 is represented by D(11,l2) = D(#1) - D(#2). Usina equation (7), D(#1,#2) can be expressed in terms of the color coordinate w by the power series EMI11.2 For the special case where #1 is the hydrogen F line (0.48613 m), #2 is the hydrogen C line (0.65627 m) and #0 is the helium d line (0.58756 m), it is of interest to note that equation (8) becomes a power series expansion in terms of the reciprocal of the Abbe number for the glass. Thin Lens Equations: Equations (6), (7) and (8) led to an elegant expression for the total dioptric power of a lens system comprisinq a number of thin lens elements in contact. For a sinqle thin lens in air, the dioptric power t is a function of wavelength A according to the relationship #(#) = = [N(X) - 1] (C1 - C2), (9) where C1 and C2 are the two curvatures of the lens. The curvatures C1 and C2 are independent of the wavelength x, and are conveniently represented by a constant K = C1 - C2 that is characteristic of the configuration of the particular lens. Thus, #(#) = [N(X) - 1] K. For the base wavelength xg, the thin lens power is b(xO) , [N0- 1] K. Since N(x) = No + #N(#), the thin lens power can be written as =#(ä0)+K#N(#). (10) In terms of the dispersive power D as defined by equation (6), equation (10) can be written in the form =#(#0) [1+D(#). (11) In terms of the color coordinate #, equation (11) can be expressed as EMI12.1 Since # # as # # #0. it follows that #(#) # #(#0) as # # #0. More qenerally, the total dioptric power # of an optical system comprisina a number of thin lens elements in contact in air is equal to the sum of the dioptric powers of the individual thin lens elements comprising the system. Thus, for an optical system comprising k thin lens elements in contact having individual lens powers #1, #2, at at the base wavelength AO, the total dioptric power # of the system at the base wavelength #0 is EMI12.2 The total dioptric power # for any wavelength # is given by k = #(#0) + # #jDj(#), (14) j=l where #j is the dioptric power of the jth lens element in the system at #0, and Dj(#) is the dispersive power of the particular type of glass from wich the fth lens element is made. For any wavelength #, n Dj(#) = #nij#i(#), (15) i=l so that the difference in the total dispersive power of the system over the wavelength range Al < x < A2, i.e., Dj(#1,#2s) = Dj(#1)-Dj(#2), is given by Dj(#1,#2) = #n ij [#i (#1) -#i(#2)], (16) and the difference in the total dioptric power of the system at the wavelengths #1 and k2 is k ##(#1,#2) = # #jDj(#1,##2). (17) j=1 Thin Lens Doublet: Applying the general equations (13) to (17) for thin lenses in contact to the particular case of a thin lens doublet (i.e., a lens system for which k = 2), the total dioptric power of the doublet at AO is #(#0) = #1 +#2. (18) From equation (14), the dioptric power of the lens doublet for any wavelenqth A is #(#) = #(#0) + #1n1(#) + #2D2(#). (19) In the case of two separated thin lenses in air, the total dioptric power at #0 is = #1 + (1-k)#2, (20) where k = d#1, where .d is the axial separation of the lenses. The parameter k is a function of wavelength according to the relationship k(#) = k[1+D1(#)]. In the case of a lens doublet comprising two different types of glasses, where the two lens elements of the doublet are cemented together, the condition that the doublet be color-corrected at two wavelenaths A1 and A2 is that #(#1) =#(#2). This implies that #1D1(#1,#2) + #2D2(#1,#2) =0, (21) where Dj(#1,#2) for j = 1, 2 is aiven by equation (16). Solving the system of equations (18) and (21) yields the dioptric powers of the individual lens elements of the thin lens doublet, to wit: =-#(#0) D2(#1,#2) /[D1(#1,#2)-D2(#1,#2)] (22) and = +(#0) D1(#1,#2) /[D1(#1,#2)-D2(#1,#2)]. (23) The set of equations (22) and (23).is equivalent to the set of equations commonly used for calculatina the dioptric powers of the individual lens elements of a twn-glass lens doublet color-corrected at the two wavelenaths Al and x2, where the dioptric powers of the lens elements comprising the doublet are expressed in terms of the Abbe numbers for the glasses from which the lens elements are made. In the neighborhood of the base wavelength xO, the dispersion dN(x) of a two-glass lens doublet can be approximated by a linear function in the color coordinate #. Thus, for a two-plass thin lens doublet, equation (5) can be written in the form DN(X) = N(AO) I #1#(#), (24) and equations (7) and (8), respectively, become D(X) - n1X(k) (25) and D(#1,#2) = n1[#(#1)-#(#2)]. (26) Equations (25) and (26) are, respectively, linear models of the dispersive power D(x) and of the difference in the dispersive power D(#1,#2) for the two-alass thin lens doublet over the wavelength range A1 < A < A2. Two-Glass Lens Doublet Color-Corrected at Two Wavelengths: In designing a two-glass thin lens doublet that is corrected for paraxial chromatic aberration at two wavelenaths, (also called a two glass two-color lens doublet), it is assumed that the dispersion properties of the optical glasses from which the lens elements of the doublet are made are substantially approximated by equations (25) and (26), i.e., by a linear dispersion model. Thus, each type of optical glass is uniquely represented by two parameters, viz., the refractive index N(#0) at the base wave-length A0, and the dispersion coefficient n1 as defined by equation (26). When #0 corresponds to the helium d line, and #1 and x2 are the hydrogen F and C lines, respectively, equation (26) becomes [N(#F) -N(#C)] /[N(#d)-1] = n1 [#(#F)-#(#C)]. (27) The left side of equation (27) is the reciprocal of the Abbe number. Since the factor [#('F) -#(#C)] is a constant, equation (27) implies that the dispersion coefficient n1 of an optical glass is directly proportional to the reciprocal of the Abbe number of the glass. The [N(xo) n1] glass parameter representation, as suggested by the foregoing analysis, is analoqous to the (Nd, Vd) representation commonly used by optical glass manufacturers for uniquely representing an optical glass, where Nd and V d are the refractive index and the Abbe number, respectively, for the alass at the wavelength of the helium d line. In terms of the dispersion coefficients n1 of the slasses from which the lens elements of a two-glass two-color lens doublet are made, the dioptric powers of the individual lens elements at the base wavelength xO can be expressed by equations in the form =-n12 #l(#0) / (n11-n12) (28) and = + n11 #(#0) / (n11-n12), (29) where n11 is called the primary dispersion coefficient for the first glass of the doublet, and n12 is called the primary dispersion coefficient for the second glass of the doublet. Ordinarily, it is desirable that the dioptric powers #1 and t2 of the lens elements of the doublet be small in value, so that the curvatures of the lens elements will be small. From equations (28) and (29), it is apparent that the absolute values of the dioptric powers 01 and #2 are small when the absolute value of the factor (n11 - n12) is large. Therefore, to obtain a aood dioptric power distribution for a lens doublet, there must be a relatively large difference between the primary dispersion coefficients of the glasses from which the lens elements of the doublet are made. The foregoing analysis has been developed with reference to the n-dispersion coefficients. However, inasmuch as #1 is directly proportional to #1, the analysis is also valid with reference to the #-dispersion coefficients. The technique of the prior art for designing a two-alass lens doublet that is color-corrected at two wavelengths is thus comprehended as a special case of the algorithm developed for the present invention, wherein a linear approximation of the power series in Buchdahl's dispersion equation (5) is used. Two-Glass Lens Doublet Color-Corrected at Three Wavelengths: An extension of the foreaoing analysis enables selection of compatible qlasses for designing a two-glass thin lens doublet that is corrected for axial chromatic aberration at three wavelengths, i.e., a so-called two-glass three-color doublet. To initiate the design of a two-al ass thin lens doublet that is color-corrected at wavelengths #1, X2 and x3, where x1 < #2 < ä2, the focal length of the doublet may be set equal to unity at the base walvength #0, SO that #(#0) = 1 in equation (18). The conditions that must be satisfied to obtain axial correction of the lens doublet at x1, x2 and #3 imply that #(#1)-#(#29 = 0 and #(#2) - #(#3) =0, These conditions lead to a set of homogeneous equations that are linear in #1 and h2. Cast in matrix form, these equations can be expressed as = 0, (30) where EMI17.1 <tb> <SEP> #D1(#1,#2) <SEP> D2(#1,#2)# <tb> <SEP> D <SEP> = <tb> #D1(#2,#3) <SEP> D2(#2,#3)# <tb> and EMI17.2 <SEP> <SEP> ##1# <tb> #'2# <tb> To express equation (30) in terms of the dispersion coefficients of the optical glasses from which the lens elements comprising the doublet are to be made, a quadratic approximation of the power series in Buchdahl's dispersion equation (5) is used to obtain axial color correction at three wavelengths. More generally, the power series in Buchdahl's dispersion equation (5) is approximated by an (n - 1)th degree polynomial in representina a two-alass lens doublet that is color-corrected at n wavelengths. Assuming that the dispersion properties of each glass of a two-glass three-color lens doublet (i.e., a two-class three-color lens system comprising k lens elements, where k = 1, 2) are approximated with substantial accuracy by a quadratic dispersion model, equation (7) becomes Dk(#) =n1k#(#)) + N2k#2(#), (31) and equation (8) becomes Dk(#i,#i) = n1k(#i-#j) + n2k(#i2 - #j2). (32) In designing a two-glass three-color lens doublet, each type of glass used in making the lens elements of the doublet is uniquely represented by the three parameters N0(#), n1 and n2, which comprise the [No(x) n1, n2] - glass parameter representation. Since n1 and n2 are proportional to #1 and v2, respectively, a [N0(#), 919 92] glass parameter representation in terms of the s-dispersion coefficients could also be used for uniquely representing each type of optical glass. Usina the [No(#), n1, n2] glass parameter representation relative to the base wavelength #0, and specifying three wavelengths #1, A2 and A3 for which color correction is desired, a system of two nonhomogeneous equations can be obtained frown equation (32) for each of the k glasses of the lens doublet, where k = 1, 2. This system of equations, however, linear in the dispersion coefficients n1k and n2k. In matrix form, this system of equations may be written as # nk = Dk, (33) where EMI19.1 <SEP> #(#1-#2) <SEP> (#12-#22)# <tb> <SEP> # <SEP> = <SEP> , <tb> <SEP> #(#2-#3) <SEP> <SEP> (#22-#32)# <tb> <SEP> <SEP> #n1k# <tb> <SEP> nk <SEP> = <tb> <SEP> #n2k# <tb> <SEP> and <tb> <SEP> #Dk(#1,#2)# <tb> <SEP> Dk <SEP> = <SEP> . <tb> <SEP> #Dk(#2,#3)# <tb> Substituting equation (33) into equation (30) yields # n #=0, (34) where EMI19.2 <SEP> #n11 <SEP> <SEP> n12# <tb> m <SEP> = <tb> <SEP> #n21 <SEP> <SEP> n22#. <tb> The elements of each column vector of the matrix are the dispersion oefficients of the glasses from which the lens elements of the two-glass three-color doublet are made. The matrix element Ti11 is called the primary dispersion coefficient of the first glass of the doublet, and the matrix element n21 is called the secondary dispersion coefficient of the first glass of the doublet. Similarly, the matrix elements n12 and n22 are called the primary and secondary dispersion coefficients, respectively, of the second glass of the doublet. The matrix n in equation (33) may be factored in the following form EMI20.1 <SEP> <SEP> #(#1-#2) <SEP> 0 <SEP> # <SEP> #1 <SEP> (#1+#2)# <tb> # <SEP> = <SEP> (35) <tb> # <SEP> 0 <SEP> <SEP> (#2-#3)# <SEP> #1 <SEP> (#2+#3)#. <tb> Since # is nonsingular, it has a unique inverse. Hence, if equation (34) is multiplied by the inverse of Q, a system of homogeneous equations is obtained in the powers of the constituent lens elements of the doublet, where the elements of the coefficient matrix Ti are the dispersion coefficients of the optical glasses comprising the doublet. Thus, Ti = U, (36) which has a nontrivial solution if and only if the determinant of the n-dispersion coefficient matrix vanishes, i.e., if and only if the determinant EMI20.2 <SEP> <SEP> #n11 <SEP> n12# <tb> <SEP> n <SEP> = <SEP> =0. <SEP> (37) <tb> <SEP> #n21 <SEP> <SEP> n22# <tb> This condition must be satisfied by the pair of glasses comprising the doublet, if axial color correction at three wavelengths is to be achieved by the thin lens doublet design. Thus, a particular pair of optical glasses can be used for designing a two-glass three-color lens doublet, if and only if the ratios of the primary dispersion coefficient to the secondary dispersion coefficient for both glasses are substantially equal, i.e., if and only if #11 = #12 . (38) #21 = #22 Since n j = Vj; ; / [N(A) - 1], equation (37) implies that the determinant of the matrix of the corresponding v-dispersion coefficients also vanishes, i.e., that EMI21.1 <tb> ##11 <SEP> <SEP> #12# <tb> <SEP> # <SEP> = <SEP> = <SEP> 0. <SEP> (39) <tb> <SEP> ##21 <SEP> <SEP> #22# <tb> Thus, using the s-dispersion coefficients, the condition that must be satisfied by a pair of optical glasses in order for those glasses to be compatible with each other in a two-glass three-color lens doublet can be expressed in terms of the ratios of the primary to secondary #-dispersion coefficients as, viz., 911 = 912 . (40) #21 #22 Equation (36) indicates that the dioptric powers of the individual lens elements comprising the two glass three-color lens doublet are functions of the dispersion coefficients of the glasses from which the lens elements comprising the doublet are made. The solution of equation (36) can be expressed in terms of the elements of either the first-row vector or the second-row vector of the matrix. In terms of the elements of the first-row vector, =+k1 n12 (41) and = -k1 n11, (42) where k1 is a proportionality factor. For a lens doublet having unit focal length at the base wavelength #0, which is the specified focal length of the two-glass three-color doublet for purposes of this analysis, kl = ll(Ti12 - n11) . (43) Similarly, in terms of the elements of the second-row vector, = +k2 n22 (44) and =-D2 n2, (45) where the proportionality factor k2 is given by k2 =1/(n22-n21) (46) for the lens doublet having unit focal length at #0. It is instructive to compare equations (41) and (42), which give the dioptric powers of the lens elements of a three-color lens doublet, with equations (28) and (29), which give the dioptric powers of the lens elements of a two-color lens doublet. In format, equations (41) and (42) are similar to equations (281 and (29). However, the values of the dispersion coefficients nij obtained from the quadratic dispersion model for the three-color doublet are in general different from the values of the dispersion coefficients nij obtained from the linear dispersion model for the two-color doublet. Two-Glass n-Color Lens Doublet: The theoretical considerations presented above for selecting pairs of glasses that are compatible for designing two-color and three-color lens doublets can be generalized and extended mathematically to define the conditions that must be satisfied in order for a pair of glasses to be compatible for designing thin lens doublets color-corrected at n wavelengths, i.e., two-glass n-color lens doublets. An n-color lens doublet has, by definition, a common paraxial focal point at wvelengts #j for j= 1,2,3,...,n. for an n-color lens doublet of unit total dioptric power (i.e., #=1), at the base wavelength #0, the dioptric powers #1 and #2 of the individual lens elements comprising the doublet-are related by the expressions #1 + 02 = 1 (47) and D #= 0, (48) where EMI23.1 <tb> <SEP> D1(A1,A2) <SEP> D2(A1'A2) <SEP> <tb> <SEP> D1(#2,#3) <SEP> D2#2,#3) <SEP> # <tb> D1(#j-1,#j) <SEP> <SEP> D2(#j-1,#j) <tb> <SEP> D1(#n-1,#n) <SEP> <SEP> D2(#n-1,#n)# <tb> <SEP> #1# <tb> <SEP> #2# <tb> and 0 is a column null vector, where Al < A2 < #3 < ... < # j-1 < A. < ... < An Equation (48), which represents a set of (n - 1) J homoaeneous equations that are linear in 61 and 62, has a nontrivial solution if and only if the rank of the coefficient matrix 0 is less than 2. The rank of the coefficient matrix D can be determined by examining all possible determinants of order 2 that can be formed by fixing any two rows of the matrix D. If all possible determinants of order 2 vanish, the rank of D is less than 2 and a nontrivial solution of equation (48) exists. Two-Glass Four-Color Lens Doublet: For a two-alass lens doublet that is color-corrected at four wavelenaths (i.e., for n = '4), submatrices A, B and C of order 2 obtained from the coefficient matrix D of equation (48) are given by EMI24.1 <SEP> <SEP> #D1(#1,#2 <SEP> <SEP> D2(#1,#2# <tb> <SEP> A <SEP> = <SEP> , <SEP> (49) <tb> <SEP> #D1(#2,#3 <SEP> <SEP> D2(#2,#3)# <tb> <SEP> #D1(#1,#2) <SEP> <SEP> D2(#1,#2)# <tb> B <SEP> = <tb> <SEP> #D1(#2,#4) <SEP> <SEP> D2(#2,#4)# <SEP> <SEP> (50) <tb> and <tb> <SEP> D1(A2,A3) <SEP> D2(A2,A3) <SEP> <tb> <SEP> C <SEP> =#D1(#3,#4) <SEP> <SEP> D2(#3,#4)#. <SEP> <SEP> (51) <tb> A necessary condition for the existence of a two-glass lens doublet color-corrected at four wavelenaths is that the determinants of the submatrices A, B and C vanish identically, which implies that the relationships D1(#1,#2) D1(#2,#3) D1(#3,#4) ######### = ######### = ######### (52) D2(#1,#2) D2(#2,#3) D2(#3,#4) must be satisfied by the pair of optical alasses comprising the doublet. To relate equation (52) to the -dispersion coefficients of the glasses, a cubic model of the dispersion polynomial is used. Thus, the submatrix A of equation (49) can be written in the form A = Ti n (53) where EMI25.1 <SEP> #(#1-#2) <SEP> <SEP> (#12-#22) <SEP> <SEP> (#13-#23)# <tb> <SEP> #A= <tb> <SEP> #(#2-#3) <SEP> <SEP> (#22-#32) <SEP> <SEP> (#23-#33) <SEP> # <tb> and <tb> <SEP> #n11 <SEP> <SEP> n12# <tb> <SEP> N <SEP> = <SEP> #n21 <SEP> <SEP> n22# <SEP> . <tb> <SEP> #n31 <SEP> <SEP> n32# <tb> The elements of the first and second column vectors of the Ti matrix are the -dispersion coefficients of the first and second optical alasses, respectively, comprisina the doublet. The matrix elements n11, n21 and n31 are called the primary, secondary and tertiary dispersion coefficients, respectively, of the first glass of the doublet; and the matrix elements 12, n22 and n32 are called the primary, secondary and teritiary dispersion coefficients, respectively, of the second glass of the doublet. In equation (53), the submatrix A may be considered as the product of the factors nA and Ti. From linear algebra, the rank of the submatrix A, written R(A), is related to the ranks of its factors A and Ti by the expression R(A) < Minimum [R(nA), R(n)] . (54) Since the determinant of the submatrix A vanishes as a necessary condition for the existence of a lens doublet that is color-corrected at four wavelenaths, the rank of A must be less than 2, i.e., R(A) < 2. The color coordinates #j are distinct in value for each wavelength. Since the highest-order nonsingular submatrix obtainable from the elements of the matrix nA is equal to 2, it follows that R(#A) = 2. Since the n-dispersion coefficients are finite in value, R() = O. Furthermore, since R(A) < 2, it follows from equation (56) that R( ) < 2. Since Rt ) must have an integral value less than 2 and areater than zero, it therefore follows that R(n) = 1. The fact that the rank of n in equation (53) is equal to unity implies that EMI26.1 <tb> #n11 <SEP> <SEP> n12# <SEP> <SEP> #n11 <SEP> <SEP> n12# <SEP> <SEP> #n21 <SEP> <SEP> n22# <tb> <SEP> = <SEP> = <SEP> =0. <SEP> (55) <tb> <SEP> #n21 <SEP> <SEP> n22# <SEP> <SEP> #n31 <SEP> <SEP> n32# <SEP> <SEP> #n31 <SEP> n32# <tb> Thus, #11 #12 ### = ### (56) #21 #22 #11 #12 ### = ### (57) #31 #32 #21 #22 ### = ### (58) #31 #32 which is to say that a particular pair of optical alasses can be used in designing a two-glass lens doublet that is color-corrected at four wavelenaths, if and only if the ratios of the primary, secondary and tertiary dispersion coefficients of the two alasses are related to each other in accordance with equations (56), (57) and (58). Just as the submatrix A in equation (49) was related to the n-dispersion coefficients by equation (53), so also the submatrix B in equation (50) and the submatrix C in equation (51) can be related to the n-dispersion coefficients by correspondina equations having the form g = B Ti and C = nC Ti. These equations for B and C differ from the correspondina equation for A only in the first factor. Thus, an analysis of the equations B = nB Ti and C = #C #C n in the same way as was done above for equation (53) leads to the same result as expressed in equations (56), (57) and (58). To understand the conditions expressed by equations (56), (57) and (58) in geometrical terms, consider each type of optical glass available to the designer to be represented bv a unique point in a three-dimensional space, called a alass space, which is defined by a coordinate system having the n-disnersion coefficients n1. n2 and n3 as orthogonal axes. Two particular optical alasses G1 and G 2 having coordinates G1 (n11, n21, n31) and G2 (n12, n22, n32), respectively, in the glass space satisfy the conditions of equations (56), (57) and (58), if and only if G1 and G2 are collinear with the origin of the coordinate system. The various optical glasses available to the designer can be represented as position vectors in space The conditions of equations (56), (57) and (58), which must be satisfied in designing a two-glass lens doublet that is color-corrected at four wavelengths, require that the two alasses G1 and G2 selected for making the lens elements of the doublet must satisfy the vector equation G1 = a G2 , (59) where G1 and t2 are the position vectors for the respective alasses, and a is a real scalar. Since the vectors 1 and C2 are collinear, the projections of G1 and A2 on the three orthogonal planes intersectina at the oriain of the coordinate system must also be collinear, which is the geometric interpretation of the ratios given in equations (56), (57) and (58). Two-Glass n-Color Lens Multiplet: In a two-alass lens multiplet, there may be any specified number of lens elements, but at least one of the lens elements is made of one type of glass and at least one other of the lens elements is made of another type of glass. A two-al ass lens doublet is a special case of a two-al ass lens multiplet 'in which there are only two lens elements. In desianina a two-al ass n-color lens doublet, an (n - 1)th degree alass dispersion model is used, which is to say that the power series in Buchdahl's dispersion equation (5) is approximated by an (n - 1)th degree polynomial when axial color correction at n wavelenaths is desired. In vector representation, each type of optical material available to the designer is reoresented as a unique glass point in an (n - 1)- dimensional vector space having the dispersion coefficients n1, n2, n3, .., nn 1 as orthogonal axes. Any two optical materials whose alass points are collinear with the oriain of the (n - 1)-dimensional vector space could in principle be used for designing a two-glass lens doublet that is color-corrected at n wavelengths. Since axial color correction of a lens multiplet is dependent upon the dispersion properties of the alasses from which the lens elements comprising the multiplet are made, and does not depend upon the desian form (i.e., the number, configuration and arranciement) of the individual lens elements, the technique described above for designing a two-glass n-color lens doublet can be extended for designina a two lass n-color lens multiplet comprising more than two lens elements. For purposes of axial color correction, a two-alass lens multiplet can be treated mathematically as a quasi-doublet, where all the individual lens elements made of one type of glass are considered collectively as the first lens element of the quasi-doublet, and where all the individual lens elements made of the other type of glass are considered collectively as the second lens'element of the quasi-doublet. Each of the two lens elements of the quasi-doublet is treated as havinq a dioptric power that is the sum of the dioptric powers of all the individual lens elements made of the same type of alass. Thus, in the mathematical analysis of a two-glass lens triplet, quadruplet, or hiaher-number multiplet treated as a quasi-doublet, at least one of the lens elements of the quasi-doublet actually comprises two or more individual lens elements made of the same type of alass. The total dioptric power of the quasi-doublet, of course, is the same as the total dioptric power obtained by summing the dioptric powers of the individual lens elements comprising the multiplet. Since correction for axial chromatic aberration does not depend upon the design form of an optical system, the degree of axial color correction that can be obtained for an optical system using a particular pair of optical alasses cannot be varied by changing the design form of the system. Thus, the same deqree of axial color correction can be obtained for anv lens multiplet using two given optical glasses, regardless of the number of lens elements comprising the multiplet, and regardless of the configurations and dispositions of the lens elements. However, the remaining optical aberrations, including lateral color, the monochromatic aberrations, and the chromatic variations of the monochromatic aberrations, are sensitive to the design form of a lens system. The selection of compatible ontical materials is a necessary condition for desianina an optical system that is color-corrected at a desired number of wavelenaths. However, it is not sufficient merely to select compatible optical materials. The designer, workina with compatible optical materials, must further apply his craft with skill in order to determine a design form that will enable the optical system to meet its specified requirements. A desianer can select a compatible pair of optical materials from among all the various types of optical materials available to him for designing a two-qlass n-color lens multiplet by: (a) Determinina the dispersion coefficients for each type of optical material, the dispersion coefficients being coordinates defining a unique "glass point" for each type of optical material in an (n - 1)-dimensional "glass space" coordinate system, where n is the number of wavelengths for which color correction is desired; (b) Calculating the slope of the hyperline connectina the origin of the "lass space" coordinate system with the "glass point" for each type of optical material; ; (c) Sorting the various types of optical materials in ascending order of the slopes of the hyperlines connecting the "glass points" with the oriain of the coordinate system; and (d) Selecting a pair of optical materials for which the hyperline slopes are substantially equal. After identifying the various pairs of optical materials that are suitable in principle for desianina the two-glass color lens multiplet, the designer then selects a preferred pair (or pairs) of optical materials to use in imDlemntina the design. Ordinarily, it would be desirable for the dioDtric powers of the individual lens elements comprisina the lens multiplet to be minimized, which occurs when the absolute value of the difference between corresponding primary dispersion coefficients of the two glasses from which the lens elements are made is a maximum. A further step in the glass selection process, therefore, would ordinarily be to calculate the value of for - n1l for each pair of alasses that could in principle be used for designing the lens multiDlet. The preferred pair of glasses is a pair for which the difference n12 - n11 j is a maximum. A particular pair of optical alasses selected accordina to the above-described procedure for desianinq a twoglass three-color lens doublet might also be found to provide color correction at more than three wavelengths. This result can occur, because the conditions for three-color correction comprise a subset of the conditions for color correction at more than three wavelengths. In general, if two glass vectors C1 and B2 are collinear, i.e., if the glass points G1 and G2 lie on the same hyperline in (n - 1)-dimensional space, the projections of the vectors G1 and G2 on the hyperplane of the next lower degeneracy, i.e., the projections of G1 and C2 on the hyperplane in (n - 2)-dimensional n-space, must also be collinear with respect to the origin. Introduction of Lens Thickness: The foregoing mathematical analysis was developed using the thin lens equations (13) to (17), which represent an idealization that ignores the effect of lens thickness. In the real world, after a compatible pair of optical materials has been selected for designing a two-al ass color-corrected lens multiplet, the individual lens elements to be made from those optical materials must be given suitable thicknesses in order to be constructible. In accordance with the present invention, an algorithm has been developed for introducing lens thickness into the design of a two-glass lens multiplet whose "thin lens" elements are to be made from optical glasses selected according to the above-described procedure. The alaorithm for lens thickening requires that the powers of the "thin lens" elements he unchanged durinq the introduction of lens thickness. Also, in order for the "thickened" multiplet to have a total dioptric power (or focal length) that is identically equal to the total dioptric power (or focal length) of the idealized thin lens multiplet that it replaces, the second principal plane of any riven lens element of the multiplet must coincide with the first principal plane of an adjacent lens element of the multiplet. The algorithm for two-alass lens multiplet thickening is described in detail below for the special cases of a cemented lens doublet and an air-spaced lens doublet. Two-Glass Cemented Lens Doublet: The thick lens dioptric powers #1 and 62, respectively, of the lens elements comprising a thickened lens doublet are given by the equations t 1= P1+P2-N1P1P2 (60) and t =P3+P4-N2 P3p4, (61) where P. (j = 1, 2, 3, 4) are the refractive powers of the lens J element surfaces in the doublet system, where t1 and t2 are the axial thicknesses of the respecti-ve lens elements of the system, and where N1 and N2 are the refractive indices of the respective glasses at the base wavelength xO. The refractive power P of a surface of a lens element is a function of the surface curvature C. (j = 1, 2, 3, 4) and of the refractive index of the particular glass from which the lens element is made, accordina to the equations P1 = C1(N1 - 1) (62) P2 = C2(1 - N1) (63) P3 = C(N2-1) (64) P4 = C3(1 - N2). (65) The requirement that adjacent principal planes of the two lens elements of the doublet coincide implies that t1P1 t2P4 #### = - #### N1#1 N2#2 which when solved for P4 yields N2#1#2#1 P4 = - ######## . (67) N1t2#1 If the two lens elements are cemented together, C2 - C3. Thus, equations (63) and (64) can be combined and solved for P3 to yield P3=P2(N2-1). (68) 1 - N1 Substituting the expressions for P4 and P3 from equations (67) and (68) into equation (61) yields =a1 P1 + a2 P2 + a3 P1 P2, (69) where a1 = -(N2 t1 #2)/N1 t2 #1 ; a2 = (N2-1)/(1-N1) ; and a3 = (N2 - 1) t1 #2/(1 - N1) N1 4 Equation (69) and the equations for a1, a2 and a3 can be solved simultaneously to yield an equation A P22 + B P2 + C = 0 , (70) which is quadratic in P2, where A = a2 b - a3; B = a2 - a1 + a3 #1 - b t2; C = al 2; and b = -t1/Nl. When the discriminant of the quadratic equation (70) is positive, there are two distinct values for P2. Usually, only one of the two values for P2 can result in a physically realizable lens system. After the values of P4, P3 and P2 have been determined, the values of P1 can be found by simple algebraic substitution in equation (66). The values of the constructional parameters of the lens system are calculated from equations (62) to (65), after the values of the refractive powers P. have been determined. 3 Two-Glass Air-Spaced Lens Doublet: The total dioptric power t of an air-spaced lens doublet is = #1+(1-k)#2, (71) where k = dD1, where d is the axial separation of the lens elements in air. The procedure used to calculate the dioptric powers #1 and of of the individual lens elements of the doublet is identical to the procedure used for the idealized case of two thin lenses in contact, except that total dioDtric power @ is given by equation (71) and the parameter k varies with wavelenqth according to the relationship k(A) =k [1 + D1(A)] , (72) where k is the value of k(x) at the base wavelength x0. Introduction of thickness into the design of an air-spaced lens doublet follows the aeneral procedure described above for designing a cemented lens doublet. The individual lens elements are "thickened" by keepina the powers 01 and 02 the same, and by keeping the axial separation of the adjacent principal planes equal to d. Two-Glass Manain Mirror: The glass selection procedure described above is applicable to catadioptric systems (i.e., systems involving both reflection and refraction of liqht)S as well as to dioptric systems involving only refraction of light. The simplest form of catadioptric system comprises a meniscus lens with spherical surfaces, one surface of which is provided with a reflective soatina to form a mirror. Such a "lens mirror" is commonly called a Manain mirror, after the French military officer who first proposed such imaoing systems. The classical Mangin mirror, which comprises only a negative singlet lens made of one optical material, is not corrected for primary chromatic aberration. In order for a Manqin mirror to be useful in imagine applications over a reasonable spectral range, it is necessary to provide color correction. The requirement for a color-corrected Mangin mirror led to the development of the so-called Manain doublet mirror, which is a compound Manain mirror in which the classical negative meniscus lens is replaced by a doublet lens system in which the two lens elements are made of different types of glasses. Mangin doublet mirrors corrected for axial chromatic aberration at two wavelengths, like ordinarily achromatic lens doublets (i.e., two-glass lens doublets corrected at two wavelenphts), were known in the prior art. Designs for Mangin doublet mirrors color-corrected at two wavelengths were described by N.v.d.W. Lessing in Appl. Opt. 8, 979 (1969), and by S. Rosin and M. Amon in Appl. Opt. 6, 963 (1967) and in U.S. Patent 3,494,688. A method for selecting pairs of optical glasses for designing cemented Mangin doublet mirrors that are color-corrected at two wavelenaths was described by N.v.d.W. Lessing in Appl. Opt. 8, 1245 (1969). However, the prior art had no unified theory for selectina optical materials for desianinq compound Mangin mirrors color-corrected at more than two wavelenaths. Algorithms developed in the prior art for selectina optical materials to be used for designing two-al ass Mangin mirrors failed to identify any combinations of alasses or other optical materials that could be used for designing any kind of catadioptric system capable of bringing more than two wavelengths to a common focus. The unified theory leading to the present invention, however, provides a method for selecting optical materials for designing Manain mirrors that are color-corrected at more than two wavelengths. Two-Glass Manin Doublet Mirror: A thin cemented Manin doublet mirror in air, having total catadioptric power ° at base wavelength #0. can be considered as a system comprising two thin lenses and a mirror in contact. For a marginal paraxial ray trace through the system, the total catadioptric power # is therefore given by °= = 2 D1 + 2 42 + #m ' (73) where #1 and #2 are the respective dioptric powers of the thin lens elements and #m is the catoptric power of the mirror element comprising the system. At a wavelenath other than xg, the total catadioptric power # of a Manain doublet mirror in terms of the dispersive powers D1(X) and D2(A) of the respective thin lens elements, as defined by equation (7), is given by = 2#1[1 + D(#)] + 2#2[1+D2(#)]+#m, (74) which after alaebraic simplification becomes =#+2#1 D1(#) +2#2D2(#). (75) The difference in the total catadioptric power of a Mangin doublet mirror at the wvelengts #i and #j, which is represented as ##(#i,#j) = #(äi)-#(#j), is given by ##(#i,#j) =2[#1D1(#i,#j)+#2D2(#i,#j], (76) where D1(#i,#j) and D2(#i,#j) represent the differences over the wavelength range from #i to #j between the dispersive powers of the respective glasses from which the lens elements comprising the Manain doublet.mirror are made. Two-Glass Manin Doublet Mirror Color-Corrected at Three Wavelenqths: The conditions that must be satisfied for a two-lass Mangin doublet mirror to be color-corrected at three wavelengths x1, z2 and #3, where #1 < #2 < #3, impy that ##(#1,#2) and ##(#2,#3)must both be identically equal to zero. In matrix form, this can be written as D#=0, (77) where EMI37.1 <SEP> #D1(#1,#2) <SEP> <SEP> D2(#1,#2)# <tb> D <SEP> = <tb> <SEP> #D1(#2,#3) <SEP> <SEP> D2(#2,#3)# <tb> and EMI38.1 <tb> <SEP> 61 <tb> 7 <SEP> <tb> <SEP> L <tb> Equation (77) is identical to equation (30), which expresses the conditions that must be satisfied for a two-glass doublet lens system to be color-corrected at three wavelengths. Thus, as suggested above in the development of equations (31) to (38), in order for two particular optical materials to be suitable for designing a Manain doublet mirror that is color-corrected at three wavelengths, it is necessary that the ratio of the primary dispersion coefficient to the secondary dispersion coefficient be substantially the same for both optical materials. Geometrically, the glass points for both optical materials in dispersion coefficient space must lie on a common line through the oriqin of the two-dimensional coordinate system defining the dispersion coefficient space. The dioptric powers of the two thin lenses comprising the Manin doublet mirror at the base wavelenath AO are given by = = K n12 (78) and 2 = K TI11 s (79) where K is a proportionality factor. Equations (78) and (79) are correspondingly similar to equations (41) and (42), respectively; although the proportionality factor K of equations (78) and (79) is in general different from the proportionality factor k1 of equations (41) and (42). For a Mangin doublet mirror having unit focal length (and therefore unit total dioptric power) at the base wavelength A0, equation (73) becomes 2 2 + 2 + hm = 1 . (80) Substituting equations (78) and (79) into equation (80) yields K = 1 - #m , (81) 2(n12-n11) which enables equations (78) and (79) to be written in the form EMI39.1 <tb> <SEP> = <SEP> #### <SEP> <SEP> ###### <SEP> <SEP> (82) <tb> and <tb> <SEP> #2= <SEP> <SEP> ###### <SEP> ######### <SEP> <SEP> (83) <tb> Equation (82) and (83) give the dioptric powers at #0 of the lens elements of the Manqin doublet mirror as a function of the -dispersion coefficients of the lens materials and the catoptric power of the mirror element. The catoptric power #m of the mirror element is independent of wavelenath variations, and can be set to a desired value by the optical desianer. For any aiven value chosen for the the powers #1 and #2 of the lens elements are inversely proportional to (Ti12 . Ti11).. Thus, in order to minimize the values of #1 and #2, the qlass pair used for designing the Mangin doublet mirror should be selected so that n12-n11 is as large as possible. In the special case where the mirror element of the Manain doublet mirror is planar, i.e., where #m = equations (82) and (83) become EMI39.2 <tb> <SEP> #1 <SEP> = <SEP> # <SEP> ######### <SEP> <SEP> (84) <tb> and <tb> <SEP> #2 <SEP> = <SEP> - <SEP> # <SEP> <SEP> ######### <SEP> (85) <tb> indicating that the dioptric power distribution of the lens elements of a Mangin doublet mirror that is color-corrected at three wavelengths has a value of one-half the dioptric power distribution of the same lens elements used for a two-glass lens doublet that is color-corrected at three wavelenaths. In the special case where the catoptric power of the mirror element of the Manain doublet mirror is given by hm = -1, equations (82) and (83) reduce to = # ######### (86) and = ######### (87) For this particular confiauration of the mirror element, the dioptric power distribution of the lens elements of a Mangin doublet mirror that is color-corrected at three wavelenaths is equal to the dioptric power distribution of the same lens elements used for a two-glass lens doublet that is color-corrected at three wavelengths. Two-Glass Mangin Doublet Mirror Color-Corrected at n Wavelengths: The procedure for selecting two different optical materials for desianina a Mangin doublet mirror that is color-corrected at n wavelenaths is the same as the procedure described above for selecting two different optical materials for designing a lens doublet that is color-corrected at n wavelengths. Each optical material available to the designer is represented as a unique glass point Gq (q = 1, 2) in an (n - 1)-dimensional vector space, where the n-disPersion coefficients of each Darticular optical material are the coordinates of the glass point renresentila that particular optical material. A pair of optical materials is suitable for designing a Mangin doublet mirror that is color-corrected at n wavelengths, if and only if the alass points G1 and G2 for the two materials obey the vector equation G1=&gamma; G2. Incomparing a Mangin doublet mirror coor-corrected at n wavelengths with a lens soublet color-corrected at n wavelengths, where the same two types of glasses are used in making the Manain doublet mirror and the lens doublet, the only difference appearing in the mathematical analysis of the system designs would be in the dioptric power distributions of the thin lens elements. Two-Glass Mangin Multiplet Mirror Color-Corrected at n Wavelengths: The procedure described above for designing a two-glass Mangin doublet mirror color-corrected at n wavelengths can be generalized for designing a twoalass Manain multiplet mirror color-corrected at n wavelenaths. The two-glass Manqin multiplet mirror can be treated mathematically as a two-glass Manain quasi-doublet mirror, where all the individual lens elements made of one type of glass are considered collectively as the first lens element of the Mangin quasi-doublet mirror, and all the individual lens elements made of the other type of glass are considered collectively as the second lens element of the Manin quasi-doublet mirror. The total dioptric power of the first lens element is the sum of the dioptric powers of all the individual lens elements made of one type of alass, and the total dioptric power of the other lens element is the sum of the dioptric powers of all the individual lens elements made of the other type of glass. The total catadioptric power # of the Mangin multiplet mirror is obtained by generalizing equation (73) into the form r s = 2 # Pi + 2 # Qi + #m , (88) i=1 j-1 m where P. (i = 1, 2, ..., r) represents the dioptric power of the ith lens element made of one type of class, and Qj (j 2 1, 2, ..., s) represents the dioptric power of the jth lens element made of the other type of alass. The splittina of the powers of the lens elements of an optical system is a useful technique in optical design to reduce spherochromatism and the hilger-order monochromatic aberrations. Color-Corrected Anamorphic Optical Systems: Each of the optical systems described above is rotationally symmetrical about a principal axis, called the optical axis, of the system. However, the class selection procedure of the present invention is generally applicable reqardless of whether such symmetry exists, and hence is also applicable to anamorphic optical systems comprising, e.g., prisms. For a thin prism of refractive index No at the base wavelength with apex angle a, the anale of deviation ss0 of a ray at wavelength AO after passina throuah the prism is given by ss0 = a [No - 1]. (89) The angle of deviation ss of a ray at wavelength A after passing through the prism is given by B (#) = &alpha; [N(#) - 1]. (90) From equation (6), N(#) - No = eN = (N0 - 1) D(A), where D(#) is the dispersive power of the glass from which the prism is made. Solving for [N(#) - 11 in terms of D(x), and substituting &alpha; = ss0/ (N0-1) from equation (89), yields ss(#) = 80 [1 + D(#)] . (91) In terms of the difference in the dispersive power D(#i, #j) of the glass over the wavelength range from #i to #j, as defined above in connection with equation (8), the chromatic dispersion of the prism from which the glass is made, i.e., #ss(#i,#j) = ss(#i) - ss(#j is given by #ss(#i,#j) = ss0 D(#i,#j). (92) Two-Glass Prism System Color-Corrected at Three Wavelengths: : Consider a prism'system comprising two thin prisms made of different optical materials havina refractive indices N1 and N2, respectively, at the base wavelength #0, and having apex angles a1 and &alpha;2, respectively. The total anaular deviation B of a ray passina through the prism system is the sum of the angular deviations produced by the individual prisms comprising the system. Thus, at the base wavelength #0, the total anaular deviation is B 2 ss1 + 82, (93) where ssl = &alpha;1(N1 - 1) and 62 = a2(N2 -1). The conditions for the prism system to have zero chromatic dispersion at, #2 and #3, where #1 < #2 < #3, are that #ss(#1,#2) and #ss(#2,#3) both identically equal zero. From equation (92), these conditions can be written in matrix form as EMI43.1 <tb> <SEP> #D1(#1,#2) <SEP> <SEP> D2(#1,#2)# <SEP> <SEP> #ss1# <tb> <SEP> = <SEP> 0. <SEP> (94) <tb> #D1(#2,#3) <SEP> D2(#2,#3)# <SEP> #ss2# <tb> Equation (94) is similar to equation (30) for a two-qlass lens doublet color-corrected at three wavelengths, and to equation (77) for a two-glass Manin doublet mirror color-corrected at three wavelengths. Using a quadratic dispersion model, the requirement for a particular pair of optical alasses to be suitable for desioning a two-glass prism system, whose chromatic dispersion at wavelengths 11, #2 and 13 is zero, is that the determinant of the n-dispersion coefficients of the glasses vanish, i.e., EMI44.1 <tb> n11 <SEP> n12 <tb> <SEP> = <SEP> 0. <SEP> (95) <tb> n21 <SEP> n22 <tb> This implies that the individual thin prisms comprising the prism system must have anaular deviations given by B1 = k n12 (96) and B2 = k k n11 ' (97) where k is another proportionalitv constant. Substituting equations (96) and (97) into equation (93), yields k B (98) n12-n11 for the proportionality constant. Thus, equations (96) and (97) can be rewritten as EMI44.2 <tb> <SEP> ss1= <SEP> ######### <SEP> <SEP> ss <SEP> (99) <tb> and <tb> <SEP> ss2 <SEP> = <SEP> ######### <SEP> <SEP> ss <SEP> (100) <tb> From equations (99) and (100), the apex angles al = B11(N1 -f1) and &alpha;2 = B2/(N1 - 1) can be written as EMI45.1 <tb> <SEP> &alpha;1 <SEP> = <SEP> ######### <SEP> ###### <SEP> (101) <tb> and <tb> <SEP> &alpha;2 <SEP> <SEP> = <SEP> ######### <SEP> <SEP> ###### <SEP> <SEP> (102) <tb> Dividing equation (101) by equation (102) yields the ratio &alpha; ;1 = - n12 (N2 - 1) (103) Q2 Ti11 (N1 - 1) ince nij = #ij/(Nj - 1), equation (103) reduces to al - 912 , (104) ## = ### which indicates that in order for a two-glass prism system to be color-corrected at three wavelenqths, the ratio of the apex angles of the individual prisms comprisina the system must be inversely proportional to the ratio of the v-dispersion coefficients of the optical materials from which the prisms are made. Equations (101) and (102) were derived using equations for thin prisms, and hence yield only approximate values. In designing a real prism system, the approximate values for al and a2 provided by thin lens theory can be adjusted hy exact ray-tracing based on Snell's law. Two-Glass Prism System Color-Corrected at More Than Three Wavelengths: Three-glass prism systems color-corrected at four wavelenaths were described by R.E. Stephens in J. Opt. Soc. Am. 56, 213 (1966). However, the prior art did not have a unified theory for selecting optical materials from which such three-glass four-color prisms could be desianed. No two-slass prism system color-corrected at more than three wavelengths has been reported in the prior art. In accordance with the present invention, the procedure for selecting optical materials for designing a two-glass prism system that has zero chromatic dispersion at more than three wavelengths is the same as the procedure described above for selecting optical materials for designing a two-al ass lens system or a two-glass catadioptric system that is color-corrected at more than three wavelengths. The glass selection procedure described above is of general validity, and can be used for desianina two-glass optical systems, e.g., lens systems, catadioptric svstems and prism systems, in which color correction at three or more wavelengths is required. Any colorcorrected optical system desiqned usinq the glass selection procedure described above would therefore be within the scope of the present invention. Extention of Theory to Include Optical Systems Comprising More Than Two Glasses: Considerina an optical multiplet comprising k thin lens elements in contact made from q different types of classes, where k > q, and where the multiplet is color-corrected at n wavelenaths, the power series expansion in Buchdahl's dispersion equation (5) is approximated by an (n - l)th decree polynomial in the color coordinate w. Thus, in equation (7), the terms hiqher than the (n - 1)th degree term are neglected, so that the dispersive power D (x) for each glass q of q the multiplet can he expressed as n-1 # niq #i, (105) Ill = i=1 where the dispersion coefficients niq in qeneral vary from glass to qlass. Usinq this (n - 1)th dearee polynomial dispersion model, each glass of the multiplet can be represented by the parameters Nq(#0), n1q, n2q,... n(n-1)q, where Nq(#is the refractive index of the qth glass at the base wavelenqth xO. Similarly, the difference in the dispersive power over a wavelength range #1 < # < #2 for each glass q, represented by Dq(#1,#2)= Dq(#1) - Dq(#2), can be expressed in terms of the color coordinate by the power series EMI47.1 It is noted that an [Nq(#0), #1q,#2q, ...,#(n-1)q] glass parameter representation could be used instead of the [Nq(#q), n1q,n2q,..., n(n-1)q] alass parameter representation. However, since the dioptric power of each lens element in the multiplet at #0 is directly proportional to [N(o) - 1], which is used in definina the n-dispersion coefficients, the n-dispersion coefficients generally lead to more compact and simpler algebraic formulations than the v-dispersfon coefficients, and are thus more desirable for rigorous mathematical analysis. Alaorithms for Determinina Dispersion Coefficients: The dispersion coefficients niq for the various types of alasses listed in the catalogs of the major optical glass manufacturers can be calculated using either equation (105) or equation (106). Since the dispersive power Dq(x) for a particular optical glass q at any wavelength # can be calculated from Nq(x) - Nq(#0) (107) q Nq(#0)-1 q usina data provided in the manufacturer's cataloa for that particular glass, it is possible to form a system of (n - 1) equations that are linear in the dispersion coefficients niq derived from equations (105) and (107), where the (n - 1) equations correspond to (n - 1) different wavelenaths that are all different from the base wavelength For For each alass q, this system of nonhomogeneous linear equations can be written in matrix form as # nq = Dq, (108) where EMI48.1 <tb> <SEP> ##1 <SEP> #12 <SEP> #13 <SEP> ... <SEP> #1n-1 <SEP> # <tb> <SEP> #2 <SEP> #22 <SEP> #32 <SEP> ... <SEP> #2n-1 <tb> <SEP> # <SEP> = <SEP> . <SEP> <SEP> . <SEP> ... <SEP> . <tb> <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> ##n-1 <SEP> <SEP> #n-12 <SEP> #n-13 <SEP> <SEP> ... <SEP> #n-1n-1# <SEP> <SEP> , <tb> <SEP> #n1q <SEP> # <tb> <SEP> nq <SEP> = <SEP> n2q <tb> <SEP> . <tb> . <tb> <SEP> . <tb> <SEP> n(n-1)q# <tb> and EMI49.1 <SEP> #Dq(#1) <SEP> # <tb> Dq <SEP> = <SEP> Dq(#2) <tb> <SEP> . <tb> <SEP> Dq(#n-1)# <SEP> . <tb> It is a property of equation (108) that the matrix n of the color coordinates # can be expressed as the product of two square matrices of order (n - 1), where one of the factors is a diagonal matrix and the other is a Wandermonde matrix. In factored form, the matrix can be written =Dag(#1, #2, #3, ...,#n-1) V(#1, #2, #3, ..., #n-1), (109) where EMI49.2 <tb> <SEP> #1 <SEP> #1 <SEP> #12 <SEP> #13 <SEP> ... <SEP> <SEP> #1n-2 <SEP> # <tb> <SEP> 1 <SEP> #2 <SEP> <SEP> #22 <SEP> #23 <SEP> ... <SEP> #2n-2 <tb> <SEP> V <SEP> = <SEP> 1 <SEP> #3 <SEP> #32 <SEP> <SEP> #33 <SEP> ... <SEP> <SEP> #3n-2 <tb> . <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> . <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> . <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> 1 <SEP> #n-1 <SEP> #n-12 <SEP> #n-13 <SEP> <SEP> ... <SEP> #n-1n-2# <SEP> <SEP> . <tb> The determinant of n is equal to the product of the determinants of its factors. Thus, EMI49.3 <SEP> n-1 <tb> det <SEP> # <SEP> = <SEP> 11 <SEP> #i <SEP> <SEP> 11 <SEP> (#j-#i), <SEP> <SEP> (110) <tb> <SEP> i=1 <SEP> i < i < j < (n-1) <tb> where II is the product symbol. For a given selection of the base wavelenath #0 and (n - 1) wavelengths #j, where #j = #0 and j = 1, 2, ..., (n-1), the corespondingcolor coordinates #j, where j = 1, 2, ...(n-1), are distinct and not equal to zero. This implies that the values of the determinants of the factors of can never be zero. Thus, viz is a nonsinaular matrix with rank equal to its order. This further implies that equation (108) has a unique solution, and that the set of values of the dispersion coefficients niq for the glasses from which the lens elements comprisina the multiplet are made is unique relative to the n wavelengths #j. According to the generalized algoritm, therefore, the (n-1)th deqree polynomial as defined by equation (105) is equivalent to a polynomial fit of the dispersive power Ddq(#) of the optical glasses for (n - 1) wavelenaths Aj relative to the base wavelength s0. The (n - 1) wavelenaths #j can be selected to be the particular wavelenaths for which color correction is required, i.e., the wavelengths for which the multiplet is designed to have a common focus. An alternative algorithm for obtaining a set of (n - 1) dispersion coefficients niq characterized the dispersion properties of an optical glass can be developed using equation (106) for the dispersive power differences relative to wavelength pairs. For each glass, n values of its refractive index at n different wavelengths Aj, where j = 1, 2, ..., n, are selected from the manufacturer's catalog. Assuming that #j # #0, and that #1 < #2 < < ... < #n-1 < a system of (n - 1) nonhomogeneous equations that are linear in the glass dispersion coefficients is obtained, from which the values of niq are calculated. This system of equation can be written in matrix form as ## nq =#Dq, (111) EMI51.1 <tb> where <tb> <SEP> #(#1 <SEP> <SEP> - <SEP> #2) <SEP> <SEP> (#12 <SEP> <SEP> - <SEP> #22) <SEP> <SEP> ... <SEP> (#1n-1 <SEP> - <SEP> #2n-1) <tb> <SEP> (#2 <SEP> <SEP> - <SEP> #3) <SEP> <SEP> (#22 <SEP> - <SEP> #32) <SEP> ... <SEP> . <tb> <SEP> ## <SEP> <SEP> = <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> #(#n-1 <SEP> - <SEP> #n) <SEP> (#n-12 <SEP> - <SEP> #n2) <SEP> ... <SEP> (#n-1n-1-#nn-1) <tb> <SEP> #n1q <SEP> # <tb> <SEP> n2q <tb> <SEP> nq <SEP> = <SEP> . <tb> <SEP> . <tb> <SEP> . <tb> <SEP> #n(n-1)q# <tb> and <tb> <SEP> Dq(#1,#2) <tb> <SEP> Dq(#2,#3) <tb> <SEP> ADq <SEP> = <tb> <SEP> Dq(#n-1),l#) <tb> This system of equations represented by the matrix equation (111) is different from the system of equations represented by the matrix equation (108) obtained using the first algorithm described above. In general, the dispersion coefficients obtained from equation (111) have values that are sliqhtly different from the dispersion coefficients obtained from equation (108) for the same types of glasses. This second algorithm using equation (111) may be viewed as a polynomial fit of the dispersive power differences of the classes in terms of (n - 1) wavelength pairs, rather than as a polynomial fit of the dispersive powers in terms of (n -.1) wavelengths as in the first algorithm using equation (108). Dioptric Powers of Lens Elements: Considerinq an optical multiplet comprisina k cemented thin lens elements in air, where the thin lens elements are made from q different types of glasses, where k > q, the total dioptric power #l of the multiplet at the base wavelength is so equal to the sum of the dioptric powers of the individual thin lens elements at the same base wavelenath xO. Thus, EMI52.1 where hj represents the subtotal dioptric power of the group of lens elements made of the same ith type of glass. For a multiplet of unit total dioptric power at #0 and color-corrected at n wavelengths #j (j = 1, 2, ..., n), the subtotal dioptric powers #i at #0 are related by the expressions #1 + + #2 #2 + . . . + #i + . + bq = 1 (113) and = ##l(#2, #3) = ... = ##(#n-1, #n)=0, (114) where EMI52.2 In matrix form, equations (113) and (114) can be represented as ê1 where EMI53.1 <SEP> 1 <SEP> 1 <SEP> 1 <SEP> # <tb> <SEP> #D1(#1, <SEP> #2) <SEP> <SEP> D2(#1, <SEP> #2), <SEP> <SEP> ... <SEP> Dq(#1, <SEP> #2), <tb> <SEP> ... <tb> <SEP> D1(#2, <SEP> <SEP> #3) <SEP> D2(#2, <SEP> #3), <SEP> <SEP> ... <SEP> Dq(#2, <SEP> #3), <tb> <SEP> ... <tb> <SEP> G <SEP> = <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> <SEP> #D1(#n-1,#n) <SEP> D(#n-1,#n) <SEP> ... <SEP> #Dq(#n-1,#n)# <SEP> , <tb> <SEP> ##1# <tb> <SEP> #3 <tb> <SEP> # <SEP> <SEP> = <SEP> . <tb> <SEP> ##q# <tb> and <tb> <SEP> #1# <tb> <SEP> 0 <tb> <SEP> 0 <tb> <SEP> ê1 <SEP> = <SEP> . <tb> <SEP> . <tb> <SEP> #0# <SEP> . <tb> A unique solution of equation (116) exists, if the determinant of the G matrix is not equal to zero. From equation (111), the G matrix can be written in terms of the dispersion coefficients niq and the color coordinates l#q of the classes. Expressing 0x as the product of two matrices, EMI53.2 <SEP> <SEP> #1 <SEP> <SEP> 0# <SEP> <SEP> #S# <tb> G <SEP> = <SEP> #0 <SEP> <SEP> ### <SEP> <SEP> #n# <SEP> <SEP> (117) <tb> where 3 = (1, 1, ..., 1) is a sum vector (i.e., a vector having unity as a value for each component) of order q, and Ti is an "(n - 1) by q" matrix in the dispersion coefficients given by EMI54.1 <tb> <SEP> #n11 <SEP> n12 <SEP> ... <SEP> n1q <tb> <SEP> n21 <SEP> n22 <SEP> ... <SEP> n2q <tb> n <SEP> = <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> #n(n-1)1 <SEP> n(n-1)2 <SEP> ... <SEP> n(n-1)q <tb> and where an is the matrix defined above by equation (111), and the 0 matrices are null matrices bf order (n - 1). Two particular cases are of special interest in considering the dioptric power distribution of the lens elements, or subqroups of lens elements, of a color-corrected multiplet made of different types of glasses, viz., the case where n = q, and the case where n > q. For the case where n = q, equation (116) represents a system of q equations that are linear in the unknown powers t (i = 1, 2, ..., q). Since the number of equations is equal to the number of unknowns when n = q, a unique solution of equation (116) exists when the determinant of G is not equal to zero. The dioptric powers hj can then readily be calculated by using Cramer's Rule, or any of a number of other methods for solving systems of linear equations. When G is written as the product of two matrices as in equation (117), the determinant of E is equal to the product of the. determinants of its factors. Thus, det G = det an det EMI54.2 <SEP> #S# <tb> #n# <SEP> <SEP> (118) <tb> where EMI55.1 <tb> <SEP> 1 <SEP> 1 <SEP> ... <SEP> 1 <tb> <SEP> n11 <SEP> n12 <SEP> ... <SEP> n1n <tb> n21 <SEP> n22 <SEP> ... <SEP> n2n <tb> <SEP> #S# <SEP> . <SEP> . <SEP> ... <SEP> . <SEP> # <SEP> # <SEP> 0 <SEP> (119) <tb> <SEP> det#n#= <SEP> <SEP> # <SEP> <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> n(n-1)1 <SEP> n(n-1)2 <SEP> ... <SEP> n(n-1)n <SEP> . <tb> By Cramer's Rule, the dioptric powers f can be expressed as =det Mi/det G (120) for i = 1, 2, 3, ..., n, where Mi is the matrix obtained from G by replacing the ith column of B by the unit column vector ê1. In terms of the dispersion coefficients niq of the glasses, the matrix Rj can be written as the product of two matrices EMI55.2 <SEP> <SEP> #1 <SEP> 0# <SEP> #S <SEP> # <tb> sMi <SEP> = <SEP> #0 <SEP> <SEP> ### <SEP> <SEP> #ni#, <SEP> <SEP> (121) <tb> where ni is the matrix obtained from the dispersion coefficients matrix Ti when the ith column of is replaced by a null column vector. Since det Mi = det ## det EMI55.3 <tb> (122) <SEP> <tb> equation (120) becomes EMI55.4 <tb> = <SEP> det <SEP> # <SEP> - <SEP> # <SEP> det <SEP> # <SEP> - <SEP> # <SEP> , <SEP> (123) <tb> EMI56.1 <SEP> <SEP> #S <SEP> <SEP> # <SEP> <SEP> #S# <tb> where <SEP> the <SEP> matrix#### <SEP> is <SEP> obtainble <SEP> from### <SEP> by <SEP> replacing <SEP> the <SEP> ith <SEP> column <tb> <SEP> <SEP> #ni# <SEP> <SEP> #n# <tb> of#n# <SEP> <SEP> with <SEP> the <SEP> unit <SEP> column <SEP> vector <SEP> ê1. <SEP> Thus, <tb> <SEP> #1 <SEP> 1 <SEP> ... <SEP> 1 <SEP> 1 <SEP> ... <SEP> 1 <SEP> # <tb> <SEP> n11 <SEP> n12 <SEP> ... <SEP> 0 <SEP> n1(i+1) <SEP> ... <SEP> n1n <tb> <SEP> n21 <SEP> n22 <SEP> ... <SEP> 0 <SEP> n2(i+1) <SEP> ... <SEP> n2n <tb> <SEP> #S <SEP> <SEP> # <SEP> . <SEP> . <SEP> ... <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> #ni# <SEP> <SEP> = <SEP> . <SEP> . <SEP> ... <SEP> . <SEP> . <SEP> ... <SEP> . <SEP> (124) <tb> <SEP> . <SEP> . <SEP> ... <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> #n(n-1) <SEP> <SEP> n(n-1)2 <SEP> ... <SEP> 0 <SEP> n(n-1)(i+1) <SEP> ... <SEP> n(n-1)n#. <tb> The determinant of EMI56.2 #S <SEP> # <tb> <SEP> #ni#, <tb> when expanded in terms of the elements of the ith column and its cofactors, yields det EMI56.3 S <tb> ni# <tb> =(-1)1+i det nis(0), (125) where ni(0) is a square matrix of order (n - 1), which is obtained from the rectangular matrix n by deleting the ith column vector of n. The determinant of EMI56.4 #n#, <tb> when expanded in terms of the elements of its first row and its cofactors, yields det EMI56.5 #n# <tb> EMI56.6 Combinina equations (125) and (126) with equation (123) yields (-1)1+i det ni(0) = ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ , (127) n j=1 det nj(0) which expresses the dioptric powers b of the lens elements, or groups of lens elements, in the multiplet as functions of the dispersion coefficients of the various types of plasses from which the lens elements are made. Dioptric Powers of Two-Glass Lens Multplet: In the simple case of a Two-glass lens multiplet color-corrected at two wavelenaths, i.e., where q = n = 2, the dispersion model is linear and the n matrix in equation (117) reduces to Ti - [Ti11 n12]. Thus, n1(0) =[n12] and n2(0) = [n11], so that the diolptric powers #i (i=1,2) for thetwo glasses, as given by equation (127), are #1 = ######### (128) and #2 = ######### (129) Equation (128) and (129) are thus seen to be identical to equations (28) and (29) derived above for the case of a two-glass doublet whose total power is equal to unity at the base wavelength. Dioptric Powers of Three-Glass Lens Multiplet: It is convenient to treat a three-class lens multiplet as a quasi-triplet (i.e., q = 3) in which each effective lens element comprises all the individual lens elements of the multiplet made from one particular type of glass. A Particular case of interest is a three-glass triplet color-corrected at three wavelengths (i.e., k = q = n = 3), for which the dispersion model is quadratic, so that the n matrix in equation (117) assumes the form EMI58.1 <SEP> #n11 <SEP> n12 <SEP> <SEP> n13# <tb> n <SEP> = <SEP> . <SEP> (130) <tb> <SEP> #n21 <SEP> n22 <SEP> n23# <tb> From equation (130), the submatrices n1(0), n2(0) and n3(0) reduce to EMI58.2 <tb> <SEP> #n12 <SEP> <SEP> n13# <SEP> <SEP> #n11 <SEP> <SEP> n13# <tb> <SEP> n1(0) <SEP> = <SEP> n21 <SEP> n23# <SEP> , <SEP> n2(0) <SEP> = <SEP> #n21 <SEP> n23# <tb> and <tb> <SEP> #n11 <SEP> n12# <tb> <SEP> n3(0) <SEP> = <SEP> #n21 <SEP> <SEP> n22# <SEP> , <tb> which when substituted into equation (127) yield the dioptric powers = (n12 n23 - n22 n13)/d (131) =-(n11 n23 - n21 n13)/d (132) = (n11 n22 - n21 n12)/d , (133) where 3 1+j d= # (-1) det nj(0), i.e., j=1 d=n11 (n22 -n33) + n12 (23 - n21) +n13 (n21 - n22). Four-Glass Lens Multiplet: Another particular case, of interest is a four-glass lens quadruplet that is color-corrected at four wavelengths, i.e., k = q = n = 4. Such a quadruplet was called a superachromatic quadruplet by N.v.d.W. Lessing in Appl. Opt. 9, 2390 (1970). Although various combinations of four different types of optical glasses suitable for designing such superachromatic quadruplets were reported in the prior art, a general technique for identifying all the optical materials that could be used for designing such superachromatic quadruplets was not developed until the present invention. In accordance with the present invention, a cubic dispersion model is used to select glasses for designing a superachromatic quadruplet. Accordingly, the Ti matrix in equation (117) assumes the form EMI59.1 <tb> <SEP> #n11 <SEP> <SEP> n12 <SEP> n13 <SEP> n14# <tb> n <SEP> = <SEP> n21 <SEP> n22 <SEP> n23 <SEP> n24 <SEP> (134) <tb> <SEP> #n31 <SEP> <SEP> n32 <SEP> n33 <SEP> n34# <tb> from which the submatrices nj(0) are obtained, and the dioptric power distributions tj(i = 1, 2, 3, 4) are calculated from equation (127). Althouqh lens multiplets comprising q different types of optical alasses color-corrected at n = q wavelengths were known in the prior art for q = 2, 3, 4, the method of the present invention whereby suitable optical materials for desianina such multiplets can be identified by expressing the dispersion characteristics of the optical materials in terms of n-dispersion coefficients is completely novel. Furthermore, it is also a novel feature of present invention that the practicality of using any particular combination of optical materials to desian a lens multiplet can be determined a priori by expressing the dioptric powers of the individual lens elements of the multiplet as functions of the -dispersion coefficients of the optical materials selected for making the lens elements. Special Case for n > q: Equation (116), G # = Ae1,represents a system of n equations that are linear in the unknown dioptric powers fj (i = 1, 2, q). For the case where n > q, the number of equations would be greater than the number of unknowns. For k = q = 2, i.e., for a two-glass doublet color-corrected at n wavelengths, equation (116) becomes EMI60.1 <tb> <SEP> #1 <SEP> <SEP> 1 <SEP> # <SEP> #1# <tb> <SEP> D1(#1, <SEP> #2) <SEP> <SEP> D2(#1, <SEP> #2) <SEP> <SEP> 0 <tb> <SEP> D1(#2, <SEP> #3) <SEP> <SEP> D2(#2, <SEP> <SEP> #3) <SEP> ##1# <SEP> 0 <tb> <SEP> . <SEP> . <SEP> ##2# <SEP> = <SEP> . <SEP> , <SEP> (135) <tb> <SEP> . <SEP> . <SEP> . <tb> <SEP> #D1(#n-1, <SEP> <SEP> #n) <SEP> <SEP> D2(#n-1, <SEP> #n)# <SEP> <SEP> #.# <tb> which is the matrix equation equivalent of equations (47) and (48) for a two-alass n-color lens doublet. In qeneral, for a lens multiplet made of q different types of glasses, the matrix D in equation (48) is an "(n - 1) x q" rectangular matrix in Dq(#j-1,#j). The conditions that must be satisfied by the individual alasses are obtained in the same way as for the doublet case, i.e., by examining the rank of the matrix D. Thus, a set of q alasses could be used for designina a lens multiplet that is colorcorrected at n wavelengths, if and only if the rank of the matrix D for that set of glasses is less than q. Special Case for n = q + 1: An interestino special case, which is instructive in describing the invention, is a lens multiplet comprisinq q different types of optical glasses color-corrected at q + 1 wavelengths. For this case, equation (116) becomes EMI61.1 <SEP> # <SEP> 1 <SEP> 1 <SEP> 1 <SEP> # <SEP> <SEP> #1# <tb> D1(#1, <SEP> #2) <SEP> <SEP> D2(#1, <SEP> #2) <SEP> <SEP> ... <SEP> Dq(#1, <SEP> #2) <SEP> ##1# <SEP> <SEP> 0 <tb> D1(#2, <SEP> <SEP> #3) <SEP> D2(#2, <SEP> #3) <SEP> ... <SEP> <SEP> Dq(#2, <SEP> #3) <SEP> <SEP> #2 <SEP> <SEP> 0 <tb> <SEP> . <SEP> . <SEP> ... <SEP> . <SEP> . <SEP> = <SEP> . <SEP> (136) <tb> <SEP> . <SEP> . <SEP> ... <SEP> . <SEP> . <SEP> . <tb> #D1(#q,#q+1) <SEP> <SEP> D2(#, <SEP> <SEP> #ql+1) <SEP> <SEP> ... <SEP> Dq(#q, <SEP> #q+1)# <SEP> ##q# <SEP> <SEP> #0# <SEP> <SEP> . <tb> Equation (136) is equivalent to the sets of equations + # 2 + ... + #q = 1 (137) and D# = 0, (138) EMI62.1 <tb> where <tb> <SEP> #D1(#1, <SEP> #2) <SEP> <SEP> D2(#1, <SEP> #2) <SEP> ... <SEP> Dq(#1, <SEP> #2) <SEP> # <tb> <SEP> D1(#2, <SEP> #3) <SEP> <SEP> D2(#2, <SEP> #3) <SEP> <SEP> ... <SEP> Dq(#2, <SEP> #3) <tb> <SEP> . <SEP> . <SEP> ... <SEP> . <tb> D <SEP> = <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> . <SEP> . <SEP> ... <SEP> . <tb> <SEP> #D1(#q, <SEP> <SEP> #ql+1) <SEP> D2(#q, <SEP> #q+1) <SEP> ... <SEP> Dq(#q, <SEP> #q+1)#, <tb> D <SEP> = <SEP> . <tb> <SEP> ##q# <tb> and 0 is a null column vector of order q. In terms of the chromatic coordinates and the dispersion coefficients of the glases, the homoqeneous matrix equation (138) can be written as hn n # = 0 , (139) where nn is defined as in equation (111), and W is the matrix of the dispersion coefficients as defined in equation (117). Both 7n and n are square matrices of order q. The matrix ## is nonsingular, so that equation (139) reduces to (140) In order for equation (140) to have a nontrivial solution, it is necessary that the determinant of n vanish1 i.e., that EMI63.1 <tb> <SEP> n11 <SEP> n12 <SEP> . <SEP> . <SEP> . <SEP> n1q <tb> <SEP> n21 <SEP> n22 <SEP> . <SEP> . <SEP> . <SEP> n2q <tb> # <SEP> . <SEP> . <SEP> . <SEP> . <SEP> . <SEP> . <SEP> # <SEP> <SEP> = <SEP> 0. <SEP> (141) <tb> <SEP> . <SEP> . <SEP> . <SEP> . <SEP> . <SEP> . <tb> <SEP> nq1 <SEP> nq2 <SEP> . <SEP> . <SEP> . <SEP> nqq <tb> Thus, equation (141) represents the condition that must be satisfied by the n-dispersion coefficients of the q different types of glasses used in designing the lens multiplet in order for the multiplet to be color-corrected at q + 1 wavelenths. The qeneral solution of the homogeneous equation (140) is = &alpha;Nij (142) for j = 1, 2, ..., q, where a is an arbitrary constant and the Nij are the cofactors of the elements of the ith row of the matrix. The constant a can be chosen to normalize the total dioptric power of the lens multiplet at the base wavelength #0. Substituting equation (142) into equation (137) yields q all 2 N. - . (143) j=1 The set of equations (142) and (143) enables the dioptric powers of the q different qroups of lens elements corresponding to the q different types of qlasses used in making the lens multiplet to be determined, where the lens multiplet is color-corrected at q + 1 wavelengths. The above analysis for the case where n = q + 1 holds true in the particular case where there is only one lens element in each of the groups of lens elements, i.e., where k = q. When k = 2, where k = q, there are only two lens elements, with each lens element being made of a different type of glass. Thus, equation (141) reduces to equation (37), and equation (142) reduces to equations (41) and (42), which were derived above for the case of a two-glass lens doublet color-corrected at three wavelengths. When k = 3, where k = q, the resulting lens multiplet is a three-glass triplet. In the case under consideration, the lens multiplet color-corrected at n = a + 1 wavelengths becomes a three-glass lens triplet color-corrected at four wavelengths, for which the designation "superachromat" was used by Herzberger in U.S. patent 3,395,962. The present invention provides a technique for identifying all possible glass combinations that could be used in designing such superachromatic lens triplets, and for selecting practical three-glass combinations in terms of dioptric power distributions. For k = q = 3, equation (141) reduces to EMI64.1 <tb> nll <SEP> nl2 <SEP> "13 <SEP> <tb> n21 <SEP> n22 <SEP> n23# <SEP> <SEP> = <SEP> 0, <SEP> (144) <tb> n31 <SEP> n32 <SEP> n33 <tb> and the dioptric powers of the individual lens elements, as given by equation (142), become = &alpha;1(n12 n23 - n22 n13) (145) #2 = -&alpha;1 (n11 n23 - n21 n13) (146) #3 = &alpha; (n11 n22 - n21 n12), (147) where &alpha;1 = 1/[n11(n22 - n23) + n12(n23 - n21) + n13(n21 - n22)]. The expressions for the dioptric Dowers #1, #2 and #3 given in equations (145), (146) and (147) are identical to those in equations (131), (132) and (133) for the case of a three-glass lens triplet color-corrected at three wavelenaths. However, a three-glass lens triplet color-corrected at four wavelengths must satisfy the additional conditions implied in equation (144). The conditions of equation (144) can be interpreted geometrically by considering each glass available to the desianer as a unique point in a three-dimensional plass space defined by the axes n1, n2 and n3. Three glasses, represented by the points G1, G2 and G3, satisfy the conditions of equation (144), if and only if G1, G2 and G3 lie in a common plane that passes through the origin of the coordinate system. Applying a series of elementary row and column operations to the matrix of equation (144) results in EMI65.1 <tb> n11/n31 <SEP> n12/n32 <SEP> n13/n33 <tb> #n21/m31 <SEP> <SEP> n22/n32 <SEP> n23/n33# <SEP> <SEP> = <SEP> 0. <SEP> (148) <tb> <SEP> 1 <SEP> 1 <SEP> 1 <tb> Defining 1 = n1/n3 and 2 = n2/n3, so that 1k = n1k/n3k and 2k = n2k/n3k for k = 1, 2, 3, the parameters 1 and '12 can be considered as axes of a two-dimensional rectanaular coordinate system into which the three-dimensional coordinate system defined by the axes n1, n2 and n3 is transformed. Equation (148) implies that when the various optical materials available to the desianer are plotted as points in the two-dimensional coordinate system with axes 1 and 2, the glass points G1( 11, 21), G2( 12, 22) and G3( 13, 23) are collinear. This two-dimensional aeometrical representation of the glasses in (P1,P2) space is more convenient than the three-dimensional representation in (n1, n2, n3) space. With the aid of a digital computer, it is relatively easy to obtain the coordinates for the glasses in ( 1, 2) space from the known values of the n-dispersion coefficients of the optical materials in (n1, n2, n3) space. When k = 4, where k = q, the resulting lens multiplet is a four-glass quadruplet. The case under consideration of a lens multiplet colorcorrected at n = q + 1 wavelenaths becomes a four-glass lens quadruplet color-corrected at five wavelengths. The dispersion model is quartic, and equation (141) becomes EMI66.1 <tb> n11 <SEP> n12 <SEP> n13 <SEP> n14 <tb> <SEP> #n21 <SEP> n22 <SEP> n23 <SEP> n24# <SEP> = <SEP> <SEP> 0. <SEP> (149) <tb> <SEP> n31 <SEP> n32 <SEP> n33 <SEP> n34 <tb> <SEP> n41 <SEP> n42 <SEP> n43 <SEP> n44 <tb> Equation (149) expresses the conditions that must be satisfied by a set of four optical materials in order for those four optical materials to be compatible with each other for use in designing a five-color lens quadruplet. The dioptric powers of the optical materials selected for designing the five-color lens quadruplet can be calculated from equation (142). Geometrically, equation (149) implies that if each optical material available to the desianer is represented by a unique point in a four-dimensional n-dispersion coefficient space with rectangular coordinate axes n1, n2, n3 and n4, the alass points G1, G2, G3 and G4 must lie in a common hyperplane that passes through the origin of the coordinate system. A more easily visualizable geometrical interpretation of equation (149) can be obtained by applying a series of elementary row and column operations to the matrix of equation (149), which results in the transformed equation EMI67.1 <tb> 11 <SEP> 12 <SEP> 13 <SEP> 14 <tb> <SEP> # 21 <SEP> 22 <SEP> 23 <SEP> <SEP> 24# <SEP> = <SEP> 0, <SEP> <SEP> (150) <tb> 31 <SEP> 32 <SEP> 33 <SEP> 34 <tb> 1 <SEP> 1 <SEP> 1 <SEP> 1 <tb> where lk = nlk/n4k, 2k = n2k/n4k and 3k = n3k/n4k for k = 1, 2, 3, 4. It is noted that the definition of the parameter '1ik (i = 1, 2, 3) for the case of a four-glass five-color lens quadruplet is different from the definition of the parameter p; (i r 1, 2) introduced above for the case of a three-glass four-color lens triplet. Equation (150) implies that if each optical material available to the designer is represented by a unique point in a three-dimensional rectangular coordinate system with axes 1, 2, and 3, the four glasses with coordinates G1( 11, 21, 31), G2( 12 22 32), G3( 13 23 33) and G4(14,24,p34) must be collinear in the three-dimensional ( 1, 2, 3) space in order to be suitable for designing a four-glass fivecolor lens quadruplet. With the aid of a digital computer, it is relatively easy to obtain the coordinates of the optical materials in the three dimensional (p1,p2,l,3) space from the known values of the n-dispersion coefficients of those materials in the four dimensional (n1, n2, n3, n4) space. Method for Selectina Three Compatible Glasses: In selecting a combination of three different optical materials for designing a "three-glass" multiplet (i.e., an optical system made of three different optical materials, whether of glass or otherwise) that is color-corrected at four wavelenaths, it is more convenient to use a two-dimensional alass point representation in ( 1, 2) space rather than a three-dimensional glass point representation in (n1, n2, n3) space for each of the available optical materials. The selection process starts with the choice of a particular optical material represented by glass point G1( 11, 21). The origin of the coordinate system defined by the axes 1 and 2 is then translated to G1, so that the "new" axes 1' and 2' (i.e., the axes after translation) are parallel to the original axes 1 and 2, respectively. The coordinates of each optical material are then expressed in terms of the translated axes P1' and 2', so that Gk( 1k, 2k) is expressed as Gk'( 1k', 2k'), where 1k' = 1k - 11 2k' = 2k - 21 EMI68.1 (151) which are the equations for transformation of coordinates. The equation of a straight line through the origin G1'(0,0) of the transformed coordinate system defined by the translated axes p11 and 2' is given by 2' = m' 1', where m' is the slope of the line referred to the translated axes. Thus, a straight line passing through 61(0,0) and a alass point Gk'('11I','12k1) has a slope = 2k'/ 1k', (152) which is the equation used to determine the slope m' for each available optical material. The arc tangent of m' is the slope angle of the glass point Gk' relative to the 1' axis. Using equation (152), a table is then made in which all available optical materials are sorted in ascending or descendina order of the values of m'. Any pair of optical materials having substantially the same value of m' (or, equivalently, havinq substantially the same value of the arc tangent of m') as the oriainally chosen optical material, whose glass point G1 is the oriqin of the translated axes,can be used in combination with that oriqinally chosen optical material for designing a "three-glass" optical system that is color-corrected at four wavelengths. Method for Selecting four Compatible Glasses: In selecting a combination of four different optical materials for designing a "four-glass" muitiplet that is color-corrected at five wavelenaths, it is more convenient to use a three-dimensional glass point representation in ( 1, 2, 3) space rather than a four-dimensional glass point representation in (n1,n2,n3,n4) space for each of the available optical materials. The selection process starts by choosing two optical materials represented by glass points G1( 11, 21, 31) and G2( 12, 22, 32), respectively. The origin of the coordinate system defined by the orthogonal axes 1, 2 and p3 is then translated to G1, so that the translated axes 1', 2' and p3' are parallel to the original axes P1, 2 and p3, respectively. The coordinates of each optical material are then expressed in terms of the translated axes, so that Gk( 1k, 2k, 3k) is expressed as Gk'( 1k', 2k', 3k'), where 1k' = 1k - 11 2k' = 2k - 21 3k' = 3k - 31 EMI69.1 (153) The equation of a straight line through the origin G1'(0,0,0) of the transformed coordinate system defined by the translated axes 1', 2' and 3' is given by 1'/ 2' = 2'/ 22' = 3'/ 32', which is equivalent to the system of equations 1'/ 12' - 2'/ 22' = 0 1'/ 12' - 3'/ 32' = 0 2'/ 22' - 3'/ 32' = 0 EMI70.1 (154) It is noted that any values for P1, u2 and 3 satisfying any two of the equations (154) also, satisfy the third equation. Equations (154) also imply that 1' = k 12' 2' = k 22' 3' = k 32' EMI70.2 (155) where k is a constant different from zero. Therefore, the glass points G2'( 12', 22', 32'), G3'( 13', 23', 33') and G4'( 14', 24', 34') are collinear with the origin G1'(0,0,0), if and only if their corresponding coordinates are proportional to each other. Optical materials represented by glass points G3' and G4' can be selected from among those optical materials having coordinates that are substantially proportional to the corresponding coordinates of G2'. DESCRIPTION OF THE DRAWING FIG. 1 is a aeometrical representation in dispersion coefficient space of an (n - 1)th degree dispersion model for an optical system comprising two different optical materials. FIG. 2 is a geometrical representation in dispersion coefficient space of a linear dispersion model for an optical system comprising two different optical materials. FIG. 3 is a geometrical representation in dispersion coefficient space of a quadratic dispersion model for an optical system comprising two different optical materials. FIG. 4 is a geometrical representation in dispersion coefficient space of a cubic dispersion model for an optical system comprising two different optical materials. FIG. 5 is a geometrical representation in dispersion coefficient space of a cubic dispersion model for an optical system comprising three different optical materials. FIG. 6A is a plot in the (n1,n2) plane of the n-dispersion coefficients for 813 different types of optical glasses listed in the catalogs of five major optical glass manufacturers. FIG. 6B is an enlargement of a portion of the plot shown in Fig. 6A. FIG. 7A is a plot in the (v1,v2) plane of the s-dispersion coefficients for the same 813 different types of optical glasses whose -dispersion coefficients are shown in FIG. 6A. FIG. 7B is an enlargement of a portion of the plot shown in Fig. 7A. FIG. 8 provides a profile drawing and a plot of paraxial marginal ray height versus wavelenath for a two-color cemented lens doublet having unit focal lenqth at xO = .54607 pm for a relative aperture of film, where the lens elements comprising the doublet are made of Schott BK7 and Schott F2 passes. FIG. 9 provides a profile drain and a plot of paraxial marginal ray height versus wavelength for a three-color cemented lens doublet of unit focal length at AO = .54607 um for a relative aperture of f/10, where the lens elements comprisina the doublet are made of Schott FK51 and Schott K51 glasses. FIG. 10 provides a profile drawing and a plot of paraxial marginal ray heiaht versus wavelength for a four-color cemented lens doublet of unit focal length at AO = .54607 vm for a relative aperture of f/10, where the lens elements comprising the doublet are made of Corninq France 486817 and Ohara LAK14 qlasses. FIG. 11 provides a profile drawing and a plot of paraxial marginal ray height versus wavelength for a four-color air-spaced lens doublet of unit focal length at =. = .54607 um for a relative aperture of f/10, where the lens elements comprising the doublet are made of the same types of glasses as for the lens doublet of FIG. 10. FIG. 12 provides a profile drawing and a plot of paraxial marginal ray height versus wavelength for a five-color air-spaced lens doublet of unit focal length at #0 = .54607 urri for a relative aperture of f/10, where the lens elements comprisina the doublet are made of Schott PK51 and Hoya LAC7 glasses. FIG. 13 provides a profile drawing and a plot of paraxial marginal ray height versus wavelength for a four-color cemented two-glass lens triplet having a focal length that is 40 times the focal length of the doublets shown in FIGS. 8 - 12 at A0 = .54607 um for a relative aperture of f/10, where the first and third lens elements are made of Corning-France 486817 glass and the second lens element is made of Corning-France 589612 glass. FIG. 14 provides a profile drawing and a plot of paraxial marginal ray height versus wavelenqth for a four-color two-glass lens triplet having a focal length that is 40 times the focal length of the doublets shown in FIGS. 8 - 12 at > 0 = .54607 um for a relative aperture of f/10, where the lens elements are made of the same types of glasses as for the lens triplet shown in FIG. 13, the first and second lens elements are cemented together, and an air gap is provided between the second and third lens elements. FIG. 15 provides a profile drawing and a plot of paraxial marginal ray height versus wavelenath for a four-color cemented two-glass lens quadruplet having a focal length that is 40 times the focal length of the doublets shown in FIGS. 8 - 12 at xO = .54607 pom for a relative aperture of f/10, where the first and third lens elements are made of Corning-France 486817 glass, and the second and fourth lens elements are made of Cornino-France 589612 qlass. FIG. 16 provides a profile drawing and a plot of paraxial marginal ray height versus wavelength for a four-color two-glass lens quadruplet having a focal length that ,is 40 times the focal length of the doublets shown in FIGS. 8 - 12 at k0 = .54607 pm for a relative aperture of f/10, where the lens elements are made of the same types of glasses as for the quadruplet shown in FIG. ls, except that the first and fourth lens elements are made of Corning-France 486817 alass, and the second and third lens elements are made of Cornina-France 589612 glass, where the first and second lens elements are cemented toaether, the third and fourth lens elements are cemented together, and an air gap is provided between the second and third lens elements. FIG. 17 provides a profile drawing and a plot of paraxial marginal ray height versus wavelenqth for a four-color two-glass lens quadruplet having a focal length that is 40 times the focal length of the lens doublets shown in FIGS. 8 - 12 at at = .54607 pm for a relative aperture of film, where the lens elements are made of the same types of glasses as for the quadruplet show in FIG. 15, where the first and third lens elements are made of Corning-France 486817 glass, and the second and fourth lens elements are made of Corninq-France 589612 glass, where the first and second lens elements are cemented together, the third and fourth lens elements are cemented together, and an air gap is provided between the second and third lens elements. FIG. 18 provides a profile drawina and a plot of paraxial marginal ray height versus wavelenath for a four-color collimator comprising a two-glass lens quadruplet, where the two glasses from which the lens elements of the quadruplet are made are Hoya FCD10 glass and Ohara LAK14 glass. FIG. 19 provides a profile drawing and a plot of paraxial marginal ray height versus wavelength for a five-color collimator comprising a two-glass lens quadruplet, where the two glasses from which the lens elements of the quadruplet are made are Schott PK51 glass and Hoya LAC7 alass. FIG. 20 provides a profile drawing and a plot of paraxial marginal ray heiaht versus wavelength for a five-color collimator comprising a lens quadruplet made of one type of optical glass and one type of crystal, where the glass is Hoya LAC7 glass and the crystal is calcium fluoride. FIG. 21 provides a profile drawina and a plot of paraxial marginal ray height versus wavelength for a five-color two-glass cemented Manqin doublet mirror system of unit focal length at 0= .54607 um for a relative aperture of fl2, where the system elements comprise a first lens element made of Hoya FDC10 glass and a second lens element made of Hoya FC3 glass, the outward facing surface of the second lens element having a reflective coating. FIG. 22 provides a profile drawing and a plot of paraxial marginal ray height versus wavelength for a four-color two-glass cemented Mangin doublet mirror system of unit focal lenath at s0 = = .54607 m for a relative aperture of f/2, where the system elements comprise a first lens element made of Hoya BAFl1 amass and a second lens element made of Hoya FL6 alass, the outward facina surface of the second lens element having a reflective coating. FIG. 23 provides a profile drawing and a plot of paraxial marginal ray height versus wavelength for a four-color two-plass cemented Mangin doublet mirror system of unit focal length at #0 = .54607 um for a relative aperture of f/2, where the system elements comprise a first lens element made of Corninq-France 486817 glass and a second lens element made of Corning-France 697554 glass, the outward facing surface of the second lens element having a reflective coating. FIG. 24 provides a profile drawing and a plot of paraxial marginal ray height versus wavelenath for a five-color two-alass air-spaced Mangin doublet mirror. system of unit focal lenqth at #0 = .54607 um for a relative aperture of f/2, where the system elements comprise a first lens element made of Schott PK51 glass and a second lens element made of Hoya LAC7 glass, the outward facing surface of the second lens element having a reflective coatina. FIG. 25 provides a profile drawing and a plot of paraxial marginal ray height versus wavelength for a five-color two-glass air spaced Mangin doublet mirror system of unit focal length at at = .54607 um for a relative aperture of f/2, where the system elements comprise a first lens element made of Hoya FCD10 glass and a second lens element made of Ohara PSK1 glass, the outward facing surface of the second lens element having a reflective coating. FIG. 26 provides a profile drawing and a plot of paraxial marginal ray height versus wavelength for a four-color two-glass air spaced Mangin doublet mirror system of unit focal length at to = .54607 m for a relative aperture of f/2, where the system elements comprise a first lens element made of Hoya FCDIO glass and a second lens element made of Hoya LAC14 glass, the outward facing surface of the second lens element having a reflective coating. FIG. 27 provides a profile drawing and a plot of paraxial marginal ray height versus wavelenath for a two-glass five-color Petzval lens system havina a focal lenqth of 600 mm at AO = .54607 um for a relative aperture of f/3.5 and an anaular field of . 60. FIG. 28 provides a profile drawina and a plot of paraxial marginal ray height versus wavelength for a two-al ass four-color Petzval lens system having a focal length of 360 mm at at = .54607 m for a relative aperture of f/3.5 and an angular field of & 60. FIG. 29 provides a profile drawing and a plot of paraxial marginal ray height versus wavelength for a two-glass three-color Petzval lens system having a focal lenqth of 100 mm at #0 = .54607 m for a relative aperture of f/2 and an anaular field of * 2.10 FIG. 30 provides-a profile drawing and a plot of change in total deviation angle versus wavelenath for a two-glass five-color doublet prism system having a total deviation angle of 60. FIG. 31 provides a profile drawina and a plot of change in total deviation angle versus wavelenath for a two-glass five-color quintuplet prism system having a total deviation anale of 300, where the apex angles of the first, second, third and fourth prism elements are equal to each other in absolute value, and where the apexes of the second and fourth prism elements have an orientation that is opposite to the orientation of the apexes of the first and third prism elements. FIG. 32 provides a profile drawing and a plot of change in total deviation angle versus wavwlength for a two-glass five-color quintuplet prism system having a total deviation angle of 30 , whwre the prism elements are made of the same types of alasses as for the corresponding prism elements of the prism system shown in FIG. 31, but where the apex angles of the five prism elements are all different in value from each other. FIG. 33 provides a profile drawing and a plot of paraxial marainal ray height versus wavelength for a three-glass lens quintuplet that is color-corrected at five wavelenoths, the quintuplet having a focal length of 1000 mm at #0 = .54607 Urn for a relative aperture of f/10, and comprisina a first lens element made of Ohara FKO1 glass, a second lens element made of Ohara KZFS8 alass and air-spaced from the first lens element, a third lens element made of Ohara FKO1 glass and cemented to the second lens element, a fourth lens element made of Ohara SF15 qlass and air-spaced from the third lens element, and a fifth lens element made of Ohara KZFS8 glass and cemented to the fourth lens element. FIG. 34 provides a profile drawing and a plot of paraxial marginal ray height versus wavelenath for a four-al ass lens quintuplet that is color-corrected at five wavelenaths, the quintuplet having a focal length of 1000 mm at x0 = .54607 vm for a relative aperture of f/10, and comprisina a first lens element made of Schott PK51 glass, a second lens element made of Schott LAK20 alass and air-spaced from the first lens element, a third lens element made of Schott PK51 glass and cemented to the second lenu element, a fourth lens element made of Schott KZFSN4 glass and air-spaced from the third lens element, and a fifth lens element made of Schott KSFS6 glass and cemented to the fourth lens element. BEST MODE OF CARRYING OUT THE INVENTION It is a feature of the present invention that combinations of optical glasses, which are compatible with each other for designing optical systems that are color-corrected at three or more wavelengths, can be readily selected from amona the various optical glasses available to the designer. Commercially available types of optical glasses are listed in catalogs published by various manufacturers. The latest edition (1980 Edition) of the Schott catalog lists 238 different types of optical glasses. The latest Ohara cataloa (distributed in 1981) lists 227 different types of optical glasses. The latest Hoya catalog (distributed in 1981) lists 206 different optical glass types. The latest Cornina-France cataloa base Edition) lists 80 different optical glass types. The latest Chance Pilkington catalog (1980 Edition) lists 62 different optical glass tvpes. These five manufacturers presently produce a total of 813 different types of optical alasses. The initial problem in desiqninq an optical system that is to be color-corrected at more than two wavelenaths is to select a suitable combination of optical materials from among the various types of optical materials available to the desiqner. The present invention provides a unified procedure for selectina suitable combinations of optical materials for use in designing color-corrected optical systems. The procedure of the present invention can be conveniently illustrated in connection with the design of a two-alass lens doublet (i.e., a multiplet comprising two lens elements made from different types of glasses), which is color-corrected at n different wavelengths, where n > 2. The principle discussed herein apply as well to the selection of alasses or other optical materials for designing color-corrected lens triplets and higher-number lens multiplets. The number of possible pairs of alasses that can be formed from the 813 different types of optical glasses listed in the cataloas published by the leading optical glass manufacturers can be determined by calculatina the combination of n things taken r at a time, i.e., C(n,r) = n'/rt(n - r)', where n = 813 and r = 2. This number, which is independent of the order in which the glasses are selected, is 330,078. Thus, if a 1,cut-and-try" approach were used to identify pairs of optical glasses that are compatible with each other for desianing a two-glass color-corrected lens doublet, more than 330,000 different combinations of glasses would have to be investigated. Very few pairs of optical glasses suitable for designing a two-glass lens doublet that is color-corrected at three wavelenaths have been reported in the literature; and those few suitable alass pairs that have been reported were discovered by cut-and-try techniques without the benefit of a unified theoretical basis for selectinq the particular glasses. Until the present invention, there has been no systematic way of knowing whether any particular alass could be paired with any other particular glass to produce an optical system that is color-corrected at more than two wavelenaths. In FIG. 1, two optical materials G1 and G2 are represented by corresponding glass points G1[n11, n21, n31, ... , n(n-1)] and G2[n12, n22, n32 .., Ti 1 in an (n - 1)-dimensional orthogonal coordinate system definina a so-called glass space. The coordinates of any particular optical material in the glass space are the -dispersion coefficients of the optical material, as derived from a generalized (n - 1)th degree dispersion model. The condition that must be satisfied in order for a two-glass optical system comprising these two particular optical materials G1 and G2 to be color-corrected at n wavelengths is that the vectors G1 and 2 in the glass space satisfy the vector equation & G 2 where a is a real scalar quantity. In graphic terms, as illustrated in FIG. 1, the glass points G1 and G2 must be substantially collinear with the origin of the coordinate system. For the special case of a two-glass optical system that is color-corrected at two wavelengths (i.e., where n = 2), the dispersion model used to derive the n-dispersion coefficients is linear. As shown in FIG. 2, a two-glass two-color optical system can be designed using any pair of optical glasses, because the glass points for all optical glasses necessarily lie on the same straioht line in the one-dimensional n-disPersion coefficient space of the linear dispersion model. Although, any two different optical glasses could in principle be used in combination with each other for designing an optical system that is color-corrected at two wavelengths, it would normally be desirable to use only those pairs of glasses for which the absolute value of the difference between their corresponding primary dispersion coefficients is as large as possible. For the special case of a two-alass optical system that is color-corrected at three wavelengths (i.e., where n = 3), the dispersion model used to derive the n-dispersion coefficients is quadratic. As shown in FIG. 3, a two-al ass three-color optical system can be designed using a pair of optical glasses whose glass points are collinear with the origin of the coordinate system defining the two-dimensional n-dispersion coefficient space of the quadratic dispersion model. Thus, if the glass points for the various optical alasses available to the designer are plotted on the (n1,n2) plane, suitable pairs of alasses that could in principle be used for designing an optical system that is color-corrected at three wavelengths can be ascertained by drawing straight lines from the orion of the coordinate system. Those glasses whose glass points are collinear with each other alona any straiaht line throuah the origin of the coordinate system are in principle suitable candidates from which glass pairs can be selected for desiqning the two-glass three-color optical system. Although any pair of alasses whose glass points are collinear with each other and with the origin of the coordinate system as shown in FIG. 3 could be used for designing a two-glass three-color optical system, it would ordinarily be desirable to select a pair of glasses from among those alasses satisfying the further condition that the absolute value of the difference between the corresoonding primary dispersion coefficients is large. The particular design form of the optical system, including a determination of the appropriate number of lens elements (e.g., doublet, triplet, or hiher-number multiplet), is determined in accordance with the principles of qeometrical optics. For the special case of a two-alass optical system that is color-corrected at four wavelengths (i.e., where n = 4), the dispersion model used to derive the -dispersion coefficients is cubic. As shown in FIG. 4, a two-lass four-color optical system can be designed using a pair of optical glasses whose glass points are collinear with the origin of the coordinate system defining the three-dimensional n-dispersion coefficient space of the cubic dispersion model. Thus, if the glass points for the various optical glasses available to the designer are plotted in the three-dimensional (n1,n2,n3) space, suitable pairs of glasses that could in principle be used for designing an optical system that is color-corrected at four wavelengths can be ascertained by drawina straiqht lines from the origin of the coordinate system. Those alasses whose alass points are linear with each other alona any straiaht line throuah the orioin of the coordinate system are in principle suitable candidates fron which glass pairs can be selected for desianing the two-al ass four-color optical system. A preferred pair of alasses would ordinarily comprise alasses for which the absolute value of the difference between their correspondina primary dispersion coefficients is as large as possible. The degree of the dispersion model used to derive the n-dispersion coefficients does not depend upon the number of glasses used in making the lens elements of the optical svstem. Therefore, the same three-dimensional plot of glass points shown in FIG. 4 in connection with the desian of a four-color optical system comprisina two different types of qlasses could also be used for designing a four-color optical system comprising three different types of glasses. A three-glass lens system must necessarily comprise at least three lens elements. For a three-glass optical system that is color-corrected at four wavelengths (i.e., where n = 4), the dispersion model used to derive the n-dispersion coefficients is cubic. As shown in FIG. 5, three glasses G1, G2 and G3 are suitable for desiqning an optical system that is color-corrected at four or more wavelenaths, if the alass points representing those three glasses in three-dimensional n-dispersion coefficient space are coplanar with each other and with the origin of the coordinate system. In general, for an optical system that is color-corrected at n wavelengths, the dispersion model used to derive the n-dispersion coefficients is an (n - 1)th deqree polynomial, where n Is the number of wavelengths for which color-correction is desired. Thus, a two-glass five-color optical system could be desianed using any pair of glasses whose glass points lie on a common hyperline through the origin of an orthogonal coordinate system defining a four-dimensional hyperspace, where the axes of the coordinate svstem are the n-dispersion coefficients accordina to a fourth degree dispersion model. Likewise, a three-glass five-color optical system could be designed usina any three glasses whose glass points lie on a common hyperDlane that passes through the origin of the coordinate system definina the same four-dimensional hyperspace. In accordance with the present invention, an (n - 1)th degree glass dispersion model is used to identify optical materials that are compatible with each other for desianino an optical system color-corrected at n wavelenoths. Each of the optical glasses available to the desianer is represented by a unique point in an (n - 1)dimensional glass space, where the dispersion coefficients of the individual glasses are the coordinates of the classes in the qlass space. In practice, it is convenient to employ a digital computer to calculate and compare dispersion coefficient ratios for the various alasses available to the designer, where the dispersion coefficients are determined from a glass dispersion model in accordance with the number of wavelengths for which color correction is required for the particular application. For most color-correction requirements, it would not be necessary to use a glass dispersion model of order higher than cubic, i.e., n = 4. For the analysis described herein, the n-dispersion coefficients are used, although the v-dispersion coefficients could have been used. In FIG. 6A, the alass points in n-dispersion coefficient space for 813 different optical glasses listed in the current cataloqs of the five leadina optical glass manufacturers are plotted in the two-dimensional n-dispersion coefficient space of the quadratic dispersion model. The values of n1 and n2, which are called the primary and secondary n-dispersion coefficients, respectively, for the glasses accordina to a quadratic dispersion model, were calculated from equation (7) using a least-squares method for seven wavelenaths in the visible region with a base wavelength of AO = 0.5740 PR. The seven wavelengths used were the solar emission lines 0.4047 m, 0.4350 pm, 0.4861 m, 0.5461 um, 0.5876 m, 0.6563 m and 0.7065 m. The optical glasses whose glass point coordinates n1 and n2 are olotted araphically in FIG. 6A are also listed in TABLE I. The 813 glasses manufactured by the five leading optical glass manufacturers are identified in TABLE I by manufacturer's name, i.e., SCHOTT, OHARA, HOYA, Cornina-France (abbreviated as CORrQ-F) and Chance Pilkington (abbreviated as CHANCE), and by cataloa number. Also given for each glass listed in TABLE I are the base refractive index at to = 0.574 m, the primary dispersion coefficient n1, thP secondary dispersion coefficient the ratio (n1In2) and the arc tangent of the ratio (n1/n2). The alasses are sorted in TABLE I in ascending order of the ratios (n1/n2). The arc tangent of the ratio (n1/n2) indicates the slope angle relative to the n1-axis, so that glasses having substantially the same arc tanaent of the ratio (n1/n2) are substantially collinear, and are therefore candidates for selection in forming pairs of alasses for designing optical systems that are color-corrected at three or more wavelenaths. FIG. 6B provides an enlargement of a portion of the plot shown in FIG. 6A. The alass selection procedure in accordance with the present invention can be illustrated graphically with reference to FIGS. 6A and 6B. In selecting a pair of glasses from among all the optical glasses whose glass points are plotted in FIG. 6A for designing a two-glass optical system that is color-corrected at three wavelengths, a designer first chooses one glass that is available to him and locates the glass point representina that one glass on the plot. The designer then draws a straiqht line extending throuah the glass point for that one glass and through the origin of the coordinate system. Other glasses that in principle are suitable for use in combination with that one glass for designing the desired two-al ass three-color lens doublet lie substantially on that same straiaht line. All class points on the same straight line through the origin of the coordinate system have the same slope angle relative to the n1-axis. Therefore, a tabulation of the available optical glasses in terms of a convenient function of the slope angle, e.n., the arc tangent of the ratio (n1/n2), as provided in Table I, can be used by an optical designer with greater convenience and accuracy than the graphical technique described above. With such a tabulation, all that the designer need do in selecting a pair of glasses for designing a two glass three-color lens doublet is to choose a first glass, and then to identify other glasses whose tabulated values for the arc tangent of the ratio (Ti11Ti2) are substantially the samp as for the chosen first glass. A suitable pair of glasses can he selected from among the glasses having substantially the same value for the arc tanaent of the ratio (n1/n2). Each of the alasses listed in TABLE I can be identified unambiguously by the manufacturer's cataloq number, which miaht be an alphanumeric desiqnation or a purely numeric designation dependina upon the manufacturer. In a case where a new type of glass is manufactured by changing the constituents or percentage composition of an older type of qlass, the new type of glass is invariably given a new catalog number by the manufacturer. Even where the new type of alass is made to meet the same optical specifications as an older type of glass, the new type of qlass is given a new cataloa number. The process of making any particular type of optical glass is ordinarily regarded by the manufacturer as proprietary information, and is ordinarily not known in detail by the optical designer who uses the glass. Accordingly, optical designers universally identify particular optical glasses by manufacturers' cataloq numbers. Considerina the portion of the plot of FIG. 6A shown in enlarged view in FIG. 6B, it is instructive to identify qlasses that could be paired with, for example, Hoya FCD10 glass for designing a two-glass optical system that is color-corrected at three wavelengths. Hoya FCD10 glass, with coordinates 1 = -0.0610293 and n2 = -0.00399528 in two-dimensional n-dispersion coordinate space (as ascertained by reference to page 10 of TABLE I), was selected for instructional purposes because the alass point for this particular optical glass is relatively isolated on the plot in FIG. 6B. A straight line, Line A, drawn through the origin of the coordinate system and the glass point for Hoya FCD10 glass indicates that, e,., Hoya FC3 glass (coordinates Til = -0.0842Q94 and n2 = -0.00547060) can be combined with Hoya FCD10 glass for designing a two-glass optical system that is color-corrected at at least three wavelengths. An examination of the cubic and quartic dispersion models for these two alasses in the same spectral region as covered by TABLE I for the quadratic dispersion model shows that this particular pair of optical alasses can yield axial color correction at up to five wavelengths. This phenomenal compatibility of the Hoya FCD10 and Hoya FC3 glasses is discussed hereinaftor in connection with a Mangin doublet mirror as illustrated in FIG. 21. Line A in FIG. 6B also shows several other glasses that could be combined with Hoya FCD10 alass to form pairs of compatible glasses for designing optical systems that are color-corrected at at least three wavelenqths. Thus, Schott BK8 glass (coordinates n1 = -0.0870925 and n2 = -0.00577220), Schott PSK50 alass (coordinates n1 = -0.0823975 and n2 = -0.00530444), Hoya PCD2 alass (coordinates n1 = -0.0878957 and "2 = -0.00577861), Hoya ZNC7 alass (coordinates n1 = -0.0905172 and n2 = -0.00582287), and Chance Pilkinaton 641601 qlass (coordinates n1 = -0.0923210 and n2 = -0.00588984) are also all substantially collinear with each other and with Hoya FCD10 alass and Hoya FC3 glass on Line A, and could in principle be considered along with Hoya FCD10 glass and Hoya FC3 glass as suitable candidates from which to select a pair of glasses for designing the desired two-glass three-color optical system. For optimum dioptric power distribution, however, it would usually be desirable to select a pair of olasses whose glass points are widely separated from each other alona Line A, so that the difference between the n1 primary dispersion coefficients for the two glasses is large. As another example, it is instructive to consider the glasses that could be combined with Schott PK51 alass (coordinates n1 = -0.0718368 and n2 = -0.00220267) for designing a two-alass optical system that is color-corrected at at least three wavelengths. A line, Line B, drawn through the oriqin of the coordinate system and the glass point for Schott PK51 glass indicates that, e.g., Hoya LAC7 glass (coordinates Ti1 = -0.0946047 and n2 = -0.00290729 could be paired with Schott PK51 glass to form a pair of compatible alasses for designina an optical system that is color-corrected at at least three wavelengths. An examination of the cubic and quartic dispersion models for these two alasses in the same spectral region as covered by TABLE I for the quadratic dispersion model shows that this particular pair of glasses can be used for designinq optical systems that are color-corrected at five wavelenaths. This phenomenal compatibility of the Schott PK51 and Hoya LAC7 alasses is demonstrated hereinefter by the lens doublet shown in FIG. 12, the lens quadruplet shown in FIG. 19, the Manin doublet mirror shown in FIG. 24, title Petzval lens system shown in FIG. 27, and the prism systems shown in FIGS. 30, 31 and 32. A glance at Line B indicates that a number of other qlasses, whose glass points lie substantially on Line B, are also suitable candidates for use in combination with Schott PK5I qlass for designing an optical system that is color-corrected at three wavelengths, e.g., Schott K11 alass (coordinates n1 = -0.0900976 and n2 = -0.00275514), Schott LAK21 glass (coordinates n1 = -0.0920718 and n2 = -0.00285003), and Cornina-France 511604 glass (coordinates nl = -0.0916603 and n2 = -0.00283942). It is important to remember that the values of n1 and n2 for the optical glasses listed in TABLE I were calculated using a least-squares method for seven selected wavelenaths in the visible spectrum extending from a minimum wavelength of approximately 0.4 um to a maximum wavelength of approximately 0.7 pm, with a base wavelength of 0.5740 um. These wavelenaths provide a statistically good representation of the entire visible spectrum. However, in a particular application, the designer might find it preferable to calculate values of n1 and n2 for the optical materials of interest by a least-squares method, or indeed by any other mathematical procedure, usina different wavelengths. For example, if the designer were concerned with color-correction for infrared wavelenaths, he could calculate a table of values for n1 and n2 for several wavelengths in the infrared wavelength band or bands of interest. If the designer were interested in obtainina color-correction at a number of different wavelength bands, as might be appropriate in designing, e.a., a color-corrected astronomical instrument having a common focal plane for radiation in the infrared and ultraviolet portions of the spectrum, he could calculate a table of values for n1 and n2 using several wavelengths in each of the wavelength bands of interest. The values calculated for n1 and n2, and therefore also the values calculated for the ratios (n1/n2) and for the arc tanaents of the ratios (n1/n2), depend upon tho wavelengths used in the quadratic dispersion model obtained from eqliÅation (7). In general, therefore, the values for n1 and n2 would differ from those shown in TABLE I, if different wavelenaths were to be used in representing the spectral range (or the discontinuous spectral bands) of interest to the designer. The values listed in TABLE I, however, are useful in illustrating the invention, and furthermore are of practical utility in selecting pairs of compatible glasses for desianing optical systems that are substantially color-corrected at at least three wavelengths in the visible spectrum. In TABLE II, the same alasses manufactured by the same five optical glass manufacturers are aqain listed and unambiguously identified by manufacturer's name and catalog number, alona with the base refractive index at 30 = 0.589 pm for each alass. Also listed for each glass in TABLE II are the primary dispersion coefficient n1, the secondary dispersion coefficient n2, the tertiary dispersion coefficient n3, and the ratios (n1/n2), (n2/n3) and (n1/n3), as calculated from equation (7) usina a least-squares fitted cubic dispersion model. For each glass, the n-dispersion coefficients n1, n2 and n3, as well as the base refractive index, were obtained for ten wavelengths in the extended spectral region from n.3650 um to 1.014 m, with a base wavelenath of #0 = 0.589 urn. The alasses are sorted in TABLE II in ascending order of the ratios (n1/n2). The ten wavelengths used were the solar emission lines 0.3650 urn, 0.4047 urn, 0.4350 urn, 0.4861 urn, 0.5461 um, 0.5876 urn, 0.6563 urn, 0.7065 urn, 0.7682 urn and 1.014 urn. Ordinarily, those optical glasses for which the corresponding ratios (n1.n2), (n2/n3) and (n1/n3) are substanyially equal to each other, and for which the glass points are substantially collinear with each other and with the origin of the coordinate system, are candidates for selection in forming pairs of compatible glasses to use for designing optical systems that are color-corrected at four wavelenaths. It is sometimes more convenient to use the arc tangents of the ratios (Ti11Ti2), (n2/n3) and (n1/n3) rather than the ratios themselves in selecting compatible pairs of glasses for designinq optical systems that are color-corrected at at least four wavelengths. Since the n-dispersion coefficients abd the #-dispersion coefficients for any optical material are related by the equation nij = #ij/(N0 - 1), the selection of alass pairs for designing a two-glass three-color optical system could also be made from a plot of the glass points in ';-dispersion coefficient space, or from a tabulation of the values for the arc tangents of the ratios (s1/v2), for the various optical glasses available to the designer. In FIG. 7A, the glass points are plotted in v-dispersion coefficient space for the same 813 qlasses whose glass points in n-dispersion coefficient space are plotted in FIG. 6A. An enlargement of a portion of the plot shown in FIG. 7A is shown in FIG. 7B. To illustrate graphically the method of selecting a pair of compatible glasses for designing a two-glass three-color optical system using the v-dispersion coefficients for the glasses available to the designer, consider Schott FK51 glass as the initial selection. Schott FK51 glass is represented in FIG. 7B by a glass point whose coordinates in v-dispersion coefficient space are v1 = -0.031926 and w2 = -0.001819, as determined by the quadratic dispersion model used to plot the glass points shown in FIGS. 7A and 7B. A straight line, Line C, drawn throuqh the origin of the coordinate system and the glass point for Schott FK51 glass indicates a number of other optical glasses whose glass points are substantially collinear with the origin and with the glass point for Schott FK51 glass. Examples of other suitable glasses lying on Line C include Schott K51 glass and Hoya ADF1 glass. All such glasses, whose glass points are substantially collinear with each other and with the origin, are suitable candidates from which to select a pair of glasses for desianin an optical system having the required color correction at three wavelengths. In FIG. 7B, straight lines could be drawn at various angles from the origin through the qlass points representina the optical glasses available to the designer, thereby identifying suitable pairs of glasses for designing two-glass three-color optical systems. Thus, Line D in FIG. 78 indicates that, e.g., Corninq-France 558525 glass and Schott BAF50 glass can be paired for designing a two-glass three-color optical system. In FIG. 6A or FIG. 7A, any pair of optical classes whose glass points lie substantially on the same straiqht line passing through the origin of the coordinate system can in principle be used for designing a two-glass three-color lens systems. Conversely, optical glasses whose glass points do not lie substantially on the same straight line cannot be used for designing a two-glass lens system that is color-corrected at three wavelengths. From equations (41) to (46), the dioptric powers and #2 of the individual lens elements of a two-glass three-color lens doublet are inversely proportional to the absolute value of the difference between the primary dispersion coefficients Ti11 and 12 of the glasses used to make the lens elements of the doublet. It is therefore necessary that the absolute value #12 - till be as larqe as possible in order to minimize the dioptric powers of the individual lens elements. ,If the dioptric powers of the lens elements were too large, the configurations of the lens elements might be so rounded (resemblina toy marbles in an extreme case) that it would be impractical to use them in most optical systems. The requirement that iTil2 - n11# be large would, therefore, ordinarily be treated as an additional condition that must be satisfied when selecting a pair of classes for designing a color-corrected optical system. In FIG. 6B or 7B, those optical classes whose glass points are substantially collinear with each other and with the origin of the coordinate system are suitable candidates from which to select a pair of glasses for designing a two-glass optical system that is color-corrected at three or more wavelenoths. Those glasses whose glass points are substantially collinear with the origin have ratios of primary to secondary dispersion coefficients that are substantially equal. Thus, in mathematical terms, when #11 #12 ### = ### #21 #22 or, equivalently, when ' 921 922 for two optical alasses, those two glasses in combination are suitable for designing a two-al ass optical system that is color-corrected at three wavelengths. This property can readily be exploited with a diqital computer by computing the slope of the line connectina each glass point with the origin, and then sortina all the glasses in ascending order of these "alass point" slopes. It was known in the prior art that any two optical glasses can in principle be used in combination with each other for desianing a lens doublet that is coldr-corrected at two wavelenqths. This prior art knowledae is seen to be a special case of the unified theory upon which the present invention is based, where n = 2. In FIG. 8, a cemented lens doublet of unit focal length at #0 = .54607 m for a relative aperture of f/10 is shown, where the lens elements comprising the doublet are made of Schott BK7 alass and Schott F2 glass. The two lens elements could be cemented toaether by any technique well-known in the art, as by using Canada balsam, optical cement or immersion oil. It can be seen by reference to paqe 9 of TABLE I that the ratio Ti11Ti2 = -13.6653 for Schott BK7 glass, and by reference to pase 7 of TABLE I that the ratio n1/n2 = -3.91263 for Schott F2 glass, are quite different in value. Thus, the unified theory upon which the present invention is based indicates that a lens doublet made of Schott BK7 and Schott F2 alasses cannot provide color correction at more than two wavelenaths. Color correction is a function of the choice of alasses used for desianina the doublet, and is independent of the particular desian form of'the doublet made from the chosen alasses. - Thus, no amount of manipulation of the design form of a lens doublet made from these two glasses can result in color correction at more that two wavelenaths. It is a feature of the present invention that the suitability or non-suitability of any particular combination of optical materials for desiqninq a color-corrected optical system can be readily determined by reference to tabulated data, such as by comparing tabulated values of the ratios n1/n2 for a pair of optical materials beinq considered. The present invention eliminates the need for "cut-and-try" methods for determininq whether any particular pair of optical materials can provide color correction at more than two wavelenaths. Although any two optical classes are suitable in principle for desiqning a two-glass two-color lens doublet, there was no unified theory in the prior art for predicting whether any two particular optical glasses would have appropriate dioptric powers so that lens elements with practical confiaurations could be made from those particular classes. It is a feature of the present invention, on the other hand, that the practicalitv or non-practicality of any two particular optical classes for desiqnina a lens doublet that is color-corrected at two or more wavelengths can be readily determined by reference to tabulated data. The cemented lens doublet shown in FIG. 8, comprising lens elements made of Schott BK7 and Schott F2 glasses, is color-corrected at only two wavelengths. Bv reference to TABLE I, it can be ascertained that the absolute value of the difference between corresponding values of n1 for Schott BK7 and Schott F2 glasses is quite large, i.e., "12 - n11# = 0.063435, indicating that the distribution of dioptric powers for lens elements made from these two glasses would be desirably small. Thus, the present invention provides a method for determininq the practicality of usinq two particular qlasses, e.g.,Schott flK7 glass and Schott F2 glass, in combination for desianinq a two-glass two-color lens doublet. As an empirical rule, it has been found that where the absolute value of the difference between the values of the primary dispersion coefficients nij(where j = 1, 2) for two optical classes is greater than about 0.02, i.e., when # #nij = nl? - nll # > 0.02, the dioptric powers of lens elements made from those two alasses will be small enough so that the lens elements will have sufficiently larqe radii of curvature to enable a lens doublet of practical configuration to be made. Also shown in FIG. 8 is a curve showing the relationship of paraxial marainal ray heiqht (conventionally desianated PY in the drawina) to wavelength for the lens doublet comprising first and second lens elements made of Schott BK7 and Schott F2 classes, respectively. Such a curve, hereinafter called a "wavelenath scan", for an optical system provides an indication of the quality of axial color correction obtainable with the optical system. The paraxial marginal ray height for an optical system at any particular wavelength is a measure of the so-caled secondary spectrum of the system at that wavelenath, i.e., a measure of the extent to which light at that particular wavelength is out-of-focus with respect to the common focus for which color-correction of the system is desired. Perfect color correction is achieved for those wavelengths at which the paraxial marainal ray heiaht is zero, i.e., for those wavelengths at which the "wavelenqth scan" curve crosses the horizontal axis. For wavelenqths at which perfect color correction is not achieved, the closeness of the "wavelength scan" curve to the horizontal axis provides a measure of the extent to which the optical system approaches perfect color correction. For the lens doublet shown in FIG. 8, color correction is obtained at one wavelength in the blue portion of the visible spectrum and at one wavelenath in the infrared spectrum. In between these two color-corrected wavelengths, however, the dispersion produced by the lens elements of the doublet is quite pronounced. The "wavelength scan" curve in FIG. 8 indicates that a lens doublet made Schott BK7 and Schott F2 alasses cannot provide a qood dearee of color correction at wavelenaths between the crossings of the horizontal axis, because the curve (i.e., the paraxial marginal ray height) departs rapidly from the horizontal axis even for wavelenaths close to the two crossings of the horizontal axis. INDUSTRIAL APPLICABILITY Two-Glass Lens Doublets: FIG. 9 illustrates a particular example of a three-color cemented lens doublet in which the optical glasses from which the two lens elements of the doublet are made were selected in accordance with the present invention. The lens doublet of FIG. 9 is of unit focal length at xO = .54607 pm for a relative aperture of f/10, and the two glasses used in making the lens elements of the doublet are Schott FK51 and Schott K51 glasses. These glasses were chosen because the ratios of their primary to secondary n-dispersion coefficients are substantially equal, and because the absolute value of the difference between corresponding values of the primary dispersion coefficient n1 for the two glasses is large. The wavelength scan curve shown in FIG. 9 crosses the horizontal axis at three discrete wavelengths in the visible spectrum, and is close to the horizontal axis throughout the entire wavelength band extending over the visible spectrum. Thus, a lens doublet made from this particular pair of optical glasses can provide very effective (if not perfect) color correction over substantially the entire visible spectrum. The design form of the lens doublet shown in FIG. 9 is specified in tabular format as follows: Surface Radius Thickness No. Ne Ve Material 1 .421 f .016 f 1.48794 84.07 Schott FK51 2 -.215 f .009 f 1.50720 59.34 Schott K51 3 7.034 f where the various lens element surfaces of the doublet system are numbered, in accordance with convantional practice, from left to right. The "Radius" listed for each surface is the radius of curvature of the surface expressed as a multiple of the focal length f of the lens system at a relative aperture of f/10. in accordance with convention, the radius of curvature of an optical surface is said to be positive if the center of curvature of the surface lies to the right of the surface, and negative if the center of curvature of the surface lies to the left of the surface. The "Thickness" listed for a particular surface is the thickness of the lens element bounded on the left by the indicated surface, where the thickness is measured along the optical axis of the lens system. The thickness of each lens element is expressed as a multiple of the focal length f of the lens system. Ne is the refractive index of- the lens element bounded on the left by the indicated surface, where the value of the refractive index is given for the mercury e line, i.e., for a wavelength of AO = 0.54607 pm. Ve is the Abbe number for the same lens element at the same base wavelength. "Material" refers to the type of optical material from which the lens element is made, where the type of optical material is identified by manufacturer and by manufacturer's catalog number. FIG. 10 illustrates a particular example of a four-color cemented lens doublet in which the optical glasses from which the two lens elements of the doublet are made were selected in accordance with the present invention. The lens doublet of FIG. 10 is of unit focal length at s0 = .54607 vm for a relative aperture of f/10. The glasses used in making the two lens elements of the doublet of FIG. 10 are Corning France 486817 and Ohara LAK14 glasses, which were chosen because their ratios (n1/n2) are substantially equal in the extended spectral region from 0.3fi5 vm to 1.014 vm, and because the difference between corresponding values of n1 for the two glasses is large. The wavelength scan curve shown in FIG. 10 crosses the horizontal axis at four discrete wavelengths in the visible and near infrared spectrum, and is close to the horizontal axis throughout this spectral range. Thus, a lens doublet made from this particular pair of optical glasses can provide very effective color correction over a wide spectral range bridging the visible and infrared wavelengths, especially in the range extending from the blue wavelengths through the near infrared wavelengths beyond 1.0 pm. The design form of the lens doublet shown in FIG. 10 is specified in tabular format as follows: Surface No. Radius Thickness Ne Ve Material 1 .257 f .016 f 1.48746 81.40 Corn-F 486817 2 -.372 f .009 f 1.69979 55.31 Ohara LAK14 3 2.022 f where the specified design parameters are as defined above in connection with FIG. 9. FIG. 11 illustrates a particular example of a four-color air-spaced lens doublet in which the two lens elements are made of the same types of optical glasses as for the cemented lens doublet shown in FIG. 10. The lens doublet of FIG. 11 is likewise of unit focal length at .54607 pm for a relative aperture of f/10. The wavelength scan curve shown in FIG. 11 crosses the horizontal axis at four discrete wavelengths in the visible and near infrared spectrum, and is close to the horizontal axis throughout the same spectral range for which the lens doublet of FIG. 10 provides effective color correction. Thus, the degree of color correction obtainable using the glasses of the cemented lens doublet shown in FIG. 10 is retained when an air space is provided between the lens elements, which implies that the quality of axial (i.e., longitudinal) color correction obtainable with a two-glass lens doublet is determined by the choice of glasses used for making the lens elements, and is independent of the design form of the doublet. The quality of correction for lateral chromatic abberation, spherochromatism and the remaining aberrations, however, depends upon the design form of the lens doublet. The design form of the lens doublet shown in FIG. 11 is specified in tabular format as follows: Surface No. Radius Thickness Ne Ve Material 1 .598 f .016 f 1.48746 81.40 Corn-F 486817 2 -.207 f .0005f Air 3 -.221 f .009 f 1.69979 55.31 Ohara LAK14 4 -.699 f FIG. 12 illustrates a particular example of a five-color cemented lens doublet in which the optical glasses from which the two lens elements of the doublet are made were selected in accordance with the present invention. The lens system of FIG. 12 is of unit focal length at to = .54607 vm for a relative aperture of f/10. The glasses used in making the two lens elements of the cemented doublet of FIG. 12 are Schott PK51 and Hoya LAC7 glasses, which were chosen because the ratios of their primary to secondary n-dispersion coefficients are substantially equal, and because the absolute value of the difference between corresponding values of nl for the two glasses is large. The wavelength scan curve shown in FI6. 12 crosses the horizontal axis at five discrete wavelengths in the spectral range extending from the ultraviolet to the near infrared wavelengths. Furthermore, the wavelength scan curve is extremely close to the horizontal axis throughout the spectral range extending from the green wavelengths to about 0.8 pm in the near infrared region. Thus, a lens doublet made from this particular pair of optical glasses can provide very effective axial color correction throughout this region of the optical spectrum. The design form of the lens doublet shown in FIG. 12 is specified ir tabular format as follows: Surface ho. Radius Thickness Ne Ve Material 1 .753 f .020 f 1.53019 76.57 Schott PK51 2 -.151 f .0004f Air 3 -.156 f .010 f 1.65426 58.15 Hoya LAC7 4 -.680 f Two-Glass Lens Triplets: FIG. 13 illustrates an example of a four-color cemented two-glass lens triplet In which the optical glasses from which the three lens elements of the triplet are made were selected in accordance with the present invention. The lens triplet as shown in FIG. 13 has a focal length that is 40 times the focal length of the lens doublets shown in FIGS. 8 - 12 at zo = .54607 pm for a relative aperture of f/10. The first and third lens elements of the lens triplet of FIG. 13 are made of Corning-France 486817 glass, and the second (i.e., middle) lens element is made of Corning-France 589612 glass. These glass types were chosen because the ratios of their primary to secondary n-dispersion coefficients are substantially equal, and because the absolute value of the difference between corresponding values of n1 for the two glasses is large. The wavelength scan curve shown in FIG. 13 crosses the horizontal axis at four discrete wavelengths in the spectral range extending from the blue to the near infrared wavelengths, and is close to the horizontal axis throughout this spectral range. Thus, a lens triplet made from this particular pair of optical glasses can provide very effective axial color correction throughout this region of the optical spectrum. It is convenient to specify the design form of the lens triplet of FIG. 13 in terms of unit focal length for a relative aperture of f/10, as was done above for the lens doublets of FIGS. 8 - 12. It is noted, however, that the depiction in FIG. 13 shows a lens triplet whose focal length is 40 times that of the lens doublets shown in FIGS. 8 - 12, In terms of the focal length f, the design form of the lens triplet of FIG. 13 As specified in the tabular format as follows: Surface No. Radius Thickness Ne Ve Material - 1 .368 f .015 f 1.48746 81.40 Corn-F 486817 2 -2.029 f .009 f 1.59129 60.94 Corn-F 589612 3 .212 f .013 f 1.48746 81.40 Corn-F 486817 4 -2.324 f FIG. 14 illustrates a particular example of a four-color two-glass lens triplet in which the three lens elements are made of the same types of optical glasses as for the cemented lens triplet shown in FIG. 13, with the first and second lens elements being cemented together, and with an air gap being provided between the second and third lens elements. The focal length of the lens triplet shown in FIG. 14 is the same as for the lens triplet shown in FIG. 13 for the same relative aperture of f/10. The wavelength scan curve shown in FIG. 14 likewise crosses the horizontal axis at four discrete wavelengths in the spectral range extending from the blue to the near infrared wavelengths, and is close to the horizontal axis throughout this spectral range. Thus, the degree of axial color correction obtainable using the pair of glasses of the cemented lens triplet shown in FIG. 13 is seen to be retained when an air space is provided between two of the lens elements. The wavelength scan thus indicates that, for a given pair of optical materials, the quality of axial color correction obtainable with a two-glass lens triplet is determined by the choice of glasses used to make the lens elements of the triplet, and is independent of the design form of the triplet. Of course, the quality of correction for lateral color aberration, spherochromatism and the higher-order monochromatic aberrations is dependent upon the design form of the lens triplet. In terms of the focal length, the design form of the lens triplet of FIG. 14 is specified in tabular format as follows: Surface No. Radius Thickness Ne Ve - Material 1 .419 f .015 f 1.48746 81.40 Corn-F 486817 2 -.449 f .009 f 1.59129 60.94 Corn-F 589612 3 .342 f .001 f Air 4 .360 f .013 f 1.48746 81.40 Corn-F 486817 5 -1.101 f Two-Glass Lens Quadruplets: FIG. 15 illustrates a particular example of a four-color cemented two-glass lens quadruplet having a focal length that is 40 times the focal length of the lens doublets shown in FIGS. 8 - 12 at xot .54607 pm for a relative aperture of f/10. The optical glasses from which the four lens elements of the quadruplet shown in FIG. 15 are made were selected in accordance with the present invention. The first and third lens elements are made of Corning-France 486817 glass, and the second and fourth lens elements are made of Corning-France 589612 glass. These glasses were chosen because the ratios of their primary to secondary n-dispersion coefficients are substantially equal, and because the absolute value of the difference between corresponding values of for the two glasses is large. The wavelength scan curve shown in FIG. 15 crosses the horizontal axis at four discrete wavelengths in the spectral range extending from the blue to the near infrared region of the optical spectrum. The wavelength scan curve is close to the horizontal axis throughout this spectral range, which indicates that a lens quadruplet made from this particular pair of glasses can provide effective axial color correction throughout this spectral range. In terms of the focal length, the design form of the lens quadruplet of FIG. 15 is'specffied in tabular format as follows: Surface No. Radius Thickness Ne Ve Material 1 .437 f .015 f 1.48746 81.40 Corn-F 486817 2 5.098 f .009 f 1.59129 60.94 Corn-F 589612 3 .285 f .015 f 1.48746 81.40 Corn-F 486817 4 -.363 f .009 f 1.59129 60.94 Corn-F 589612 5 -1.147 f FIG. 16 illustrates a particular example of a four-color two-glass lens quadruplet in which the four lens elements are made of the same types of optical glasses as for the cemented lens quadruplet shown in FIG. 15, with the first and second lens elements being cemented together, the third and fourth lens elements being cemented together, and an air gap being provided between the second and third lens elements. The focal length of the lens quadruplet shown in FIG. 16 is the same as for the lens quadruplet shown in FIG. 15 for the same relative aperture of f/10. The wavelength scan curve shown in FIG. 16 likewise crosses the horizontal axis at four discrete wavelengths in the spectral range extending from the blue to the near infrared region of the optical spectrum. The wavelength scan curve of FIG. 16 is likewise close to the horizontal axis throughout this spectral range. As can be seen by comparing the wavelength scan of FIG. 16 with the wavelength scan of FIG. 15, the degree of axial color correction obtainable using the pair of glasses of the cemented lens quadruplet of FIG. 15 is retained when an air space is provided between two of the lens elements. In terms of the focal length, the design form of the lens quadruplet of FIG. 16 is specified in tabular format as follows: Surface No. Radius Thickness Ne Ve Material 1 .948 f .015 f 1.48746 81.40 Corn-F 486817 2 -.375 f .009 f 1.59129 60.94 Corn-F 589612 3 1.280 f .001 f Air 4 .499 f .009 f 1.59129 60.94 Corn-F 589612 5 .274 f .015 f 1.48746 81.40 Corn-F 486817 6 -1.150 f FIG. 17 illustrates a particular example of a four-color two-glass lens quadruplet in which the four lens elements are made of the same types of optical glasses as for the lens quadruplets shown in FIGS. 15 and 16, except that the first and third lens elements are made of Corning-France 486817 glass and the second and fourth lens elements are made of Corning-France 589612 glass. The focal length of the lens quadruplet shown in FIG. 17 is the same as for the lens quadruplets shown in FIGS. 15 and 16 for the same relative aperture of f/10. As with the lens quadruplet shown in FIG. 16, the first and second lens elements of the lens quadruplet shown in FIG. 17 are cemented together, the third and fourth lens elements are cemented together, and an air gap is provided between the second and third lens elements. The wavelength scan curve shown in FIG. 17 likewise crosses the horizontal axis at four discrete wavelengths in the spectral range extending from the blue to the near infrared region of the optical spectrum. The wavelength scan curve of FIG. 16 is likewise close to the horizontal axis throughout this spectral range. When compared with the wavelength scans shown in FIGS. 15 and 16, the wavelength scan shown in FIG. 17 further indicates that the quality of axial color correction obtainable with a lens multiplet is determined by the choice of glasses used for designing the multiplet, and Is independent of the design form of the multiplet. In terms of the focal length; the design form of the lens quadruplet of FIG. 17 is specified in tabular format as follows: Surface No. Radius Thickness Ne Ve Material 1 .823 f .015 f 1.48746 81.40 Corn-F 486817 2 -.400 f .009 f 1.59129 60.94 Corn-F 589612 3 1.069 f .001 f Air 4 .645 f .015 f 1.48746 81.40 Corn-F 486817 5 -.337 f .009 f 1.59129 60.94 Corn-F 589612 6 -.758 f Two-Glass Collimators: FIG. 18 shows a four-color collimator comprising a two-glass lens quadruplet, which can be used for precise collimation of a beam of light having a spectral range from blue to near infrared. The collimator of FIG. 18 comprises a lens,quadruplet wherein the consecutive lens elements are all air-spaced. The first and fourth lens elements of the collimator are made of Hoya FCDlO glass, and the second and third lens elements are made of Ohara LAK14 glass. The wavelength scan curve shown in FIG. 18 crosses the horizontal axis at four discrete wavelengths, and is close to the horizontal axis throughout a wavelength band that bridges the visible and near infrared spectral regions. In fact, the wavelength scan curve of FIG. 18 substantially coincides with the horizontal axis throughout the near infrared spectral range, which illustrates the suitability of this particular combination of optical glasses for correcting paraxial chromatic aberration in the near infrared spectral range. The collimator shown in FIG. 18, in addition to being substantially color-corrected in the near infrared spectral range, is also wellcorrected for the various monochromatic aberrations. In terms of the focal length for a relative aperture of f/10, the design form of the collimator of FIG. 18 is specified in detail in tabular format as follows: Surface No. Radius Thickness Ne Ve Material 1 1.244 f .015 f 1.45770 90.32 Hoya FCD10 2 - .381 f .010 f Air 3 - .381 f .009 f 1.69979 55.31 Ohara LAK14 4 - .542 f .002 f Air 5 - .539 f .00q f 1.69979 55.31 Ohara LAK14 6 -3.845 f 000of Air 7 .715 f .015 f 1.45770 90.32 Hoya FCD10 8 -1.025 f FIG. 19 shows a five-color collimator comprising a two-glass lens quadruplet. The first and fourth lens elements of the collimator of FIG. 19 are made of Schott PK51 glass, and the second and third lens elements are made of Hoya LAC7 qlass. These two optical glasses were selected because of the substantial collinearity of their respective glass points with the origin of the coordinate system in fourdimensional n-dispersion coefficient space, and also because the absolute value of the difference between their respective primary dispersion coefficients is large. The wavelength scan curve shown in FIG. 19 crosses the horizontal axis at five discrete wavelengths in the spectral range extending from about 0.38 vm to about 0.80 pm. These five wavelengths can therefore be precisely focussed using the collimator of FIG. 19. The other wavelengths in this spectral range can be focussed with a degree of precision indicated by the closeness with which the wavelength scan curve approaches the horizontal axis. The collimator shown in FIG. 19 is well-corrected for the various monochromatic aberrations, especially spherochromatism. In terms of the focal length for a relative aperture of f/10, the design form of the collimator of FIG. 19 is specified in tabular format as follows: Surface No. Radius Thickness Ne Ve Material 1 -1.314 f .018 f 1.53019 76.57 Schott PK51 2 - .295 f .025 f Air 3 - .269 f .010 f 1.65426 58.15 Hoya LAC7 4 -1.795 f .003 f Air 5 .469 f .010 f 1.65426 58.15 Hoya LAC7 6 .233 f .002 f Air 7 .232 f .015 f 1.53019 76.57 Schott PK51 8 - .697 f FIG. 20 shows a five-color collimator comprising a lens quadruplet having a focal length that is 40 times the focal length of the doublets shown in FIGS. 8 - 12 at AO = .54607 um for a relative aperture of f/8. The first and fourth lens elements of the collimator of FIG. 20 are made of calcium fluoride crystal, and the second and third lens elements are made of Hoya LAC7 glass. Use of calcium fluoride crystal as one of the optical materials enables a larger aperture (i.e., a lower f-number) to be used than would be possible if both optical materials were glasses. With the collimator of FIG. 20, a light beam of large diameter can be collimated without significant error due to spherochromatism. The wavelength scan curve shown in FIG. 20 crosses the horizontal axis at five wavelengths, and therefore indicates that precise collimation can be obtained at five wavelengths, in the spectral range from ultraviolet to near infrared. The closeness of the wavelength scan curve to the horizontal axis throughout this spectral range indicates that a high degree of collimation can be obtained for the other wavelengths in this range. In terms of the focal length for a relative aperture of f/8, the design form of the collimator of FIG. 20 is specified in tabular format as follows: Surface No. Radius Thickness Ne Ve Material 1 - .668 f .08 f 1.43500 95.06 Calcium Fluoride 2 - .268 f .032 f Air 3 - .250 f .010 f 1.65426 58.15 Hoya LAC7 4 - .565 f .001 f Air 5 .455 f .010 f 1.65426 58.15 Hoya LAC7 6 .384 f .001 f Air 7 .424 f .015 f 1.43500 95.06 Calcium Fluoride 8 - .635 f Two-Glass Mangin Mirrors: FIG. 21 illustrates a particular example of a cemented Mangin doublet mirror, which is color-corrected at five wavelengths. The Mangin doublet mirror of FIG. 21 has unit focal length at A0 .54607 m for relative aperture of f/2, and comprises a first lens element made of Hoya FCD10 glass and a second lens element made of Hoya FC3 glass. The outward facing surface of the second lens element is provided with a reflective coating, which could comprise a conventional reflecting material such as, e.g., silver or aluminum. The Hoya FCD10 and Hoya FC3 passes, used in combination, provide color correction at five wavelengths. The design form of the particular Mangin doublet mirror shown in FIG. 21 is specified in tabular format as follows: Surface Radius Thickness No. Ne Ve Material 1 - .421 f .036 f 1.45770 90.32 Hoya FCD10 2 4.200 f .057 f 1.46619 65.49 Hoya FC3 3 -1.572 f - .057 f 1.46619 65.49 Hoya FC3 4 4.200 f - Q?,6 f 1.45770 90.32 Hoya FCD10 5 - .958 f where the negative values of thickness listed for the lens element after the third surface, as numbered in accordance with conventional practice from left to right in the drawing, indicate that reflection occurs at the third surface. Thus, the fourth surface is the same as the second surface, and the fifth surface is the same as the first surface. Light at a color-corrected wavelength passing consecutively through the first and second surfaces is reflected from the third surface back consecutively through the second (i.e., fourth) and first (i.e., fifth) surfaces to the focal plane of the Mangin doublet mirror. The wavelength scan for the Mangin doublet mirror shown in FIG. 21 indicates that precise color correction occurs at five discrete wavelengths in the optical spectrum, and that a high degree of axial color correction is achieved over a band of wavelengths extending from the far ultraviolet to the near infrared regions of the spectrum. In general, in accordance with the present invention, dispersive effects can be substantially eliminated from Mangin mirrors by the proper choice of optical materials from which the lens elements are made. FIG. 22 illustrates another example of a cemented Mangin doublet mirror, which provides substantially complete axial color correction from the blue to the near infrared regions of the spectrum. The Mangin doublet mirror of FIG. 22 has unit focal length at to x0 = .54607 pm for a relative aperture of f/2, and comprises a first lens element made of Hoya BAF11 glass and a second lens element made of Hoya FL6 glass. The outward facing surface of the second lens element is provided with a reflective coating. The design form of the Mangin doublet mirror shown in FIG. 22 is specified in tabular format as follows: Surface No. Radius Thickness Ne Ve Material 1 -1.897 f .025 f 1.67000 47.97 Hoya BAF11 2 3.607 f .040 f 1.57047 42.57 Hoya FL6 3 -1.825 f - .oao f 1.57047 42.57 Hoya FL6 4 3.607 f - .025 f 1.67000 47.97 Hoya BAF11 5 -1.897 f The wavelength scan for the Mangin doublet mirror of FIG. 22 shows that precise axial color correction (i.e., crossing of the horizontal axis) occurs at four discrete wavelengths, and that a high degree of axial color correction (i.e., only insignificant paraxial marginal ray height) occurs throughout the spectral range extending from the blue to beyond 0.8 pm in the near infrared regions of the spectrum. FIG. 23 illustrates an example of a cemented Mangin doublet mirror, which provides substantially complete color correction from the blue to well into the near infrared regions of the optical spectrum. The Mangin doublet mirror of FIG. 23 has unit focal length at to = .54607 pm for relative aperture of f/2, and comprises a first lens element made of Cornina-France 486817 glass and a second lens element made of Corning-France 697554 glass. The outward facing surface of the second lens element is provided with a reflective coating. The design form of the Mangin doublet mirror shown in FIG. 23 is specified in tabular format as follows: Surface No. Radius Thickness Ne Ve Material 1 - .7!53 f .042 f 1.48746 81.40 Corn-F 486817 2 -7.4100 f .066 f 1.70000 55.18 Corn-F 697554 3 -1.536 f - .066 f 1.70000 55.18 Corn-F 697554 4 -7.400 f - .042 f 1.48746 81.40 Corn-F 486817 5 - .753 f The wavelength scan for the Mangin doublet mirror of FIG. 23 shows that precise axial color correction occurs at four discrete wavelengths, and that a high degree of axial color correction occurs throughout the spectral range extending from the blue to beyond 1.0 pm in the near infrared region of the spectrum. FIG. 24 illustrates a particular example of an air-spaced Mangin doublet mirror, which is color-co*rected at five wavelengths. The Mangin doublet mirror of FITS. 24 has unit focal length at x0 = .54607 vm for a re lative aperture of f/2, and comprises a first lens element made of Schott PK51 glass and a second lens element made of Hoya LAC7 glass. The two lens elements are separated by an air gap, and the outward facing surface of the second lens element is provided with a reflective coating. The design form of the Mangin doublet mirror shown in FIG. 24 is specified in tabular format as follows: Surface No. Radius Thickness Ne Ve Material 1 - .775 f .040 f 1.53019 76.57 Schott PK51 2 3.799 f .007 f Air 3 4.568 f .061 f 1.65426 58.15 Hoya LAC7 4 -1.501 f - .061 f 1.65426 58.15 Hoya LAC7 5 4.568 f - .007 f Air 6 3.799 f - .040 f 1.53019 76.57 Schott PK51 7 - .775 f The wavelength scan for the Mangin doublet mirror of FIG. 24 indicates that precise color correction occurs at five discrete wavelengths, and that a high decree of axial color correction occurs throughout the spectral range extending from the violet to the near infrared regions of the optical spectrum. FIG. 25 illustrates an example of an air-spaced Mangin doublet mirror, which provides substantially complete axial color correction throughout the visible and into the near infrared portions of the optical spectrum. The Mangin doublet mirror of FIG. 25 has unit focal length at A0 = .54607 pm for a relative aperture of off2, and comprises a first lens element made of Hoya FCD10 glass and a second lens element made of Ohara PSK1 glass. The two lens elements are separated by an air gap, and the outward facing surface of the second lens element is provided with a reflective coating. The design form of the Mangin doublet mirror shown in FIG. ? is specified in tabular format as follows: Surface No. Radius Thickness Ne Ve Material 1 - .736 f .036 f 1.45770 90.32 Hoya FCD10 2 8.012 f .004 f Air 3 8.273 f .057 f 1.54979 62.60 Ohara PSK1 4 -1.476 f - .057 f 1.54979 62.60 Ohara PSK1 5 8.273 f - .004 f Air 6 8.012 f - .036 f 1.45770 90.32 Hoya FCDlO 7 - .736 f The wavelength scan curve shown in FIG. 25 substantially coincides with the horizontal axis throughout the visible portion of the optical spectrum, although a larger scale plot would show that the crossings of the horizontal axis actually occur at five discrete wavelengths. Technically, therefore, the Mangin doublet mirror of FIG. 25 is color-corrected at only fiye wavelengths. However, for many practical applications, this Mangin doublet mirror can be considered to be substantially color-corrected throughout the visible wavelength band. FIG. 26 illustrates an example of an air-spaced Mangin doublet mirror, which provides substantially complete axial color correction from the green region of the visible spectrum to well into the infrared wavelengths. The Mangin doublet mirror of FIG. 26 has unit focal length at x0 - .54607 pm for a relative aperture of f/2, and comprises a first lens element made of Hoya FCD10 glass and a second lens element made of Hoya LAC14 glass. The two lens elements are separated by an air gap, and the outward facing surface of the second lens element is provided with a reflective coating. The design form of the Mangin doublet mirror shown in FIG. 26 is specified in tabular format as follows: Surface No. Radius Thickness Ne Ve Material 1 - .661 f .029 f 1.45770 90.32 Hoya FCD10 2 -2.254 f .010 f Air 3 -3.628 f .054 f 1.69980 55.25 Hoya LAC14 4 -1.519 f - .054 f 1.69980 55.25 Hoya LAC14 5 -3.628 f - .010 f Air 6 -2.254 f - .029 f 1.45770 9.32 Hoya FCD10 7 - .661 f The wavelength scan curve shown in FIG. 26 substantially coincides with the horizontal'axis from the green wavelength region to beyond 1.0 pm in the near infrared wavelength region of the spectrum. A larger scale plot would show that crossings of the horizontal axis actually occur at only four discrete wavelengths. Technically, therefore, the Mangin doublet mirror of FIG. 26 is color-corrected at only four wavelengths. However, for many practical applications, particularly applications in the near infrared region of the spectrum, the Mangin doublet mirror of FIG. 26 can be considered to be substantially color-corrected throughout the wavelength band of interest. Two-Glass Petzval Lens Systems: The designation "Petzval lens system" is generally applied to a lens system comprising two widely separated lens groups, each of which has a net positive dioptric power, followed by a negative lens element or a lens group having a net negative dioptric power. The positive lens groups in combination provide good resolution at high aperture for narrow to moderate fields of view. The negative lens element or lens group functions as a field flattener. A lens group is said to have positive dioptric power when it causes light rays passing through it to converge, and to have negative dioptric power when it causes light rays passing through it to diverge. Often, each lens group of a Petzval lens system is a doublet. However, for a particular application, either one (or all) of the lens groups of a Petzval lens system could be a singlet, a triplet or a high-number multiplet. The spacing between the two positive lens groups of a Petzval lens system is large in comparison with the thicknesses of the individual lens elements comprising each lens group. Within a lens group, the individual lens elements could be cemented or air-spaced. It is usual for a negative lens element or lens group functioning as a field flattener to be positioned immediately in front of the image plane of the system to correct for field curvature. A Petzval lens system that includes a field flattener is called, appropriately, a flat-field Petzval lens system. For a given optical design, aberrations scale linearly with the physical size of the system. Thus, a lens system that is reasonably well-corrected for a relatively short focal length (say, less than 10 mm) might have very severe aberration problems at a focal length of more than 100 mm. In the prior art, Petzval lens systems were typically used only in short-focus applications, e.g., in projectors for 16 mm and 8 mm motion-picture films. For very long-focus applications (e.g., more than 200 mm), Petzval-type lens systems were not generally used because of the difficulty in designing high-aperature long-focus Petzval lens systems that are well-corrected. The lens groups of Petzval lens systems of the prior art were typically 'achromats", :.e., doublets color-corrected at only two wavelengths. Furthermore, Petzval lens systems of the prior art were typically used only in relatively narrow field-angle applications. An example of a short-focus narrow field-angle Petzval lens system is described in U.S. patent 3,255,664. FIG. 27 shows a two-glass flat-field lens system of the Petzval type made of the same two types of optical glasses as used for the lens doublet shown in FIG. 12, i.e., Schott PK51 and Hoya LAC7 glasses. The last lens element 'iri the system, which is a biconcave lens made of Hoya LAC7 glass, functions as a field flattener. The Petzval lens system of FIG. 27 is color-corrected at five wavelengths in the optical spectrum from .4 pm to .7 pm, and is also well-corrected for monochromatic aberrations in this spectral range. The design form of the Petzval lens system of FIG. 27, in terms of the focal length for a relative aperture of f/3.5, is specified in tabular format as follows: Surface No. Radius Thickness Ne Ve Material 1 .342 f .031 f 1.53019 76.57 Schott PK51 2 - .497 f .006 f Air 3 -1.190 f .020 f 1.65426 58.15 Hoya LAC7 4 1.465 f .015 f Air 5 - .299 f .020 f 1.65426 58.15 Hoya LAC7 6 .522 f .001 f Air 7 .350 f .028 f 1.53019 76.57 Schott PK51 8 - .438 f ' .274 f Air 9 .508 f .023 f 1.53019 76.57 Schott PK51 10 - .593 f .016 f Air 11 - .225 f .018 f 1.65426 58.15 Hoya LAC7 12 1.483 f .oia f Air 13 .417 f .025 f 1.53019 76.57 Schott PK51 14 - .356 f .?68 f Air 15 - .241 f .013 f 1.65426 58.15 Hoya LAC7 16 2.412 f The wavelength scan for the Petzval lens system of FIG. 27 shows three crossings of the horizontal axis in the visible spectral range, as well as single crossings in the ultraviolet and infrared portions of the spectrum. For the visible wavelengths from the blue region into the red region, the paraxial marginal ray height is insignificant, indicating that very substantial axial color correction occurs throughout that portion of the visible spectrum. The design form of this Petzval lens system also provides superb correction of the monochromatic aberrations, and the chromatic variation of spherical aberration and coma. The Petzval lens system of FIG. 27 is noteworthy for having a long focal length (f = 600 mm) at a relative aperture of fl3.5, while providing a field of view of 120. This particular Petzval lens system is without precedent in enabling diffraction limited performance to be provided at such a large aperture and wide field of view. FIG. 28 shows a two-glass flat-field lens system of the Petzval type made of the same two types of optical glasses as used for the lens doublets shown in FIGS. 10 and 11, i.e., Corning-France 486817 and Ohara LAK14 glasses. The Petzval lens system of FIG. 28 is color-corrected at four wavelengths, two in the visible region and two in the infrared region. This system is also well-corrected for spherochromatism and the monochromatic aberrations. The design form of the Petzval lens system of FIG. 28, in terms of the focal length for a relative aperture of f/3.5, is specified in tabular format as follows: Surface No. Radius Thickness Ne Ve Material 1 .305 f .020 f 1.48746 81.40 Corn-F 486817 2 - .900 f .005 f Air 3 - .337 f .013 f 1.69979 55.31 Ohara LAK14 4 .398 f .001 f Air 5 .192 f .018 f 1.48746 81.40 Corn-F 486817 6 - .692 f .166 f Air 7 .441 f .016 f 1.48746 81.40 Corn-F 486817 8 - .385 f .010 f Air 9 - .146 f .011 f 1.69979 55.31 Ohara LAK14 10 - .552 f .OOq f Air 11 .393 f .060 f 1.48746 81.40 Corn-F 486817 12 - .240 f .187 f Air 13 - .162 f .014 f 1.69979 55.31 Ohara LAK14 14 .789 f The wavelength scan for thp Petzval lens system of FIG. 28 shows very substantial (if not perfect) color-correction throughout the spectral range extending from the blue wavelength region to beyond 1.0 pm in the near infrared region. It is remarkable that such color correction can be obtained for a Petzval lens system using only two different optical glasses. The Petzval lens system of FIG. 28 has a long focal length (f = 380 mm) at a relative aperture of f/3.5, while providing a field of view of approximately 120 The design form of this Petzval lens system provides diffraction limited performance throughout the spectral range for which it is color-corrected. FIG. 29 shows another long-focus flat-field Petzval lens system whose lens elements are made of only two different types of optical glasses, viz., Schott FK51 and Schott LAKN14 glasses. This Petzval lens system is color-corrected at three wavelengths, two in the visible region and one in the infrared region. The system is also well-corrected for spheróchromatism and the monochromatic aberrations, and provides diffraction limited performance throughout the spectral range for which it is color-corrected. The design form of the Petzval lens system of FIG. 29, in terms of the focal length for a relative aperture of f/2 (i.e., an extremely wide aperture), is specified in tablar format as follows: Surface No. Radius Thickness Ng Va Material 1 2.066 f .094 f 1.48794 84.07 Schott FK51 2 - 1.933 f .156 f Air 3 4.568 f .087 f 1.48794 84.07 Schott FK51 4 - 1.026 f .004 f Air 5 - .991 f .037 f 1.69980 55.19 Schott LAKN14 6 24.483 f .033 f Air 7 - 1.339 f .037 f 1.69980 55.19 Schott LAKN14 8 63.427 f .001 f Air 9 .850 f .087 f 1.48794 84.07 Schott FK51 10 - 5.545 f .873 f Air 11 .422 f .050 f 1.48794 84.07 Schott FK51 12 - .55 f .010 f Air 13 - .473 f .0?5 f 1.69980 55.19 Schott LAKN14 14 - 5.724 f .032 f Air 15 - 2.021 f .020 f 1.69980 55.19 Schott LAKN14 16 .969 f .001 f Air 17 .340 f .050 f 1.48794 84.07 Schott FK51 18 - .798 f .24q f Air 19 - .252 f .025 f 1.69980 Schott LAKN14 20 5.189 f The wavelength scan for the Petzval lens system of FIG. 29 shows that precise axial color-correction occurs at the wavelengths 0.527 pm, 0.640 um, and 0.778 m. In the range from 0.527 m to 0.778 m, the degree of color-correction obtainable is very high. The Petzval lens system of FIG. 29 has a focal length of 1000 mm, and a field angle of 4.2 . Two-Glass Prism Systems: FIG. 30 illustrates a two-alass cemented doublet prism system having a deviation angle of 60 for which very substantial color correction (i.e., only insignificant dispersion) occurs throughout the visible spectrum. The deviation angle nf a prism is defined as the angle through which a ray changes direction after passing through the prism, i.e., the angle between the direction of the ray entering the system and the direction of the ray exiting from the system. The prism system of FIG. 30 comprises a first prism element made of Schott PK51 glass and having an apex angle of al = 42.02390, and a second prism element made of Hoya LAC7 glass and having an apex angle of a2 = 25.5872O. The negative sign for a 2 is a convention indicating that the orientation of the apex of the second prism element is inverted with respect to the orientation of the apex of the first prism element. Also shown in FIG. 30 is a plot of change in angular deviation (in degrees) versus wavelength (in micrometers) for this particular doublet prism system for a 6 total deviation angle. The curve in FIG. 30 crosses the horiontal axis at five discrete wavelengths, which indicates that chromatic dispersion from a total deviation angle of 6o is precisely zero at those discrete wavelengths. It is particularly noteworthy, however, that the curve in FIG. 30 is very close to the horizontal axis throughout the entire visible region extending well into the infrared region of the spectrum to about 0.8 pm. For those wavelengths at which the total deviation angle differs from 60, the difference is approximately 0.0001 degree throughout this wavelength band. Thus, for many applications, the prism system of FIG. 30 can be considered to be color-corrected (i.e., as having substantially zero dispersion) for a deviation angle of 60 throughout this rather wide wavelength band, which includes the entire visible region. The plot of change in angular deviation versus wavelength shown in FIG. 30 describes a "real" ray trace, not a paraxial ray trace as in the foregoing plots for dioptric and catadioptric systems. The plots shown in FIG. 30 and in the following examples of other prism systems were based upon data obtained from ray traces according to Snell's law. FIG. 31 illustrates a to-glass cemented quintuplet prism system, which provides a high degree of color correction throughout the visible spectrum for a total deviation of 30 . The prism system of FIG. 31 comprimes a first prism element made of Schott PK51 glass and having an apex angle of &alpha;1 = 43.1695 , a second prism element made of Hoya LAC7 glass and having an apex angle of a2 = -43.1695O a third prism element made Schott PK51 glass and having an apex angle of &alpha;3 = 43.1695 , a fourth prism element made of Hoya LAC7 glass and having an apex angle of &alpha;4 = -43.1695 , and a fifth prism element made of Schott PK51 glass and having am apex angle of &alpha;5 = 57.5776 . From a manufacturing standpoint, it is of special interest that a1, a2, a3 and a4 have the same value, where the negative sign given for a2 and a4 indicates that the orientations of the second and fourth prism elements are inverted with respect to the orientations of the first, third and fifth prism elements. A plot of change in angular deviation versus wavelength shown in FIG. 31 indicates that chromatic dispersion from a total deviation angle of 300 is precisely zero at five discrete wavelengths. It is to be noted that a total deviation angle of 300 is a large total deviation angle. The 300 deviation of a beam of light that is produced by the prism system of FIG. 31 is equivalent to the deviation produced by the marginal zone of a lens with a relative aperture of f/1.0. The plot of change in angular deviation versus wavelength in FIG. 31 indicates that the change in total angular deviation from 300 is only about 0.0005 degree for any wavelength in the spectral band that includes the entire visible region and a portion of the near infrared region extending to almost 0.8 um. The change in total angular deviation from 300 is in fact zero at five discrete wavelengths in this spectral band. FIG. 32 illustrates a two-glass cemented quintuplet prism system, which is designed using the same types of glasses as the quintuplet prism system of FIG. 31. The only difference between the prism system of FIG. 32 and the prism system of FIG. 31 is that the apex angles of the prism elements of the system shown in FIG. 32 have different values. Thus, for the first prism element &alpha;1 = 83.1964 , for the second prism elemeny &alpha;2 = -44.9953 , for the third prism element = = 40.85760, for the fourth prism element a4 = -46.9210 , and for the fifth prism element ag = 37.50190 Optical Systems Comprising More Than Two Glasses: The present invention provides the designer with the ability to design optical systems that are color-corrected at three or more wavelengths using only two different optical materials. Thus, as a result of the present invention, complicated multiglass optical systems of the prior art can be replaced by simpler two-glass optical systems that provide comparable, or better, color correction. This ability to simplify complicated optical systems while improving performance is a major advantage inherent in the present invention. The method of the present invention for selecting more than two optical materials for designing color-corrected optical systems is of general interest in terms of demnnstrating the unified theory. Ordinarily, in practical anplications, a two-glass optical system is to be preferred to a system having the same capabilities but comprising more than two optical materials. In particular applications, however, where color correction at particular wavelengths is required, optical systems comprising three or more different optical materials might be used to provide optimum color correction for specified operational requirements. FIG. 33 illustrates a particular example of a three-glass lens multiplet for which the lens elements comprising the multiplet were selected in accordance with the present invention. The lens multiplet of FIG. 33 is a quintuplet having a focal length of 1000 mm at = .54607 um for a relative aperture of f/10, and provides color correction at five wavelengths. In accordance with conventional practice, the five lens elements comprising'the lens quintuplet are described consecutively from left to right as shown in drawing. The design form of the lens quintuplet of FIG. 33 is specified in tabular format as follows: Surface No. Radius Thickness Ne Ve Material 1 .493 f .0l5 f 1.49845 81.22 Ohara FKO1 2 - .660 f .034 f Air 3 - .538 f .01? f 1.72538 34.49 Ohara KZFS8 4 1.078 f .012 f 1.49845 81.22 Ohara FKO1 5 -2.457 f .001 f Air 6 -5.045 f .013 f 1.70443 29.89 Ohara SF15 7 - .288 f .013 f 1.72538 34.49 Ohara KZFS8 8 - .953 f The wavelength scan for the three-glass multiplet shown in FIG. 33 indicates that a lens system can be designed using Ohara FKO1, Ohara KZFS8 and Ohara FK01 glasses for bringing five wavelength from the ultraviolet through the visible to the near infrared regions of the spectrum to a common focus. The wavelength scan further indicates that substantially complete axial color correction can be provided by these three glasses in combination for wavelengths in the near infrared region up to at least 1.0 pm. FIG. 34 illustrates a particular example of a four-glass lens multiplet for which the lens elements comprising the multiplet were selected in accordance with the present invention. The lens multiplet of FIG. 34 is a quintuplet having a focal length of 1000 mm at = .54607 pm for a relative aperture of f/10, and provides color correction at five wavelengths. The design form of the lens quintuplet of FIG. 34 is specified in tabular format as follows: Surface No. Radius Thickness Ne Ve Material 1 .425 f.015 f 1.53019 76.57 Schott PK51 2 - .749 f .008 f Air 3 - .369 f .012 f 1.69669 51.28 Schott LAK20 4 .416 f .015 f 1.53019 76.57 Schott PK51 5 - .385 f .001 f Air 6 .546 f .015 f 1.61669 44.07 Schott KZFSN4 7 - .170 f .012 f 1.59487 48.29 Schott KZFS6 8 .434 f The wavelength scan for the four-glass multiplet shown in FIG. 34 indicates that a lens system can be designed using Schott PK51, Schott LAK20, Schott KZFSN4 and Schott KZFS6 glasses for bringing five wavelengths from the ultraviolet through the visible to the near infrared regions of the spectrum to a common focus. The wavelength scan further indicates that substantially complete color correction can be provided by these four glasses in combination for wavelengths in the range from about 0.60 pm to 0.85 pm. CONCLUSION This invention has been described above in terms of particular optical systems designed using particular glasses and other types of optical materials that are commercially available at the present time. However, other kinds of optical systems, which could be designed using other types of glasses and optical materials, could be made by designers skilled in the art on the basis of the foregoing disclosure in conjunction with the accompanying drawing. Therefore, the novel optical systems described above are to be considered as merely illustrative of the invent ion. The legal definition of the invention is provided more generally by the following claims and their equivalents. TABLE I (1 of 12) ***LEAST SQUARES FITIED COEFFICIENTS*** ORDER BASE WVL MlN VL MAX WVL 2.0 0.5740 0.400 0.700 CAT NAME ETA1/ETA2 INDEX ETA1 ETA2 ARCTAN(ETA1/ETA2) OHARA SK4 -.500727+05 1.613471 -.939625-01 .187652-05 -89.998856 OHARA LAK010 -.344490+04 1.726980 -.102990+00 .317391-04 -89.982343 OHARA LAK11 -.294092+04 1.659127 -.962812-01 .327384-04 -89.980517 CHANGE 691547 -.192659+04 1.691914 -.100937+00 .523916-04 -89.970261 SCHOTT SK15 -.148992+04 1.623767 -.951161-01 .638397-04 -89.961544 OHARA ZK1 -.113189+04 1.533817 -.952528-01 .841541-04 -89.949380 SCHOTT SK51 -.882619+03 1.621646 -.915519-01 .103728-03 -89.935084 SCHOTT BAK5 -.863211+03 1.557397 -.941415-01 .109060-03 -89.933624 SCHOTT ZK1 -.542770+03 1.533815 -.952493-01 .175487-03 -89.894439 OHARA LAK8 -.505624+03 1.713954 -.102540+00 .202799-03 -89.886683 CORN-F 713538 -.420221+03 1.713958 -.102594+00 .244142-03 -89.863654 HOYA LAC12 -.391017+03 1.678786 -.9994099-01 .254234-03 -89.853470 OHARA SK15 -.360639+03 1.623767 -.949577-01 .263304-03 -89.841127 HOYA C12 -.346402+03 1.523719 -.941556-01 .271810-03 -89.834599 HOYA C3 -.307862+03 1.518870 -.936381-01 .304156-03 -89.813891 OHARA ZK4 -.297025+03 1.512537 -.949230-01 .319579-03 -89.807101 SCHOTT SK13 -.245242+03 1.592544 -.946779-01 .386058-03 -89.766372 CHANGE 572577 -.238564+03 1.572917 -.956311-01 .400862-03 -89.759831 CORN-F 651559 -.207410+03 1.651968 -.987661-01 .476189-03 -89.723757 OHARA BAK1 -.203696+03 1.573218 -.956013-01 .469332-03 -89.718722 HOYA BACD13 -.195377+03 1.592545 -.946756-01 .484579-03 -89.706745 CORN-F 658572 -.193118+03 1.658335 -.965192-01 .499794-03 -89.703314 OHARA K2 -.172343+03 1.516673 -.972221-01 .564120-03 -89.667551 OHARA BAK5 -.165965+03 1.557399 -.941142-01 .567071-03 -89.654778 OHARA KO1 -.146523+03 1.523717 -.944011-01 .644277-03 -89.608969 OHARA LAK12 -.138588+03 1.678787 -.997704-01 .719909-03 -89.586580 CORN-F 691548 -.127310+03 1.691921 -.100767-01 .791505-03 -89.549962 SCHOTT SK52 -.953341+02 1.639373 -.993953-01 .104260-02 -89.399022 OHARA SK10 -.921555+02 1.623589 -.966943-01 .104925-02 -89.378296 OHARA LAK13 -.907372+02 1.674441 -.103439+00 .113999-02 -89.368575 OHARA LAK011 -.897967+02 1.742014 -.104780+00 .116686-02 -89.361963 OHARA LAK013 -.830518+02 1.641813 -.969394-01 .116722-02 -89.310151 SCHOTT K10 -.824042+02 1.502014 -.978985-01 .118803-02 -89.304731 OHARA SK19 -.787332+02 1.614193 -.961291-01 .122095-02 -89.272317 SCHOTT SK19 -.783834+02 1.614195 -.961830-01 .122708-02 -89.269073 HOYA BACD10 -.768258+02 1.623591 -.969209-01 .126157-02 -89.254251 SCHOTT BAK1 -.751939+02 1.573219 -.958644-01 .127490-02 -89.238069 HOYA BACD1 -.743045+02 1.611028 -.974048-01 .131089-02 -89.228950 HOYA LACL2 -.727112+02 1.651040 -.992233-01 .136462-02 -89.212060 HOYA BACD6 -.716787+02 1.614541 -.978361-01 .136493-02 -89.200707 SCHOTT LAKN22 -.715624+02 1.651973 -.987132-01 .137940-02 -89.199411 CHANGE 623569 -.657657+02 1.623589 -.969717-01 .147450-02 -89.128858 SCHOTT SK10 -.654909+02 1.623593 -.969513-01 .148038-02 -89.125200 HOYA SBF5 -.591198+02 1.522013 -.104595+00 .176920-02 -89.030948 OHARA LASK01 -.581632+02 1.756042 -.105438+00 .181279-02 -89.015014 SCHOTT SK2 -.566100+02 1.608157 -.973525-01 .171971-02 -88.987988 CORN-F 623569 -.561077+02 1.623593 -.969182-01 .172736-02 -88.978932 CHANCE 569561 -.560878+02 1.569560 -.982912-01 .175245-02 -88.978572 CHANGE 678552 -.556141+02 1.678788 -.999158-01 .179659-02 -88.969873 SCHOTT SK1 -.524111+02 1.611029 -.972537-01 .185559-02 -88.906936 CORN-F 614564 -.520142+02 1.611029 -.972537-01 .187957-02 -88.898597 HOYA BACD2 -.519914+02 1.608159 -.972569-01 .187064-02 -88.898108 HOYA ADC1 -.515199+02 1.620722 -.886488-01 .172067-02 -88.888030 HOYA BAC4 -.500459+02 1.569563 -.984724-01 .196764-02 -88.855289 OHARA BAK6 -.497699+02 1.575177 -.976194-01 .196141-02 -88.848944 SCHOTT LAKN16 -.481711+02 1.734527 -.106819+00 .221749-02 -88.810749 CHANGE 691548 -.474013+02 1.691911 -.100650+00 .212337-02 -88.791434 SCHOTT SK6 -.472162+02 1.614537 -.977687-01 .207066-02 -88.786704 OHARA SK1 -.470107+02 1.611035 -.975581-01 .207523-02 -88.781403 SCHOTT BAK4 -.466145+02 1.569563 -.982860-01 .210849-02 -88.771045 OHARA BAK4 -.465233+02 1.569563 -.982470-01 .211178-02 -88.768640 OHARA LAK04 -.461629+02 1.651835 -.982167-01 .212761-02 -88.759029 SCHOTT BAK6 -.446430+02 1.575176 -.978150-01 .219105-02 -88.716792 OHARA SK6 -.445799+02 1.614537 -.978164-01 .219418-02 -88.714978 SCHOTT LAKN12 -.438037+02 1.678788 -.998759-01 .228008-02 -88.692214 TABLE 1 (2 Or 12) HOYA BACD8 -.438015+02 1.611961 -.988673-01 .225717-02 -88.692147 HOYA BAC1 -.418595+02 1.573217 -.959622-01 .229248-02 -88.631498 OHARA SK2 -.415061+02 1.608152 -.970336-01 .233782-02 -88.619845 CHANGE 734517 -.399053+02 1.734527 -.106738-01 .267478-02 -88.564508 SCHOTT SK8 -.396332+02 1.611961 -.985867-01 .248748-02 -88.554654 OHARA KZF5 -.386798+02 1.522016 -.104984+00 .271418-02 -88.519047 OHARA LAK09 -.386447+02 1.735028 -.107216+00 .277441-02 -88.517697 OHARA KF3 -.382488+02 1.515220 -.100854+00 .263679-02 -88.502365 CORN-F 569560 -.377078+02 1.569531 -.984073-01 .260973-02 -88.480890 CORN-F 734514 -.374738+02 1.734545 -.107304+00 .286344-02 -88.471407 OHARA SK8 -.370859+02 1.611956 -.985702-01 .265789-02 -88.455426 OHARA ZK5 -.369012+02 1.534444 -.992690-01 .269013-02 -88.447699 SCHOTT SKN18 -.361546+02 1.639374 -.994923-01 .175186-02 -88.415658 HOYA TAC4 -.359864+02 1.735038 -.108040+00 .300226-02 -88.408251 HOYA BAC6 -.349833+02 1.575178 -.978458-01 .279693-02 -88.362641 HOYA BACD18 -.343625+02 1.639374 -.994040-01 .289281-02 -88.333075 SCHOTT LAK28 -.331265+02 1.745347 -.108591+00 .327807-02 -88.270920 CORN-F 639555 -.330270+02 1.639336 -.993028-01 .300671-02 -88.265717 HOYA BACED4 -.326817+02 1.618461 -.999157-01 .305724-02 -88.247398 CORN-F 529518 -.323428+02 1.529735 -.106441+00 .329102-02 -88.229052 HOYA TAF1 -.321194+02 1.773625 -.111086+00 .345853-02 -88.216740 SCHOTT KF3 -.321153+02 1.515220 -.100799+00 .313867-02 -88.216505 HOYA ZNC5 -.317057+02 1.534442 -.995644-01 .314026-02 -88.193491 SCHOTT KZF2 -.308127+02 1.530180 -.106733+00 .346394-02 -88.141160 CHANGE 639554 -.303756+02 1.639373 -.994654-01 .327451-02 -88.114441 SCHOTT SSK4 -.301555+02 1.618460 -.999556-01 .331467-02 -88.100686 OHARA SK18 -.298634+02 1.639372 -.995302-01 .333286-02 -88.082115 SCHOTT ZK5 -.298507+02 1.534448 -.996534-01 .333839-02 -88.081308 HOYA NBF3 -.297358+02 1.736068 -.110662+00 .372151-02 -88.073895 CORN-F 618551 -.293313+02 1.618415 -.999977-01 .340924-02 -88.047360 HOYA NBF1 -.292015+02 1.744391 -.111894+00 .383180-02 -88.038677 HOYA BACD9 -.290570+02 1.614853 -.100019+00 .344216-02 -88.028940 OHARA SSK4 -.289407+02 1.618457 -.100125+00 .345966-02 -88.021023 OHARA SK9 -.284730+02 1.614854 -.998924-01 .357262-02 -87.951707 OHARA KZF2 -.284730+02 1.614855 -.100310+00 .352300-02 -87.988535 SCHOTT SK9 -.283086+02 1.530181 -.106660+00 .376777-02 -87.976865 HOYA LACL4 -.279606+02 1.614854 -.998924-01 .357262-02 -87.951707 HOYA C10 -.276702+02 1.670540 -.106749+00 .385792-02 -87.930225 HOYA LAC10 -.274406+02 1.502013 -.979219-01 .356850-02 -87.912933 OHARA LAK07 -.272641+02 1.721032 -.109430+00 .401369-02 -87.899438 HOYA SBF6 -.271081+02 1.678819 -.103231+00 .380814-02 -87.887345 SCHOTT KZF6 -.262344+02 1.527567 -.107951+00 .411488-02 -87.817054 HOYA CF3 -.259432+02 1.527563 -.107860+00 .415756-02 -87.792576 OHARA LAF03 -.257701+02 1.515220 -.100945+00 .391714-02 -87.777769 HOYA LACL3 -.251758+02 1.665698 -.103219+00 .409993-02 -87.725368 SCHOTT LAK10 -.251349+02 1.721031 -.109349+00 .435050-02 -87.721663 CHANGE 694533 -.249047+02 1.694439 -.103288+00 .414735-02 -87.700623 HOYA SBF2 -.248584+02 1.530180 -.106777+00 .429543-02 -87.696345 SCHOTT LAF28 -.245516+02 1.774263 -.110825+00 .451397-02 -87.667597 OHARA KZF6 -.245076+02 1.527565 -.107804+00 .439881-02 -87.663412 HOYA LAC13 -.244463+02 1.694439 -.103295+00 .422538-02 -87.657568 HOYA LACL8 -.240411+02 1.678813 -.103123+00 .428944-02 -87.618134 SCHOTT LAKN13 -.240258+02 1.694440 -.103269+00 .429827-02 -87.616606 OHARA LASK02 -.239434+02 1.787636 -.110169+00 .460124-02 -87.608415 CORN-F 720503 -.237201+02 1.721037 -.109518+00 .461709-02 -87.585937 HOYA BAFL6 -.232615+02 1.589840 -.103892+00 .446626-02 -87.538402 OHARA SSK1 -.227995+02 1.618021 -.101915+00 .447008-02 -87.488567 OHARA LASF16 -.226136+02 1.773624 -.111103+00 .491310-02 -87.467966 HOYA BACED1 -.225050+02 1.618029 -.102142+00 .453864-02 -87.455758 HOYA BAFL4 -.215062+02 1.580352 -.102543+00 .476805-02 -87.337774 SCHOTT SSK1 -.208156+02 1.618028 -.102159+00 .490781-02 -87.249574 OHARA LAF010 -.207334+02 1.744286 -.111697+00 .538727-02 -87.238701 HOYA LACL5 -.205079+02 1.694488 -.108445+00 .528796-02 -87.208372 CHANGE 720504 -.201899+02 1.721028 -.109283+00 .541278-02 -87.164460 SCHOTT BALF4 -.199801+02 1.580348 -.102533+00 .513175-02 -87.134751 SCHOTT KZFS6 -.198362+02 1.592846 -.113651+00 .572949-02 -87.113990 CORN-F 623531 -.191719+02 1.623348 -.103671+00 .540746-02 -87.014169 OHARA LAK10 -.190226+02 1.721029 -.109318+00 .574673-02 -86.990791 HOYA BACED2 -.189050+02 1.623146 -.103722+00 .548647-02 -86.972110 OHARA LAK05 -.188067+02 1.659188 -.103006+00 .547712-02 -86.956287 CORN-F 548535 -.187923+02 1.548492 -.103039+00 .548307-02 -86.953961 OHARA BALF4 -.185250+02 1.580346 -.102511+00 .553369-02 -86.910091 SCHOTT SSK51 -.183513+02 1.604421 -.102659+00 .559412-02 -86.880909 OHARA K10 -.180011+02 1.502013 -.976985-01 .542737-02 -86.820360 TABLE I (3 OF 12) HOYA BAFL3 -.173226+02 1.572127 -.103848+00 .599494-02 -86.696095 OHARA SSK2 -.173201+02 1.623140 -.103469+00 .597395-02 -86.695603 SCHOTT SSK2 -.173039+02 1.623147 -.103564+00 .598502-02 -86.692524 SCHDTT LGSK2 -.172411+02 1.586683 -.900992-01 .522584-02 -86.680509 SCHDTT LAK20 -.172277+02 1.694457 -.106718+00 .619455-02 -86.677938 SCHOTT BALF5 -.172238+02 1.548128 -.102659+00 .596028-02 -86.677194 CORN-F 659510 -.172101+02 1.659435 -.107970+00 .627367-02 -86.674529 SCHDTT KF6 -.170349+02 1.518136 -.105524+00 .619459-02 -86.640413 HOYA TAF4 -.169853+02 1.789195 -.115886+00 .682271-02 -86.630638 SCHDTT BALF6 -.169177+02 1.589843 -.103831+00 .613740-02 -86.617210 DHARA BALF5 -.168985+02 1.548131 -.102838+00 .608566-02 -86.613349 HOYA BACED20 -.168637+02 1.649381 -.103805+00 .615554-02 -86.606387 DHARA SSKD1 -.168448+02 1.649380 -.103806+00 .616250-02 -86.602592 OHARA BALF6 -.168344+02 1.589839 -.103456+00 .614550-02 -86.600507 SCHDTT BALF3 -.162086+02 1.572132 -.103962+00 .641400-02 -86.469576 CHANCE 788674 -.161986+02 1.789510 -.116133+00 .716935-02 -86.468387 DHARA KF6 -.159867+02 1.518131 -.105272+00 .658496-02 -86.420706 HOYA CF6 -.159558+02 1.518135 -.105600+00 .661829-02 -86.413781 DHARA BALF3 -.158921+02 1.572130 -.104100+00 .655047-02 -86.399423 HOYA CF2 -.155826+02 1.527040 -.107825+00 .691960-02 -86.328115 CORN-F 788674 -.154159+02 1.789201 -.116099+00 .753114-02 -86.288522 HOYA NBF2 -.151928+02 1.758144 -.115302+00 .758923-02 -86.234198 SCHDTT SSK50 -.151161+02 1.618802 -.104581+00 .691854-02 -86.215121 SCHDTT KZFSN9 -.149861+02 1.599477 -.117431+00 .783599-02 -86.182401 DHARA LASF14 -.149352+02 1.789196 -.116005+00 .776721-02 -86.169432 CORN-F 689496 -.148607+02 1.690010 -.110800+00 .745588-02 -86.150294 SCHDTT LAF21 -.147798+02 1.789509 -.116094+00 .785489-02 -86.129281 HOYA TAF3 -.144778+02 1.805449 -.118302+00 .817125-02 -86.048793 SCHDTT KF9 -.144754+02 1.524146 -.106917+00 .738611-02 -86.048134 DHARA LAK08 -.144013+02 1.694480 -.108231+00 .751536-02 -86.027864 CHANCE 689495 -.143658+02 1.690002 -.111148+00 .773696-02 -86.018091 CHANCE 530512 -.143418+02 1.531074 -.107543+00 .749857-02 -86.011436 SCHDTT KF50 -.143387+02 1.531630 -.107670+00 .750908-02 -86.010559 SCHDTT LAF24 -.143385+02 1.758334 -.115078+00 .802579-02 -86.010528 SCHDTT BALF51 -.142959+02 1.574727 -.105621+00 .738818-02 -85.998683 HOYA LAF3 -.140928+02 1.718078 -.114629+00 .813393-02 -85.941167 DHARA LAF04 -.140362+02 1.758138 -.114841+00 .818176-02 -85.924891 DHARA KF4 -.140292+02 1.534323 -.106679+00 .760410-02 -85.922841 CHANCE 717479 -.137641+02 1.718078 -.114898+00 .834764-02 -85.844612 SCHDTT SSK52 -.137302+02 1.659372 -.108066+00 .787070-02 -85.834369 CORN-F 803467 -.136712+02 1.804243 -.117728+00 .861139-02 -85.816465 SCHDTT KZF1 -.135468+02 1.551949 -.110788+00 .817815-02 -85.778192 DHARA LASK15 -.134563+02 1.805240 -.117893+00 .876120-02 -85.749886 HOYA CF4 -.134532+02 1.534323 -.106780+00 .793714-02 -85.748924 SCHDTT BALF50 -.133403+02 1.589757 -.107074+00 .802632-02 -85.713098 SCHDTT LASF30 -.131945+02 1.804429 -.118405+00 .897384-02 -85.665875 HOYA CF5 -.130901+02 1.523840 -.108017+00 .825177-02 -85.631474 DHARA LAK03 -.129607+02 1.670935 -.106504+00 .821740-02 -85.588040 HOYA ADC2 -.129435+02 1.597777 -.995685+00 .769256-02 -85.582163 DHARA BALF8 -.127337+02 1.554389 -.107435+00 .843705-02 -85.509683 HOYA LACL9 -.127122+02 1.678871 -.108695+00 .855048-02 -85.502096 DHARA KF5 -.125473+02 1.523841 -.108162+00 .862031-02 -85.443265 DHARA LASF12 -.125343+02 1.804240 -.117789+00 .939727-02 -85.438573 HOYA CF1 -.124764+02 1.541179 -.108055+00 .956075-02 -85.417464 HOYA BACED3 -.124276+02 1.615704 -.107456+00 .864660-02 -85.399525 DHARA KF2 -.124217+02 1.527038 -.107455+00 .865053-02 -85.397401 HOYA SBF1 -.124038+02 1.551953 -.111168+00 .896239-02 -85.390770 DHARA LAK06 -.123576+02 1.678861 -.108356+00 .876843-02 -85.373568 DHARA SSK5 -.122989+02 1.659370 -.108016+00 .878259-02 -85.351607 OHARA LASF09 -.122734+02 1.817261 -.117859+00 .960282-02 -85.341990 CORN-F 717480 -.121961+02 1.718088 -.114541+00 .939161-02 -85.312608 HOYA BACED5 -.121267+02 1.659369 -.108146+00 .891800-02 -85.285908 SCHDTT KZFS1 -.120820+02 1.614096 -.124112+00 .102724-01 -85.268574 SCHDTT KF1 -.120276+02 1.541174 -.107640+00 .894940-02 -85.247248 SCHDTT SSK3 -.119842+02 1.615703 -.107446+00 .896566-02 -85.230095 SCHDTT BALF8 -.117921+02 1.554389 -.107425+00 .910997-02 -85.152740 HOYA TAF2 -.117637+02 1.795759 -.121061+00 .102911-01 -85.141108 CHANCE 717480 -.117480+02 1.718076 -.114518+00 .974783-02 -85.134682 SCHDTT SSKN5 -.117271+02 1.659373 -.108028+00 .921187-02 -85.126008 HOYA FEL6 -.116556+02 1.532505 -.112562+00 .965740-02 -85.096244 DHARA SSK3 -.116501+02 1.615705 -.107440400 .921912-02 -82.093989 DHARA BALF7 -.115927+02 1.589580 -.107363+00 .926134-02 -85.069760 DHARA KF1 -.114950+02 1.541172 -.107786+00 .937680-02 -85.028093 OHARA BALF2 -.114715+02 1.571798 -.108026+00 .941691-02 -85.017970 TABLE I (b or 12) CHANCE 658509 -.113934+02 1.659369 -.108049+00 .948349-02 -84.983988 HOYA BAFL2 -.113366+02 1.571798 -.108081+00 .953379-02 -84.959005 CORN-F 800456 -.112482+02 1.801265 -.120513+00 .107140-01 -84.919575 CORN-F 616444 -.110961+02 1.617001 -.123860+00 .111726-01 -84.845672 DHARA LASF17 -.110210+02 1.796261 -.121371+00 .110127-01 -84.815415 HOYA LAFL2 -.109266+02 1.698033 -.113261+00 .103656-01 -84.770881 SCHDTT LAF23 -.104049+02 1.690005 -.111022+00 .106701-01 -84.510280 OHARA LLF6 -.102947+02 1.532500 -.112374+00 .109157-01 -84.451853 HOYA NBFD14 -.100981+02 1.803002 -.123911+00 .122708-01 -84.344487 HOYA TAFD1 -.100908+02 1.816026 -.124285+00 .123166-01 -84.340487 CORN-F 613443 -.100236+02 1.614396 -.124203+00 .123790-01 -84.302802 DHARA LAF06 -.999756+01 1.687003 -.111708+00 .111736-01 -84.287985 SCHDTT KZFSN4 -.992835+01 1.614398 -.124113+00 .125009-01 -84.248456 SCHDTT SSKNB -.989874+01 1.618614 -.110403+00 .111532-01 -84.231401 HOYA TAFD10 -.987546+01 1.816820 -.123359+00 .124914-01 -84.217907 SCHDTT LLF6 -.987203+01 1.535205 -.112704+00 .114165-01 -84.215878 SCHDTT LAFN3 -.683210+01 1.718074 -.114425+00 .116379-01 -84.192550 DHARA LASF04 -.982992+01 1.816858 -.123542+00 .125679-01 -84.191297 DHARA SSK9 -.978441+01 1.621018 -.110591+00 .113028-01 -84.164426 HOYA BACED9 -.970537+01 1.621015 -.110247+00 .113594-01 -84.117236 CORN-F 624469 -.964415+01 1.624957 -.117036+00 .121355-01 -84.080138 DHARA K2F4 -.959733+01 1.571262 -.114147+00 .118936-01 -84.051504 SCHDTT LAF20 -.956524+01 1.683496 -.113922+00 .119100-01 -84.031681 HOYA NBFD11 -.952474+01 1.787185 -.125047+00 .131287-01 -84.006467 DHARA LAF3 -.950536+01 1.718081 -.114514+00 .120473-01 -83.994361 SCHDTT BAF54 -.949968+01 1.667716 -.113891+00 .119889-01 -83.990808 SCHDTT BAF5 -.949139+01 1.608175 -.111149+00 .117105-01 -83.985587 HOYA LAFL1 -.945834+01 1.687005 -.111199+00 .117567-01 -83.964728 DHARA BAF2 -.943387+01 1.570481 -.111286+00 .117964-01 -83.949199 DHARA LAF09 -.936908+01 1.698037 -.113150+00 .120770-01 -83.907633 DHARA BAF5 -.930348+01 1.608177 -.111627+00 .119985-01 -83.864978 DHARA SSKB -.924203+01 1.618614 -.110229+00 .119269-01 -83.814557 CHANCE 614439 -.915702+01 1.615006 -.125205+00 .136731-01 -83.767671 HOYA ADFA -.912199+01 1.613480 -.122486+00 .134276-01 -83.743897 SCHDTT LASF11 -.895934+01 1.802962 -.124033+00 .138439-01 -83.631311 DHARA BAF6 -.893555+01 1.589873 -.112906+00 .126356-01 -83.914452 HOYA LAFL3 -.892589+01 1.701356 -.114758+00 .128568-01 -83.607579 CORN-F 670471 -.891792+01 1.671029 -.116510+00 .130647-01 -83.601938 SCHDTT BAFN11 -.886361+01 1.667712 -.113380+00 .127917-01 -83.563025 SCHDTT BAFN6 -.875482+01 1.588974 -.113357+00 .129479-01 -83.483784 DHARA KZF54 -.874898+01 1.614407 -.125294+00 .143195-01 -83.480115 DHARA BAF11 -.873308+01 1.667711 -.113624+00 .130108-01 -83.467654 DHARA LASF06 -.867922+01 1.842396 -.126901+00 .146212-01 -83.427512 HOYA BAF5 -.865291+01 1.608178 -.111318+00 .128648-01 -83.407685 CORN-F 648462 -.864701+01 1.648755 -.118797+00 .137386-01 -83.403180 CORN-F 667484 -.863608+01 1.667688 -.113290+00 .131182-01 -83.394959 DHARA LAF01 -.858138+01 1.701046 -.114132+00 .133000-01 -83.353202 HOYA TAF05 -.850256+01 1.836398 -.127685+00 .150173-01 -83.292139 HOYA BAF6 -.847460+01 1.588976 -.112148+00 .133514-01 -83.270249 CHANCE 744448 -.844983+01 1.745195 -.122607+00 .145099-01 -83.250734 CORN-F 744448 -.843366+01 1.745195 -.122509+00 .145262-01 -83.237867 SCHDTT LAF10 -.840519+01 1.785717 -.125057+00 .148786-01 -83.215154 HOYA FEL2 -.840377+01 1.541543 -.116334+00 .138431-01 -83.214029 HOYA BAF3 -.836181+01 1.583573 -.118003+00 .141122-01 -83.180280 CHANCE 541472 -.835964+01 1.541542 -.116414+00 .139257-01 -83.178566 SCHDTT TIF1 -.835750+01 1.511902 -.107733+00 .128906-01 -83.176814 SCHDTT BAF9 -.831442+01 1.644242 -.114405+00 .137599-01 -83.141773 HOYA BAF9 -.827768+01 1.644243 -.114451+00 .138265-01 -83.111640 SCHDTT LLF2 -.824244+01 1.541544 -.116392+00 .141211-01 -83.082477 DHARA LASF01 -.819622+01 1.787175 -.124162+00 .151487-01 -83.043862 DHARA LLF2 -.819503+01 1.541546 -.116287+00 .141899-01 -83.042887 SCHDTT BAF53 -.818865+01 1.671053 -.116514+00 .142287-01 -83.037509 DHARA BAF1 -.816264+01 1.557725 -.113001+00 .138437-01 -83.015524 HOYA FF1 -.811881+01 1.511899 -.107640+00 .132581-01 -82.978203 SCHDTT LLF3 -.809326+01 1.560985 -.116392+00 .143814-01 -82.956232 HOYA BAF21 -.797430+01 1.665194 -.112192+00 .140692-01 -82.852256 DHARA LASF05 -.797197+01 1.836212 -.128378+00 .161037-01 -82.850178 HOYA BAF8 -.785487+01 1.624693 -.116626+00 .148476-01 -82.744730 DHARA BAF9 -.783248+01 1.644246 -.114641+00 .146366-01 -82.724218 HOYA BAF10 -.777140+01 1.671048 -.116242+00 .149577-01 -82.667629 HOYA NBFD1 -.771675+01 1.790331 -.128262+00 .166212-01 -82.616309 SCHDTT BAFN10 -.770727+01 1.671054 -.116443+00 .151082-01 -82.607309 HOYA BAF11 -.769951+01 1.667712 -.113467+00 .147369-01 -82.599946 OHARA LLF3 -.765676+01 1.560987 -.116739+00 .152466-01 -82.559049 TABLE II (5 OF 12) SCHDTT LASF9 -4.074 1.850066 -.155145+00 .380864-01 .147781-01 2.577 -10.498 DHARA SF8 -4.050 1.688770 -.161032+00 .397613-01 .175491-01 2.266 -9.176 SCHDTT SF8 -4.045 1.688772 -.160524+00 .396840-01 .180977-01 2.193 -8.870 HDYA FD8 -4.030 1.688771 -.160675+00 .398746-01 .181835-01 2.193 -8.836 CHANCE 706300 -3.904 1.705688 -.166420+00 .426291-01 -.125649-02 -33.927 -132.448 SCHDTT SF52 -3.813 1.688358 -.163202+00 .428023-01 .179492-01 2.385 -9.092 CDRN-F B36302 -3.799 1.836206 -.165259+00 .435053-01 .274394-02 15.855 -60.227 CDRN-F 699301 -3.746 1.698834 -.165739+00 .442431-01 .127899-01 3.459 -12.959 HDYA FD15 -3.705 1.698777 -.166066+00 .448226-01 .113998-01 3.932 -14.567 SCHDTT SF15 -3.702 1.698783 -.165953+00 .448271-01 .116878-01 3.835 -14.199 DHARA SF15 -3.691 1.698780 -.165577+00 .448647-01 .116099-01 3.864 -14.262 CHANCE 699301 -3.651 1.698778 -.166161+00 .455060-01 .144051-01 3.159 -11.535 DHARA SF1 -3.631 1.717187 -.169088+00 .465651-01 .195078-01 2.387 -8.668 SCHDTT SF1 -3.624 1.717185 -.169134+00 .466728-01 .116878-01 2.403 -8.708 HDYA FD1 -3.597 1.717184 -.169250+00 .470500-01 .198544-01 2.370 -8.525 HDYA FD1 -3.587 1.720047 -.170467+00 .475280-01 .161718-01 2.939 -10.541 CHANCE 717295 -3.578 1.717189 -.169016+00 .472341-01 .181433-01 2.603 -9.316 HOYA FD18 -3.576 1.721329 -.170626+00 .477197-01 .189655-01 2.516 -8.997 SCHDTT SF18 -3.561 1.721332 -.170563+00 .479035-01 .193173-01 2.480 -8.830 DHARA SF01 -3.533 1.720041 -.170120+00 .481532-01 .196576-01 2.450 -8.654 DHARA SF18 -3.531 1.721328 -.170537+00 .482918-01 .197161-01 2.449 -8.650 SCHDTT TISF1 -3.526 1.673225 -.172328+00 .488749-01 -.942108-02 -5.188 18.292 CDRN-F 717295 -3.512 1.717235 -.168890+00 .480868-01 .128491-01 3.742 -13.144 SCHDTT SF53 -3.416 1.728118 -.173616+00 .508275-01 .165347-01 3.074 -10.500 HDYA FD52 -3.403 1.728117 -.173734+00 .510503-01 .169420-01 3.013 -10.255 SCHDTT LAF9 -3.379 1.794836 -.175409+00 .519128-01 .173355-01 2.995 -10.118 CDRN-F 728284 -3.370 1.728119 -.175210+00 .519861-01 .122161-01 4.256 -14.343 HDYA FD10 -3.347 1.728067 -.175779+00 .525203-01 .102814-01 5.108 -17.097 DHARA SF10 -3.331 1.728065 -.174981+00 .525319-01 .137174-01 3.830 -12.756 CDRN-F 740281 -3.328 1.739811 -.176848+00 .531469-01 .104692-01 5.077 -16.892 CHANCE 728284 -3.321 1.728063 -.175405+00 .528124-01 .139044-01 3.798 -12.615 SCHDTT SF10 -3.318 1.728065 -.175217+00 .528054-01 .127250-01 4.150 -13.770 SCHDTT SF3 -3.317 1.739812 -.176532+00 .532265-01 .199391-01 2.669 -8.854 HDYA FD3 -3.309 1.739810 -.176226+00 .532600-01 .197209-01 2.701 -8.936 DHARA SF3 -3.283 1.739809 -.175936+00 .535928-01 .207575-01 2.582 -8.476 SCHDTT SF54 -3.279 1.740610 -.177244+00 .540529-01 .188731-01 2.864 -9.391 CHANCE 748278 -3.259 1.748224 -.178804+00 .548708-01 .210530-01 2.606 -8.493 DHARA SFO4 -3.219 1.750644 -.179544+00 .557806-01 .178977-01 3.117 -10.032 HDYA FD4 -3.219 1.755001 -.180410+00 .560502-01 .157490-01 3.559 -11.445 CHANCE 755276 -3.206 1.755007 -.180326+00 .562432-01 -.196885-01 2.857 -9.159 CDRN-F 755276 -3.197 1.755006 -.180036+00 .563099-01 .123656-02 4.554 -14.559 SCHDTT SF63 -3.193 1.748205 -.179540+00 .562238-01 .191761-01 2.932 -9.363 SCHDTT SF4 -3.192 1.755004 -.180351+00 .564958-01 .205532-01 2.749 -8.775 DHARA SF13 -3.166 1.740577 -.178843+00 .564814-01 .132034-01 4.278 -13.545 DHARA SF4 -3.154 1.755002 -.180714+00 .572879-01 .196616-01 2.914 -9.191 SCHDTT SF61 -3.149 1.750645 -.180774+00 .574082-01 .195867-01 2.831 -9.229 CDRN-F 762269 -3.141 1.761598 -.184460+00 .587192-01 .118663-01 4.948 -15.545 HDYA FD13 -3.140 1.740582 -.179728+00 .572369-01 .210715-01 2.722 -8.547 SCHDTT SF13 -3.128 1.740578 -.179992+00 .575388-01 .889124-02 6.471 -20.244 SCHDTT TISF6 -3.054 1.616359 -.160015+00 .523949-01 -.253322-01 -2.068 6.317 DHARA SF55 -3.049 1.761595 -.183071+00 .600488-01 .170045-01 3.531 -10.766 HDYA FD55 -3.046 1.761600 -.184171+00 .604674-01 .131237-01 4.608 -14.033 SCHDTT SF55 -3.040 1.761596 -.184320+00 .606329-01 .189400-01 3.201 -9.732 DHARA SFL14 -3.030 1.761615 -.187228+00 .617896-01 .149891-03 -412.230 1249.090 DHARA SFSL3 -2.984 1.784482 -.188637+00 .632232-01 .214489-02 26.181 -16.892 CDRN-F 734265 -2.969 1.733821 -.186901+00 .629605-01 .296774-02 -21.215 62.978 CDRN-F 785259 -2.931 1.784776 -.191216+00 .652490-01 .116685-01 5.592 -16.387 DHARA SF14 -2.917 1.761613 -.186558+00 .639638-01 .888133-02 7.202 -21.008 SCHDTT SF14 -2.903 1.761614 -.186734+00 .643310-01 .591584-02 10.874 -31.565 DHARA SF53 -2.902 1.784486 -.188982+00 .651195-01 .178789-01 3.642 -10.570 SCHDTT SF56 -2.895 1.784485 -.190232+00 .657154-01 .189545-01 3.467 -10.036 HDYA FD14 -2.895 1.761617 -.186961+00 .645879-01 .151099-01 4.275 -12.373 HDYA FD53 -2.884 1.784484 -.190638+00 .660970-01 .217325-01 3.041 -8.772 DHARA SFL11 -2.879 1.784504 -.193021+00 .670424-01 .456981-03 146.707 -422.383 DHARA SFL6 -2.858 1.804954 -.194939+00 .682144-01 .459951-02 14.831 -42.383 CDRN-F 805255 -2.841 1.804867 -.194059+00 .683118-01 .152341-01 4.484 -12.738 CHANCE 805254 -2.834 1.804952 -.195132+00 .688456-01 .265278-01 2.595 -7.356 HDYA FD11 -2.820 1.784496 -.191123+00 .677795-01 .118843-01 -5.703 16.082 SCHDTT SF6 -2.815 1.804954 -.194617+00 .691471-01 .186358-01 3.710 -10.443 CHANCE 785258 -2.810 1.784501 -.192403+00 .684671-01 .128753-01 5.318 -14.224 HDYA FD6 -2.803 1.804957 -.194363+00 .693396-01 .188400-01 3.680 -10.316 DHARA SF11 -2.796 1.784502 -.192467+00 .688348-01 .584361-02 11.780 -32.936 SCHDTT SF11 -2.787 1.784502 -.192107+00 .689216-01 .605232-02 11.388 -31.741 DHARA SF6 -2.779 1.804950 -.194546+00 .699951-01 .202121-01 3.463 -9.625 TABLE I (6 OF 12) DHARA LF6 -.559211+01 1.568272 -.127770+00 .228483-01 -79.861323 DHARA BAFO3 -.558236+01 1.686896 -.124389+00 .228824-01 -79.844049 CHANCE 582421 -.552595+01 1.583140 -.130084+00 .235406-01 -79.742502 DHARA LF1 -.545623+01 1.574057 -.128470+00 .235456-01 -79.614264 DHARA LF3 -.544102+01 1.583143 -.129985+00 .238897-01 -79.585934 SCHDTT LF3 -.542358+01 1.583143 -.130057+00 .239800-01 -79.553095 SCHDTT LASF15 -.540814+01 1.879649 -.143284+00 .264941-01 -79.523978 HDYA FL7 -.537239+01 1.576004 -.131817+00 .245361-01 -79.455771 SCHDTT BASF5 -.535886+01 1.604248 -.128770+00 .240293-01 -79.429816 HDYA TAFD17 -.533073+01 1.879648 -.143186+00 .268606-01 -79.375233 SCHDTT LF4 -.531969+01 1.574489 -.131542+00 .247273-01 -79.353765 DHARA LF7 -.529916+01 1.575999 -.131817+00 .248751-01 -79.313421 OHARA LASF13 -.528160+01 1.805855 -.138191+00 .261646-01 -79.278728 SCHOTT LF7 -.526935+01 1.576004 -.131848+00 .250216-01 -79.254414 SCHDTT LAF265 -.526858+01 1.747309 -.136722+00 .259505-01 -79.252824 DHARA BASF5 -.526487+01 1.604251 -.129208+00 .245415-01 -79.245464 SCHDTT TIF2 -.524856+01 1.533389 -.119097+00 .226913-01 -79.212844 HDYA FL1 -.522402+01 1.574054 -.128324+00 .245643-01 -79.163304 HDYA FL3 -.521652+01 1.583143 -.130129+00 .249455-01 -79.148149 CHANCE 700412 -.521161+01 1.701222 -.132836+00 .254884-01 -79.138177 HDYA BAFD5 -.521098+01 1.604252 -.129013+00 .247579-01 -79.136869 DHARA LAF8 -.520302+01 1.736482 -.133072+00 .255759-01 -79.120646 CHANCE 581409 -.518228+01 1.582463 -.133802+00 .258191-01 -79.078160 CDRN-F 702411 -.517080+01 1.703028 -.133019+00 .257251-01 -79.054454 SCHDTT BASF57 -.515333+01 1.652589 -.130517+00 .253268-01 -79.018248 DHARA LAF08 -.514535+01 1.721225 -.129925+00 .252510-01 -79.001640 CDRN-F 581408 -.507744+01 1.582416 -.133988+00 .263888-01 -78.858253 HDYA FL2 -.506272+01 1.590242 -.133416+00 .263527-01 -78.826607 DHARA LF4 -.506138+01 1.579448 -.131702+00 .260211-01 -78.823695 DHARA LF2 -.504860+01 1.590234 -.133114+00 .263665-01 -78.796182 HDYA FF2 -.503419+01 1.533392 -.119221+00 .236822-01 -78.764947 HDYA FL5 -.502675+01 1.582455 -.133718+00 .266013-01 -78.748707 SCHDDT LF5 -.502089+01 1.582460 -.133830+00 .266547-01 -78.735891 DHARA LLF8 -.501965+01 1.533396 -.119225+00 .237516-01 -78.733232 SCHDTT BASF6 -.501596+01 1.668691 -.130373+00 .259916-01 -78.725145 SCHDTT LF2 -.498130+01 1.590243 -.133529+00 .268061-01 -78.648690 HDYA BAFD6 -.495304+01 1.668691 -.130381+00 .263235-01 -78.585609 DHARA BASF6 -.494074+01 1.668691 -.130359+00 .263844-01 -78.558018 DHARA LF5 -.492576+01 1.582461 -.134113+00 .272268-01 -78.524123 CHANCE 579411 <RTI ID=126.2> -.492155+01 1.579607 -.132868+00 .269971-01 -78.514577 DHARA BASF07 -.491985+01 1.702758 -.132646+00 .269614-01 -78.510674 CHANCE 702410 -.481428+01 1.703034 -.133197+00 .276670-01 -78.265675 HDYA NBFD5 -.481376+01 1.763356 -.135651+00 .281799-01 -78.264393 DHARA LAF05 -.473415+01 1.763361 -.136243+00 .287787-01 -78.072703 HDYA BAFD3 -.470271+01 1.608248 -.135419+00 .287960-01 -77.995222 CDRN-F 696365 -.468160+01 1.697353 -.149696+00 .319754-01 -77.942689 OHARA BASF3 -.463616+01 1.608246 -.135671+00 .292636-01 -77.828046 OHARA F8 -.460518+01 1.596595 -.139289+00 .302460-01 -77.748667 OHARA BASF7 -.459808+01 1.702754 -.132468+00 .288095-01 -77.730225 SCHDTT F8 -.458732+01 1.596597 -.139423+00 .303931-01 -77.702365 HDYA F8 -.458564+01 1.596601 -.139300+00 .303774-01 -77.698002 HDYA BAFD7 -.458385+01 1.702763 -.132739+00 .289580-01 -77.693317 DHARA LASF10 -.455572+01 1.835606 -.146922+00 .322499-01 -77.619716 SCHDDT LAF13 -.453378+01 1.776974 -.144324+00 .318330-01 -77.561641 CORN-F 650392 -.452662+01 1.651393 -.139385+00 .307922-01 -77.542600 SCHDTT KZFSN7 -.448614+01 1.681949 -.146956+00 .327578-01 -77.433705 HDYA BAFD10 -.444249+01 1.651340 -.138758+00 .312344-01 -77.314174 SCHDTT BASF51 -.441666+01 1.725087 -.143230+00 .324294-01 -77.242480 HDYA NBFD4 -.439865+01 1.832225 -.149417+00 .339688-01 -77.191944 SCHDTT F14 -.438161+01 1.602525 -.142795+00 .325895-01 -77.143821 DHARA F9 -.436390+01 1.621615 -.143209+00 .328166-01 -77.093400 SCHDTT LASF13 -.436139+01 1.857116 -.149118+00 .341905-01 -77.086157 HDYA BAFD1 -.435910+01 1.627203 -.139565+00 .320170-01 -77.079582 HDYA F5 -.434251+01 1.604552 -.143573+00 .330622-01 -77.031920 HDYA NBFD10 -.434016+01 1.835598 -.146158+00 .336758-01 -77.025099 HDYA TAFD13 -.433808+01 1.857070 -.149204+00 .343940-01 -77.019126 SCHDTT F5 -.433060+01 1.604555 -.143537+00 .331449-01 -76.997434 SCHDTT BASF10 -.429826+01 1.651348 -.139390+00 .324293-01 -76.903029 DHARA BASF1 -.428723+01 1.627202 -.139561+00 .325527-01 -76.870468 DHARA BASF10 -.427365+01 1.651338 -.138503+00 .324085-01 -76.830230 DHARA F5 -.426141+01 1.604555 -.143543+00 .336844-01 -76.793684 DHARA BASF1 -.428723+01 1.627202 -.139561+00 .325527-01 -76.870468 CDRN-F 604381 -.426071+01 1.604631 -.143232+00 .336168-01 -76.791644 DHARA BASF08 -.425820+01 1.724781 -.143442+00 .336861-01 -76.784068 TABLE I (7 OF 12) HOYA F9 -.425569+01 1.621611 -.143327+00 .336789-01 -76.776564 SCHOTT BASF1 -.425307+01 1.627210 -.140057+00 .329309-01 -76.768662 SCHOTT F15 -.423545+01 1.606796 -.144250+00 .340579-01 -76.715557 OHARA BASF12 -.421880+01 1.671199 -.138730+00 .328837-01 -76.665069 SCHOTT BASF12 -.421877+01 1.671202 -.139189+00 .329928-01 -76.664951 SCHOTT F9 -.418601+01 1.621616 -.143307+00 .342348-01 -76.564344 HOYA BAFD4 -.413166+01 1.652493 -.142370+00 .344582-01 -76.394194 SCHOTT BASF50 -.411723+01 1.711586 -.148997+00 .361886-01 -76.348269 SCHOTT TIF3 -.411567+01 1.548577 -.129389+00 .314381-01 -76.343284 HOYA LAF7 -.410307+01 1.751029 -.155645+00 .379336-01 -76.302975 SCHOTT F3 -.407382+01 1.614114 -.147267+00 .361497-01 -76.208272 CORN-F 724380 -.406406+01 1.724851 -.143517+00 .353137-01 -76.176455 SCHOTT KZFSB -.403840+01 1.721957 -.157593.00 .390237-01 -76.091992 HOYA F3 -.403026+01 1.614114 -.147563+00 .366139-01 -76.064973 OHARA F3 -.401354+01 1.614111 -.147333+00 .367090-01 -76.009242 OHARA BASF4 -.400294+01 1.652501 -.142588+00 .356208-01 -75.973665 SCHOTT BASF13 -.398318+01 1.698903 -.141393+00 .354976-01 -75.906810 OHARA KZFSB -.398234+01 1.721949 -.157077+00 .394435-01 -75.903951 SCHOTT F4 -.396937+01 1.617794 -.148869+00 .375045-01 -75.859752 SCHOTT LAFN7 -.395001+01 1.751034 -.156046+00 .394054-01 -75.827716 HOYA BAFD8 -.392267+01 1.617791 -.148893+00 .379571-01 -75.698284 HOYA F4 -.392267+01 1.617791 -.148893+00 .379571-01 -75.698284 OHARA F10 -.391907+01 1.624858 -.149166+00 .380616-01 -75.685695 SCHOTT F2 -.391263+01 1.621528 -.149901+00 .383121-01 -75.663106 OHARA F4 -.390157+01 1.617790 -.148793+00 .381367-01 -75.624152 HOYA F2 -.389279+01 1.621260 -.150179+00 .385788-01 -75.593061 SCHOTT LAF22 -.388108+01 1.783297 -.146991+00 .378738-01 -75.551401 HOYA F1 -.387472+01 1.627131 -.152428+00 .393390-01 -75.528740 OHARA F2 -.386980+01 1.621262 -.150304+00 .388404-01 -75.511025 CHANCE 620364 -.386932+01 1.621259 -.149839+00 .387249-01 -75.509355 CORN-F 620363 -.385979+01 1.621230 -.150183+00 .389097-01 -75.475066 SCHOTT F13 -.380709+01 1.623605 -.151201+00 .397156-01 -75.282714 OHARA BASF8 -.379440+01 1.724781 -.143612+00 .378484-01 -75.235631 SCHOTT BASF56 -.376732+01 1.658126 -.148317+00 .393695-01 -75.134134 CHANCE 626357 -.376047+01 1.627129 -.152618+00 .405849-01 -75.108277 SCHOTT F1 -.375478+01 1.627133 -.152611+00 .406446-01 -75.086694 CORN-F 637353 -.374590+01 1.637779 -.154265+00 .411822-01 -75.053026 HOYA NBFD6 -.373363+01 1.758188 -.149908+00 .401507-01 -75.006072 OHARA F1 -.372919+01 1.627133 -.152573+00 .409131-01 -74.989038 HOYA F6 -.372321+01 1.637641 -.154091+00 .413867-01 -74.965958 CORN-F 626356 -.368321+01 1.627157 -.153021+00 .415457-01 -74.810177 OHARA F6 -.366983+01 1.637641 -.153964+00 .419539-01 -74.757449 HOYA NBFD7 -.366029+01 1.784548 -.151063+00 .412707-01 -74.719572 SCHOTT F6 -.365072+01 1.637644 -.154102+00 .422114-01 -74.681369 HOYA F7 -.364428+01 1.266178 -.153009+00 .419861-01 -74.655564 SCHOTT F7 -.364290+01 1.626616 -.153153+00 .420416-01 -74.650002 HOYA BAFD2 -.362186+01 1.665778 -.151722+00 .418906-01 -74.565116 HOYA NBFD8 -.361176+01 1.809021 -.153117+00 .423939-01 -74.524049 SCHOTT BASF2 -.357610+01 1.665783 -.151969+00 .424958-01 -74.377166 OHARA SF1 -.356282+01 1.641118 -.157459+00 .441952-01 -74.321763 SCHOTT SF7 -.354192+01 1.641120 -.157306+00 .444127-01 -74.233868 HOYA FD7 -.349147+01 1.641123 -.157450+00 .450956-01 -74.017641 OHARA LAF012 -.347733+01 1.784545 -.150611+00 .433121-01 -73.956038 SCHOTT LASF18 -.346436+01 1.915483 -.167528+00 .483576-01 -73.899012 OHARA BASF2 -.344610+01 1.665783 -.151837+00 .440604-01 -73.818210 SCHOTT SF16 -.342867+01 1.647464 -.159812+00 .466103-01 -73.740301 CORN-F 648339 -.341481+01 1.649352 -.160369+00 .469628-01 -73.677746 OHARA LAF015 -.339933+01 1.751025 -.155605+00 .457753-01 -73.607368 HOYA FD9 -.339567+01 1.655845 -.161352+00 .475170-01 -73.590678 SCHOTT SF9 -.339174+01 1.655847 -.161676+00 .476675-01 -73.572718 SCHOTT LASF33 -.338732+01 1.807636 -.158904+00 .469113-01 -73.552548 OHARA SF2 -.338224+01 1.649055 -.160939+00 .475835-01 -73.529069 SCHOTT SF2 -.337068+01 1.649052 -.160726+00 .476834-01 -73.475689 OHARA LAF2 -.336786+01 1.751015 -.154634+00 .459147-01 -73.462530 HOYA FD2 -.335505+01 1.649057 -.160788+00 .479242-01 -73.402875 OHARA SF9 -.335368+01 1.655846 -.161900+00 .482753-01 -73.396485 SCHOTT SF12 -.335230+01 1.649675 -.160766+00 .479569-01 -73.390026 SCHOTT SF17 -.335175+01 1.651546 -.161571+00 .482050-01 -73.387432 CHANCE 648338 -.334365+01 1.649677 -.160751+00 .480765-01 -73.349392 HOYA F11 -.333766+01 1.622194 -.151489+00 .453878-01 -73.321196 HOYA BAFD14 -.333152+01 1.701106 -.155796+00 .467643-01 -73.292152 SCHOTT FN11 -.333151+01 1.622185 -.150518+00 .451800-01 -73.292165 CHANCE 653335 -.333047+01 1.654867 -.162480+00 .487860-01 -73.287169 OHARA F11 -.332182+01 1.622189 -.151750+00 .456827-01 -73.246145 TABLE 1 (8 OF 12) SCHOTT BASF14 -.331917+01 1.709107 -.155615+00 .468839-01 -73.233424 HOYA FD12 -.331257+01 1.649675 -.160929+00 .485813-01 -73.201967 SCHOTT BASF55 -.331112+01 1.701248 -.156886+00 .473815-01 -73.195038 OHARA SF19 -.330308+01 1.668237 -.164555+00 .498187-01 -73.156416 CORN-F 667331 -.327995+01 1.668432 -.164248+00 .500766-01 -73.044371 SCHOTT SF19 -.326298+01 1.668239 -.164748+00 .504901-01 -72.961339 CHANCE 850322 -.326209+01 1.852142 -.168651+00 .517003-01 -72.956974 SCHOTT TIF4 -.322509+01 1.585187 -.146933+00 .455594-01 -72.772945 HOYA FD19 -.321631+01 1.668233 -.164381+00 .511085-01 -72.728721 SCHOTT LAFN11 -.320719+01 1.758620 -.170944+00 .533003-01 -72.682533 CDRN-F 673323 -.318517+01 1.674180 -.168239+00 .528196-01 -72.570020 HOYA NBFD9 -.316344+01 1.758593 -.170915+00 .540284-01 -72.457594 SCHOTT SF50 -.314834+01 1.656144 -.165279+00 .524971-01 -72.378737 SCHOTT SF5 -.314487+01 1.674185 -.168709+00 .536458-01 -72.360465 SCHOTT SF51 -.313750+01 1.661675 -.164957+00 .525761-01 <RTI ID=128.4> -72.321562 SCHOTT LASF8 -.313135+01 1.809228 -.171939+00 .549090-01 -72.289032 OHARA F16 -.312662+01 1.593887 -.153036+00 .489462-01 -72.263928 HOYA FD5 -.312442+01 1.674190 -.168891+00 .540586-01 -72.251181 OHARA LASF21 -.311521+01 1.852133 -.168309+00 .540281-01 -72.203088 OHARA SF5 -.309993+01 1.674192 -.169243+00 .545956-01 -72.120972 SCHOTT SF62 -.309010+01 1.682857 -.170099+00 .550464-01 -72.067698 HOYA FF5 -.307661+01 1.593893 -.153424+00 .498679-01 -71.994116 SCHOTT TIFN5 -.306922+01 1.594745 -.153142+00 .498961-01 -71.953566 HOYA TAFD9 -.301491+01 1.852179 -.168822+00 .559957-01 -71.650099 CORN-F 689312 -.300391+01 1.690574 -.174022+00 .579318-01 -71.587436 SCHOTT SF8 -.299049+01 1.690503 -.174160+00 .582379-01 -71.510421 OHARA SF8 -.297801+01 1.690507 -.174702+00 .586640-01 -71.438223 SCHOTT LASF9 -.297257+01 1.852133 -.168426+00 .566603-01 -71.406512 HOYA FD8 -.296749+01 1.690503 -.174275+00 .587279-01 -71.377003 SCHOTT BASF54 -.289811+01 1.737899 -.168843+00 .582595-01 -70.962937 SCHOTT SF52 -.284569+01 1.690119 -.177173+00 .622601-01 -70.638090 OHARA SF1 -.277434+01 1.719089 -.183742+00 .662288-01 -70.178579 SCHOTT LASF32 -.276608+01 1.805371 -.178500+00 .645317-01 -70.123956 SCHOTT SF1 -.275419+01 1.719087 -.183734+00 .667106-01 -70.044926 CORN-F 699301 -.274146+01 1.700651 -.180120+00 .657022-01 -69.959596 SCHOTT SF18 -.272083+01 1.723262 -.185368+00 .681295-01 -69.819778 OHARA SF01 -.271515+01 1.721963 -.184925+00 .681086-01 -69.781050 HOYA FD1 -.271396+01 1.719086 -.183727+00 .676972-01 -69.772860 CHANCE 717295 -.271283+01 1.719090 -.183675+00 .677062-01 -69.765126 HOYA FD18 -.271048+01 1.723258 -.185364+00 .683877-01 -69.749100 OHARA SF18 -.270769+01 1.723258 -.185348+00 .684524-01 -69.729891 OHARA SF15 -.268086+01 1.700595 -.179933+00 .671176-01 -69.543760 SCHOTT SF15 -.268069+01 1.700601 -.180303+00 .672598-01 -69.542593 HOYA FD15 -.266205+01 1.700596 -.180349+00 .677481-01 -69.411311 CHANCE 699301 -.265997+01 1.700596 -.180374+00 .678107-01 -69.396501 SCHOTT SFN64 -.264749+01 1.707504 -.179020+00 .676190-01 -69.307568 HOYA F020 -.264393+01 1.721969 -.185068+00 .699972-01 -69.282167 CORN-F 717295 -.261491+01 1.719138 -.183728+00 .702618-01 -69.072000 SCHOTT SF53 -.259177+01 1.73C102 -.188827+00 .728564-01 -68.901551 SCHOTT SF3 -.257858+01 1.741863 -.192066+00 .744853-01 -68.803162 HOYA FDS2 -.257473+01 1.730102 -.188881+00 .733595-01 -68.774325 CORN-F 836302 -.257217+01 1.838371 -.179359+00 .697694-01 -68.755099 SCHOTT LAF9 -.256742+01 1.797027 -.190736+00 .742911-01 -68.719235 OHARA SF3 -.256772+01 1.741853 -.191425+00 .745793-01 -68.714080 HOYA FD3 -.256638+01 1.741857 -.191715+00 .747027-01 -68.711455 CHANCE 706300 -.255413+01 1.707527 -.180644+00 .707264-01 -68.618481 CHANCE 748278 -.252592+01 1.750323 -.194421+00 .769700-01 -68.401712 SCHOTT SF54 -.251467+01 1.742670 -.192740+00 .766461-01 -68.313977 CORN-F 728284 -.251456+01 1.730123 -.190680+00 .758309-01 -68.313045 CHANCE 755276 -.249572+01 1.757145 -.196256+00 .786372-01 -68.164672 SCHOTT SF4 -.249448+01 1.757142 -.196269+00 .786815-01 -68.154840 OHARA SF04 -.249191+01 1.752762 -.195466+00 .784402-01 -68.134485 CORN-F 740281 -.248406+01 1.741869 -.192609+00 .775380-01 -68.071918 HOYA FD4 -.247971+01 1.757144 -.196511+00 .792476-01 -68.037105 OHARA SF10 -.246937+01 1.730063 -.190214+00 .770293-01 -67.953959 SCHOTT SF63 -.246009+01 1.750313 -.195287+00 .793819-01 -67.878828 SCHOTT SF10 -.245780+01 1.730067 -.190535+00 .775228-01 -67.860112 OHARA SF4 -.245714+01 1.757145 -.196693+00 .800493-01 -67.854864 CHANCE 728284 -.245550+01 1.730064 -.190621+00 .776304-01 -67.841390 HOYA FD10 -.244881+01 1.730075 -.191179+00 .780702-01 -67.786772 SCHOTT SF61 -.243636+01 1.752775 -.196666+00 .807210-01 -67.684441 CORN-F 755276 -.241616+01 1.757143 -.196095+00 .811598-01 -67.516314 CORN-F 762269 -.238586+01 1.763809 -.201033+00 .842603-01 -67.259656 OHARA SF13 -.238101+01 1.742657 -.194646+00 .817492-01 -67.218124 TABLE I (9 OF 12) OHARA SF55 -.237461+01 1.763788 -.199484+00 .840071-01 -67.162971 HDYA FD13 -.237294+01 1.742663 -.195067+00 .822049-01 -67.148528 SCHDTT SF55 -.236292+01 1.763801 -.200664+00 .849223-01 -67.061605 HDYA FDS5 -.234664+01 1.763809 -.200827+00 .855807-01 -66.919139 SCHDTT SF13 -.230283+01 1.742671 -.195912+00 .850744-01 -66.527199 DHARA SF53 -.229004+01 1.786820 -.206096+00 .899966-01 -6.410396 CHANCE 805254 -.227076+01 1.807417 -.212405+00 .935391-01 -66.232224 SCHDTT TJSF1 -.226756+01 1.675043 -.187210+00 .825602-01 -66.202369 SCHDTT SF56 -.226331+01 1.786829 -.207228+00 .915596-01 -66.162707 HDYA FD53 -.225619+01 1.786830 -.207464+00 .919536-01 -66.095797 CORN-F 785259 -.224900+01 1.787139 -.208574+00 .927408-01 -66.028050 SCHDTT SF6 -.223844+01 1.807421 -.212348+00 .948645-01 -65.927739 DHARA SF6 -.222790+01 1.807416 -.212284+00 .952842-01 -65.826954 HDYA FD6 -.222728+01 1.807421 -.212038+00 .952005-01 -65.820946 CORN-F 805255 -.222501+01 1.807326 -.211744+00 .951654-01 -65.799128 HDYA FD14 -.220890+01 1.763852 -.203560+00 .921545-01 -65.643063 DHARA SF14 -.219571+01 1.763848 -.203384+00 .926280-01 -65.513864 SCHDTT SF14 -.215204+01 1.763850 -.203549+00 .945845-01 -65.076799 DHARA SFSL3 -.213910+01 1.786805 -.205349+00 .959976-01 -64.944611 CHANCE 785258 -.213763+01 1.786872 -.209608+00 .980564-01 -64.929408 DHARA SFL14 -.212526+01 1.763851 -.203665+00 .958305-01 -64.801605 CORN 734265 -.211212+01 1.735978 -.203755+00 .964694-01 -64.664419 DHARA SF11 -.209162+01 1.786877 -.209933+00 .100369+00 -64.447530 SCHDTT SF11 -.208404+01 1.786872 -.209512+00 .100532+00 -64.366498 DHARA SFL6 -.207789+01 1.807416 -.212223+00 .102134+00 -64.300446 HDYA FD11 -.207581+01 1.786875 -.209578+00 .100962+00 -64.278046 DHARA SFL11 -.205802+01 1.786881 -.210162+00 .102119+00 -64.084599 HDYA FDS9 -.205150+01 1.849166 -.226160+00 .110242+00 -64.013018 SCHDTT SF57 -.205007+01 1.849171 -.226170+00 .110323+00 -63.997438 DHARA SF03 -.204471+01 1.849159 -.225686+00 .110376+00 -63.938182 SCHDTT TIF6 -.188663+01 1.617905 -.174161+00 .923130-01 -62.074440 <RTI ID=129.4> SCHDTT SF58 -.179407+01 1.920613 -.249868+00 .139274+00 -60.865129 DHARA SF501 -.176690+01 1.925912 -.252358+00 .142826+00 -60.491622 DHARA SF51 -.168930+01 1.925965 -.256990+00 .152128+00 -59.376132 SCHOTT SF59 -.166253+01 1.955781 -.263360+00 .158409+00 -58.973417 SCHOTT LF8 -.607584+00 1.565361 -.125182+00 -.206033-01 -99.346334 SCHDTT FK5 .870540+01 1.487994 -.790093-01 -.907590-02 -96.552917 HDYA BSC3 .883498+01 1.498866 -.853725-01 -.966302-02 -96.457629 CORN-F 487704 .915227+01 1.487751 -.788591-01 -.861635-02 -96.235550 DHARA BK10 .921173+01 1.498363 -.831851-01 -.903035-02 -96.195613 DHARA BK9 .924626+01 1.494420 -.841124-01 -.909691-02 -96.172651 DHARA FK5 .937660+01 1.487996 -.792314-01 -.844991-02 -96.087499 SCHDTT BK10 .948819+01 1.498363 -.830447-01 -.875243-02 -96.016432 HOYA FC5 .953238+01 1.487993 - .789354-01 -.828076-02 -95.988739 CORN-F 488658 .958277+01 1.488042 -.845033-01 -.881825-02 -95.957476 DHARA PK1 .972404+01 1.504328 -.831612-01 -.855213-02 -95.871542 SCHDTT BK3 .972749+01 1.498869 -.854339-01 -.878274-02 -95.869477 SCHDTT PK1 .992166+01 1.504329 -.830549-01 -.837107-02 -95.755382 HDYA PCS1 .100388+02 1.517825 -.797593-01 -.794509-02 -95.688657 HDYA PC1 .102555+02 1.504328 -.831214-01 -.810504-02 -95.569218 DHARA BK4 .102743+02 1.501034 -.841968-01 -.819491-02 -95.559113 SCHDTT FK1 .105349+02 1.471198 -.825028-01 -.783140-02 -95.422431 DHARA PK2 .106726+02 1.518786 -.854542-01 -.800685-02 -95.352846 DHARA BK3 .107940+02 1.498866 -.854179-01 -.791344-02 -95.292991 HDYA FC1 .108373+02 1.471197 -.825422-01 -.761653-02 -95.272003 SCHDTT PK50 .108546+02 1.521083 -.796732-01 -.734003-02 -95.263615 DHARA FK3 .111977+02 1.465011 -.842295-01 -.752205-02 -95.103216 DHARA PK51 .113430+02 1.517818 -.797889-01 -.703421-02 -95.038185 DHARA FK1 .115831+02 1.471198 -.824182-01 -.711539-02 -94.934268 SCHDTT FK3 .117421+02 1.465014 -.844297-01 -.719035-02 -94.867778 SCHDTT FK54 .120508+02 1.437351 -.611695-01 -.507598-02 -94.743646 HDYA PC2 .121075+02 1.518788 -.851916-01 -.703627-02 -94.721540 SCHDTT PK2 .122813+02 1.518790 -.853260-01 -.694761-02 -94.654999 CORN-F 465657 .123644+02 1.465014 -.843988-01 -.682594-02 -94.623858 CORN-F 518651 .124691+02 1.518778 -.852578-01 -.683755-02 -94.585223 HDYA BSC7 .126988+02 1.517384 -.864635-01 -.680879-02 -94.502611 SCHDTT PK3 .127884+02 1.526010 -.858252-01 -.671118-02 -94.471197 DHARA BK12 .129958+02 1.519324 -.860235-01 -.661931-02 -94.400107 HDYA PC3 .134431+02 1.526011 -.858534-01 -.638644-02 -94.254268 CHANCE 517642 .135229+02 1.517382 -.864826-01 -.639526-02 -94.229240 CORN-F 517642 .135812+02 1.517389 -.864021-01 -.636190-02 -94.211164 SCHDTT BK7 .136653+02 1.517385 -.864656-01 -.632739-02 -94.185336 CHANGE 510644 .137233+02 1.510273 -.861023-01 -.627415-02 -94.167694 SCHDTT UBK7 .137359+02 1.517385 -.863121-01 -.628369-02 -94.163899 TABLE I (10 OF 12) DHARA BK7 .137436+02 1.516915 -.864910-01 -.629317-02 -94.161563 DHARA PSK3 .137567+02 1.552953 -.869995-01 -.632415-02 -94.157620 DHARA PK3 .141636+02 1.526007 -.859593-01 -.606904-02 -94.038589 SCHDTT BK8 .150883+02 1.520745 -.870925-01 -.577220-02 -93.791827 HDYA PCD2 .152105+02 1.569385 -.878957-01 -.577861-02 -93.761437 HDYA FCD10 .152753+02 1.456866 -.610293-01 -.399528-02 -93.745521 HDYA FC3 .153931+02 1.465015 -.842094-01 -.547060-02 -93.716953 SCHDTT PSK50 .155337+02 1.558131 -.823975-01 -.530444-02 -93.683403 HDYA ZNC7 .155451+02 1.509074 -.905172-01 -.582287-02 -93.680701 CHANGE 641601 .156746+02 1.641270 -.923210-01 -.588984-02 -93.650374 DHARA PSK1 .161505+02 1.548344 -.881099-01 -.545554-02 -93.543085 DHARA LAK01 .163213+02 1.640772 -.922437-01 -.565175-02 -93.506116 SCHDTT PSK3 .163302+02 1.552954 -.873711-01 -.535026-02 -93.504190 SCHDTT ZKN7 .164635+02 1.509073 -.906253-01 -.550463-02 -93.475906 DHARA ZK7 .165143+02 1.509077 -.911171-01 -.551746-02 -93.465229 CORN-F 510635 .165281+02 1.510575 -.872466-01 -.527870-02 -93.462358 HDYA BSC1 .167237+02 1.510675 -.873966-01 -.522591-02 -93.421946 DHARA PSK2 .168792+02 1.569383 -.877116-01 -.519644-02 -93.390503 SCHDTT PSK2 .169834+02 1.569385 -.878687-01 -.517380-02 -93.369743 CHANGE 508612 .172982+02 1.508191 -.906602-01 -.524101-02 -93.308551 SCHDTT FK51 .175476+02 1.486979 -.655603-01 -.373614-02 -93.261635 SCHDTT BK1 .178859+02 1.510673 -.873263-01 -.488241-02 -93.200073 CORN-F 486817 .192375+02 1.486475 -.677108-01 -.351973-02 -92.975659 DHARA BK1 .192502+02 1.510673 -.870835-01 -.452377-02 -92.973700 HDYA PCD3 .194229+02 1.552952 -.873730-01 -.449844-02 -92.947297 CHANCE 569631 .195119+02 1.569383 -.878305-01 -.450139-02 -92.933891 DHARA BK6 .195970+02 1.531743 -.886865-01 -.452553-02 -92.921178 DHARA FK01 .197991+02 1.497441 -.678377-01 -.342631-02 -92.891407 HDYA LACL6 .200987+02 1.640776 -.920358-01 -.457919-02 -92.848371 SCHDTT BK6 .202252+02 1.531750 -.891374-01 -.440724-02 -92.830582 SCHDTT FK52 .214118+02 1.486484 -.676504-01 -.315949-02 -92.673953 HDYA BSC6 .214496+02 1.531749 -.891886-01 -.415805-02 -92.669247 DHARA BK2 .216654+02 1.507162 -.893758-01 -.412529-02 -92.642707 SCHDTT PSK52 .233739+02 1.603769 -.846166-01 -.362012-02 -92.449769 DHARA K1 .238599+02 1.510363 -.891660-01 -.373707-02 -92.399940 SCHDTT K51 .243787+02 1.505796 -.930316-01 -.381609-02 -92.348915 CORN-F 564609 .245040+02 1.564676 -.908447-01 -.370733-02 -92.336918 DHARA SK20 .246088+02 1.560289 -.904751-01 -.367653-02 -92.326981 SCHDTT SK5 .257685+02 1.589828 -.903533-01 -.350635-02 -92.222368 HDYA C7 .262127+02 1.511735 -.914766-01 -.348978-02 -92.184742 CORN-F 542734 .262662+02 1.542737 -.753406-01 -.286835-02 -92.180299 CORN-F 518603 .270791+02 1.518824 -.918428-01 -.339165-02 -92.114906 HDYA BACD5 .275634+02 1.589827 -.903801-01 -.327899-02 -92.077779 CHANCE 589613 .299354+02 1.589826 -.903610-01 -.301853-02 -91.913267 DHARA SK11 .299784+02 1.564512 -.911508-01 -.304055-02 -91.910527 HDYA BACD165 .301388+02 1.621164 -.924448-01 -.306730-02 -91.900365 SCHDTT 5K20 .311164+02 1.560294 -.903862-01 -.290478-02 -91.840705 HDYA LACL7 .312404+02 1.670844 -.964946-01 -.308878-02 -91.833405 CORN-F 589612 .319377+02 1.589696 -.904002-01 -.283052-02 -91.793402 CORN-F 511604 .322814+02 1.511613 -.916603-01 -.283942-02 -91.774321 SCHDTT LAK21 .323056+02 1.641269 -.920718-01 -.285003-02 -91.772991 HDYA LAC7 .325405+02 1.652408 -.946047-01 -.290729-02 -91.760199 SCHDTT PK51 .326136+02 1.529052 -.718368-01 -.220267-02 -91.756261 SCHDTT K11 .327016+02 1.500720 -.900976-01 -.275514-02 -91.751530 HDYA BACD16 .333124+02 1.621155 -.917238-01 -.275344-02 -91.719435 SCHDTT UK50 .336648+02 1.523199 -.916329-01 -.272192-02 -91.701448 DHARA LAK7 .338735+02 1.652403 -.942570-01 -.278262-02 -91.690973 CHANCE 697562 .339006+02 1.698236 -.984705-01 -.290468-02 -91.689619 HDYA BACD11 .344348+02 1.564512 -.909246-01 -.264048-02 -91.663421 SCHDTT SK16 .347019+02 1.621157 -.917065-01 -.264269-02 -91.650625 DHARA SK14 .349146+02 1.603833 -.911086-01 -.260947-02 -91.640578 SCHDTT LAK31 .354878+02 1.697628 -.980691-01 -.276349-02 -91.614111 OHARA SK5 .360112+02 1.589827 -.906992-01 -.251864-02 -91.590646 OHARA LAK014 .361383+02 1.697691 -.979264-01 -.270977-02 -91.585055 CHANCE 603606 .362407+02 1.603830 -.912762-01 -.251861-02 -91.580577 SCHDTT SK11 .362732+02 1.564512 -.909578-01 -.250757-02 -91.579158 SCHDTT SK14 .363318+02 1.603832 -.912752-01 -.251227-02 -91.576617 CORN-F 540597 .366064+02 1.540160 -.926842-01 -.253191-02 -91.564794 SCHDTT K50 .368838+02 1.523201 -.919227-01 .,249222-02 -91.553029 HDYA BACL3 .369534+02 1.518973 -.916143-01 -.247919-02 -91.550112 OHARA LAK6 .375794+02 1.643293 -.947540-01 -.252143-02 -91.524297 HOVA BACD14 .375934+02 1.603831 -.910845-01 -.242289-02 -91.523735 CHANCE 564608 .389388+02 1.564511 -.909646-01 -.233609-02 -91.471107 HDYA LAC6 .390387+02 1.643302 -.953703-01 -.244297-02 -91.467346 Tabel I (11 OP 12) CHANGE 620603 .397432+02 1.621154 -.196871-01 -.230699-92 -91.441346 CORN-F 620603 .404871+02 1.621151 -.916950-01 -.226480-02 -91.414876 SCHOTT K2FSN2 .414694+02 1.559109 -.102222+00 -.246500-02 -91.381373 HDYA LAC11 .416691+02 1.659130 -.965613-01 -.231733-02 -91.374750 CHANCE 519604 .422941+02 1.519611 -.915426-01 -.216443-02 -91.354446 CORN-F 641601 .439338+02 1.641267 -.919855-01 -.209373-02 -91.303914 HOYA LAC15 .444092+02 1.697695 -.985518-01 -.221917-02 -91.289957 SCHOTT K7 .449551+02 1.511734 -.951112-01 -.203650-02 -91.274299 CORN-F 652585 .450442+02 1.652407 -.944992-01 -.209792-02 -91.271780 SCHOTT BALKN3 .450955+02 1.519112 -.917996-01 -.203567-02 -91.270334 CORN-F 697562 .451971+02 1.697899 -.983871-01 -.217685-02 -91.267482 OHARA BALK1 .456965+02 1.527056 -.921451-01 -.201646-02 -91.253633 HOYA LAC14 .466141+02 1.697713 -.997339-01 -.213956-02 -91.228959 CHANCE 697554 .470812+02 1.697710 -.998106-01 -.211997-02 -91.216775 HOYA BACD12 .471840+02 1.583840 -.928865-01 -.196860-02 -91.214122 SCOTT PSK53 .482711+02 1.620848 -.870163-01 -.180266-02 -91.186790 OHARA LAK14 .486738+02 1.697706 -.994448-01 -.204309-02 -91.176973 OHARA BALK3 .497837+02 1.518974 -.917072-01 -.184211-01 -91.150737 HOYA LAC9 .522504+02 1.691912 -.101030+00 -.193358-02 -91.096432 HOYA TAC1 .543995+02 1.726985 -.103520+00 -.190295-02 -91.053118 OHARA SK16 .559137+02 1.621156 -.917056-01 -.164013-02 -91.024611 SCHOTT LAKN14 .576174+02 1.697711 -.997837-01 -.173183-02 -90.994316 OHARA PSKO1 .586782+02 1.617713 -.880364-01 -.150033-02 -90.976349 OHARA SK12 .596787+02 1.583841 -.930734-01 -.155957-02 -90-959978 OHARA BAK2 .633248+02 1.540616 -.927256-01 -.146429-02 -90.904719 CORN-F 523594 .679816+02 1.523633 -.929572-01 -.136739-02 -90.842753 OHARA K7 .690021+02 1.511733 -.914017-01 -.132462-02 -90.830289 OHARA K50 .721590+02 1.523196 -.921678-01 -.127729-02 -90.793972 HOYA BACD7 .747049+02 1.608032 -.928925-01 -.124346-02 -90.766915 CHANCE 524592 .747616+02 1.524639 -.933783-01 -.124901-02 -90.766332 SCHOTT LAKN7 .749037+02 1.652407 -.944376-01 -.126079-02 -90.764882 CHANCE 652585 .757398+02 1.652404 -.944566-01 -.124712-02 -90.756438 CORN-F 697554 .760379+02 1.697916 -.998003-01 -.131251-01 -90.753474 HOYA LACL1 .780667+02 1.641669 -.972321-01 -.124550-02 -90.733893 SCHOTT SK7 .798809+02 1.608030 -.929450-01 -.116354-02 -90.717224 SCHOTT SK12 .836981+02 1.583842 -.929417-01 -.111044-02 -90.684521 SCHOTT BALK1 .871857+02 1.527057 -.920710-01 -.105603-02 -90.657138 SCHOTT BAK50 .875947+02 1.568446 -.952900-01 -.108785-02 -90.654072 HOYA BAC5 .890026+02 1.667397 -.942542-01 -.105900-02 -90.643723 CORN-F 613585 .897103+02 1.613451 -.944049-01 -.105233-02 -90.638648 CHANCE 607595 .897382+02 1.608030 -.929421-01 -.103570-02 -90.638449 SCHOTT TIK1 .924535+02 1.479281 -.941893-01 -.101877-02 -90.619698 SCHOTT K5 .939519+02 1.523126 -.929097-01 -.988908-03 -90.609818 HOYA ZNC1 .957631+02 1.533814 -.951004-01 -.993080-03 -90.598286 OHARA LAK18 .997389+02 1.730123 -.101009+00 -.101274-02 -90.574442 SCHOTT BAK2 .103271+03 1.540615 -.925331.01 -.896020-03 -90.554791 CORN-F 604640 .109857+03 1.604192 -.863228-01 -.785775-03 -90.521534 OHARA SK7 .110102+03 1.608032 -.930232-01 -.844881-03 -90.520373 SCHOTT LAK11 .110909+03 1.659134 -.965050-01 -.870126-03 -90.516586 OHARA LAKO2 .114422+03 1.670846 -.963556-01 -.842108-03 -90.500729 OHARA SK3 .116368+03 1.609560 -.937132-01 -.805320-03 -90.492356 OHARA PSKO2 .125723+03 1.618706 -.871342-01 -.693063-03 -90.455719 HOYA LAC8 .128627+03 1.713957 -.102430+00 -.796330-03 -90.445430 HOYA C5 .152053+03 1.523124 -.929279-01 -.611157-03 -90.376810 HOYA BACD15 .152779+03 1.623771 -.950835-01 -.622358-03 -90.375017 CHANCE 669574 .156946+03 1.669663 -.962691-01 -.613390-03 -90.365062 SCHOTT SK3 .158337+03 1.609558 -.937522-01 -.592104-03 -90.361854 HOYA BACLI .165873+03 1.527052 -.919471-01 -.554323-03 -90.345415 SCHOTT K3 .177587+03 1.518866 -.936677-01 -.527447-03 -90.322632 CHANCE 643580 .179454+03 1.643299 -.953194-01 -.531164-03 -90.319275 OHARA K5 .192279+03 1.523127 -.924409-01 -.480765-03 -90.297979 HOYA BAC2 .198263+03 1.540616 -.925125-01 -.466615-03 -90.288986 CORN-F 609590 .208907+03 1.609502 -.935670-01 -.447888-03 -90.274261 CHANCE 713538 .211681+03 1.713958 -.102639+00 -.484875-03 -90.270667 OHARA LAK9 .222992+03 1.691914 -.100754+00 -.451830-03 -90.256941 CORN-F 623581 .225515+03 1.623780 -.951191-01 -.421786-03 -90.254064 HOYA ADF1 .228995+03 1.565769 -.104320-01 -.455555-03 -90.250203 SCHOTT LAK23 .235819+03 1.669660 -.962547-01 -.408172-03 -90.242963 SCHOTT LAKN6 .237437+03 1.643302 -.952892-01 -.401324-03 -90.241308 SCHOTT LAK9 .257817+03 1.691917 -.100967+00 -.391624-03 -90.222234 SCHOTT LAK8 .280438+03 1.713962 -.102629+00 -.365959-03 -90.204307 SCHOTT SK4 .306677+03 1.613477 -.942118-01 -.307202-03 -90.186827 HOYA BACD4 .371294+03 1.613475 -.942747-01 -.253908-03 -90.154312 HOYA BACD3 .416634+03 1.609561 -.938263-01 -.225201-03 -90.137521 TABLE I I 12 OF 12) CHANCE 613586 .428948+03 1.613475 -.942101-01 -.219630-03 -90.133572 CHANCE 658573 .484001+03 1.659131 -.964698-01 -.199317-03 -90.118379 OHARA K3 .569286+03 1.518865 -.937249-01 -.164636-03 -90.100645 SCHOTT K4 .572325+03 1.519606 -.962542-01 -.168181-03 -90.100111 CORN-F 678555 .581978+03 1.678889 -.994888-01 -.170950-03 -90.098450 CHANCE 623581 .670154+03 1.623764 -.951456-01 -.141976-03 -90.085497 HOYA TAC2 .914435+03 1.742017 -.104919-00 -.114737-03 -90.062657 CORN-F 573575 .116669+05 1.573219 -.961053-01 -.823742-05 -90.004910 TABLE II (1 OF 12) ...LEST SOUARES FITTED COEFFICIENTS... ORDER BASE WVL MIN WVL MAX WVL 3.0 0.5890 0.360 1.014 CAT NAME ETA1/ETA2 INDEX ETA 1 ETA2 ETA3 ETA2/ETA3 ETA1/ETA3 CORN-F 558525 -1050.530 1.557434 -.974752-01 .927867-04 -.390622-02 -.024 24.954 SCHOTT LASF 11 -752.430 1.801525 -.115759+00 .153847-03 .524469-02 .029 -22.072 OHARA BAF5 -594.102 1.607198 -.104136+00 .927867-04 .390622-02 .032 -18.791 SCHOTT BAFN11 -377.046 1.666620 -.105738+00 .280437-03 .413480-02 .068 -25.573 HOYA LAFL4 -351.383 1.712584 -.118572+00 .337443-03 .277293-02 .122 -42.760 HOYA SSK5 -344.527 1.669924 -.108569+00 .315124-03 .207762-02 .152 -52.256 OHARA BAF5 -323.740 1.658342 -.100614+00 .310787-03 .104009-01 .030 -9.674 SCHOTT BAF5 -263.952 1.607199 -.103629+00 .392606-03 .601944-02 .065 24.954 SCHOTT LAF23 -245.436 1.588914 -.974752-01 .927867-04 .390622-02 .024 -17.216 HOYA BAF6 -234.257 1.688900 -.103472+00 .421584-03 .421584-03 .053 -13.003 SCHOTT LAF20 -231.441 1.588914 -.105634+00 .450934-03 .482195-02 .094 -21.907 HOYA NBFD11 -231.215 1.682372 -.106185+00 .458798-03 .612522-02 .075 -17.336 OHARA NBFD2 -203.299 1.785765 -.116614+00 .504353-03 .718313-02 .070 -16.234 HOYA BAF5 -189.571 1.569565 -.103725+00 .510213-03 .582092-02 .088 -17.819 CORN-F 548457 -171.777 1.607020 -.103909+00 .548126-03 .549668-02 .100 -18.904 OHARA LAF01 -154.399 1.699891 -.106472+00 .689593-03 .486976-02 .142 -21.864 OHARA LAF09 -139.242 1.696897 -.105456+00 .757380-03 .640845-02 .118 -16.456 SCHOTT LAF10 -118.034 1.784300 -.116661+00 .988369-03 .515218-02 .192 -22.643 SCHOTT BAF53 -112.012 1.669925 -.108658+00 .970051-03 .386597-02 .251 -28.106 CHANGE 548456 -107.436 1.547602 -.112271+00 .104501-02 .241304-02 .433 -46.527 OHARA BAF6 -100.221 1.588912 -.105204+00 .104972-02 .566316-02 .185 -18.577 HOYA LAFL3 -97.646 1.700195 -.106981+00 .109560-02 .639820-02 .171 -16.720 HOYA FEL3 -89.849 1.560033 -.108708+00 .120990-02 .310242-02 .390 -35.040 HOYA BAF21 -89.124 1.664119 -.104787+00 .117575-02 .578126-02 .203 -18.125 OHARA LAF3 -81.326 1.716894 -.106686+00 .131184-02 .806100-02 .163 -13.235 OHARA BAF1 -80.823 1.556816 -.105401+00 .103410-02 .509190-02 .256 -20.700 OHARA BAF11 -77.909 1.666617 -.105827+00 .135835-02 .544010-02 .250 -19.453 SCHOTT LLF7 -69.953 1.548743 -.112723+00 .161141-02 .233046-02 .691 -48.369 OHARA LLF3 -69.160 1.560042 -.108884+00 .157438-02 .372003-02 .423 -29.270 HOYA BAF9 -68.508 1.643179 -.106698+00 .155745-02 .564904-02 .276 -18.888 SCHOTT KZFSN5 -65.662 1.653997 -.129255+00 .196849-02 -.310441-02 -.634 41.636 SCHOTT LLF1 -63.655 1.548053 -.111850+00 .175712-02 .253850-02 .692 -44.061 OHARA LASF01 -63.641 1.785766 -.115810+00 .181975-02 .673988-02 .270 -17.183 SCHOTT LAFN3 -60.968 1.716888 -.106539+00 .174745-02 .955062-02 .183 -11.155 CORN-F 670471 -58.527 1.669901 -.108558+00 .185484-02 .814704-02 .228 -13.325 HOYA FF2 -57.558 1.532476 -.111413+00 .193568-02 -.109276-01 -.177 10.196 SCHOTT BAFN10 -54.216 1.669927 -.108512+00 .200146-02 .413130-02 .484 -26.266 OHARA LASF06 -53.532 1.840854 -.118293+00 .220977-02 .901010-02 .245 -13.129 OHARA LLF1 -53.174 1.548053 -.111719+00 .210102-02 .330115-02 .636 -33.843 OHARA LLF7 -52.684 1.548601 -.112212+00 .212992-02 .302928-02 .703 -37.042 HOYA FEL1 -51.632 1.548049 -.111508+00 .215968-02 .364425-02 .593 -30.598 SCHOTT TIF2 -51.036 1.532474 -.111177+00 .217838-02 -.947587-02 -.230 11.733 HOYA LAF2 -49.984 1.743876 -.114058+00 .228190-02 .341337-02 .669 -33.415 HOYA TAFD5 -48.089 1.834857 -.119028+00 .247515-02 .924471-02 .268 -12.875 SCHOTT BAF9 -45.451 1.643179 -.106557+00 .234445-02 .706099-02 .332 -15.091 OHARA KZFS5 -44.759 1.653994 -.128928+00 .288054-02 -.161015-02 -1.789 80.072 HOYA FEL7 -44.140 1.548741 -.112447+00 .254752-02 .376192-02 .677 -29.891 OHARA BAF9 -40.296 1.643181 -.106837+00 .265129-02 .686698-02 .386 -15.558 OHARA BAF10 -39.937 1.669925 -.108092+00 .270654-02 .493908-02 .548 -21.885 OHARA LASF05 -39.539 1.834664 -.119657+00 .302656-02 .845778-02 .358 -14.148 SCHOTT LLF4 -37.349 1.561290 -.113002+00 .302554-02 .337006-02 .898 -33.531 HOYA LAFL1 -36.213 1.685902 -.103528+00 .285890-02 .119049-01 .240 -8.696 HOYA NBFD1 -34-398 1.788694 -.119434+00 .347212-02 .725389-02 .479 -16.465 HOYA BAF11 -34.301 1.666619 -.105769+00 .308354-02 .795536-02 .388 -13.295 HOYA BAF8 -33.837 1.623642 -.108554+00 .320811-02 .707055-02 .454 -15.353 HOYA FEL4 -33.462 1.561288 -.113039+00 .337814-02 .462977-02 .730 -24.416 OHARA LLF8 -32.139 1.532480 -.111282001 .346255-02 -.794041-02 -.436 14.015 OHARA LLF4 -30.955 1.561288 -.113115+00 .365418-02 .425506-02 .859 -26.584 SCHOTT BAF8 -29.261 1.623643 -.108607+00 .371162-02 .742686-02 .500 -14.623 OHARA BAF8 -28.362 1.623643 -.108774+00 .383526-02 .718593-02 .543 -15.137 SCHOTT BAF3 -27.953 1.582578 -.109864+00 .393029-02 .656866-02 .598 -16.725 CORN-F 667484 -26.737 1.666597 -.105345+00 .394003-02 .112015-01 .352 -9.405 HOYA BAF3 -24.490 1.582578 -.109451+00 .446919002 .820470-02 .545 -13.340 HOYA BAF7 -24.292 1.607917 -.110450+00 .454684-02 .674832-02 .674 -16.367 SCHOTT BAF52 -23.590 1.608493 -.109821+00 .465544-02 .636994-02 .731 -17.240 TABLE II (2 OF 12) CORN-F 606439 -23.512 1.605508 -.116186+00 .494161-02 .131351-02 3.762 -88.454 HOYA NBFD12 -23.111 1.799364 -.120496+00 .521386-02 .102631-01 .508 -11.741 HOYA TAFD2 -22.942 1.837551 -.121732+00 .530614-02 .118741-01 .447 -10.252 OHARA LAF2 -22.723 1.743877 -.114027+00 .501816-02 .900490-02 .557 -12.663 OHARA BAF3 -22.658 15825798 -.110049+00 .485696-02 .780848-02 .655 -14.096 OHARA LASF02 -22.164 1.799377 -.120641+00 .544307-02 .803180-02 .678 -15.020 OHARA BAF01 -20.498 1.682384 -.113654+00 .554431-02 -3196551-02 -1.734 -35.553 SCHOTT BAF12 -19.769 1.639197 -.112813+00 .570667-02 .570551-02 1.000 -19.773 SCHOTT BASF52 -19.185 1.701684 -.124359+00 .648195-02 .301104-02 2.153 -41.301 SCHOTT BAF51 -19.184 1.652135 -.113428+00 .591270-02 .806229-02 .733 -14.069 SCHOTT LF8 -19.124 1.564341 -.116535+00 .609355-02 .539743-02 1.129 -21.591 SCHOTT BAF13 -19.106 1.682613 -.114474+00 .599166-02 .852320-02 703 -13.413 HOYA BAF13 -18.841 1.668807 -.113565+00 .602752-02 .568205-02 1.061 -19.987 HOYA FL6 -18.794 1.567227 -.119041+00 .633390-02 .410144-02 1.544 -29.024 HOYA LAFL5 -18.320 1.719877 -.115979+00 .633086-02 .685298-02 .924 -16.924 OHARA LF8 -18.227 1.564346 -.116391+00 .638568-02 .576779-02 1.107 -20.180 SCHOTT BAF139 -17.549 1.668811 -.113273+00 .645484-02 .633754-02 1.019 -17.873 OHARA LAF011 -17.479 1.719887 -.110611+00 .632831-02 .120600-01 .525 -9.172 SCHOTT LAFN2 -17.470 1.743879 -.137316+00 .651028-02 .113526-01 .573 -10.018 SCHOTT LAF25 -17.388 1.784133 -.123364+00 .709495-02 .450414-02 1.575 -27.389 HOYA BAF22 -17.185 1.682384 -.114314+00 .665199-02 .665086-02 1.000 -17.188 OHARA BAF13 -16.928 1.668813 -.113226+00 .668836-02 .660533-02 1.013 -17.141 OHARA LASF07 -16.700 1.862845 -.122676+00 .734572-02 .118988-01 .617 -10.310 SCHOTT LF6 -16.551 1.567223 -.118934+00 .718604-02 .544410-02 1.320 -21.846 CHANGE 567428 -16.328 1.567221 -.118977+00 .728671-02 .571840-02 1.274 -20.806 OHARA BAF03 -16.241 1.685664 -.115724+00 .712537-02 .376098-02 1.895 -30.770 HOYA LAFL6 -16.040 1.719874 -.120916+00 .753820-02 .637544-02 1.182 -18.966 SCHOTT LAFN8 -15.804 1.735068 -.122469+00 .774926-02 .579672-02 1.337 -21.127 HOYA BAF20 -15.734 1.685663 -.115826+00 .736131-02 .575338-02 1.279 -20.132 HOYA BAF12 -15.690 1.639198 -.112862+00 .719328-02 .669007-02 1.075 -16.870 HOYA NEFD12 -15.464 1.797057 -.123831+00 .800752-02 .109175-01 .733 -11.342 HOYA FL4 -15.210 1.578346 -.121940+00 .801715-02 .442920-02 1.810 -27.531 OHARA BAF12 -14.896 1.639196 -.113404+00 .761280-02 .909745-02 .837 -12.465 CHANGE 573426 -14.766 1.572989 -.119598+00 .809957-02 .675199-02 1.200 -17.713 SCHOTT LAF26 -14.692 1.745837 -.127243+00 .866046-02 .373026-02 2.322 -34.111 SCHOTT LASFN3 -14.611 1.807865 -.124911+00 .854927-02 .843706-02 1.013 -14.805 OHARA LASF03 -14.547 1.805953 -.124719+00 .857340-02 .894751-02 1.009 -14.677 CHANGE 582421 -14.544 1.582047 -.121034+00 .832200-02 .618517-02 1.345 -19.568 SCHOTT LF1 -14.220 1.572991 -.119537+00 .828961-02 .659340-02 1.257 -18.130 OHARA LF6 -14.084 1.567226 -.118862+00 .843972-02 .734061-02 1.150 -16.192 HOYA BAFD15 -14.064 1.701858 -.126284+00 .897935-02 .846666-02 1.061 -14.916 OHARA LF3 -14.044 1.582050 -.120905+00 .860920-02 .582093-02 1.479 -20.771 OHARA LAF07 -13.840 1.712728 -.117774+00 .850955-02 .693729-02 1.227 -16.977 SCHOTT LF3 -12.696 1.582050 -.120955+00 .883166-02 .613708-02 1.439 -19.709 HOYA NBFD13 -13.631 1.805957 -.124868+00 .916079-02 .111698-01 .820 -11.179 OHARA LAF02 -13.622 1.719879 -.116357+00 .854199-02 .881268-02 .969 -13.203 SCHOTT LASF31 -13.091 1.880513 -.123721+00 .945100-02 .172923-01 .547 -7.155 CHANGE 606439 -13.083 1.605513 -.115836+00 .885368-02 .978139-02 .905 -11.842 SCHOTT LF4 -13.066 1.578349 -.122313+00 .936105-02 .616887-02 1.517 -19.827 SCHOTT BAF4 -12.972 1.605519 -.115760+00 .892355-02 .980315-02 .929 -12.054 OHARA LF1 -12.902 1.572993 -.119457+00 .925863-02 .779907-02 1.872 -15.317 SCHOTT LF7 -12.737 1.574910 -.122605+00 .962558-02 .651416-02 1.478 -18.821 HOYA FL3 -12.685 1.582049 -.121048+00 .954243-02 .652345-02 1.463 -18.556 HOYA BAF4 -12.677 1.605519 -.115915+00 .914392-02 .992630-02 .921 -11.678 SCHOTT KZFSN7 -12.518 1.680506 -.136829+00 .109307-02 .137634-02 -7: :942 99.454 CORN-F 696365 -12.487 1.695850 -.139493+00 .111714-01 .324357-02 3.444 -43.006 SCHOTT TIF3 -12.443 1.547555 -.120418+00 .967782-02 -7264161-02 -1.332 16.577 OHARA LASF13 -12.438 1.804250 -.128526+00 .103335-01 .786269-02 1.314 -16.346 HOYA FL1 -12.431 1.572992 -.119456+00 .960991-02 .818230-02 1.174 -14.599 OHARA LF7 -12.209 1.574905 -.122511+00 .100343-01 .729838-02 1.375 -16.766 OHARA LASF08 -12.208 1.882839 -.124635+00 .102113-01 .165761-01 .616 -7.620 HOYA FL7 -11.928 1.574909 -.122437+00 .102643-01 .792764-02 1.295 -15.444 CHANGE 700412 -11.906 1.699880 -.123488+00 .103720-01 .760631-02 1.762 -16.232 OHARA BAF4 -11.837 1.605519 -.116199+00 .981703-01 .984560-02 .363 -11.802 SCHOTT LASF15 -11.816 1.877832 -.133184+00 .112711-02 .102777-01 1.097 -12.959 SCHOTT BASF57 -11.777 1.651362 -.121285+00 .102987-01 .661943-02 1.556 -18.322 HOYA NBFD3 -11.652 1.804355 -.128592+00 .110078-01 .119855-01 .918 -10.701 HOYA BAFD5 -11.543 1.603128 -.119932+00 .103984-01 .846102-02 1.229 -14.175 OHARA LF4 -11.473 1.578249 -.122479+00 .106757-01 .766185-02 1.393 -15.986 CHANGE 581409 -11.410 1.581340 -.124300+00 .108938-01 .764572-02 1.425 -16.257 SCHOTT BASF5 -11.378 1.603127 -.119614+00 .105128-01 .927692-02 1.333 -12.594 CORN-F 581408 -11.181 1.581928 -.124582+00 .111423-01 .857334-02 1.300 -88.531 HOYA FL2 -11.000 1.589106 -.123975+00 .112707-01 .791513-02 1.424 -88.663 OHARA LF5 -10.755 15813358 -.124689+00 .115920-01 .795933-02 1.456 -88.666 TABLE II (3 OP 12) OHARA LAFOB -10.587 1.719874 -.120601+00 .113914-01 .844621-02 1.349 -14.279 OHARA BASF5 -10.543 1.603126 -.119991+00 .113807-01 .105922-01 1.074 -11.328 SCHOTT LF5 -10.512 1.581336 -.124312+00 .118254-01 .854312-02 1.384 -14.551 HDYA FL5 -10.500 1.581333 -.124247+00 .118332-01 .915481-02 1.293 -13.572 SCHOTT LF2 -10.439 1.589107 -.124023+00 .118811-01 .819465-02 1.450 -15.135 OHARA LAF8 -10.387 1.735068 -.123420+00 .118826-01 .865996-02 1.372 -14.252 OHARA LF2 -10.360 1.589102 -.123610+00 .119316-01 .894944-02 1.333 -13.812 OHARA BASF07 -10.064 1.701415 -.123199+00 .122419-01 .876093-02 1.397 -14.062 CORN-F 702411 -10.014 1.701680 -.123468+00 .123294-01 .109797-01 1.123 -11.245 SCHOTT BASF6 -9.784 1.667435 -.120949+00 .123619-01 .912665-02 1.354 -13.252 CORN-F 865401 -9.744 1.864842 -.126497+00 .129823-01 .168720-01 .769 -7.497 HDYA BAFD6 -9.686 1.667434 -.121015+00 .124935-01 .954491-02 1.309 -12.679 OHARA BASF7 -9.469 1.701412 -.122947+00 .129837-01 .578976-02 2.243 -21.235 OHARA BASF6 -9.396 1.667435 -.120931+00 .128704-01 .979036-02 1.315 -12.352 OHARA LAFO5 -9.241 1.761862 -.126401+00 .136777-01 .822010-02 1.664 -15.377 HDYA TAFD17 -9.096 1.877831 -.132602+00 .145775-01 .138075-01 1.056 -9.604 SCHDTT F8 -8.832 1.595399 -.129421+00 .146544-01 .915673-02 1.600 -14.134 OHARA LASF24 -8.775 1.906827 -.132194+00 .150656-01 .213980-01 .704 -6.178 CORN-F 650392 -8.771 1.650085 -.129383+00 .147510-01 .854240-02 1.727 -15.146 HOYA F8 ' -8.686 1.595403 -.129279+00 .148832-01 .959313-02 1.551 -13.476 CHANCE 579411 -8.585 1.578497 -.123176+00 .143473-01 .125785-01 1.141 -9.793 OHARA LASF10 -8.554 1.833837 -.136365+00 .159424-01 .103311-01 1.543 -13.199 OHARA BASF3 -8.533 1.607057 -.125960+00 .147607-01 .115804-01 1.275 -10.877 <RTI ID=135.9> HDYA BASD3 -8.526 1.607061 -.125537+00 .147239-01 .101656-01 1.448 -12.349 OHARA F8 -8.415 1.595398 -.129199+00 .153527-01 .104838-01 1.464 -12.324 HDYA BAFD7 -8.369 1.701418 -.123029+00 .147006-01 .887196-02 1.657 -13.867 HOVA F9 -8.298 1.620328 -.133035+00 .160322-01 .675076-02 2.375 -19.707 CHANCE 702410 -8.138 1.701684 -.123408+00 .151639-01 .128015-01 1.185 -9.640 OHARA F9 -8.138 1.620332 -.132829+00 .163217-01 .840122-02 1.943 -15.811 SCHDTT LAF13 -8.126 1.775358 -.133827+00 .164687-01 .108661-01 1.516 -12.316 HDYA NBFD5 -7.957 1.761863 -.125708+00 .157988-01 .144103-01 1.096 -8.723 SCHDTT F14 -7.859 1.601285 -.132434+00 .168516-01 .103818-01 1.623 -12.759 SCHDTT BASF51 -7.745 1.723590 -.132751+00 .171397-01 .106527-01 1.609 -12.432 HDYA NBFD10 -7.742 1.833838 -.135598+00 .175154-01 .112216-01 1.561 -12.084 SCHDTT K2FS58 -7.719 1.720318 -.146318+00 .189559-01 .723483-02 2.620 -20.224 SCHDTT F9 -7.715 1.620332 -.132927+00 .172300-01 .816536-02 2.110 -16.279 HDYA NBFD4 -7.715 1.830433 -.138304+00 .179275-01 .858925-02 2.087 -16.102 SCHDTT BASF50 -7.704 1.710058 -.138257+00 .179462-01 .773877-02 2.319 -17.865 SCHDTT F5 -7.614 1.603305 -.133082+00 .174794-01 .107518-01 1.626 -12.378 HDYA LAF7 -7.548 1.749345 -.144365+00 .191270-01 .804394-02 2.378 -17.947 HDYA TAFD13 -7.526 1.855226 -.138205+00 .183641-01 .100732-01 1.823 -13.720 OHARA K2FS8 -7.515 1.720316 -.145803+00 .194066-01 .712757-02 2.722 -20.456 CORN-F 604381 -7.498 1.603383 -.132845+00 .177178-01 .109889-01 1.612 -12.089 HDYA F15 -7.455 1.605534 -.133509+00 .179078-01 .110112-01 1.626 -12.125 SCHDTT F15 -7.303 1.605535 -.133736+00 .183130-01 .113792-01 1.609 -11.753 SCHDTT LAFN7 -7.270 1.749346 -.144760+00 .199107-01 .758794-02 2.624 -19.078 OHARA F5 -7.206 1.603304 -.133048+00 .184644-01 .121634-01 1.518 -10.938 HDYA F5 -7.177 1.603301 -.132990+00 .185296-01 .127475-01 1.454 -10.433 SCHDTT BASF12 -7.152 1.669855 -.128903+00 .180238-01 .101709-01 1.772 -12.674 HDYA BAFD10 -7.114 1.650037 -.128408+00 .180496-01 .129905-01 1.389 -9.885 OHARA BASF12 -7.018 1.669856 -.128397+00 .182949-01 .101700-01 1.799 -12.625 SCHDTT BASF1 -7.013 1.625944 -.129741+00 .185012-01 .124187-01 1.490 -10.447 HDYA NBFD7 -6.998 1.782841 -.140110+00 .200213-01 .234134-02 8.551 -59.841 SCHDTT BASF13 -6.990 1.697479 -.130948+00 .187347-01 .716289-02 2.616 -18.281 OHARA BASF1 -6.879 1.625941 -.129235+00 .187870-01 .135298-01 1.389 -9.552 OHARA BASF08 -6.850 1.723282 -.132830+00 .193904-01 .135401-01 1.432 -9.810 SCHDTT FN11 -6.827 1.620837 -.139550+00 .204406-01 -.595771-02 -3.431 23.423 SCHDTT F3 -6.777 1.612811 -.136443+00 .201321-01 .118564-01 1.698 -11.508 HDYA BAFD8 -6.767 1.723278 -.132746+00 .196157-01 .593488-02 3.305 -22.367 HDYA F11 -6.766 1.620837 -.140410+00 .207514-01 -.576843-02 -3.597 24.341 OHARA F11 -6.751 1.620830 -.140703+00 .208427-01 -5462656-02 -3.815 25.757 HDYA F3 -6.670 1.612808 -.136691+00 .204946-01 .116985-01 1.752 -11.684 SCHDTT BASF10 -6.667 1.650040 -.128991+00 .193478-01 .144917-01 1.335 -8.901 SCHDTT LAF22 -6.643 1.718638 -.136077+00 .204842-01 .762574-02 2.686 -17.845 SCHDTT LASF13 -6.603 1.855273 -.137989+00 .208967-01 .169617-01 1.232 -8.135 OHARA F3 -6.561 1.612807 -.136506+00 .208068-01 .127433-01 1.633 -10.712 OHARA BASF10 -6.551 1.650038 -.128157+00 .195643-01 .149071-01 1.312 -8.597 HDYA BAFD4 -6.550 1.651154 -.131869+00 .201397-01 .143726-01 1.401 -9.175 OHARA BASF8 -6.525 1.723282 -.133052+00 .203923-01 .807924-02 2.524 -16.468 HDYA BAFD1 -6.508 1.625941 -.128946+00 .198145-01 .143214-01 1.384 -9.004 SCHDTT F4 -6.456 1.616469 -.137862+00 .213540-01 .121536-01 1.760 -11.360 OHARA F10 -6.315 1.623516 -.138187+00 .218811-01 .131919-01 1.659 -10.475 HDYA F10 -6.246 1.616466 -.137878+00 .219691-01 .129832-01 1.692 -10.620 OHARA BASF4 -6.257 1.651161 -.131957+00 .210898-01 .134255-01 1.571 -9.829 TABLE II (4 OF 12) CORN-F 724380 -6.233 1.723352 -.132593+00 .212715-01 .120268-01 1.769 -11.025 OHARA F4 -6.228 1.616466 -.137789+00 .221243-01 .130243-01 1.690 -10.525 SCHDTT F2 -6.223 1.619916 -.138788+00 .223030-01 .131183-01 1.700 -10.580 SCHDTT TIF4 -6.214 1.583949 -.136144+00 .219042-01 -.423007-02 -5.178 32.178 CORN-F 620363 -6.144 1.619886 -.139062+00 .226337-01 .130501-01 1.734 -10.656 OHARA F2 -6.102 1.619917 -.139131+00 .228023-01 .131765-01 1.731 -10.559 CHANCE 620364 -6.084 1.619918 -.138657+00 .227899-01 .128088-01 1.779 -10.825 HDYA F2 -6.074 1.619916 -.139000700 .228849-01 .139599-01 1.639 -9.958 HDYA F1 -6.016 1.625753 -.140925+00 .234266-01 .122319-01 1.915 -11.521 SCHDTT F13 -5.977 1.622246 -.139915+00 .234103-01 .127246-01 1.840 -10.996 CHANCE 626357 -5.919 1.625751 -.141288+00 .238684-01 .132134-01 1.806 -10.693 CORN-F 637353 -5.808 1.636362 -.142766+00 .245799-01 .138303-01 1.777 -10.323 SCHDTT F1 -5.803 1.625754 -.141185+00 .243285-01 .133309-01 1.825 -10.591 OHARA F1 -5.776 1.625754 -.141188+00 .244442-01 .135281-01 1.807 -10.437 HDYA NBFD8 -5.736 1.807236 -.141680+00 .247020-01 .108494-01 2.277 -13.059 OHARA LAF012 -5.701 1.782843 <RTI ID=136.3> -.139314+00 .244377-01 .703459-02 3.474 -19.804 CORN-F 626356 -5.697 1.625775 -.141656+00 .248670-01 .142208-01 1.749 -9.961 SCHDTT BADF56 -5.691 1.657019 -.137123+00 .240955-01 .136697-01 1.763 -10.031 SCHDTT TIFN5 -5.630 1.593434 -.141761+00 .251788-01 -.388728-02 -6.477 36.468 HDYA FF5 -5.598 1.592582 -.142075+00 .253793-01 -.249450-02 -10.174 56.955 SCHDTT BASF55 -5.591 1.699664 -.145113+00 .259548-01 .348875-02 7.440 -41.595 SCHDTT LASF18 -5.578 1.913275 -.155052+00 .277982-01 .999495-02 2.781 -15.513 OHARA F6 -5.565 1.636227 -.142394+00 .255880-01 .140436-01 1.822 10.140 OHARA F16 -5.563 1.592579 -.141625+00 .254589-01 -.133843-02 -19.021 105.814 HDYA F6 -5.509 1.636225 -.142381+00 .258436-01 .145002-01 1.782 -9.819 SCHDTT F6 -5.486 1.636228 -.142495+00 .259741-01 .143701-01 1.808 -9.916 SCHDTT F7 -5.457 1.625233 -.141604+00 .259511-01 .143641-01 1.807 -9.858 HDYA F7 -5.419 1.625235 -.141451+00 .261046-01 .146792-01 1.778 -9.636 OHARA LAF7 -5.279 1.749342 -.142977+00 .270864-01 .944421-02 2.868 -15.129 SCHDTT SF7 -5.274 1.639667 -.145428+00 .275734-01 .145731-01 1.892 -9.979 SCHDTT BASF2 -5.257 1.664325 -.140417+00 .267122-01 .144307-01 1.851 -9.730 HDYA FD7 -5.233 1.639669 -.145636+00 .278294-01 .147764-01 1.883 -9.856 OHARA SF7 -5.213 1.639664 -.154596+00 .279095-01 .151326-01 1.844 -9.614 HDYA NBFD6 -5.193 1.756551 -.138386+00 .266493-01 .177375-01 1.502 -7.802 SCHDTT BASF14 -5.120 1.699536 -.143764+00 .280794-01 .905315-02 3.102 -15.880 HDYA BAFD14 -5.098 1.699533 -.143909+00 .282298-01 .956098-02 2.953 -15.052 HDYA BAFD2 -5.084 1.664323 -.140014+00 .275421-01 .162454-01 1.695 -8.619 SCHDTT SF12 -5.019 1.648171 -.148531+00 .295908-01 .122520-01 2.415 -12.123 CHANCE 648338 -5.010 1.648173 -.148536+00 .296460-01 .123944-01 2.392 -11.984 SCHDTT SF16 -4.983 1.645974 -.147645+00 .296315-01 .152709-01 1.940 -9.668 CORN-F 648339 -4.948 1.647853 -.148505+00 .300116-01 .201143-01 1.492 -7.383 SCHDTT SF9 -4.921 1.654320 -.149368+00 .303534-01 .154365-01 1.966 -9.676 HDYA FD2 -4.904 1.647554 -.148559+00 .302920-01 .146703-01 2.065 -10.127 SCHDTT LASF33 -4.895 1.805788 -.146754+00 .299778-01 .149144-01 2.010 -9.840 HDYA FD9 -4.885 1.654321 -.149021+00 .305049-01 .155978-01 1.956 -9.554 SCHDTT SF2 -4.863 1.647550 -.148460+00 .305265-01 .154254-01 1.979 -9.624 HDYA FD12 -4.850 1.648169 -.148675+00 .306537-01 .141316-01 2.169 -10.521 OHARA SF9 -4.845 1.654317 -.149580+00 .308741-01 .158054-01 1.953 -9.464 OHARA SF2 -4.834 1.647550 -.148652+00 .307503-01 .163419-01 1.882 -9.096 OHARA BASF2 -4.825 1.664327 -.140209+00 .290599-01 .172396-01 1.686 -8.133 SCHDTT SF17 -4.817 1.650030 -.149220+00 .309753-01 .155351-01 1.994 -9.605 CHANCE 653335 -4.805 1.653335 -.150134+00 .312471-01 .161343-01 1.937 -9.305 OHARA SF19 -4.736 1.666653 -.152025+00 .320978-01 .164376-01 1.953 -9.249 OHARA LAFO15 -4.713 1.749342 -.143590+00 .304670-01 .171232-01 1.779 -8.386 SCHDTT SF19 -4.680 1.666653 -.152114+00 .325027-01 .151201-01 2.150 -10.060 SCHDTT LAFN11 -4.677 1.756753 -.157878+00 .337572-01 .140857-01 2.397 -11.208 CORN-F 667331 -4.674 1.666851 -.151698+00 .324574-01 .164434-01 1.974 -9.225 SCHDTT SF51 -4.641 1.660103 -.152222+00 .327980-01 .102301-01 3.206 -14.880 HDYA TAFD9 -4.604 1.850107 -.155881+00 .338585-01 .750431-02 4.512 -20.772 SCHDTT LASF8 -4.539 1.807225 -.158724+00 .349707-01 .135055-01 2.589 -11.753 CORN-F 673323 -4.477 1.672548 -.155397+00 .347024-01 .177009-01 1.960 -8.777 HDYA NBFD9 -4.477 1.756726 -.157724+00 .352326-01 .155215-01 2.270 -10.162 CHANCE 850322 -4.471 1.850071 -.155534+00 .347844-01 .178619-01 1.947 -8.708 OHARA LASF21 -4.461 1.850068 -.155280+00 .348101-01 .133600-01 2.606 -11.623 HDYA FD19 -4.400 1.666651 -.151620+00 .344628-01 .179466-01 1.920 -8.448 SCHDTT SF50 -4.391 1.654583 -.152470+00 .347218-01 .160027-01 2.170 -9.528 SCHDTT SF5 -4.349 1.672547 -.155022+00 .357873-01 .170565-01 2.098 -9.124 SCHDTT SF62 -4.274 1.681185 -.156885+00 .367053-01 .167365-01 2.193 -9.374 HDYA FD5 -4.266 1.672550 -.155753+00 .365086-01 .179888-01 2.030 -8.658 OHARA SF5 -4.255 1.672549 -.156105+00 .366839-01 .177050-01 2.072 -8.817 SCHDTT LASF32 -4.205 1.803302 -.164710+00 .391719-01 .491177-02 7.975 -33.524 SCHDTT SFN64 -4.116 1.705682 -.165302+00 .401588-01 .252126-02 15.928 -65.563 SCHDTT BASF54 -4.095 1.736105 -.155574+00 .379897-01 .114353-01 3.322 -13.605 CORN-F 689312 -4.082 1.688844 -.160491+00 .393157-01 .188028-01 2.091 -8.532 TABLE I (5 .158511-01 12) HOYA LAFL4 -.762216+01 1.713888 -.126836+00 .166404-01 -82.525701 CHANCE 548456 -.758952+01 1.548553 -.120302+00 OF -82.493895 CORN-F 548457 -.758480+01 1.548960 -.120033+00 .158254-01 -82.489323 HOYA FEL1 -.756928+01 1.548997 -.119676+00 .158107-01 -82.474092 SCHOTT BAF8 -.755166+01 1.624694 -.116669+00 .154494-01 -82.456735 OHARA BAF10 -.754804+01 1.671049 -.116054+00 .153754-01 -82.453126 HOYA FEL3 -.748347+01 1.560980 -.116432+00 .155586-01 -82.388767 OHARA KF8 -.748140+01 1.511900 -.107585+00 .143803-01 -82.386711 OHARA LAFO11 -.739885+01 1.721126 -.119064+00 .160922-01 -82.302780 HOYA NBFD12 -.739653+01 1.800860 -.129473+00 .175045-01 -82.300406 OHARA LLF1 -.735086+01 1.549002 -.119827+00 .163011-01 -82.253117 OHARA BAF8 -.732767+01 1.624696 -.116808+00 .159407-01 -82.228893 OHARA LLF7 -.732480+01 1.549555 -.120369+00 .164331-01 -82.225887 HOYA FEL7 -.732475+01 1.549698 -.120672+00 .164746-01 -82.225824 HOYA ADF8 -.731999+01 1.687649 -.128009+00 .174876-01 -.82.220849 HOYA TAFD2 -.725452+01 1.839131 -.130614+00 .180045-01 -82.151518 SCHOTT LLF7 -.723611+01 1.549700 -.120796+00 .166935-01 -82.131801 SCHOTT LLF1 -.721689+01 1.549001 -.119877+00 .166106-01 -82.111117 OHARA LAF2 -.721056+01 1.745194 -.122533+00 .169936-01 -82.104247 SCHOTT LAFN2 -.717331+01 1.745195 -.122407+00 .170642-01 -82.063804 SCHOTT BAF3 -.716396+01 1.583571 -.117980+00 .164686-01 -82.053539 OHARA BAF3 -.709528+01 1.583575 -.118294+00 .166722-01 -81.977648 HOYA LAF2 -.706147+01 1.745189 -.122231+00 .173095-01 -81.939768 SCHOTT LASF31 -.700163+01 1.882209 -.133272+00 .190344-01 -81.871775 HOYA BAF7 -.691393+01 1.608959 -.118645+00 .171603-01 -81.770058 SCHOTT BAF52 -.684565+01 1.609531 -.118000+00 .172372-01 -81.689131 HOYA FEL4 -.683556+01 1.562271 -.121229+00 .177350-01 -81.677047 SCHOTT LLF4 -.683225+01 1.562272 -.121198+00 .177391-01 -81.673051 SCHOTT BAF50 -.683160+01 1.683828 -.123135+00 .180242-01 -81.672325 CORN-F 558525 -.679080+01 1.558274 -.104451+00 .153812-01 -81.622959 OHARA LASF02 -.678640+01 1.800873 -.129573+00 .190930-01 -81.617603 OHARA LASF07 -.674292+01 1.864490 -.131905+00 .195620-01 -81.564310 SCHOTT BAF51 -.667683+01 1.653284 -.121957+00 .182657-01 -81.482031 HOYA LAFL5 -.663890+01 1.721176 -.124870+00 .188089-01 -81.434055 CORN-F 655401 -.661610+01 1.656673 -.136700+00 .206617-01 -81.405012 OHARA LLF4 -.661334+01 1.562271 -.121299+00 .183416-01 -81.401454 OHARA LASF08 -.657825+01 1.884553 -.134296+00 .204152-01 -81.356277 HOYA LAFL6 -.643226+01 1.721231 -.130376+00 .202691-01 -81.163168 SCHOTT BAF12 -.634602+01 1.640316 -.121262+00 .191084-01 -81.044998 HOYA NBF02 -.623651+01 1.798590 -.133088+00 .213402-01 -80.890365 SCHOTT BAF13 -.619665+01 1.669988 -.121811+00 .196576-01 -80.832764 OHARA BAF12 -.616833+01 1.640323 -.122011+00 .197803-01 -80.791384 HOYA NBFD13 -.612790+01 1.807522 -.134409+00 .219340-01 -80.731686 HOYA BAF13 -.610432+01 1.669986 -.122007+00 .199870-01 -80.696530 HOYA BAF12 -.609516+01 1.640320 -.121479+00 .199305-01 -80.682753 OHARA BAF13 -.609495+01 1.669989 -.121732+00 .199726-01 -80.682481 HOYA BAF20 -.607026+01 1.686899 -.124740+00 .205493-01 -80.645282 SCHOTT KZFSN5 -.606110+01 1.655302 -.138283+00 .228149-01 -80.631338 OHARA LF8 -.603928+01 1.565365 -.125051+00 .207062-01 -80.598153 OHARA KZFS5 -.596388+01 1.655297 -.137983+00 .231365-01 -80.481395 OHARA LASF03 -.588457+01 1.807515 -.134140+00 .227952-01 -80.355525 OHARA LAF02 -.587444+01 1.721182 -.125227+00 .213173-01 -80.339188 SCHOTT LASFN3 -.585438+01 1.809432 -.134322+00 .229438-01 -80.306747 SCHOTT BAF4 -.583744+01 1.606609 -.124605+00 .213459-01 -80.279103 CHANCE 606439 -.582678+01 1.606604 -.124645+00 .213917-01 -80.261711 CORN-F 606439 -.579984+01 1.606597 -.124659+00 .214936-01 -80.217294 HOYA FL6 -.578924+01 1.568274 -.127818+00 .220785-01 -80.199783 OHARA LASF24 -.578901+01 1.908697 -.142651+00 .246417-01 -80.199378 OHARA BAF01 -.578563+01 1.683593 -.122490+00 .211714-01 -80.193776 SCHOTT LF6 -.575725+01 1.568270 -.127797+00 .221976-01 -80.146363 SCHOTT LAF25 -.575068+01 1.785634 -.132542+00 .230481-01 -80.135318 CORN-F 865401 -.571089+01 1.866547 -.136374+00 .238797-01 -80.067945 CHANCE 567428 -.570883+01 1.568268 -.127810+00 .223881-01 -80.064467 HOYA BAF4 -.569557+01 1.606610 -.124698+00 .218901-01 -80.043463 SCHOTT LAFN8 -.569485+01 1.736465 -.131618+00 .231117-01 -80.040579 HOYA BAFD15 -.565905+01 1.703234 -.135739+00 .239861-01 -79.978856 SCHOTT BASF52 -.565096+01 1.703037 -.133478+00 .236204-01 -79.964772 OHARA LAF07 -.565078+01 1.714032 -.126717+00 .224247-01 -79.964451 HOYA BAF22 -.564805+01 1.683591 -.122573+00 .217019-01 -79.959669 OHARA BAF4 -.564077+01 1.606613 -.125148+00 .221864-01 -79.946979 CHANCE 573426 -.563933+01 1.574053 -.128546+00 .227946-01 -79.944473 HOYA FL4 -.562263+01 1.579442 -.131186+00 .233318-01 -79.915234 SCHOTT LF1 -.560199+01 1.574055 -.128516+00 .229412-01 -79.878821 HOYA NBF03 -.559747+01 1.805959 -.138026+00 .246586-01 -79.870863 TABLE lI (6 OF 12) SCHOTT SF57 -2.563 1.846408 -.206927+00 .807402-01 .162222-01 4.977 - 12.756 HOYA FDS9 -2.552 1.846403 -.206914+00 .810766-01 .174143-01 4.656 - 11.882 OHARA SF03 -2.533 1.846404 -.206695+00 .816138-01 .215868-01 3.781 - 9.575 SCHOTT SF58 -2.235 1.917309 -.228319+00 .102142-00 .149349-01 6.839 - 15.288 OHARA SFS01 -2.208 1.922555 -.230396+00 .104355-00 .113419-01 9.201 - 20.314 OHARA SFS1 -2.128 1.922547 -.234526+00 .110212-00 .744372-02 14.806 - 31.507 SCHOTT SF59 -2.109 1.952164 -.240117+00 .113849+00 .162320-02 70.139 -147.928 OHARA BK9 2.861 1.493821 -.803643-01 -.280896-01 -.204052-01 1.377 3.938 SCHOTT FK5 2.865 1.487438 -.753913-01 -.263180-01 -.189047-01 1.392 3.988 HOYA FC5 2.905 1.487438 -.753744-01 -.259430-01 -.188962-01 1.373 3.989 CORN-F 488658 2.919 1.487447 -.807348-01 -.276601-01 -.194901-01 1.419 4.142 HOYA BSC3 2.952 1.498252 -.813643-01 -.275662-01 -.193049-01 1.428 4.215 OHARA FK5 2.960 1.487438 -.756632-01 -.255643-01 -.170814-01 1.497 4.430 SCHOTT BK10 2.960 1.497766 -.792124-01 -.267620-01 -.192149-01 1.393 4.122 SCHOTT BK3 2.991 1.496254 -.814789-01 -.272409-01 -.195328-01 1.395 4.171 CORN-F 487704 2.993 1.487196 -.752048-01 -.251274-01 -.167875-01 1.497 4.480 OHARA BK10 3.025 1.497765 -.792615-01 -.262056-01 -.177864-01 1.473 4.456 SCHOTT BK1 3.075 1.503725 -.791244-01 -.257320-01 -.180104-01 1.429 4.393 OHARA BK4 3.126 1.500426 -.802655-01 -.256745-01 -.169697-01 1.513 4.730 SCHOTT FK1 3.163 1.470638 -.785719-01 -.248440-01 -.170414-01 1.458 4.611 HOYA PC1 3.178 1.503723 -.791104-01 -.248895-01 -.168196-01 1.480 4.703 OHARA BK3 3.185 1.498251 -.813600-01 -.255469-01 -.174240-01 1.466 4.669 OHARA PK1 3.188 1.503723 -.790943-01 -.248065-01 -.162424-01 1.527 4.870 OHARA PK2 3.242 1.518146 -.812802-01 -.250680-01 -.170427-01 1.471 4.769 HOYA PC1 3.259 1.470636 -.785432-01 -.240986-01 -.159417-01 1.512 4.927 OHARA FK3 3.275 1.464446 -.801760-01 -.244804-01 -.161796-01 1.513 4.955 SCHOTT PK50 3.298 1.520484 -.757644-01 -.229694-01 -.150775-01 1.523 5.025 OHARA FK1 3.343 1.470638 -.784884-01 -.234806-01 -.143948-01 1.631 5.453 SCHOTT FK3 3.377 1.464448 -.802741-01 -.237720-01 -.157250-01 1.512 5.105 CORN-F 465657 3.379 1.464448 -.803645-01 -.237823-01 -.151281-01 1.572 5.312 SCHOTT PK2 3.397 1.518151 -.811341-01 -.238813-01 -.160876-01 1.484 5.043 HOYA PC2 3.429 1.518151 -.809744-01 -.236126-01 -.154907-01 1.524 5.227 CORN-F 518651 3.477 1.518140 -.810585-01 -.233110-01 -.146698-01 1.589 5.526 OHARA PKS1 3.486 1.517222 -.757358-01 -.217277-01 -.135002-01 1.609 5.610 HOYA PCS1 3.493 1.517229 -.756531-01 -.216566-01 -.118306-01 1.831 5.395 SCHOTT PK3 3.512 1.525358 -.815369-01 -.232167-01 -.151485-01 1.533 5.383 OHARA PK3 3.535 1.525355 -.817364-01 -.231251-01 -.153467-01 1.507 5.326 HOYA FC3 3.566 1.464450 -.802805-01 -.225129-01 -.131702-01 1.709 5.096 HOYA PC3 3.588 1.525360 -.815538-01 -.227293-01 -.144528-01 1.573 5.643 SCHOTT BK7 3.595 1.516740 -.821247-01 -.228469-01 -.147828-01 1.545 5.555 HOYA BSC7 3.597 1.516738 -.820635-01 -.228162-01 -.143071-01 1.595 5.736 SCHOTT UBK7 3.623 1.516740 -.819592-01 -.226221-01 -.144807-01 1.562 5.660 OHARA BK12 3.627 1.518679 -.816145-01 -.225015-01 -.143862-01 1.564 5.673 CORN-F 517642 3.627 1.516744 -.820742-01 -.226262-01 -.138974-01 1.628 5.906 OHARA BK7 3.667 1.516270 -.821115-01 -.223890-01 -.138449-01 1.617 5.931 CHANCE 510644 3.682 1.509639 -.816942-01 -.221864-01 -.140498-01 1.579 5.815 CHANCE 517642 3.704 1.516736 -.820335-01 -.221500-01 -.137473-01 1.611 5.967 CHANCE 641601 3.706 1.640416 -.876494-01 -.236528-01 -.159457-01 1.483 5.497 OHARA PSK3 3.760 1.552259 -.825119-01 -.219468-01 -.131672-01 1.667 6.266 SCHOTT BKB 3.839 1.520091 -.825798-01 -.215109-01 -.132199-01 1.627 6.247 OHARA LAK01 3.856 1.639919 -.875043-01 -.226923-01 -.143658-01 1.580 6.091 HOYA ZNC7 3.900 1.508409 -.858151-01 -.220015-01 -.132040-01 1.666 6.499 SCHOTT ZKN7 3.914 1.508407 -.859278-01 -.219515-01 -.135941-01 1.615 6.321 CORN-F 510635 3.945 1.509933 -.827472-01 -.209770-01 -.123052-01 1.705 6.725 CHANCE 508612 3.952 1.507526 -.859436-01 -.217458-01 -.137590-01 1.580 6.246 HOYA PCD2 4.003 1.568663 -.831973-01 -.207821-01 -.122812-01 1.692 6.774 OHARA ZK7 4.006 1.508408 -.833600-01 -.215569-01 -.125222-01 1.721 6.897 SCHOTT PSK3 4.017 1.552257 -.827823-01 -.206068-01 -.119426-01 1.725 6.932 HOYA BSC1 4.059 1.510031 -.827665-01 -.203921-01 -.120206-01 1.696 6.885 SCHOTT PSK50 4.060 1.557468 -.780233-01 -.192169-01 -.105060-01 1.829 7.427 SCHOTT K51 4.098 1.505117 -.881892-01 -.215198-01 -.151929-01 1.416 5.805 SCHOTT PSK2 4.101 1.568663 -.832147-01 -.202894-01 -.115953-01 1.750 7.177 SCHOTT BK1 4.108 1.510030 -.827070-01 -.201308-01 -.119323-01 1.687 6.931 OHARA PSK2 4.128 1.568662 -.830341-01 -.201158-01 -.114936-01 1.750 7.224 SCHOTT KZFSN2 4.129 1.558285 -.970219-01 -.234949-01 -.187953-01 1.250 5.162 SCHOTT FK54 4.131 1.436964 -.577929-01 -.139897-01 -.573847-01 2.438 10.071 OHARA BK1 4.179 1.510032 -.825826-01 -.197592-01 -.103512-01 1.909 7.978 OHARA PSK1 4.183 1.547646 -.833594-01 -.199288-01 -.108206-01 1.842 7.704 HOYA PCD3 4.295 1.552255 -.827597-01 -.192709-01 -.992002-01 1.943 8.343 SCHOTT BK6 4.356 1.531066 -.843429-01 -.193615-01 -.107182-01 1.806 7.869 CHANCE 569631 4.362 1.568661 -.831007-01 -.190507-01 -.101752-01 1.872 8.167 OHARA BK6 4.459 1.531062 -.839051-01 -.188158-01 -.907099-01 2.074 9.250 SCHOTT K11 4.520 1.500069 -.852812-01 -.188674-01 -.121052-01 1.559 7.045 CORN-F 518603 4.533 1.518137 -.869053-01 -.191735-01 -.111896-01 1.714 7.767 TABLE 11 (7 OF 12) OHARA BK2 4.606 1.506507 -.844496-01 -.183355-01 -.948703-02 1.933 8.902 CORN-F 564609 4.654 1.563936 -.859088-01 -.184594-01 -.927684-02 1.990 9.261 HOYA LACL6 4.704 1.639924 -.868927-01 -.184710-01 -.882896-02 2.141 10.070 HOYA BSC6 4.709 1.531064 -.842204-01 -.178850-02 -.870653-02 2.054 9.673 CHANCE 589613 4.770 1.589057 -.854452-01 -.179132-02 -.941120-02 1.903 9.079 CORN-F 540597 4.851 1.539438 -.876151-01 -.180594-01 -.102980-01 1.754 8.508 SCHOTT SK5 4.875 1.589059 -.853376-01 -.175035-01 -.825204-02 2.121 10.341 OHARA SK20 4.884 1.559557 -.854291-01 -.174927-01 -.809035-02 2.162 10.559 HOYA FCD10 4.904 1.456463 -.575592-01 -.117369-01 -.235336-02 4.987 24.458 SCHOTT LAK31 4.909 1.696641 -.926829-01 -.188813-01 -.103613-01 1.822 8.945 SCHOTT PSK52 4.969 1.603031 -.798370-01 -.160673-01 -.689272-02 2.331 11.583 OHARA K1 4.980 1.509706 -.841213-01 -.168921-01 -.744747-02 2.268 11.295 OHARA LAKO14 5.015 1.696705 -.925209-01 -.184487-01 -.951720-02 1.938 9.721 HOYA BACD5 5.026 1.589057 -.853142-01 -.169741-01 -.765990-02 2.216 11.138 CHANCE 697562 5.048 1.697243 -.929825-01 -.184184-01 -.940164-02 1.959 9.890 SCHOTT UK50 5.057 1.522507 -.865220-01 -.171107-01 -.854471-02 2.002 10.126 CORN-F 486817 5.064 1.486000 -.638663-01 -.126120-01 -.337675-02 3.735 18.914 CORN-F 511604 5.127 1.510937 -.865685-01 -.168846-01 -.727218-02 2.322 11.904 OHARA SK11 5.140 1.563770 -.860269-01 -.167378-01 -.734932-02 2.277 11.705 SCHOTT K50 5.158 1.522507 -.867957-01 -.168285-01 -.805276-02 2.090 10.778 SCHOTT LAK21 5.183 1.640417 -.868864-01 -.167639-01 -.758897-02 2.209 11.449 SCHOTT FK51 5.195 1.486518 -.617162-01 -.118794-01 -.295916-02 4.014 20.856 CORN-F 697562 5.201 1.696908 -.929539-01 -.178730-01 -.870714-02 2.053 10.676 CORN-F 589612 5.201 1.588927 -.853444-01 -.164087-01 -.673590-02 2.436 12.670 SCHOTT SK20 5.221 1.559563 -.852772-01 -.163329-01 -.702539-02 2.325 12.138 HOYA BACD 5.244 1.620333 -.865455-01 -.165044-01 -.727648-02 2.268 11.894 OHARA LAK6 5.246 1.642414 -.894287-01 -.170461-01 -.800976-02 2.128 11.165 OHARA FK01 5.273 1.496953 -.639181-01 -.121214-01 -.282021-02 4.298 22.664 OHARA LAK14 5.280 1.696705 -.939134-01 -.177852-01 -.877056-02 2.028 10.708 HOYA LACL7 5.283 1.669910 -.910488-01 -.172354-01 -.690969-02 2.494 13.177 HOYA ADF1 5.284 1.564918 -.985658-01 -.186537-01 -.125719-01 1.484 7.840 CORN-F 523594 5.284 1.522931 -.878077-01 -.166168-01 -.907534-02 1.831 9.675 CHANCE 697554 5.305 1.696705 -.942321-01 -.177644-01 -.873633-02 2.033 10.786 SCHOTT SK16 5.308 1.620335 -.865128-01 -.162986-01 -.709247-02 2.298 12.198 OHARA LAK7 5.324 1.651515 -.889115-01 -.166990-01 -.712987-02 2.342 12.470 SCHOTT BALKN3 5.354 1.518425 -.866198-01 -.161787-01 -.781501-02 2.070 11.084 OHARA K50 5.384 1.522501 -.869886-01 -.161616-01 -.901797-02 1.792 9.646 HOYA LAC14 5.399 1.696709 -.941316-01 -.174345-01 -.799765-02 2.180 11.770 HOYA C7 5.425 1.511059 -.861484-01 -.158813-01 -.577050-02 2.752 14.929 SCHOTT TIK1 5.446 1.478630 -.889197-01 -.163273-01 -.906127-02 1.802 9.813 SCHOTT LAKN14 5.458 1.696707 -.941778-01 -.172531-01 -.835559-02 2.065 11.271 CHANCE 603606 5.467 1.603035 -.860735-01 -.157455-01 -.621115-02 2.535 13.858 OHARA SK5 5.472 1.589055 -.855443-01 -.156340-01 -.591099-02 2.645 14.472 SCHOTT K7 5.485 1.511058 -.863398-01 -.157415-01 -.709100-02 2.220 12.176 HOYA BACD14 5.497 1.603037 -.859069-01 -.156274-01 -.598718-02 2.610 14.349 HOYA LAC6 5.505 1.642416 -.899007-01 -.163322-01 -.705862-02 2.314 12.736 SCHOTT SK11 5.515 1.563771 -.857460-01 -.155488-01 -.607616-02 2.559 14.112 CORN-F 697554 5.518 1.696912 -.942449-01 -.170810-01 -.808880-02 2.112 11.651 HOYA LAC15 5.536 1.696703 -.930117-01 -.168024-01 -.636116-02 2.641 14.622 SCHOTT SK14 5.540 1.603037 -.860309-01 -.155286-01 -.604468-02 2.569 14.232 OHARA SK14 5.546 1.603039 -.858583-01 -.154822-01 -.694749-02 2.603 14.436 CORN-F 641601 5.546 1.640416 -.867823-01 -.156484-01 -.606702-02 2.579 14.304 CHANCE 519604 5.551 1.518924 -.862977-01 -.155461-01 -.661172-02 2.351 13.052 CHANCE 564608 5.563 1.563770 -.857603-01 -.154164-01 -.594402-02 2.594 14.428 OHARA BALK3 5.569 1.518287 -.865144-01 -.155354-01 -.650411-02 2.389 13.301 HOYA BACD11 5.580 1.563771 -.856229-01 -.153440-01 -.627898-02 2.444 13.636 HOYA BACD165 5.606 1.620335 -.870460-01 -.155275-01 -.543135-02 2.859 16.027 CORN-F 620603 5.621 1.620330 -.864614-01 -.153816-01 -.551740-02 2.788 15.671 CHANCE 620603 5.698 1.620332 -.863890-01 -.151603-01 -.556257-02 2.725 15.530 OHARA K7 5.723 1.511058 -.862441-01 -.150695-01 -.606722-02 2.484 14.215 CORN-F 652585 5.741 1.651517 -.890910-01 -.155172-01 -.540970-02 2.868 16.469 SCHOTT FK52 5.757 1.486008 -.636069-01 -.110490-01 -.176256-02 6.269 36.088 HOYA LAC7 5.793 1.651516 -.890710-01 -.153745-01 -.463508-02 3.317 19.217 OHARA PSK01 5.814 1.616928 -.830255-01 -.142800-01 -.507654-02 2.813 16.355 HOYA LAC11 5.858 1.658211 -.909119-01 -.155199-01 -.562700-02 2.758 16.156 OHARA PSK01 5.814 1.616928 -.830255-01 -.142800-01 -.507654-02 2.813 16.355 OHARA PSK01 5.814 1.616928 -.830255-01 -.142800-01 -.507654-02 2.813 16.355 HOYA LAC11 5.858 1.658211 -.909119-01 -.155199-01 -.562700-02 2.758 16.156 HOYA LAC11 5.858 1.658211 -.909119-01 -.155199-01 -.562700-02 2.758 16.156 OHARA PSK01 5.814 1.616928 -.830255-01 -.142800-01 -.507654-02 2.813 16.355 CORN-F 652585 5.741 1.651517 -.890910-01 -.155172-01 -.540970-02 2.868 16.469 HOYA LAC11 5.858 1.658211 -.909119-01 -.155199-01 -.562700-02 2.758 16.156 SCHOTT FK52 5.757 1.486008 -.636069-01 -.110490-01 -.176256-02 6.269 36.088 SCHOTT FK52 5.757 1.486008 -.636069-01 -.110490-01 -.176256-02 6.269 36.088 TABLE II (8 OF 12) CHANGE 713538 6.147 1.712901 -.967482-O1 -.157384-01 -.675252-02 2.331 14.328 OHARA K5 6.150 1.522429 -.871256-O1 -.141669-01 -.590165-02 2.400 14.763 SCHOTT LAKB 6.151 1.712905 -.967281-O1 -.157262-01 -.711774-02 2.209 13.590 HOYA BACD12 6.203 1.583057 -.873666-O1 -.140851-01 -.440023-02 3.201 19.855 SCHOTT LAKN7 6.213 1.651518 -.889269-O1 -.143121-01 -.481842-02 2.970 18.456 CHANGE 607595 6.216 1.607215 -.875668-O1 -.140868-01 -.458911-02 3.070 19.081 OHARA LAK9 6.218 1.690909 -.949531-O1 -.152697-01 -.629513-02 2.426 15.084 CORN-F 613585 6.232 1.612616 -.889349-O1 -.142702-01 -.464760-02 3.070 19.136 SCHOTT LAK11 6.233 1.658216 -.909186-O1 -.145874-01 -.523021-02 2.789 17.383 SCHOTT BAK50 6.237 1.567664 -.897380-O1 -.143880-01 -.501834-02 2.867 17.882 CHANGE 652585 6.241 1.651515 -.889501-O1 -.142526-01 -.459356-02 3.103 19.364 SCHOTT LAK9 6.277 1.690909 -.951366-O1 -.151571-01 -.622629-02 2.434 15.280 OHARA SK12 6.313 1.583056 -.875952-O1 -.138698-01 -.431570-02 3.214 20.289 CHANGE 524592 6.327 1.523932 -.878863-O1 -.138896-01 -.445128-02 3.120 19.744 SCHOTT K3 6.336 1.518164 -.882051-O1 -.139217-01 -.551445-02 2.525 15.995 CORN-F 623581 6.368 1.622924 -.896154-O1 -.140731-01 -.509693-02 2.761 17.582 HOYA BACL1 6.376 1.526353 -.866298-O1 -.135861-01 -.445183-02 3.052 19.459 HOYA SBF5 6.382 1.521226 -.986168-O1 -.154515-01 -.988293-02 1.563 9.978 SCHOTT BALK1 6.383 1.526356 -.866673-O1 -.135777-01 -.425036-02 3.194 20.391 HOYA LAC8 6.449 1.712902 -.964279-O1 -.149521-01 -.514611-02 2.906 18.738 OHARA LAK02 6.499 1.669913 -.906677-O1 -.139503-01 -.471304-02 2.960 19.238 SCHOTT PSK53 6.508 1.620068 -.817978-O1 -.125688-01 -.266930-02 4.709 30.644 OHARA BAK2 6.520 1.539892 -.872133-O1 -.133754-01 -.336242-02 3.978 25.937 SCHOTT BAK2 6.556 1.539893 -.870826-O1 -.132837-01 -.374755-02 3.545 23.237 SCHOTT SK12 6.568 1.583058 -.874398-O1 -.133138-01 -.353850-02 3.763 24.711 HOYA TAC1 6.590 1.725898 -.927090-O1 -.147516-01 -.457236-02 3.226 21.260 SCHOTT 5K7 6.590 1.607214 -.874337-O1 -.132673-01 -.337933-02 3.926 25.873 CORN-F 713538 6.606 1.712902 -.966678-O1 -.146339-01 -.535544-02 2.733 18.050 OHARA K01 6.610 1.523003 -.889419-O1 -.134552-01 -.583532-02 2.306 15.242 HOYA BAC2 6.622 1.539894 -.870947-O1 -.131533-01 -.391689-02 3.358 22.236 HOYA C3 6.658 1.518169 -.882289-O1 -.132510-01 -.465668-02 2.846 18.947 HOYA ZNC1 6.663 1.533081 -.894813-O1 -.134302-01 -.328172-02 4.092 27.267 SCHOTT K10 6.695 1.501305 -.921918-O1 -.137707-01 -.724901-02 1.900 12.718 HOYA C5 6.713 1.522423 -.875458-O1 -.130419-01 -.233649-02 5.582 37.469 OHARA LAK010 6.714 1.725900 -.969928-O1 -.144462-01 -.477007-02 3.029 20.334 OHARA K3 6.721 1.518164 -.882441-O1 -.131296-01 -.392919-02 3.342 22.459 <RTI ID=140.8> OHARA K2F5 6.796 1.521226 -.989376-O1 -.145579-01 -.962169-02 1.513 10.263 SCHOTT SK3 6.812 1.608733 -.881775-O1 -.129447-01 -.355097-02 3.645 24.832 CHANGE 669574 6.830 1.663732 -.905610-O1 -.132587-01 -.336905-02 3.935 26.880 HOYA C12 6.844 1.523007 -.886949-O1 -.129586-01 -.370803-02 3.495 23.920 SCHOTT LAK23 6.851 1.668729 -.905576-O1 -.132185-01 -.358112-02 3.691 25.287 HOYA BACD7 6.855 1.607216 -.873371-O1 -.127414-01 -.214358-02 5.943 40.738 OHARA K2 6.860 1.515949 -.914926-O1 -.133366-01 -.549090-02 2.429 16.663 OHARA LAK8 6.895 1.712897 -.965187-O1 -.139977-01 -.452127-02 3.096 21.348 SCHOTT ZK1 6.901 1.533081 -.896179-O1 -.129867-01 -.447048-02 2.905 20.047 CORN-F 573575 6.931 1.572425 -.904539-O1 -.130502-01 -.351043-02 3.718 25.767 HOYA LACL2 6.953 1.650109 -.934514-O1 -.134408-01 -.589840-02 2.279 15.844 OHARA SK7 6.958 1.607216 -.874465-O1 -.125676-01 -.262312-02 4.791 33.337 CORN-F 678555 6.987 1.677914 -.935998-O1 -.134144-01 -.352755-02 3.803 26.534 CAHNGE 658573 7.029 1.658213 -.907356-01 -.129095-01 -.329672-02 3.916 27.523 SCHOTT PK51 7.035 1.528503 -.673937-O1 -.957963-02 -.453233-03 -21.136 -148.695 CHANGE 643580 7.044 1.642414 -.896155-O1 -.127217-01 -.285256-02 4.460 31.416 OHARA 5K3 7.093 1.608735 -.880631-O1 -.124147-01 -.235977-02 5.261 37.319 SCHOTT 5K4 7.117 1.612643 -.885774-O1 -.124460-01 -.283700-02 4.387 31.222 CORN-F 529518 7.163 1.528923 -.100340+00 -.140072-01 -.820824-02 1.706 12.224 CHANGE 572577 7.177 1.572126 -.899434-01 -.125326-01 -.381528-02 3.285 23.575 SCHOTT LAKN6 7.183 1.642417 -.895749-01 -.124711-01 -.250159-02 4.985 35.807 OHARA BAK1 7.186 1.572428 -.899356-01 -.125151-01 -.366446-02 3.415 24.543 HOYA BACD15 7.211 1.622915 -.892737-01 -.123807-01 -.308693-02 4.011 28.920 CHANGE 691547 7.229 1.690906 -.949247-01 -.131317-01 -.307996-02 4.264 30.820 SCHOTT K2F2 7.233 1.529364 -.100562-01 -.139033-01 -.883979-02 1.573 11.376 OHARA ZK1 7.241 1.533083 -.895476-01 -.123663-01 -.319562-02 3.870 28.022 HOYA BAC5 7.254 1.556638 -.883840-01 -.121843-01 -.324910-02 3.750 27.203 CHANGE 613586 7.301 1.612640 -.885524-01 -.121292-01 -.232589-02 5.215 38.073 OHARA LAK011 7.317 1.740893 -.986297-01 -.134798-01 -.417016-02 3.232 23.651 CORN-F 609590 7.373 1.608679 -.879735-01 -.119318-01 -.107720-02 11.077 81.669 OHARA KZF2 7.403 1.529366 -.100437+00 -.135712-01 -.873342-02 1.554 11.505 CHANGE 623581 7.415 1.622907 -.894283-01 -.120602-01 -.198530-02 5.075 45.045 HOYA BACD4 7.444 1.612640 -.885957-01 -.119024-01 -.171424-02 6.943 51.682 HOYA BACD3 7.459 1.608735 -.881444-01 -.118178-01 -.203789-02 5.799 43.253 OHARA LAK13 7.462 1.693404 -.972759-01 -.130362-01 -.437388-02 2.980 22.240 SCHOTT SK15 7.532 1.622911 -.893772-01 -.118666-01 -.213001-02 5.571 41.961 HOYA SBF6 7.598 1.526746 -.101704+00 -.133847-01 -.827299-02 1.618 12.293 SCHOTT KZF56 7.605 1.591875 -.107110+00 -.140833-01 -.115092-01 1.224 9.306 TABLE Il (9 OF 12) SCHOTT K2FG 7.606 1.526743 -.101593+00 -.133562-01 -.862104-02 1.549 11.784 OHARA PSKO2 7.643 1.617927 -.818372-01 -.107073-01 -.110198-03 97.164 742.638 HOYA SBF2 7.646 1.529364 -.100648+00 -.131629-01 -.780821-02 1.686 12.890 DHARA LAK11 7.657 1.658211 -.904552-01 -.118128-01 -.170177-02 6.941 53.154 SCHOTT BAK5 7.677 1.556640 -.884378-01 -.115204-01 -.178067-02 6.470 49.665 CORN-F 6S1559 7.682 1.651038 -.928350-01 -.120842-01 -.210084-02 5.752 44.189 DHARA ZK4 7.685 1.511834 -.892013-01 -.116065-01 -.192179-02 6.039 46.416 SCHOTT SK51 7.688 1.620824 -.859845-01 -.111842-01 -.188495-02 5.933 45.616 HOYA C10 7.703 1.501305 -.923216-01 -.119846-01 -.567892-02 2.110 16.257 HOYA TAC2 7.741 1.740893 -.984759-01 -.127209-01 -.236823-02 5.371 41.582 OHARA LAK013 7.747 1.640915 -.911302-01 -.117626-01 -.317403-02 3.706 28.711 DHARA SK15 7.779 1.622912 -.892144-01 -.114685-01 -.154793-02 7.409 57.635 CORN-F 691548 7.823 1.690915 -.947209-01 -.121087-01 -.207882-02 5.825 45.565 OHARA SK4 7.852 1.612638 -.882629-01 -.112411-01 -.811949-03 13.844 108.705 SCHOTT SK52 7.868 1.638455 -.934108-01 -.118722-01 -.268132-02 4.428 34.838 CORN-F 658572 7.983 1.657418 -.906808-01 -.113589-01 -.118132-02 9.615 76.783 DHARA K2F6 8.073 1.526745 -.101431+00 -.125642-01 -.806489-02 1.558 12.577 HOYA BACD13 8.081 1.591735 -.889125-01 -.110026-01 -.112692-02 9.763 78.898 DHARA LASK01 8.106 1.754892 -.991531-01 -.122321-01 -.261430-02 4.679 37.927 SCHOTT SK13 8.157 1.591734 -.888920-01 -.108980-01 -.861306-03 12.653 103.206 DHARA LAK09 8.164 1.733892 -.100890+00 -.123579-01 -.374200-02 3.302 26.961 SCHOTT LAKN16 8.186 1.733395 -.100420+00 -.122675-01 -.353129-02 3.474 28.437 HOYA BAC4 8.396 1.568754 -.925165-01 -.110188-01 -.271226-02 4.063 34.110 DHARA BAK5 8.442 1.556642 -.883742-01 -.104688-01 .113065-04 -925.906 -7816.220 CORN-F 604640 8.470 1.603439 -.809551-01 -.955736-02 .201133-02 -4.752 -40.249 SCHOTT BAK6 8.480 1.574364 -.918813-01 -.108344-01 -.311720-02 3.476 29.476 OHARA SK19 8.485 1.613341 -.902771-01 -.106402-01 -.113363-02 9.386 79.635 HOYA LAC12 8.544 1.677812 -.932141-01 -.109101-01 -.446700-03 24.424 208.673 DHARA SK10 8.731 1.622718 -.907040-01 -.103893-01 -.105581-02 9.840 85.909 SCHOTT KF3 8.780 1.514471 -.947050-01 -.107861-01 -.380584-02 2.834 24.884 SCHOTT BAK4 8.842 1.568755 -.922830-01 -.104366-01 -.200230-02 5.212 46.089 CHANCE 569561 8.976 1.568752 -.922182-01 -.102743-01 -.154966-02 6.630 59.509 DHARA LAK12 8.976 1.677809 -.935008-01 -.104171-01 -.405546-03 25.687 230.555 SCHOTT SK19 9.015 1.613342 -.902379-01 -.100103-01 -.251304-03 39.833 359.078 SCHOTT LAK10 9.053 1.719894 -.102773+00 -.113521-01 -.488559-02 2.324 21.036 HOYA BAC6 9.077 1.574366 -.919426-01 -.101259-01 -.220226-02 4.598 41.735 SCHOTT LAKN22 9.114 1.651044 -.926400-01 -.101646-01 .130301-03 -78.009 -710.970 DHARA LAK04 9.118 1.650910 -.921923-01 -.101114-01 -.135790-02 7.446 67.894 HOYA CF3 9.168 1.514470 -.948556-01 -.103464-01 -.392678-02 2.635 24.156 OHARA K10 9.179 1.501306 -.9t8246-01 -.100037-01 -.722028-02 1.385 12.718 SCHOTT KZFSN9 9.220 1.598463 -.110530+00 -.119880-01 -.993952-02 1.206 11.120 OHARA LAF03 9.263 1.734887 -.103971+00 -.112248-01 -.398197-02 2.819 26.111 CRON-F 569560 9.314 1.568722 -.924370-01 -.992437-02 -.959931-03 10.339 96.295 SCHOTT LAK28 9.335 1.744179 -.101990+00 -.109256-01 -.222904-02 4.901 45.755 SCHOTT BAK1 9.337 1.572426 -.899074-01 -.962889-02 .348458-03 -27.633 -258.015 OHARA BAK4 9.365 1.568756 -.921768-01 -.984275-02 -.991787-03 9.924 92.940 OHARA BAK6 9.392 1.574366 -.916184-01 -.975546-02 -.244339-03 39.926 374.964 HOYA TAC4 9.414 1.733893 -.101592+00 -.107914-01 .141620-03 -76.200 -717.353 HOYA BAC1 9.426 1.572424 -.901217-01 -.956143-02 -.168226-03 56.837 535.719 SCHOTT SKN18 9.569 1.638456 -.933396-01 -.975467-02 -.181507-02 5.374 51.425 SCHOTT SK10 9.598 1.622720 -.908955-01 -.947032-02 .369531-03 -25.628 -245.976 OHARA KF3 9.645 1.514470 -.946095-01 -.980925-02 -.134816-02 7.276 70.177 CHANCE 623569 9.672 1.622716 -.909436-01 -.940274-02 .958374-03 -9.811 -94.894 CORN-F 734514 9.796 1.733407 -.100712+00 -.102813-01 -.543492-03 18.917 185.305 CHANCE 678552 9.798 1.677809 -.937135-01 -.956504-02 .811637-03 -11.785 -115.462 OHARA SK18 9.850 1.638454 -.933611-01 -.947800-02 -.242891-02 3.902 38.437 SCHOTT SK1 9.906 1.610171 -.912011-01 -.920641-02 .728678-03 -12.634 -125.160 CHANCE 734517 10.006 1.733395 -.100140+00 -.100080-01 .441798-04 -226.528 -2266.650 HOYA BACD10 10.054 1.622719 -.908052-01 -.903132-02 .146881-02 -6.149 -61.822 CORN-F 548535 10.127 1.547678 -.968188-01 -.956016-02 -.428149-02 2.233 22.613 CRON-F 623569 10.167 1.622720 -.908938-01 -.894014-02 .186653-02 -4.790 -48.597 HOYA BACD1 10.204 1.610168 -.912395-01 -.894152-02 .160556-02 -5.569 -56.827 SCHOTT SK2 10.234 1.607302 -.912395-01 -.891538-02 .132736-02 -6.717 -68.737 CHANCE 639554 10.318 1.638455 -.932891-01 -.904120-02 -.105759-02 8.549 88.209 HOYA BACD18 10.325 1.638456 -.932041-01 -.902681-02 -.515061-03 17.526 180.957 SCHDTT KZFS1 10.361 1.612997 -.116813+00 -.112746-01 -.107927-01 1.045 10.823 HOVA BACD2 10.377 1.607305 -.912003-01 -.878874-02 .199064-02 -4.415 -45.815 CORN-F 614564 10.505 1.613418 -.916306-01 -.872255-02 .178191-02 -4.895 -51.423 CHANCE 691548 10.549 1.690906 -.943467-01 -.894354-02 .160095-02 -5.586 -58.932 HOYA BACD6 10.585 1.613673 -.916544-01 -.865859-02 .263028-02 -3.292 -34.846 HOYA BACD8 10.730 1.611087 -.926409-01 -.863371-02 .127109-02 -6.792 -72.883 OHARA SK6 10.806 1.613669 -.916329-01 -.847967-02 .125900-02 -6.735 -72.782 HOYA NBF3 10.831 1.734892 -.103717+00 -.957616-02 -.966783-03 9.905 107.280 SCHOTT SK6 10.863 1.613669 -.915980-01 -.843184-02 .180368-02 -4.675 -50.784 TABLE II (10 OF 12) SCHOTT SKB 10.923 1.511090 -.923874-01 -.845805-02 .132397-02 -6.388 -69.780 HOYA ADC2 10.942 1.596919 -.933579-01 -.853277-02 -.980123-02 .871 9.525 OHARA SK1 11.050 1.610174 -.913639-01 -.826836-02 .177398-02 -4.661 -51.502 OHARA SK8 11.072 1.611085 -.923511-01 -.834113-02 .103501-02 -8.059 -59.227 HOYA TAF1 11.091 1.772385 -.104132+00 -.938892-02 .632043-03 -14.855 -164.754 SCHOTT LANK12 11.169 1.677809 -.935780-01 -.837855-02 .226014-02 -3.707 -41.404 OHARA SK2 11.276 1.607300 -.909568-01 -.806679-02 .270714-02 -2.980 -33.599 HOYA ADC1 11.314 1.619928 -.831119-01 -.734596-02 .378705-02 -1.940 -21.946 SCHOTT LAF28 11.449 1.773025 -.103947+00 -.907951-02 .145718-03 62.309 713.343 HOYA ZNC5 11.466 1.533674 -.933141-01 -.813812-02 .133897-02 -6.078 -69.691 HOYA LACL3 11.476 1.664706 -.966720-01 -.842380-02 .139428-02 6.042 59.335 SCHOTT KF6 11.549 1.517348 -.990185-01 -.857394-02 .357701-02 -2.397 27.682 SCHOTT ZK5 11.879 1.533679 -.933704-01 -.786021-02 .143778-02 -5.467 -64.941 OHARA LAF010 11.990 1.743087 -.104735+00 -.873505-02 .111923-02 7.804 93.577 HOYA BACD9 12.004 1.613965 -.937155-01 -.780691-02 .155036-02 -5.036 -60.448 OHARA LASF16 12.026 1.772383 -.104200+00 -.866460-02 .250196-03 -34.631 -416.471 SCHOTT SSK4 12.138 1.617567 -.936250-01 -.771354-02 .170370-02 -4.528 -54.954 CORN-F 623531 12.187 1.622416 -.972221-01 -.797728-02 .122081-02 6.534 79.637 CORN-F 616444 12.201 1.615900 -.116471+00 -.954589-02 .872605-02 1.094 13.347 HOYA CF6 12.229 1.517346 -.990930-01 -.810337-02 .296959-02 2.729 33.369 CORN-F 720503 12.249 1.719898 -.102682+00 -.838272-02 .931710-02 -8.997 -110.208 OHARA LASK02 12.262 1.786384 -.103301+00 -.842462-02 .113170-02 -7.444 -91.280 HOYA BACED4 12.367 1.617569 -.935749-01 -.756683-02 .257686-02 -2.936 -36.314 OHARA SSK4 12.461 1.617563 -.937492-01 -.752339-02 .161793-02 -4.650 -57.944 CHANCE 720504 12.481 1.719891 -.102491+00 -.821181-02 -.617128-04 133.065 1660.770 SCHOOT SK9 12.495 1.613968 -.935765-01 -.748881-02 .195235-02 -3.836 -47.930 OHARA ZK5 12.558 1.533678 -.928794-01 -.739597-02 .263766-02 -2.804 -35.213 HOYA LACL4 12.573 1.669507 -.997206-01 -.793134-02 .131342-02 6.039 75.924 HOYA NSF1 12.797 1.743188 -.104665+00 -.817900-02 .104589-02 -7.820 -100.072 OHARA BALF5 12.811 1.547317 -.964399-01 -.752779-02 -.164868-02 4.566 58.495 CORN-F 618551 12.905 1.617522 -.936587-01 -.725764-02 .290431-02 -2.499 -32.248 OHARA SK9 12.927 1.613965 -.938917-01 -.726304-02 .198750-02 -3.654 -47.241 CORN-F 639555 12.947 1.638420 -.929858-01 -.718212-02 .354561-02 -2.026 -26.226 SCHOOT KF9 13.444 1.523338 -.100273+00 -.745843-02 -.291589-02 2.558 34.389 OHARA KF6 13.639 1.517344 -.986996-01 -.723664-02 -.135495-02 5.341 72.844 SCHOTT BALF4 13.740 1.579490 -.960428-01 -.698979-02 .744760-03 -9.385 -128.958 HOYA LACL8 13.877 1.677803 -.965912-01 -.696055-02 .289141-02 -2.407 -33.406 HOYA LAC10 13.936 1.719893 -.102337+00 -.734346-02 .230514-02 -3.186 -44.395 SCHOTT KZF1 14.155 1.551068 -.103919+00 -.734141-02 -.286232-02 2.565 36.306 OHARA LAC07 14.187 1.677804 -.965340-01 -.680458-02 .253105-02 -2.688 -38.140 HOYA SBF1 14.214 1.551069 -.104347+00 -.734135-02 -.358390-02 2.048 29.115 CHANCE 694533 14.319 1.693404 -.966723-01 -.675121-02 .301339-02 -2.240 -32.081 HOYA ADF4 14.818 1.612398 -.115112+00 -.776814-02 -.954514-02 .814 12.060 CHANCE 530512 14.971 1.530250 -.100802+00 -.673296-02 -.139736-02 4.818 72.137 SCHOOT KF50 15.057 1.530805 -.100922+00 -.670262-02 --126310-02 5.306 79.900 CORN-F 659510 15.061 1.658408 -.101156+00 -.671657-02 .105713-02 -6.354 -95.689 CHANCE 717479 15.086 1.716888 -.107691+00 -.713844-02 -.227627-02 3.136 47.310 SCHOOT SSK1 15.101 1.617117 -.956034-01 -.633102-02 .213161-02 -2.970 -44.850 HOYA CF5 15.338 1.523024 -.101296+00 -.660428-02 -.188990-02 3.495 53.599 OHARA BALF4 15.431 1.579487 -.959797-01 -.622008-02 .173836-02 -3.578 -55.213 HOYA BALF4 15.545 1.579492 -.958654-01 -.616684-02 .187385-02 -3.291 -51.160 OHARA LAC05 15.547 1.658208 -.964179-01 -.620174-02 .175631-02 -3.531 -54.898 CORN-F 613443 15.685 1.613297 -.116508+00 -.742786-02 -.678856-02 1.094 17.162 SCHOTT KZFSN4 16.142 1.613300 -.116512+00 -.721776-02 -.671142-02 1.075 17.360 SCHOTT SSK51 16.233 1.603525 -.960450-01 -.591653-02 .170910-02 -3.462 -56.196 CHANCE 788474 16.262 1.788187 -.108792+00 -.668985-02 .152448-02 -4.388 -71.363 OHARA SSK1 16.306 1.617111 -.952664-01 -.584239-02 .324455-02 -1.801 -29.362 SCHOTT BALF5 16.447 1.547316 -.960768-01 -.584179-02 .151808-02 -3.848 -63.289 CORN-F 788474 16.507 1.787879 -.108794+00 -.659072-02 .145711-02 -4.523 -74.664 HOYA BAFL6 16.509 1.588954 -.970442-01 -.587840-02 .272633-02 -2.156 -35.595 HOYA BACED1 16.647 1.617119 -.956235-01 -.574419-02 .531776-02 -1.080 -17.982 SCHOTT LACN13 16.651 1.693405 -.965749-01 -.580002-02 .470656-02 -1.232 -20.519 HOYA CF2 16.697 1.526220 -.100885+00 -.604216-02 -.325851-02 185.427 3096.060 HOYA BACED2 16.822 1.622213 -.969745-01 -.576476-02 .200675-02 -2.873 -48.324 HOYA CF4 17.216 1.533501 -.100100+00 -.581455-02 .488402-02 -11.905 -204.955 OHARA KF5 17.262 1.523024 -.101342+00 -.583240-02 -.153240-02 3.831 66.132 SCHOTT LAF24 17.540 1.757075 -.107786+00 -.614507-02 .763045-03 -8.053 -141.257 OHARA SSKK01 17.750 1.648407 -.970851-01 -.546945-02 .179478-02 -3.047 -54.093 OHARA LASF14 18.277 1.787875 -.108668+00* -.594573-02 .244923-02 -2.428 -44.368 SCHOTT BALF6 18.277 1.588959 -.971123-01 -.531324-02 .239830-02 -2.215 -40.492 SCHOTT SSK28 18.640 1.622215 -.968524-01 -.519584-02 .291178-02 -1.784 -33.262 HOYA LACL9 18.652 1.677806 -.101805+00 -.545801-02 -.407621-03 13.390 249.755 SCHOTT LAF21 18.706 1.788187 -.108670+00 -.580932-02 .169762-02 -3.422 -64.013 OHARA KF2 18.719 1.526221 -.100681+00 -.537852-02 .243004-03 22.134 414.316 TABLE II (11 Or 12) HOYA TAF4 18.749 1.787875 -.108413+00 -.578226-02 .330225-02 -1.751 -32.830 HOYA LAF3 19.027 1.716481 -.107419+00 -.564562-02 .261948-02 -2.155 -41.008 OHARA LAK10 19.066 1.719891 -.102216+00 -.537107-02 .445067-02 -1.205 -22.967 SCHOTT TIF1 19.159 1.511107 -.100985+00 -.527083-02 -.886545-02 .595 11.391 HOYA CF1 19.423 1.540336 -.101153+00 -.520780-02 -.527047-03 9.881 191.924 OHARA BALF6 19.469 1.588958 -.967387-01 -.496895-02 .306967-02 -1.619 -31.514 SCHOTT KF1 19.848 1.540334 -.100772+00 -.507724-02 -.886894-03 5.725 113.623 HDYA FF1 20.191 1.511105 -.100973+00 -.500089-02 -.796293-02 .628 12.680 HOVA LAC13 20.254 1.693403 -.964648-01 -.476272-02 .649559-02 -.733 -14.851 CHANCE 614439 20.474 1.613896 -.117400+00 -.573407-02 -.599192-02 .957 19.593 MOYA BACED20 20.529 1.648408 -.970644-01 -.472826-02 .392752-02 -1.204 -24.714 SCHOTT BALF51 20.561 1.573851 -.987925-01 -.178928-02 .178928-02 -2.685 -55.214 OHARA 5SK2 20.641 1.622210 -.967020-01 -.468498-02 .375988-02 -1.246 -25.719 OHARA BALF8 20.937 1.553529 -.100465+00 -.479854-02 -.339661-03 14.127 295.781 OHARA LAFO4 21.195 1.756882 -.107470+00 -.507061-02 -.257934-02 -1.966 -41.666 CORN-F BO3467 21.559 1.802877 -.110198+00 -.511139-02 -.268763-02 -1.902 -41.002 OHARA LASF15 21.760 1.803870 -.110339+00 -.507084-02 -.234348-02 -2.164 -47.083 SCHOTT BALF50 22.529 1.588846 -.100140+00 -.444402-02 -.176678-02 -2.516 -56.679 SCHOTT SSK50 22.629 1.617868 -.977415-01 -.431922-02 .310087-02 -1.393 -31.521 OHARA KF4 22.700 1.533500 -.997623-01 -.439479-02 .265009-02 -1.658 -37.645 HOYA NBF2 22.805 1.756882 -.107835+00 -.472864-02 .432778-02 -1.093 -24.917 HOYA BAFL2 23.295 1.571269 -.969991-01 -.416399-02 .475507-02 -.876 -20.399 OHARA KFB 24.035 1.511105 -.100728+00 -.419082-02 -.103850-01 .404 9.899 SCHOTT LASF30 24.230 1.803055 -.110777+00 -.457199-02 .311257-02 -1.469 -35.590 OHARA K2FS4 24.658 1.613297 -.117432+00 -.476240-02 -.497424-02 .957 23.608 SCHOTT BALF3 25.410 1.571273 -.971088-01 -.382163-02 .499134-02 -.766 -19.455 SCHOTT SSK52 25.644 1.658344 -.101000+00 -.393850-02 .319719-02 -1.232 -31.590 HOYA TAF3 25.839 1.804074 -.110596+00 -.428013-02 .479869-02 -.892 -23.047 OHARA LASF12 27.378 1.802873 -.1.10166+00 -.402388-02 .323075-02 -1.245 -34.099 OHARA K2F4 28.093 1.570322 -.106837+00 -.380300-02 -.185012-02 2.056 57.746 OHARA KF1 28.415 1.540330 -.100853+00 -.354933-02 .233569-02 -1.520 -43.179 OHARA BALF3 28.705 1.571270 -.972122-01 -.339658-02 .578056-02 -.586 -16.817 SCHOTT BALF8 29.064 1.553529 -.100435+00 -.345567-02 .214805-02 -1.609 -46.756 SCHOTT LAK20 30.727 1.693387 -.996050+01 -.324156-02 .715069-02 -.453 -13.929 HOYA FEL6 31.142 1.531640 -.105050+00 -.337320-02 .342800-03 -9.840 -306.446 SCHOTT LLF6 31.422 1.531639 -.105432+00 -.335532-02 -.436874-03 7.680 241.334 OHARA LAK03 32.351 1.669904 -.994844+01 -.307520-02 .399695-02 -.769 -24.890 CORN-F 624469 34.682 1.623903 -.109483+00 -.315675-02 -.166283-03 18.984 658.417 SCHOTT SSKN5 35.061 1.656345 -.100884+00 -.287739-02 .249156-02 -1.155 -40.490 HOYA BACED5 35.924 1.658340 -.100946+00 -.280997-02 .284249-02 -.989 -35.513 OHARA LAK08 36.549 1.693394 -.101018+00 -.276392-02 .607351-02 -.455 -16.632 HOYA LACL5 37.367 1.693399 -.100887+00 -.269993-02 .732856-02 -.368 -13.766 CORN-F 800456 39.017 1.799872 -.112702+00 -.288856-02 .456701-02 -.632 -24.678 OHARA LASF17 39.614 1.794867 -.113455+00 -.286402-02 .359110-02 -.798 -31.593 OHARA SSK3 40.938 1.614751 -.100315+00 -.245043-02 .383497-02 -.639 -26.158 SCHOTT SSKN8 42.626 1.617629 -.103142+00 -.241973-02 .731294-02 -3.309 -141.041 OHARA LLF6 43.533 1.531637 -.104948+00 -.241078-02 .143303-02 -1.682 -73.235 SCHOTT SSK3 44.156 1.614748 -.100322+00 -.227196-02 .459550-02 -.494 -21.830 CHANCE 658509 45.108 1.658341 -.100900+00 -.223684-02 .389522-02 -.574 -25.904 OHARA SSK8 47.221 1.617630 -.103089+00 -.218311-02 .103056-02 -2.118 -100.033 OHARA LAK06 51.478 1.677799 -.101095+00 -.196383-02 .530494-02 -.370 -19.057 CD9N-F 717480 52.282 1.716901 <RTI ID=143.15> -.106944+00 -.204553-02 .633514-02 -.323 -16.881 CHANCE 689495 52.735 1.688895 -.103672+00 -.196592-02 .808088-02 -.243 -12.829 HOYA BACED9 54.952 1.620028 -.102983+00 -.187407-02 .177196-02 -1.058 -58.119 HOYA BACED3 59.401 1.614749 -.100224+00 -.168724-02 .583482-02 -.289 -17.177 CHANCE 689496 61.615 1.688907 -.103341+00 -.167993-02 .946179-02 -.178 -10.922 HDYA TAF2 67.909 1.794368 -.112925+00 -.166289-02 .595338-02 -.279 -18.968 CORN-F 648462 68.088 1.647644 -.111090+00 -.163156-02 .108405-02 -1.505 -102.476 HOYA BAFL2 75.831 1.570906 -.100876+00 -.133027-02 .601909-02 -.221 -16.759 HOYA BAFL2 80.252 1.696892 -.105622+00 -.131613-02 .446973-02 -.294 -23.631 SCHOTT BAFN6 82.245 1.588910 -.105894+00 -.128755-02 .101844-02 -1.264 -103.978 OHARA LASFO9 86.389 1.815871 -.109998+00 -.127328-02 .866117-02 -.147 -12.700 OHARA BALF7 86.735 1.588666 -.108727+00 -.115469-02 .627747-02 -.184 -15.929 OHARA BALF2 93.719 1.570906 -.100739+00 -.107491-02 .600537-02 -.179 -16.775 CHANCE 717480 96.594 1.716889 -.106822+00 -.110588-02 .723681-02 -.153 -14.761 HOYA ADF8 104.577 1.686380 -.119723+00 -.114483-02 -.294973-02 .388 40.588 SCHOTT LLF3 109.564 1.560043 -.108768+00 -.992740-03 .346505-04 -28.650 -3139.010 CHANCE 541472 122.952 1.540633 -.108770400 -.884652-03 .119341-02 -.741 -91.142 OHARA SSK9 143.292 1.620027 -.103179+00 -.720058-03 .410703-02 -.175 -25.122 OHARA LASFO4 143.537 1.815402 -.115359+00 -.803689-03 .568507-02 -.141 -20.292 SCHOTT BAF54 149.969 1.666619 -.106286+00 -.708719-03 .385235-02 -.184 -27.590 SCHOTT LLF2 171.906 1.540635 -.108727+00 -.632476-03 .125404-02 -.504 -86.701 CHANCE 744448 183.119 1.743877 -.114507+00 -;625315-03 .184080-02 -.340 -62.205 HOVA FEL2 184.340 1.540634 -.108625+00 -.589262-03 .142463-02 -.414 -76.247 TABLE 11 (12 Or 12) CORN-F 744448 192.746 1.743879 -.114440+00 -.593733-03 .220180-02 -.270 -51.976 HOYA TAFD1 205.243 1.814564 -.115954+00 -.565007-03 .622681-02 -.091 -18.623 HOYA NBFD14 224.677 1.801566 -.115564+00 -.514356-03 .564119-02 -.091 -20.486 HOYA TAFD10 258.348 1.815368 -.115241+00 -.446069-03 .763394-02 -.058 -15.096 OHARA LLF2 363.647 1.540638 -.108587+00 -.298606-03 .161587-02 -.185 -67.200 SCHOTT LGSK2 452.288 1.585919 -.837990-01 -.185278-03 .107401-01 -.017 -7.802 OHARA LAFO6 987.209 1.685896 -.104144+00 -.016464-03 .570256-02 -.019 -18.263 CORN-F 655401 1271.950 1.655380 -.127954+00 -.100597-03 .301127-02 -.033 42.492

Claims: CLAIMS 1. A method of selecting optical materials for designing an optical system that is color-corrected at a number of wavelengths, each optical material having a characteristic dispersive power, said method comprising: a) representing the dispersive power of each optical material by a polynomial expression in a variable that is a function of wavelength, the polynomial expression for each optical material being of a degree that is numerically one less than the number of wavelengths for which color correction is required; b) comparing a ratio of coefficients in the polynomial expression for one of said optical materials with corresponding ratios of coefficients in the polynomial expressions for others of said optical materials; ; c) identifying particular optical materials from among said others of said optical materials for which said corresponding ratios of coefficients are substantially equal to said ratio of coefficients for said one optical material; and d) choosing optical materials for designing said system from among those particular optical materials for which said corresponding ratios of coefficients are substantially equal. 2. The method of claim 1 further comprising: a) determining absolute values of differences between a coefficient in said polynomial expression for said one optical material and corresponding coefficients in the polynomial expressions for those particular optical materials for which said corresponding ratios of coefficients are substantially equal to said ratio of coefficients for said one optical material; and b) selecting optical materials for designing said system from among those particular optical materials for which said corresponding ratios of coefficients are substantially equal, and for which the absolute values of differences between said corresponding coefficients are sufficiently large to permit construction of optical elements having dioptric powers of appropriate configuration for said system. 3. The method of claim I wherein the dispersive power of each optical material is represented by a polynomial expression of the form EMI146.1 where D(x) is the dispersive power, # is the wavelength, W( ) is said variable that is a function of wavelength, w(X) being defined by the expression a(A) = ##/(1 + a dx), where ## represents change in wavelength with respect to a base wavelength and a is a constant that is substantial lv independent of the dispersive power of the optical material; where ni are the coefficients in said polynomial expression; and where n is the degree of said polynomial. 4. The method of claim 3 wherein absolute values are determined for differences between a coefficient ni in the polynomial expression for said one optical material and corresponding coefficients ni in the polynomial expressions for the particular optical materials for which corresponding ratios (ni/nj), where j # i, are substantially equal to the ratio (ni/nj) for said one optical material. 5. The method of claim 3 wherein said polynomial expression is of (n - 1)th degree. 6. The method of claim 5 wherein, when said polynomial expression is quadratic, the ratio (nl/n2) for said one optical material is compared with the corresponding ratios (n1/n2) for the others of said optical materials. 7. The method of claim 6 wherein said optical materials for designing said system are selected from the group consisting of optical glasses listed in TABLE I, which is incorporated herein by reference, each optical glass listed in TABLE I being described in terms of refractive index at a base wavelength of 0.574 micrometers, and in terms of numerical values for said coefficients TiI (i = 1, 2) for a wavelength range extending from approximately 0.40 micrometers to approximately 0.70 micrometers. 8. The method of claim 5 wherein, when said polynomial expression is cubic, the ratios (n1/n2), (n2/n3) and (nl/n3) for said one optical material are compared with the corresponding ratios (n1/n2), (n2/n3) and (nl/n3) for the others of said optical materials. 9. The method of claim 8 wherein said optical materials for designing said system are selected from the group consisting of optical glasses listed in TABLE II, which is incorporated herein by reference, each optical glass listed in TABLE II being described in terms of refractive index at a base wavelength of 0.589 micrometers, and in terms of numerical values for said coefficients Tii (i = 1, 2, 3) for a wavelength range extending from approximately 0.36 micrometers to approximately 1.01 micrometers. 10. An optical system that is color-corrected at a number of wavelengths, said system comprising optical elements made of different optical materials each of said optical materials having a characteristic dispersive power, said system being made by a process that includes selection of said optical materials, said optical materials beinq selected by: : a) representing the disporsive power of each optical material by a polynomial expression in a variable that is a function of wavelength, the polynomial expression for each optical material being of a degree that is numerically one less than the number of wavelengths for which color correction is required; b) comparing a ratio of coefficients in the polynomial expression for one of said optical materials with corresponding ratios of coefficients in the polynomial expressions for others of said optical materials; c) identifying particular optical materials for which said corresponding ratios of coefficients in said polynomial expressions are substantially equal; and d) choosing optical materials for designing said system from among those particular optical materials for which said corresponding ratios of coefficients are substantially equal. 11. The optical system of claim 10 wherein said optical materials are further selected by: a) determining absolute values of differences between a coefficient in said polynomial expression for said one optical material and corresponding coefficients in the polynomial expressions for those particular optical materials for which said corresponding ratios of coefficients are substantially equal to said ratio of coefficients for said one optical material; and b) selecting optical materials for designing said system from among those particular optical materials for which said corresponding ratios of coefficients are substantially equal, and for which the absolute values of differences between said corresponding coefficirnts are sufficiently large to permit construction of optical elements having dioptric powers of appropriate configuration for said system. 12. The optical system of claim 10 wherein the dispersive power of each optical material is represented by a polynomial expression of the form EMI149.1 where D(X) is the dispersive power, A is the wavelength, w(A) is said variable that is a function of wavelength; #(#) being defined by the expression 0,(\ = ##(1 + a ##), where ## represents change in wavelength with respect to a base wavelength and a is a constant that is substantially independent of the dispersive power of the optical material; where ni are the coefficients in said polynomial expression; and where n is the degree of said polynomial. 13. The optical system of claim 12 wherein absolute values are determined for differences between a coefficient ni in the polynomial expression for said one optical material and corresponding coefficients ni in the polynomial expressions for the particular optical materials for which corresponding ratios (ni/nj), where j f i, are substantially equal to the ratio (nilrli) for said one optical material. 14. The optical system of claim 12 wherein said polynomial expression is of (n - 1)th degree. 15. The optical system of claim 14, wherein when said polynomial expression i-s quadratic, the ratio (nlfn2) for said one optical material is compared with the corresponding ratios (n1/n2) for the others of said optical materials. 16. The optical system of claim 15 wherein said optical materials for designing said system are selected from the group consisting of optical glasses listed in TABLE I, which is incorporated herein by reference, each optical glass listed in TABLE I being described in terms of refractive index at a base wavelength of 0.574 micrometers, and in terms of numerical values for said coefficients ni (i = 1, 2) for a wavelength range extending from approximately 0.40 micrometers to approximately 0.70 micrometers. 17. The optical system of claim 14 wherein, when said polynomial expression is cubic, the ratios (Ti11Ti2), (n2/n3) and (n1/n3) for said one optical material are compared with the corresponding ratios (n1/n2), (n2/n3) and (n1/n3) tor the others of said optical materials. 18. The optical system of claim 17 wherein said optical materials for designing said system are selected from the group consisting of optical glasses listed in TABLE II, which is incorporated herein by reference, each optical glass listed in TABLE II being described in terms of refractive index at a base wavelength of 0.589 micrometers, and in terms of numerical values for said coefficients n; (i = 1, 2, 3) for a wavelength range extending from approximately 0.36 micrometers to approximately 1.01 micrometers. 19. An optical system color-corrected at least at two wavelengths, said system comprising two lens elements, each lens element being made of a different optical material, each optical material having a characteristic dispersive power, the dispersive power of each optical material being represented by a polynomial expression in a variable that is a function of wavelength, said polynomial expression being of the form D(x) = nl (i)() + n? w (#) where D(x) is the dispersive power, X is the wavelength, (X) is the variable that is a function of wavelength, #(#= being defined by the expression w(A) = 61/(1 + a ##), where dA represents change in wavelength with respect to a base wavelength and a effectively a constant that is substantially independent of the dispersive power of the optical material, and where Ti1 and n2 are coefficients in said polynomial expression, said optical system being made by a process that includes selection of said optical materials, said optical materials being selected by ascertaining that corresponding coefficients in the polynomial expressions for each of said optical materials have an absolute value difference that permits construction of optical elements having dioptric powers appropriate for said system. 20. An optical system color-corrected at more than two wavelengths, said system comprising only two different optical materials. 21. The optical system of claim 20 wherein said system is a lens system. 22. The optical system of claim 21 wherein said lens system is color-corrected at more than three wavelengths. 23. The optical system of claim 20 wherein said system is catadioptric. 24. The optical system of claim 23 wherein said catadioptric system comprises a Mangin mirror. 25. The optical system of claim 20 wherein said system is anamorphic. 26. The optical system of claim 25 wherein said anamorphic system comprises a prism. 27. An optical svstem rotationally symmetric about an axis, said system comprising a lens doublet having a common focal length on said axis for three optical wavelengths, said lens doublet comprising a first lens element made of an optical material having refractive index of approximately 1.49 and an Abbe number of approximately 84.07 at a base wavelength of 0.546 micrometers, and a second lens element made of an optical material having a refractive index of approximately 1.50 and an Abbe number of approximately 59.34 at said base wavelength. 28. The optical system of claim 27 having a design form wherein said first and second lens elements are positioned in contact with each other to define first, second and third surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said second and third surfaces, said first surface having a positive radius of curvature of approximately 0.421 times the focal length of said doublet, said second surface having a negative radius of curvature of approximately 0.215 times said focal length, said third surface having a positive radius of curvature of approximately 7.034 times said focal length, said first lens element having a thickness along said axis of approximately 0.016 times said focal length, said second lens element having a thickness along said axis of approximately 0.009 times said focal length. 29. A lens doublet that is color-corrected at more than three wavelengths. 30. An optical system rotationally symmetric about an axis, said system comprising a lens doublet having a common focal length on said axis for four optical wavelengths, said lens doublet comprising a first lens elempnt made of an optical material having a refractive index of approximately 1.49 and an Abbe number of approximately 81.40 at a basP wavelength of 0.546 micrometers, and a second lens element niadP of an optical material having a refractive index of approximately 1.70 and an Abbe number of approximately 55.31 at said base wavelength. 31. The optical system of claim 30 having a design form wherein said first and second lens elements are positioned in contact with each other to define first, second and third surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said second and third surfaces, said first surface having a positive radius of curvature of approximately 0.257 times the focal length of said doublet, said second surface having a negative radius of curvature of approximately 0.372 times said focal length, said third surface having a positive radius of curvature of approximately 2.022 times said focal length, said first lens element having a thickness along said axis of approximately 0.016 times said focal length, said second lens element having a thickness along said axis of approximately 0.009 times said focal length. 32. The optical system of claim 30 having a design form wherein said first and second lens elements are positioned with respect to each other to define first, second, third and fourth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said third and fourth surfaces, said first surface having a positive radius of curvature of approximately 0.598 times the focal length of said doublet, said second surface having a negative radius of curvature of approximately 0.207 times said focal length, said third surface having a negative radius of curvature of approximately 0.221 times said focal length, said fourth surface having a negative radius of curvature of approximately 0.699 times said focal length, said first lens element having a thickness along said axis of approximately 0.016 times said focal length, said second lens element being separated from said first lens element along said axis by approximately o.ooo. times said focal length, said second lens element having a thickness along said axis of approximately 0.009 times said focal length. 33. A lens doublet that is color-corrected at more than four optical wavelengths - 34. An optical system rotationally symmetric about an axis, said system comprising a lens doublet having a common focal length on said axis for five optical wavelengths, said lens doublet comprising a first lens element made of an optical material having a refractive index of approximately 1.53 and an Abbe number of approximately 76.57 at a base wavelength of 0.546 micrometers, and a second lens element made of an optical material having a refractive index of approximately 1.65 and an Abbe number of approximately 58.15 at said base wavelength. 35. The optical system of claim 34 having a design form wherein said first and second lens elements are positioned with respect to each other to define first, second, third and fourth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said third and fourth surfaces, said first surface having a positive radius of curvature of approximately 0.753 times the focal length of said doublet, said second surface having a negative radius of curvature of approximately 0.151 times said focal length, said third surface having a negative radius of curvature of approximately 0.156 times said focal length, said fourth surface having a negative radius of curvature of approximately 0.680 times said focal length, said first lens element having a thickness along said axis of approximately 0.020 times said focal length, said second lens element being separated from said first lens element along said axis by approximately 0.0004 times said focal length, said second lens element.having a thickness along said axis of approximately 0.010 times said focal length. 36. An optical system rotationally symmetric about an axis, said system comprising a lens triplet having a common focal length on said axis for four optical vavelengths, said lens triplet comprising a first lens element made of an optical material having a refractive index of approximately 1.49 and an Abbe number of approximately R1.40 at a hase wavelength of 0.546 micrometers, a second lens element made of an optical material having a refractive index of approximately 1.59 and an Abbe number of approximately 60.94 at said base wavelength, and a third lens element made of the same optical material as said first lens element. 37. The optical system of claim 36 having a design form wherein said lens elements are positioned so that said first and second lens elements are in contact with each other, and so that said second and third lens elements are in contact with each other, thereby defining first, second, third and fourth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said second and third sur faces, said third lens element being bounded by said third and fourth surfaces, said first surface having a positive radius of curvature of approximately 0.368 times the focal length of said triplet, said second surface having a negative radius of curvature of approximately 2.029 timers said focal length, said third surface having a positive radius of curvature of approximately 0.212 times said focal length, said fourth surface having a negative radius of curvature of approximately 2.324 times said focal length, said first lens element having a thickness along said axis of approximately 0.015 times said focal length, said second lens element having a thickness along said axis of approximately 0.009 times said focal length, said third lens element having a thickness along said axis of approximately 0.013 times said focal length. 38. The optical system of claim 36 having a design form wherein said lens elements are positioned so that said first and second lens elements are in contact with each other, thereby defining first, second, third, fourth and fifth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said second and third surfaces, said third lens element being hounded by said fourth and fifth surfaces, said first surface having a positive radius of curvature of approximatoly 0.419 times the focal length of said triplet, said second surface haying a negative radius of curvature of approximately 0.449 times said focal length, said third surface having a positive radius of curvature of approximately 0.342 times said focal length, said fourth surface having a positive radius of curvature of approximately 0.360 times said focal length, said fifth surface having a negative radius of curvature of approximately 1.101 times said focal length, said first lens element having a thickness along said axis of approximately 0.015 times said focal length, said second lens element having a thickness along said axis of approximately 0.009 times said focal length, said third lens element being separated from said focal length, said third lens element being separated from said second lens element along said axis by approximately 0.001 times said focal length, said third,lens element having a thickness along said axis of approximately 0.013 times said focal length. 39. An optical system rotationally symmetric about an axis, said system comprising a lens quadruplet having a common focal length on said axis for four optical wavelengths, said lens quadruplet comprising a first lens element made of an optical material having a refractive index of approximately 1.49 and an Abbe number of approximately 81.40 at a base wavelength of 0.546 micrometers, a second lens element made of an optical material having a refractive index of approximately 1.59 and an Abbe number of approximately 60.94 at said base wavelength, a third lens element and a fourth lens element, one of said third and fourth lens elements being made of the same optical material as said first lens element, and another one of said third and fourth lens elements being made of the same optical material as said second lens element, 40. The optical system of claim 39 wherein said third lens element is made of the same optical material as said first lens element, said optical system having a design form wherein said lens elements are positioned so that said first and second lens elements are in contact with each other, said second and third lens elements are in contact with each other, and said third and fourth lens elements are in contact with each other, thereby defining first, second, third, fourth and fifth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said second and third surfaces, said third lens element being bounded by said third and fourth surfaces, said fourth lens element being bounded by said fourth and fifth surfaces, said first surface having a positive radius of curva ture of approximately 0.437 times the focal length of said quad ruplet, said second surface having a positive radius of curvature of approximately 5.098 times said focal length, said third surface having a positive radius of curvature of 0.285 times said focal length, said fourth surface having a negative radius of curvature of approximately 0.363 times said focal length, said fifth surface having a negative radius of curvature of approximately 1.147 times said focal length, said first lens element having a thickness along said axis of approximately 0.015 times said focal length, said second lens element having a thickness along said axis of approxi mately 0.009 times said focal length, said third lens element having a thickness along said axis of approximately 0.015 times said focal length, said fourth lens element having a thickness along said axis of approximately 0.009 times said focal length. 41. The optical system of claim 39 wherein said third lens element is made of the same optical material as said second lens element, said optical system having a design form wherein said lens elements are positioned so that said first and second lens elements are in contact with each other, and so that said third and fourth lens elements are in contact with each other, thereby defining first, second, third, fourth, fifth and sixth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said second and third surfaces, said third.lens element being bounded by said fourth and fifth surfaces, said fourth lens element being bounded by said fifth and sixth surfaces, said first surface having a positive radius of curvature of approximately 0.948 times the focal length of said quadruplet, said second surface having a negative radius of curvature of approximately 0.375 times said focal length, said third surface having a positive radius of curvature of approximately 1.280 times said focal length, said fourth surface having a positive radius of curvature of approximately 0.499 times said focal length, said fifth surface having a positive radius of curvature of approximately 0.274 times said focal length, said sixth surface having a negative radius of curvature of approximately 1.150 times said focal length, said first lens element having a thickness along said axis of approximately 0.015 times said focal length, said second lens element having a thickness along said axis of approximately 0.009 times said focal length, said third lens element being separated from said second lens element along said axis by approximately 0.001 times said focal length, said third lens element having a thickness along said axis of approximately 0.009 times said focal length, said fourth lens element having a thickness along said axis of approximately 0.015 times said focal length. 42. The optical system of claim 39 wherein said third lens element is made of the same optical material as said first lens element, said optical system having a design form wherein said lens elements are positioned so that said first and second lens elements are in contact with each other, and so that said third and fourth lens elements are in contact with each other, thereby defining first, second, third, fourth, fifth and sixth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said second and third surfaces, said third lens elements being bounded by said fourth and fifth surfaces, said fourth lens elements being bounded by said fifth and sixth surfaces, said first surface having a positive radius of curvature of approximately 0.823 times the focal length of said quadruplet, said second surface having a negative radius of curvature of approximately 0.400 times said focal length, said third surface having a positive radius of curvature of approximately 1.OF; ;o times said focal length, said fourth surface having a positive radius of curvature of approximately Q.645 times said focal length, said fifth surface having a negative radius of curvature of approximately 0.337 times said focal length, said sixth surface having a negative radius of curvature of approximately 0.758 times said focal length, said first lens element having a thickness along said axis of approximately 0.015 times said focal length, said second lens element having a thickness along said axis of approximately 0.009 times said focal length, said third lens element being separated from said second lens element along said axis by approximately 0.001 times said focal length, said third lens element having a thickness along said axis of approximately 0.015 times said focal length, said fourth lens element having a thickness along said axis of approximately 0,009 times said focal length. 43. An optical system for collimating more than two optical wavelengths, said system comprising only two optical materials. 44. The optical system of claim 43, said system being a lens multiplet for collimating four optical wavelengths. 45. The optical system of claim 44 wherein said lens multiplet comprises a lens quadruplet having a common focal length along an axis for said four optical wavelengths, said lens quadruplet comprising a first lens element made of an optical material having a refractive index of approximately 1.46 and an Abbe number of approximately 90.32 at a base wavelength of 0.546 micrometers, a second lens element made of an optical material having a refractive index of approximately 1.70 and an Abbe number of approximately 55.31 at said base wavelength, a third lens element made of the same optical material as said second lens element, and a fourth lens element made of the same optical material as said first lens element. 46. The optical system of claim 45 having a design form wherein said lens elements are positioned with respect to each other to define first, second, third, fourth, fifth, sixth, seventh and eighth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said third and fourth surfaces, said third lens element being bounded by said fifth and sixth surfaces, said fourth lens element being bounded by said seventh and eighth surfaces, said first surface having a positive radius of curvature of approximately 1.244 times the focal length of said quadruplet, said second surface having a negative radius of curvature of approximately 0.381 times said focal length, said third surface having a negative radius of curvature of approximately 0.381 times said focal length, said fourth surface having a negative radius of curvature of approximately 0.542 times said focal length, said fifth surface having a negative radius of curvature of approximately 0.539 times said focal length, said sixth surface having a negative radius of curvature of approximately 3.8aS times said focal length, said seventh surface having a positive radius of curvature of approximately 0.715 times said focal length, said eighth surface having a negative radius of curvature of approximately 1.025 times said focal length, said first lens element having a thickness along said axis of approximately 0.015 times said focal length, said second lens element being separated from said first lens element along said axis by approximately 0.010 times said focal length, said second lens element having a thickness along said axis of approximately 0.009 times said focal length, said third lens element being separated from said second lens element along said axis by approximately 0.002 times said focal length, said third lens element having a thickness along said axis of approximately 0.009 times said focal length, said fourth lens element beinq separated from said third lens element along said axis by approximately 0.0005 tines said focal length, said fourth lens element having a thickness along said axis of approximately 0.015 times said focal lenath. 47. The optical system of claim 43, said system comprising a lens multiplet for collimating five optical wavelengths. 48. The optical system of claim 47 wherein said lens multiplet comprises a lens quadruplet having a common focal length along said axis for said five optical wavelengths, said lens quadruplet comprising a first lens element made of an optical material having a refractive index of approximately 1.53 and an Abbe number of approximately 76.57 at a base wavelength of 0.546 micrometers, a second lens element made of an optical material having a refractive index Qf approximately 1.65 and an Abbe number of approximately 58.15 at said base wavelength, a third lens element made of the same optical material as said second lens element, and a fourth lens element made of the same optical material as said first lens element. 49. The optical system of claim 48 having a design form wherein said lens elements are positioned with respect to each other to define first, second, third, fourth, fifth, sixth, seventh and eighth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said third and fourth surfaces, said third lens element being bounded by said fifth and sixth surfaces, said fourth lens element being bounded by said seventh and eighth surfaces, said first surface having a negative radius of curvature of approximately 1.314 times the focal length of said quadruplet, said second surface having a negative radius of curvature of approximately 0.295 times said focal length, said third surface having a negative radius of curvature of approximately 0.2he times said focal length, said fourth surface having a negative radius of curvature of approximately 1.795 times said focal length, said fifth surface having a positive radius of curvature of approximately 0.469 times said focal lenqth, said sixth surface having a positive radius of curvature of approximately 0.233 times said focal length, said seventh surface having a positive radius of curvature of approximately 0.23? times said focal length, said eighth surface having a negative radius of ctirvature of approximately 0.697 times said focal length, said first lens element having a thickness along said axis of approximately 0.018 times said focal length, said second lens element beinq separated from said first lens element along said axis by approximately 0.025 times said focal length, said second lens element having a thickness along said axis of approximately 0.010 times said focal length, said third lens element being separated from said second lens element along said axis by approximately 0.003 times said focal length, said third lens element having a thickness along said axis of approximately 0.010 times said focal length, said fourth lens element being separated from said third lens element along said axis by approximately 0.002 timers said focal length, said fourth lens element having a thickness along said axis of approximately 0.015 times said focal length. 50. The optical system of claim 4 wherein one of said optical materials comprises a crystal. 51. The optical system of claim 50, said system being a lens multiplet for collimating five optical wavelengths. 52. The optical system of claim 51 wherein said lens multiplet comprises a lens quadruplet having a common focal length along said axis for said five optical wavelengths, said lens quadruplet comprising a first lens element made of calcium fluoride, a second lens element made of an optical material having a refractive index of approximately 1.65 and an Abbe number of approximately 58.15 at a base wavelength of 0.546 micrometers, a third lens element made of the same optical material as said second lens element, and a fourth lens element made of calcium fluoride. 53. The optical system of claim 52 having a design form wherein said lens elements are positioned with respect to each other to define first, second, third, fourth, fifth, sixth, seventh and eighth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said third and fourth surfaces, said third lens element being bounded by said fifth and sixth surfaces, said fourth lens element being bounded by said seventh and eighth surfaces, said first surface having a negative radius of curvature of approximately 0.668 times the focal length of said quadruplet, said second surface having a negative radius of curvature of approximately 0.268 times said focal length, said third surface having a negative radius of curvature of approximately 0.250 times said focal length, said fourth surface having a negative radius of curvature of approximately 0.565 times said focal length, said fifth surface having a positive radius of curvature of approximately 0.455 times said focal length, said sixth surface having a positive radius of curvature of approximate,ly 0.384 times said focal length, said seventh surface having a positive radius of curvature of approximately 0.424 times said focal length, said eighth surface having a negative radius of curvature of approximately 0.635 times said focal length, said first lens element having a thickness along said axis of approximately 0.018 times said focal length, said second lens element being separated from said first lens element along said axis by approximately 0.032 times said focal length, said second lens element having a thickness along said axis of approximately 0.010 times said focal length, said third lens element being separated from said second lens element along said axis by approximately 0.001 times said focal length, said third lens element having a thickness along said axis of approximately 0.010 times said focal length, said fourth lens element being separated from said third lens element along said axis by approximately 0.001 times said focal length, said fourth lens element being separated from said third lens element along said axis by approximately 0.001 times said focal length, said fourth lens element having a thickness along said axis of approximately 0.015 times said focal length. 54. A catadioptric optical system rotationally symmetric about an axis, said system having a common focal length along said axis for more than two optical wavelengths. 55. The catadioptric system of claim 54, said system comprising lens elements made of different optical materials, a surface portion of one of said lens elements having a coating that reflects optical wavelengths incident thereon from within said one lens element. 56. The catadioptric system of claim 55 comprising a first lens element and a second lens element, said first and second lens elements being positioned in contact with each other to define first, second and third surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said second and third surfaces, said third surface having said reflective coating. 57. The catadioptric system of claim 56 wherein said first lens element is made of an optical material having a refractive index of approximately 1.46 and an Abbe number of approximately 90.32 at a base wavelength of 0.546 micrometers, and said second lens element is made of an optical material having a refractive index of approximately 1.47 and an Abbe number of approximately 65.49 at said base wavelength. 58. The catadioptric system of claim 57 having a design form wherein said first surface has a negative radius of curvature of approximately 0.958 times the focal length of said system, said second surface has a positive radius of curvature of approximately 4.200 times said focal length, said third surface has a negative radius of curvature of approximately 1.572 times said focal length, said first lens element having a thickness along said axis of approximately 0.036 times said focal length, said second lens element having a thickness along said axis of approximately 0.057 times said focal length. 59. The catadioptric system of claim 56 wherein said first lens element is made of optical material having a refractive index of approximately 1.67 and an Abbe number of approximately 47.97 at a base wavelength of 0.546 micrometers, and said second lens element. is made of an optical material having a refractive index of approximately 1.57 and an Ahbe number of approximately 42.57 at said base wavelength. 60. The catadioptric system of claim 9 having a design form wherein said first surface has a negative radius of curvature of approximately 1.897 times the focal length of said system, said second surface has a positive radius of curvature of approximately 3.607 times said focal length, said third surface has a negative radius of curvature of approximately 1.825 times said focal length, said first lens element having a thickness along said axis of approximately 0.025 times said focal length, said second lens element have a thickness along said axis of approximately 0.040 times said focal length. 61. The catadioptric system of claim 56 wherein said first lens element is made of an optical material having a refractive index of approximately 1.49 and an Abbe number of approximately 81.40 at a base wavelength of 0.546 micrometers, and said second lens element is made of an optical material having a refractive index of approximately 1.70 and an Abbe number of approximately 55.18 at said base wavelength. 62. The catadioptric system of claim 61 having a design form wherein said first surface has a negative radius of curvature of approximately 0.753 times the focal length of said system, said second surface has a negative radius of curvature of approximately 7.400 times said focal length, said third surface has a negative radius of curvature of approximately 1.536 times said focal length, said first lens element having a thickness along said axis of approximately 0.042 times said focal length, said second lens element having a thickness along said axis of approximately 0.066 times said focal length. 63. The catadioptric system of claim 55 comprising a first lens element and a second lens element, said first and second lens elements being spaced apart from each other to define first, second, third and fourth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said third and fourth surfaces, said fourth surface having said reflective coating. 64. The catadioptric system of claim 53 wherein said first lens element is made of an optical material having a refractive index of approximately 1.53 and an Abbe number of approximately 76.57 at a base wavelength of 0.54h micrometers, and said second lens element is made of an optical material having a refractive index of approximately 1.65 and an Abbe number of approximately 58.15 at said base wavelength. t;5. The catadioptric system of claim 64 having a design form wherein said first -surface has a negative radius of curvature of approximately 0.775 times the focal length of said system, said second surface has a positive radius of curvature of approximately 3.799 times said focal length, said third surface has a positive radius of curvature of approximately 4.568 times said focal length, said fourth surface has a negative radius of curvature of approximately 1.501 times said focal length, said first lens element having a thickness along said axis of approximately 0.040 times said focal length, said second lens element being separated from said first lens element along said axis by approximately 0.007 times said focal length, said second lens element having a thickness along said axis of approximately 0.061 times said focal length. 66. The catadioptric system of claim 63 wherein said first lens element is made of an optical material having a refractive index of approximately 1.46 and an Abbe number of approximately 90.32 at a base wavelength of 0.546 micrometers, and said second lens element is made of an optical material having a refractive index of approximately 1.55 and an Abbe number of approximately 62.60 at said base wavelength. 67. The catadioptric system of claim 66 having a design form wherein said first surface has a negative radius of curvature of approximately 0.736 times the focal length of said system, said second surface has a positive radius of curvature of approximately 8.012 times said focal length, said third surface has a positive radius of curvature-of approximately 8.273 times said focal length, said fourth surface has a negative radius of curvature of approximately 1.476 times said focal length, said first lens element having a thickness'along said axis of approximately 0.036 times said focal length, said second lens element being separated from said first lens element along said axis by approximately 0.004 times said focal length, said second lens element having a thickness along said axis of approximately 0.057 times said focal length. 68. The catadioptric system of claim 63 wherein said first lens element is made of an optical material having a refractive index of approximately 1.46 and an Abhe number of approximately 90.32 at a base wavelength of 0.546 micrometers, and said second lens element is made of an optical material having a refractive index of approximately 1.70 and an Abbe number of approximately 55.25 at said base wavelength. 69. The catadioptric system of claim 68 having a design form wherein said first surface has a negative radius of curvature of approximately 0.661 times the focal length of said system, said second surface has a negative radius of curvature of approximately 2.254 times said focal length, said third surface has a negative radius of curvature of approximately 3.628 times said focal length, said fourth surface has a negative radius of curvature of approximately 1.519 times said focal length, said first lens element having a thickness along said axis of approximately 0.029 times said focal length, said second lens element being separated from said first lens element along said axis by approximately 0.010 times said focal length, said second lens element having a thickness along said axis of approximately 0.054 times said focal length. 70. An optical lens system comprising a first group of lens elements and a second group of lens elements, said lens system being rotationally symmetric about an axis and having a common focal length along said axis for more than two optical wavelengths, said lens system being made of only two different optical materials. 71. A field-flattened Petzval lens system comprising only two different optical materials, said Petzval lens system being color-corrected at more than two optical wavelengths. 72. The Petzval lens system of claim 71 comprising a first group of lens elements, a second group of lens elements, and a lens element functioning as a field flattener, said lens elements having a rotationally symmetric disposition about an axis, said system having a common focal length on said axis for five optical wavelengths. 73. The Petzval lens system of claim 72 wherein said two optical materials comprise a first glass having a refractive index of approximately 1.53 and an Abbe number of approximately 76.57 at a base wavelength of 0.546 micrometers, and a second glass having a refractive index of approximately 1.65 and an Abbe number of approximately 58.15 at said base wavelength. 74. The Petzval lens system of claim 73 wherein said first group of lens elements comprises first, second, third and fourth lens elements, said second group of lens elements comprises fifth, sixth and seventh lens elements, and said field flattener comprises an eighth lens element, said lens elements being disposed so as to define first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, twelfth, thirteenth, fourteenth, fifteenth and sixteenth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said third and fourth surfaces, said third lens element being bounded by said fifth and sixth surfaces, said fourth lens element being bounded by said seventh and eighth surfaces, said fifth lens element being bounded by said ninth and tenth surfaces, said sixth lens element being bounded by said eleventh and twelfth surfaces, said seventh lens element being bounded by said thirteenth and fourteenth surfaces, said eighth lens'element being bounded by said fifteenth and sixteenth surfaces, said first surface having a positive radius of curvature of approximately 0.342 times the focal length of said system, said second surface having a negative radius of curvature of approximately 0.497 times said focal length, said third surface having a negative radius of curvature of approximately 1.190 times said focal length, said fourth surface having a positive radius of curvature of approximately 1.465 times said focal length, said fifth surface having a negative radius of curvature of approximately 0.299 times said focal length, said sixth surface having a positive radius of curvature of approximately 0.522 times said focal length, said seventh surface having a positive radius of curvature of approximately 0.350 times said focal length, said eighth surface having a negative radius of curvature of approximately 0.438 times said focal length, said ninth surface having a positive radius of curvature of approximately 0.508 times said focal length, said tenth surface having a negative radius of curvature of approximately 0.593 times said focal length, said eleventh surface having a negative radius of curvature of approximately 0.225 times said focal length, said twelfth surface having a positive radius of curvature of approximately 1.483 times said focal length, said thirteenth surface having a positive radius of curvature of 0.417 times said focal length, said fourteenth surface having a negative radius of curvature of approximately 0.356 times said focal length, said fifteenth surface having a negative radius of curvature of approximately 0.241 times said focal length, said sixteenth surface having a positive radius of curvature of approximately 2.412 times said focal length, said first lens element having a thickness along said axis of approximately 0.031 times said focal length, said second lens element being separated from said first lens element along said axis by approximately 0.006 times said focal length, said second lens element having a thickness along said axis of approximate,ly 0.020 times said focal length, said third lens element being separated from said second lens element along said axis by approximatelv 0.015 times said focal length, said third lens element having a thickness along said axis of approximately 0.020 times said focal length, said fourth lens element having a thickness along said axis of approximately 0.028 times said focal length, said fifth lens element being separated from said fourth lens element along said axis by approximately 0.274 times said focal length, said fifth lens element having a thickness along said axis of approximately 0.023 times said focal length, said sixth lens element being separated from said fifth lens element along said axis by approximately 0.016 times said focal length, said sixth lens element having a thickness along said axis of approximately 0.018 times said focal length, said seventh lens element being separated from said first lens element along said axis by approximately 0.014 times said focal length, said seventh lens element having a thickness along said axis of approximately 0.025 times said focal length, said eighth lens element being separated from said seventh lens element along said axis by approximately 0.268 times said focal length, said eighth lens element having a thickness along said axis of approximately 0.013 times said focal length. 75. The Petzval lens system of claim 71 comprising a first group of lens elements, a second group of lens element, and a lens element functioning as a field flattener, said lens elements having a rotationally symmetric disposition about an axis, said system having a common focal length on said axis for four optical wavelengths. 76. The Petzval lens system of claim 75 wherein said two optical materials comprise a first glass having a refractive index of approximately 1.49 and an Abbe number of approximately 81.40 at a base wavelength of 0.546 micrometers, and a second glass having a refractive index of approximately .1.70 and an Abbe number of approximately 55.31 at said base wavelength. 77. The Petzval lens system of claim 76 wherein said first group of lens elements comprises first, second and third lens elements, said second group of lens 'elements comprises fourth, fifth and sixth lens elements, and said field flattener comprises a seventh lens elements, said lens elements being disposed so as to define first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, twelfth, thirteenth and fourteenth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said third and fourth surfaces, said third lens element being bounded by said fifth and sixth surfaces, said fourth lens element being bounded by said seventh and eighth surfaces, said fifth lens element being bounded by said ninth and tenth surfaces, said sixth lens element being bounded by said eleventh and twelfth surfaces, said seventh lens element being bounded by said thirteenth and fourteenth surfaces, said first surface having a positive radius of curvature of approximately 0.305 times the focal length of said system, said second surface having a negative radius of curvature of approximately 0.900 times said focal length, said third surface having a negative radius of crvature of approximately 0.337 times said focal length, said fourth surface having a positive radius of curvature of approximately 0.398 times said focal length, said fifth surface having a positive radius of curvature of approximately 0.192 times said focal length, said sixth surface having a negative radius of curvature of approximately 0.692 times said focal length, said seventh surface having a positive radius of curvature of approximately 0.441 times said focal length, said eighth surface having a negative radius of curvature of approximately 0.385 times said focal length, said ninth surface having a negative radius of curvature of approximately 0.146 times said focal length, said tenth surface having a negative radius of curvature of approximately 0.52 times said focal length, said eleventh surface having a positive radius of curvature of approximately 0.393 times said focal length, said twelfth surface having a negative radius of curvature of approximately 0.240 times said focal length, said thirteenth surface having a negative radius of curvature of approximately 0.162 times said focal length, said fourteenth surface having a positive radius of curvature of approximately-0.789 times said focal length, said first lens element having a thickness along said axis of approximately 0.020 times said focal length, said second lens element being separated from said first lens element by approximately 0.005 times said focal length, said second lens element having a thickness along said axis of approximately 0.013 times said focal length, said third lens element being separated from second lens element along said axis by approximately 0.001 times said focal length, said third lens element having a thickness along said axis of approximately 0.018 times said focal length, said fourth lens element being separated from said third lens element along said axis by approximately 0.166 times said focal length, said fourth lens element having a thickness along said axis of approximately 0.n16 times said focal length, said fifth lens element being separated from said fourth lens element along said axis by approximately 0.010 times said focal length, said fifth lens element having i thickness along said axis of approximately 0.011 times said focal length, said sixth lens element being separated from said fifth lens element along said axis by approximately 0.009 times said focal length, said sixth lens element having a thickness along said axis of approximately 0.060 times said focal length, said seventh lens element being separated from said sixth lens element along said axis by approximately 0.187 times said focal length, said seventh lens element having a thickness along said axis of approximately 0.014 times said focal length. 78. The Petzval lens system of claim 71 comprising a first group of lens elements, a second group of lens elements, and a lens element functioning as a field flattener, said lens elements having a rotationally symmetric disposition about an axis, said system having a common focal length on said axis for three optical wavelengths. 79. The Petzval lens system of claim 78 wherein said two optical materials comprise a first glass having a refractive index of approximately 1.48 and an Abbe number of approximately 84.07 at a base wavelength of 0.546 micrometers, and a second glass having a refractive index of approximately 1.69 and an Abbe number of approximately 55.19 at said base wavelength. 80. The Petzval lens system of claim 79 wherein said first group of lens elements comprises first, second, third, fourth and fifth lens elements, said second group of lens elements comprises sixth, seventh, eighth and ninth lens elements, and said field flattener comprises a tenth lens element, said lens elements being disposed so as to define first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, twelfth, thirteenth, fourteenth, fifteenth, sixteenth, seventeenth, eighteenth, nineteenth and twentieth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said third and fourth surfaces, said third lens element being bounded hy said fifth and sixth surfaces, said fourth lens element being hounded by said seventh and eighth surfaces, said fifth lens element being bounded by said ninth and tenth surfaces, said sixth lens element being bounded by said eleventh and twelfth surfaces, said seventh lens element being bounded by said thirteenth and fourteenth surfaces, said eighth lens element being bounded by said fifteenth and sixteenth surfaces, said ninth lens element being bounded by said seventeenth and eighteenth surfaces, said tenth lens element being bounded by said nineteenth and twentieth surfaces, said first surface having a positive radius of curvature of approximately 2.066 times the focal length of said system, said second surface having a negative radius of curvature of approximately 1.933 times said focal length, said third surface having a positive radius of curvature of approximately 4.5he times said focal length, said fourth surface having a negative radius of curvature of approximately 1.026 times said focal length, said fifth surface having a negative radius of curvature of approximately 0.991 times said focal length, said sixth surface having a positive radius of curvature of approximately 2a.483 times said focal length, said seventh surface having a negative radius of curvature of approximately 1.339 times said focal length, said eighth surface having a positive radius of curvature of approximately 63.427 times said focal length, said ninth surface having a positive radius of curvature of approximately 0.850 times said focal length, said tenth surface having a negative radius of curvature of approximately 5.545 times said focal length, said eleventh surface having a positive radius of curvature of approximately 0.422 times said focal length, said twelfth surface having a negative radius of curvature of approximately 0.555 times said focal length, said thirteenth surface having a negative radius of curvature of approximately 0.473 times said focal length, said fourteenth surface having a negative radius of curvature of approximately 5.724 times said focal length, said fifteen surface having a negative radius of curvature of approximately 2.021 times said focal length, said sixteenth surface having a positive radius of curvature of approximatelv (1.969 times said focal length, said seventeenth surface having a positive radius of curvature of approximately (1.30 times said focal length, said eighteenth surface having a negative radius of curvature of approximately 0.798 times said focal length, said nineteenth surface having a negative radius of curvature of approximately 0.252 times said focal length, said twentieth surface having a positive radius of curvature of approximately 5.189 times said focal length, said first lens element having 3 thickness along said axis of approximately 0.094 times said focal length, said second lens element being separated from said first lens element along said axis by approximately 0.156 times said focal length, said second lens element having a thickness along said axis of approximately 0.087 times said focal length, said third lens element being separated from said second lens element along said axis by approximately 0.004 times said focal length, said third lens element having a thickness along said axis of approximately 0.037 times said focal length,, said fourth lens element being separated from said third lens element along said axis by approximately 0.033 times said focal length, said fourth lens element having a thickness along said axis'of approximately 0.037 times said focal length, said fifth lens element being separated from said fourth lens element along said axis by approximately 0.001 times said focal length, said fifth lens element having a thickness along said axis of approximately 0.087 times said focal length, said sixth lens element being separated from said fifth lens element along said axis by approximately 0.873 times said focal length, said sixth lens element having a thickness along said axis of approximately 0.050 times said focal length, said seventh lens element being separated from said sixth lens element along said axis by approximately 0.010 times said focal length, said seventh lens element having a thickness along said axis of approximately 0.025 times said focal length, said eighth lens element being separated from said seventh lens element along said axis by approximately 0,032 times said focal length said eighth lens element having a thickness along said axis of approximately O.Q25 times said focal length, said ninth lens element being separated from said eighth lens element along said axis by approximately 0.001 times said focal length, said ninth lens element having a thickness along said axis of approximately 0.050 times said focal length, said tenth lens element being separated from said ninth lens element along said axis by approximately 0.249 times said focal length, said tenth lens element having a thickness along said axis of approximately o.n24 times said focal length. 81. An anamorphic optical system comprising a plurality of prism elements, said system being made of only two different optical materials, said system providing a substantially identical deviation angle for more than two optical wavelengths. 82. The anamorphic system of claim 81 comprising only two prism elements. 83. The anamorphic system of claim 81 comprising a first prism element made of an optical material having a refractive index of approximately 1.53 and an Abbe number of approximately 76.57 at a base wavelength of 0.546 micrometers, and a second prism element made of an optical material having a refractive index of approximately 1.65 and an Abbe number of approximately 58.15 at said base wavelength. 84. The anamorphic system of claim 83 wherein said first prism element has an apex angle of approximately 42.02 degrees, and said second prism element has an apex angle of approximately 25.59 degrees. 85. The anamorphic system of claim 81 comprising first, second, third, fourth and fifth prism elements, said first, third and fifth prism elements being made of an optical material having a refractive index of approximately 1.53 and an Abbe number of approximately 76.57 at a base wavelength of 0.546 micrometers, said second and fourth prism elements being made of an optical material having a refractive index of approximatfnly 1.65 and an Abbe number of approximately 58.15 at said base wavelength. 86. The anamorphic system of claim BF wherein four of said prism elements have apex angles that are substantially equal. 87. The anamorphic system of claim 86 wherein each of said first, second, third and fourth prism elements has an apex angle of approximately 43.17 degrees, ad said fifth prism element has an apex angle of approximately 57.58 degrees. 88. The anamorphic system of claim 85 wherein said first prism element has an apex angle of approximately 83.20 degrees, said second prism element has an apex angle of approximately 44.96 degrees, said third prism element has an apex angle of approximately 40.86 degrees, said fourth prism element has an apex angle of approximately 4fi.92 degrees, and said fifth prism element has an apex angle of approximately 37.50 degrees. 89. An optical system rotationally symmetric about an axis, said system comprising a lens multiplet having a common focal length along said axis for at least five optical wavelengths, said lens multiplet comprising an optical material having a refractive index of approximately 1.50 and an Ahbe number of approximately 81.22 at a base wavelength of 0.546 micrometers, an optical material having a refractive index of approximately 1.73 and an Abbe number of approximately 34.49 at said base wavelength, and an optical material having refractive index of approximately 1.70 and an Abbe number of approximately 29.89 at said base wavelength. 90. The optical system of claim 89 wherein said lens multiplet is a quintuplet comprising a first lens element made of said optical material having a refractive index of approximately 1.50 and an Abbe number of approximately 81.22, a second lens element made of said optical material having a refractive index of approximately 1.73 and an Abbe number of approximately 34.49, a third lens element made of the same optical material as said first lens element, a fourth lens element made of said optical material having a refractive index of approximately 1.70 and an Abbe number of approximately 29.89, and fifth lens element made of the same optical material as said second lens element. 91. The optical system of claim 90 having a design form wherein said lens elements are positioned so that said second and third lens elements are in contact with patch other, and so that said fourth and fifth lens elements are in contact with each other, thereby defining first, second, third, fourth, fifth, sixth, seventh and eighth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said third and fourth surfaces, said third lens element being bounded by said fourth and fifth surfaces, said fourth lens element being bounded by said sixth and seventh surfaces, said fifth lens element being bounded by said seventh and eighth surfaces, said first surface having a positive radius of curvature of approximately 0.493 times tp focal length of said quintuplet, said second surface having a negative radius of curvature of approximately 0.660 times said focal length, said third surface having a negative radius of curvature of approximately 0.538 times said focal length, said fourth surface having a positive radius of curvature of approximately 1.078 times said focal length, said fifth surface having a negative radius of curvature of approximately 2.457 times said focal length, said sixth surface having a negative radius of curvature of approximately 5.045 times said focal length, said seventh surface having a negative radius of curvature of approximately 0.288 times said focal length, said eighth surface having a negative radius of curvature of approximately 0.953 times said focal length, said first lens element having a thickness along said axis of approximately 0.015 times said focal length, said second lens element being separated from said first lens element along said axis by approximately 0.034 times said focal length, said second lens element having a thickness along said axis of approximately 0.012 times said focal length, said third lens element having a thickness along said axis of approximately 0.012 times said focal length, said fourth lens element being separated from said third lens element along said axis by approximately 0.001 times said focal length, said fourth lens element having a thickness along said axis of approximately 0.013 times said focal lengths, said fifth lens element having a thickness along said axis of approximately 0.013 times said focal length. 92. An optical system rotationally symmetric about an axis, said system comprising a lens multiplet having a common focal length along said axis for at least five optical wavelengths, said lens multiplet comprising an optical material having a refractive index of approximately 1.53 and an Abbe number of approximately 76.57 at a base wavelength of 0.546 micrometers, an optical material having a refractive index of approximately 1.69 and an Abbe number of approximately 51.28 at said base wavelength, an optical material having a refractive index of approximately 1.62 and an Abbe number of approximately 44.07 at said base wavelength, and an optical material having a refractive index of approximately 1.59 and an Abbe number of approximately 48.29 at said base wavelength. 93. The optical system of claim 92 wherein said lens multiplet is a quintuplet comprising a first lens element made of said optical material having a refractive index of approximately 1.53 and an Abbe number of approximately 76.57, a second lens element made of said optical material having a refractive index of approximately 1.69 and an Abbe number of approximately 51.28, a third lens element made of the same optical material as said first lens element, a fourth lens element made of said optical material having a refractive index of approximately 1.62 and an Abbe number of approximately 44.07, and a fifth lens element made of said optical material having a refractive index of approximately 1.59 and an Abbe number of approximately 48.29. 94. The optical system of claim 93 having a design form wherein said lens elements are positioned so that said second and third lens elements are in contact with each other, and so that said fourth and fifth lens elements are in. contact with each other, thereby defining first', second, third, fourth, fifth, sixth, seventh and eighth surfaces, said first lens element being bounded by said first and second surfaces, said second lens element being bounded by said third and fourth surfaces, said third lens element being bounded by said fourth and fifth.surfaces, said fourth lens element being bounded by said sixth and seventh surfaces, said fifth lens element being bounded by said seventh and eight surfaces, said first surface having a positive radius of curvature of approximately 0.425 times the focal length of said quintuplet, said second surface having a negative radius of curvature of approximately 0.749 times said local length, said third surface having a negative radius of curvature of approximately 0.369 times said focal length, said fourth surface having a positive radius of curvature of approximately 0.416 times said focal length, said fifth surface having a negative radius of curvature of approximately 0.385 times said focal length, said sixth surface having a positive radius of curvature of approximately 0.546 times said focal length, said seventh surface having a negative radius of curvature of approximately 0.170 times said focal length, said eighth surface having a positive radius of curvature of approximately 0.434 times said focal length, said first lens element having a thickness along said axis of approximately 0.015 times said focal length, said second lens element being separated from said first lens element along said axis by approximately 0.008 times said focal length, said second lens element having a thickness along said axis of approximately 0.012 times said focal length, said third lens element having a thickness along said axis of approximately 0.015 times said focal length, said fourth lens element being separated from said third lens element along said axis by approximately 0.001 times said focal length, said fourth lens element having a thickness along said axis of approximately 0.015 times said focal length, said fifth lens element having a thickness along said axis of approximately 0.012 times said focal length. 95. A method of selecting optical materials for making an optical system that is color-corrected at a plurality of wavelengths, each optical material having a characteristic dispersive power that is a function of wavelength, said method comprising: a) representing the dispersive power of each optical material by a polynomial expression in a variable that is a function of wavelength; b) comparing a ratio of coefficients in a polynomial expression for one of said optical materials with corresponding ratios of coefficients in the polynomial expressions for others of said optical materials; c) identifying particular optical materials from among said others of said optical materials for which said corresponding ratios of coefficients are substantially equal to said ratio of coefficients for said one optical material; and d) choosing optical materials for making said system from among those particular optical materials for which said corresponding ratios of coefficients are substantially equal. 96. A dioptric optical system color-corrected at three wavelengths, said system comprising only two optical materials, namely, Schott FK51 glass and Schott K51 glass. 97. The optical system of claim 96, said system being a lens doublet. 98 A dioptric optical system color-corrected at four wavelengths, said system comprising only two optical materials, namely, Corning-France 486817 glass and Ohara LAK14 glass. 99. The optical system of claim 98, said system being a lens doublet. 100. The optical system of claim 99, said lens doublet comprising two air-spaced lens elements. 101. A dioptric optical system color-corrected at five wavelengths, said system comprising only two optical materials, namely, Schott PK51 glass and Hoya LAC7 glass. 102. The optical system of claim 101, said system being a lens doublet. 103. The optical system of claim 102, said lens doublet comprising two air-spaced lens elements. 104. A dioptric optical system color-corrected at four wavelengths, said system comprising only two optical materials, namely, Corning-France 486817 glass and Corning-France 589612 glass. 105. The optical system of claim 104, said system being a lens triplet. -106. The optical system of claim 105, said lens triplet comprising three lens elements, two of said lens elements being air-spaced. 107. The optical system of claim 104, said system being a lens quadruplet. 108. The optical system of claim 107, said lens quadruplet comprising four lens elements, two of said lens elements being air-spaced. 109. A dioptric optical system color-corrected at four wavelengths, said system comprising only two optical materials, namely, Hoya FCD10 glass and Ohara LAK14 glass. 110. The optical system of claim 109, said system being a collimator. 111. The optical system of claim-llO, said collimator comprising four lens elements. 112. The optical system of claim 111, said lens elements being air-spaced. 113. A dioptric optical system color-corrected at five wavelengths,, said system comprising only two optical materials, namely, Schott PK51 glass and Hoya LAC7 glass. 114. The optical system of claim 113, said system being a collimator. 115. The optical system of claim 114, said collimator comprising four lens elements. 116. The optical system of claim 115, said lens elements being air-spaced. 117. A dioptric optical system color-corrected at five wavelengths, said system comprising bnly two optical materials, namely, calcium fluoride crystal and Hoya LAC7 glass. 118. The optical system of claim 117, said system being a collimator. 119. The optical system of claim 118, said collimator comprising four lens elements. 120. The optical system of claim 119, said lens elements being air-spaced. 121. A catadioptric optical system color-corrected at five wavelengths, said system comprising only two optical materials, namely, Hoya FCD10 glass and Hoya FC3 glass. 122. A catadioptric optical system color-corrected at four wavelengths, said system comprising only two optical materials, namely, Hoya BAFIl glass and Hoya FL6 glass. 123. A catadioptric optical system color-corrected at four wavelengths, said system comprising only two optical materials, namely, Corning-France 486817 glass and Corning-France 697554 glass. 124. A catadioptric optical system color-corrected at five wavelengths, said system comprising only two optical materials, namely, Schott PK51 glass and Hoya LAC7 glass. 125. The catadioptric optical system of claim 124, said system comprising two lens elements, said lens elements being air-spaced. 126. A catadioptric optical system color-corrected at five wavelengths, said system comprising only two optical materials, namely, Hoya FCD10 glass and Ohara PSK1 glass. 127. The catadioptric optical system of claim 126, said system comprising two lens elements, said lens elements being air-spaced. 128. A catadioptric optical system color-corrected at four wavelengths, said system comprising only two optical materials, namely, Hoya FCD10 glass and Hoya LAC14 glass. 129. The catadioptric optical system of claim 128, said system comprising two lens elements, said lens elements being air-spaced. 130. A flat-field lens system of the Petzval type color-corrected at five wavelengths, said system comprising only two optical materials, namely, Schott PK51 glass and Hoya LAC7 glass. 131. A flat-field lens system of the Petzval type color-corrected at four wavelengths, said systPm comprising only two optical materials, namely, Corning-France 486817 glass and Ohara LAK14 glass. 132. A flat-field lens system of the Petzval type color-corrected at three wavelengths, said system comprising only two optical materials, namely, Schott FK51 glass and Schott LAKN14 glass. 133. A prism system whose chromatic dispersion from a given total deviation angle is zero at five wavelengths, said prism system comprising only two optical materials. 134. The prism system of claim 133 wherein said two optical materials are Schott PK51 glass and Hoya LAC7 glass. 135. The prism system of claim l34 wherein said system comprises only two prism elements. 136. The prism system of claim 135 wherein said prism elements are configured to have a total deviation angle of six degrees. 137. The prism system of claim 134 wherein said system comprises five prism elements. 138. The prism system of claim 137 wherein said prism elements are configured to have a total deviation angle of thirty degrees. 139. A dioptric optical system color-corrected at five wavelengths, said system comprising only three optical materials, namely, Ohara FKO1 glass, Ohara KZFS8 glass and Ohara SF15 glass. 140. The optical system of claim 139, said system being a lens quintuplet. 141. A dioptric optical systems cnlor-corrected at five wavelengths, said system comprising only rour optical materials, namely, Schott PK51 glass, Schott LAK20 glass, Schott KZFSN4 glass and Schott KZFS6 glass. 142. The optical system of claim 141, said system being a lens quintuplet. 143. A method of selecting optical materials for designing an optical system that is color-corrected at a number of wavelengths in a particular wavelength region, each optical material having a characteristic dispersive power D(A) represented by an nth degree polynomial in a variable #(#), said polynomial being of the form: EMI186.1 where #(#) = ##/(1 + &alpha; ##), where ## represents change in wavelenght with respect to a base wavelength and oc is a constant that is substantially independent of optical material; and where #i are coefficients of terms in said variable S(A), said polynomial having n terms in said variable e(2); said method comprising use of a digital computer for: a) calculating said coefficients #i for a plurality of specified wavelengths in said wavelength region for each optical material; b) calculating ratios #i/#j, where j#i, for each optical material; c) comparing corresponding ratios #i/#j for said optical materials; and d) identifying candidate optical materials for designing said system from among those optical materials for which said corresponding ratios #i/#j are substantially equal. 144. The method of claim 143 wherein said coefficients vli are calculated using a least-squares technique. 145. The method of claim 143 wherein said polynomial is quadratic, the coefficients #1 and #2 being calculated for each optical material, and wherein said candidate optical materials for designing said system are identified from among those optical materials for which corresponding ratios #1/#2 are substantially equal. 146. The method of claim 145 wherein optical materials for designing said system are selected by forming paired combinations of said candidate optical materials for which cerresponding ratios #1/#2 are substantially equal, subtracting corresponding values of #1 for each paired combination of said candidate optical materials, and selecting optical materials for designing said system from among those paired combinations for which the absolute value of the difference between corresponding values of #1 is greater than a specified value appropriate for said system. 147. The method of claim 143 wherein said polynomial is cubic, the coefficients #1, #2 and and being calculated for each optical material, and wherein said carldidate optical materials for designing said system are identified frnrll. among those optical materials for which corresponding ratios (#1/#2), (#2/#3) and (#1/#3) are substantially equal. 148. The method of claim 147, said method being used to select three different optical materials from among said candidate optical materials for designing said system, said method further comprising: a) locating each candidate optical material with respect to a three-dimensional coordinate system defined by axes corresponding to the coefficients ZZi' #2 and b) designating a first one of said candidate optical materials as a reference optical material; c) defining a two-dimensional transformed coordinate system by axes 1 and 2, with origin at the location of said reference optical material; d) locating the other-candidate optical materials with respect to said transformed coordinate system; ; e) calculating the ratio 2/ 1 for each of said other candidate optical materials; and f) selecting a second one and a third one of said candidate optical materials from among those other candidate optical materials having substantially the same value as said reference optical material for the ratioAA1.

Inventors: MERCADO, ROMEO IQUICO, ROBB, PAUL NEWELL
Applicants: LOCKHEED MISSILES & SPACE COMPANY, INC.
Application year: 1983
Main classification: G02B1
IPC codes: G02B13, G02B9, G02B1