Abstract:
Variable power lens systems for use with electronic imaging systems, e.g., systems employing CCDs, are provided. The systems take advantage of the fact that the images detected by electronic imaging systems are small, e.g., the image diagonal can be 5.5 millimeters or less. The lens systems employ thick lens elements, whose diameters and thicknesses are large relative to the image size, and large air spaces between lens elements. The systems also employ weak lens units. In this way, simplified lens designs having excellent optical properties at less cost are provided. In certain embodiments, the lens systems contain only three lens elements, e.g., a negative first lens element, a positive second lens element for zooming, and a positive third lens element, with the first and/or the third lens element serving as a compensator.

Description:
FIELD OF THE INVENTION 
     This invention relates to variable power lens systems, particularly zoom lens systems, for use in producing small images. In certain embodiments of the invention, the small images produced by the lens system are detected by an electronic imaging system, e.g., a system employing a charged coupled device (CCD) or similar light sensitive electronic component. Such systems are well known in the art and descriptions thereof can be found in various references, including Rose et al., &#34;Physical Limits to the Performance of Imaging Systems,&#34; Physics Today, September 1989, pages 24-32 and the references cited therein; and Sequin et al., &#34;Charge Transfer Devices,&#34; Advances in Electronics and Electron Physics, suppl. 8, L. Marton editor, Academic Press, New York, 1975, the relevant portions of all of which are incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     Electronic imaging systems have the advantage of being able to work with images of small size. For example, CCDs having a diagonal of approximately 4 mm (known as 1/4 inch CCDs) are widely available. CCDs having diagonals of 5.5 mm (1/3 inch CCDs) are also widely used. Within this small size, a typical CCD will have over 200,000 pixels, thus giving the device a resolution on the order of 70 cycles per millimeter at the surface of the CCD. 
     In the past, fixed focal length lens systems have been used with CCDs. For many applications, such systems are inadequate because a fixed focal length system cannot simultaneously provide a large angle of view and sufficient resolution to allow detailed examination of specific parts of the field of view. Although electronic zooming can be performed, i.e., zooming wherein a portion of the field is selected and electronically magnified to fill the entire viewing screen, such zooming does not increase the resolution of the original image captured by the CCD. Alternatively, the resolution of the original image can be improved by increasing the number of CCD pixels, but this approach significantly adds to the cost of the device and diffraction effects limit the extent to which pixel size can be reduced. 
     There thus exists a need for variable power lens systems for use with electronic imaging systems. As known in the art, variable power lens systems can have a discrete number of focal lengths at which the image is in focus at a fixed location, e.g., a dual power system, or can have a focal length which can vary continuously while producing a focused image at a fixed location, e.g., a zoom lens system. Alternatively, the image location need not be kept fixed, in which case, either the detecting device, e.g., the CCD, or the lens system can be moved as the focal length of the lens system is varied either discretely or continuously. The present invention provides variable power lens systems for use with any of these configurations. 
     A variety of zoom lens systems are known in the art. Examples include Tsuchida et al., U.S. Pat. No. 4,810,071, Mihara et al., U.S. Pat. No. 4,906,079, Hata, U.S. Pat. No. 5,009,491, and Ozawa, U.S. Pat. No. 5,054,897. Lens systems of these types have been developed in accordance with the following principles of conventional lens design practice: 
     (1) The manufacturing cost of a lens element is primarily determined by the volume of the element and its surface area. For this reason, for most commercial applications, lens designers try to minimize lens element diameters and thicknesses relative to the image size. 
     (2) In zoom lens design, one or both of the pupils typically moves during zooming. This means that lens diameters must be increased to transmit the entire imaging bundle throughout the zooming range. To minimize this increase in lens diameters (see principle (1) above), lens designers typically use lens elements of relatively large powers. This, in turn, results in increased aberration contributions because of the large powers, and necessitates the inclusion of more lens elements for aberration correction. Conventional wisdom, however, has been to opt for more lens elements, as opposed to larger elements. 
     Ohno, U.S. Pat. No. 5,357,374, discloses a zoom lens system for use in a photographic camera that employs three lens elements in a negative-positive-negative or a negative-positive-positive arrangement. The Ohno lens system employs strong, thin lens elements which introduce substantial aberrations into the system such that the smallest f-number reported for any of Ohno&#39;s examples is 7.6. The Ohno system is limited to such relatively small apertures since the aberrations of the system would become excessive if the aperture were increased. In contrast, the lens systems of the present invention achieve large apertures through the use of weak, thick lens elements. 
     SUMMARY OF THE INVENTION 
     In accordance with the present invention, it has been found that the conventional approaches discussed above lead to overly expensive and complicated designs when applied to the problem of providing a large aperture, variable power lens system which produces a small image suitable for detection by an electronic imaging system. Specifically, in accordance with the invention, it has been found that by increasing the thicknesses of lens elements relative to the image size, as well as by increasing air spaces between lens elements, simplified lens designs having excellent optical properties at less cost can be provided. In particular, in certain embodiments, lens units containing only one lens element can be used with the system still having excellent overall aberration correction. 
     This effect occurs because although manufacturing costs are reduced as the volume of a lens element goes down, a point is reached where this cost reduction levels off. This point of diminishing cost reduction generally corresponds to lens elements whose diameters are less than about 10 millimeters. As such, these diameters are large relative to the size of the images which are detected by electronic imaging systems, even though from a cost point of view the lens elements are small. 
     Accordingly, thick lens elements whose diameters and thicknesses are large relative to the image size, but whose absolute size is small, are used in the practice of the present invention. Such thick lens elements allow for the use of lens surfaces having reduced power. This, in turn, reduces the aberrations produced by the surfaces. In addition, because the lens elements have an overall small absolute size, they can be economically molded in either glass or plastic. Such molding, in turn, permits the use of aspherical surfaces, which can be configured to further reduce the aberrations of the system. 
     The variable power lens systems of the invention include three lens units. The first and second lens units from the object end of the system have a negative and a positive power, respectively. The third lens unit generally has a positive power, but may be negative in some cases. Each of the three lens units includes one or more lens elements. 
     The first and second units have powers whose magnitudes are small relative to the overall strongest power of the system. In particular, the absolute values of the focal lengths of at least one and preferably both of the first and second units of the lens system is greater than about 1.3 times f min , where f min  is the focal length of the system at its shortest focal length position, i.e., its widest field of view. Similarly, the third lens unit is generally also weak, i.e., its focal length is generally greater than about 1.3 times f min . 
     In addition to having weak lens units, the lens systems of the invention also have thick lens elements. In particular, the lens systems include at least one lens element whose thickness is greater than about 0.5 times f min , and preferably include at least two such lens elements and in some cases at least three such elements. In some embodiments, one of the thick lens elements may be part of a color correcting doublet (see Example 7). 
     In certain embodiments of the invention, the first lens unit and/or the second lens unit includes a surface which has a relatively strong power in comparison to the overall power of the unit in which it is contained. These strong surfaces serve to provide aberration correction for the lens system. 
     In other embodiments, the third lens unit has a positive power and includes a surface at its image side that is concave to the image. This surface also provides aberration correction for the lens system. 
     As illustrated by the examples presented below, the invention can provide variable power lens systems and, in particular, zoom lens systems having a limited number of lens elements, each of low power relative to the overall power of the system, e.g., in some cases, only three lens elements of relatively low power, rather than many lens elements at least some of which are very strong, as in the prior art. Such lens systems provide a cost effect way to produce small images of varying magnification for detection by an electronic imaging system. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIGS. 1 through 9 are schematic side views of lens systems constructed in accordance with the invention. The upper portion of each of these figures shows the lens system in its short effective focal length (EFL) configuration, while the lower portion shows it in its long EFL configuration. 
    
    
     These drawings, which are incorporated in and constitute part of the specification, illustrate the preferred embodiments of the invention, and together with the description, serve to explain the principles of the invention. It is to be understood, of course, that both the drawings and the description are explanatory only and are not restrictive of the invention. 
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     As discussed above, the present invention relates to variable focal length lens systems employing weak lens units and lens elements of substantial thickness. By utilizing weak units, thick elements, and aspheric surfaces,the invention can achieve large apertures of f/2.0 or less and a wide totalfield of view of 70 degrees or more. 
     Also, a wide range of zoom ratios can be achieved. In particular, in the simplest case, a 2:1 zoom ratio can be achieved using just three single lens elements, i.e., a negative first lens element, a positive second lenselement that moves to effect a change of internal magnification during zooming, and a positive third lens element, where either or both of the first and third lens elements moves to provide compensation when zooming. 
     If the focal length is increased, either by increasing the zoom ratio or bychanging the zooming region to longer focal lengths, then correction of residual chromatic aberrations may be necessary. This can be achieved by compounding only the third lens unit. (As used herein and in the claims, acompounded component, e.g., a doublet, is not a &#34;single lens element.&#34;) 
     As an alternative, the third lens unit can include a diffractive surface tocorrect the chromatic aberration, e.g., the third lens unit can be composedof an element that is fabricated as a refractive-diffractive hybrid element. The fabrication of such elements is well known in the art. See, for example, C. Londono, &#34;Design and Fabrication of Surface Relief Diffractive Optical Elements, or Kinoforms, with Examples for Optical Athermalization,&#34; Ph.D. diss., Tufts University, 1992, and the references cited therein, the relevant portions of all of which are incorporated herein by reference. Diffractive surfaces have the problem of diffraction efficiency, i.e., all orders do not come to a perfect focus. This effect is often seen as &#34;glare&#34;. For an electronic imaging system application, the diffraction efficiency problem can be addressed by digital processing of the electronic image. 
     If desired, chromatic aberration can be corrected in the first and/or the second lens units, either alone or in combination with correction in the third lens unit, although correction in just the third lens unit is most preferred. 
     For monochromatic CCDs, it is generally not important that the exit pupil of the lens system is telecentric. In this case, the preferred location ofthe aperture stop is after the second unit. When a telecentric or near telecentric exit pupil is required, e.g., for color CCDs, the aperture stop can be moved to a position before or within the second unit. 
     If only a change of focal length (field of view) between two extremes is required, the first and third units can be fixed and a positive second unit can be moved to change focal length without requiring refocusing for the two extremes. 
     To increase the zoom range, a fixed positive lens unit (U4) can be placed before the negative first lens unit. In this design, the negative first lens unit becomes the focal length variator for zooming and the positive second lens unit becomes the compensator. As illustrated in Example 6, thesecond and third lens units can be moved together for compensating, if desired. 
     Because the lens units making up the lens systems of the invention have small mass, they can be easily moved using low powered devices, such as, small motors, electromagnetics, and the like. Accordingly, the lens systems can be mounted directly on a circuit board which carries a CCD or similar device. 
     EXAMPLES 
     Without intending to limit it in any manner, the present invention is illustrated by the examples of FIGS. 1-9 and the corresponding prescriptions of Tables 1-9. Lens units, lens elements, and lens surfaces are identified by &#34;U&#34;, &#34;L&#34;, and &#34;S&#34; numbers, respectively, in the figures. 
     As is conventional, the figures are drawn with the long conjugate on the left and the short conjugate on the right. Accordingly, in the typical application of the invention, the object to be viewed will be on the left and an electronic imaging system, e.g., a system employing a CCD, will be on the right. 
     The glasses and plastics referred to in Tables 1-9 are set forth in Table 10, where the glass names are the SCHOTT and HOYA designations. Equivalentmaterials made by other manufacturers can be used in the practice of the invention. 
     The aspheric coefficients set forth in the tables are for use in the following equation: ##EQU1##where z is the surface sag at a distance y from the optical axis of the system, c is the curvature of the lens at the optical axis, and k is a conic constant, which is zero except where indicated. 
     The abbreviations used in the tables are as follows: SN--surface number; CLR. AP.--clear aperture; FIELD--half field of view; EFL--effective focal length; FVD--front vertex distance; f/--f-number; BFL--back focal length; ENP--entrance pupil; EXP--exit pupil, and BRL--barrel length. The designations &#34;a&#34; and &#34;ac&#34; associated with various surfaces represent &#34;aspheric&#34; and &#34;aspheric with a conic constant&#34;, respectively. The asterisks used in Tables 4 and 5 represent a diffractive surface. All dimensions given in the tables are in millimeters. 
     Example 1 
     This example shows a three element zoom lens system having a negative firstlens unit, a positive second lens unit, and a positive third lens unit. Thefirst lens unit is fixed during zooming, the second lens unit provides the change in magnification of the system, and the third lens unit is the compensator. This system provides a 1.7 zoom ratio from 3.8 mm to 6.5 mm. 
     Example 2 
     This example shows another three element zoom lens system having a negativefirst lens unit which remains fixed during zooming, a positive second lens unit which moves to change the system&#39;s focal length, and a positive thirdlens unit which serves as the compensator. This system has a 2.0 zoom ratioand a maximum field of view of 72° at an aperture of f/1.7. The lenssystem of this example has a larger field of view, i.e., a shorter focal length, than that of Example 1 and uses the thickness of the front lens element to provide a higher level of field curvature correction than in Example 1. 
     Example 3 
     This example illustrates the use of a color correcting doublet in the thirdlens unit. As in Examples 1 and 2, the first lens unit is negative and remains fixed during zooming, the second lens unit is positive and moves to change the system&#39;s focal length, and the third lens unit is positive and serves as the compensator. The zoom ratio for this system is 1.84. 
     Examples 4 and 5 
     These examples illustrate the use of a diffractive surface (S6/S7) in the third lens unit to provide for color correction. The asterisks in the tables for these examples represent the index of refraction and the Abbe numbers used in the Sweatt model for a diffractive surface, e.g., a N e  value of 9999 and a V e  value of -3.4. See W. C. Sweatt, &#34;Mathematical Equivalence between a Holographic Optical Element and an Ultra High Index Lens,&#34; Journal of the Optical Society of America, 69:486-487, 1979. In each of these examples, the first lens unit is negative and fixed, the second lens unit is positive and moves for zooming, and the third lens unit is positive and serves as the compensator. 
     Example 6 
     This example illustrates the use of a positive lens unit (U4) on the objectside of the first lens unit (U1). This positive lens unit serves to increase the zooming range of the system, in this case, to 2.25. The system of this example moves the first lens unit for zooming and the second and third lens units for compensating. The third lens unit includesa color correcting doublet. 
     Example 7 
     This example illustrates a system having a distant exit pupil. The first lens unit is negative and fixed during zooming. The second lens unit is positive and moves between the first and third lens units to provide dual power without a change in focus position. The third lens unit is a positive doublet which provides color correction. The aperture stop for this system is within the second lens unit and moves with that unit. For certain applications, e.g., the viewing of documents, the system can be focused at different object distances for its different focal lengths for a constant image distance, e.g., the system can be focused at infinity forits short focal length position and can be focused at a closer distance, e.g., 25-50 centimeters, for its long focal length position. 
     Example 8 
     This example is similar to the lens system of Example 2 wherein the third unit has been compounded for color correction. Surfaces S6 and S7 are eachapproximately paraboloidal so as to provide large surface powers for effective color correction. 
     Example 9 
     This example is also similar to the lens system of Example 2. In this case,the third unit is composed of two identical lens elements which allows for enhanced aberration correction without a substantial increase in the overall cost of the system. 
     Of the foregoing examples, Examples 1-6 are zoom systems, while Examples 7-9 are dual power systems. In particular, Examples 7-9 are designed to produce a 2:1 change in magnification between their long and short focal length positions. 
     In the case of dual power systems, it should be noted that the same opticalelements can be used to produce a magnification range other than 2:1 by simply changing the limits of motion of the second lens unit and the spacing between the lens system and the image plane. This can be done through the use of a lens barrel that includes changeable stops for the second lens unit and a mounting system for the lens barrel which allows for changes in the spacing between the barrel and the image plane. Alternatively, the same lens elements can be used with different lens barrels having different stops and/or with different lens barrel mounts which provide different spacings between the lens system and the image plane. 
     Tables 11-14 summarize various properties of the lens systems of FIGS. 1-9.In particular, Table 11 sets forth the powers of the first, second, and third units (Φ U1 , Φ U2 , Φ U3 ), and the powers of the strongest concave-to-the-image surface of the first and second units (Φ U1S , Φ U2S ). Note that the second unit of the lens system of Example 7 does not include a surface that is concave to the image. As shown by this table, all of the lens systems of the invention include at least one concave-to-the-image surface which is strong relativeto the power of the unit, i.e., Φ U1S  /Φ U1  &gt;1.0 or Φ U2S  /Φ U2  &gt;1.0, and many of the systems have such a surface in both the first and second units, i.e., Φ U1S  /Φ U1  &gt;1.0 and Φ U2S  /Φ U2  &gt;1.0. 
     Table 12 sets forth the operating magnification of each of the units at itsshort focal length position (M w ) and its long focal length position (M t ). In Examples 1-5 and 7-9, the first unit is at the object end ofthe lens system and thus its operating magnification is always zero. Accordingly, Table 12 does not contain entries for the first unit for these examples. 
     As is well known, the focal length of an optical system can be expressed asthe product of the focal length of the system&#39;s unit closest to the object and the product of the operating magnifications of the following units. Accordingly, for a variable focal length system, the unit which contributes most to the change in focal length of the system between its maximum and minimum focal lengths can be determined by forming the ratio of the operating magnifications of the units of the system at the maximum and minimum focal lengths of the system, i.e., M t  /M w . This ratio is set forth in Table 12 and shows that for the lens systems of the invention, it is the second unit which provides the majority of the changein focal length of the system between its maximum and minimum effective focal lengths. 
     Table 13 sets forth the focal lengths of the first, second, and third units(f 1 , f 2 , f 3 ) and compares those focal lengths to the minimumfocal length of the system (f min ). As can be seen in this table, for all of the examples, the first and second lens units are relatively weak in that their focal lengths are greater than 1.3 times the minimum focal length of the system. Similarly, the f 3  /f min  ratio is greater than 1.3 for all of the examples. 
     Table 14 sets forth the ratios of the thicknesses (T 1 , T 2 , T 3 , T 4 , and T 5 ) of the various lens elements of Examples 1-9 to f min . As shown in this table, all of the examples have at least one lens element for which the ratio is greater than 0.5, two of theexamples (Examples 3 and 9) have two lens elements of this type, five of the examples (Examples 1, 2, 4, 6, and 8) have three such lens elements, and one example (Example 7) has four such elements. The use of thick lens elements in the lens systems of the invention is thus evident from Table 14. 
     Although specific embodiments of the invention have been described and illustrated, it is to be understood that a variety of modifications which do not depart from the scope and spirit of the invention will be evident to persons of ordinary skill in the art from the foregoing disclosure. Thefollowing claims are intended to cover the specific embodiments set forth herein as well as such modifications, variations, and equivalents. 
     
                                           TABLE 1__________________________________________________________________________SN.   RADIUS   THICKNESS          GLASS              CLR. AP.__________________________________________________________________________1a 10.6068   2.94249          SK5 8.782  2.8047   space 1    4.813  2.7212   3.09514          FK5 4.244ac   9.2271   space 2    2.885a 4.8690   2.53252          SK5 2.346  127.0755        2.69__________________________________________________________________________CONICS SURF. CONST. - k__________________________________________________________________________4 -1.0000E+00__________________________________________________________________________ZOOM THICKNESSESEFL   space 1  space 2__________________________________________________________________________3.8   6.123  0.0004.9   4.484  1.2006.5   2.736  2.026__________________________________________________________________________EVEN POLYNOMIAL ASPHERESSN  AD     AE    AF    AG     AH     AI__________________________________________________________________________1 1.5125E-04    6.0814E-06          1.3343E-07                -1.1696E-10                       -1.8823E-11                              0.0000E+004 9.1628E-03    1.4307E-03          3.3105E-04                1.5987E-04                       2.5426E-06                              7.5636E-065 -6.5629E-03    2.1341E-03          8.2481E-04                -3.0731E-04                       -2.7285E-04                              6.4932E-05__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 1FIELD: 32.0°  f/2.80STOP: 0.00 after surface 4. DIA: 1.8567__________________________________________________________________________EFL:   3.80557  FVD:     18.2149         ENP:            6.94365BFL:   3.52208  BRL:     14.6929         EXP:            -1.57966__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 2FIELD: 23.0°  f/2.80STOP: 1.20 after surface 4. DIA: 1.9723__________________________________________________________________________EFL:   4.89295  FVD:     18.1558         ENP:            7.42769BFL:   3.90117  BRL:     14.2547         EXP:            -1.57966__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 3FIELD: 19.0°  f/2.80STOP: 2.03 after surface 4. DIA: 2.3075__________________________________________________________________________EFL:   6.49324  FVD:     18.1529         ENP:            7.93326BFL:   4.82045  BRL:     13.3325         EXP:            -1.57966__________________________________________________________________________ 
    
     
                                           TABLE 2__________________________________________________________________________SN.   RADIUS   THICKNESS          GLASS               CLR. AP.__________________________________________________________________________1a 13.3243   4.38830          ACRYLIC               11.742a 2.5110   Space 1     4.833a 5.3905   4.12155          FC5  3.744  -3.9133   Space 2     2.625a 3.0405   3.81871          FC5  3.336a 3.4578           3.89__________________________________________________________________________ZOOM THICKNESSEFL   Space 1  Space 2__________________________________________________________________________ 2.75   4.398  0.4684.0   2.249  2.7975.5   0.644  3.998__________________________________________________________________________EVEN POLYNOMIAL ASPHERESSN  AD     AE     AF     AG     AH     AI__________________________________________________________________________1 1.4639E-03    2.6163E-05           -4.8682E-07                  -5.8626E-09                         7.8908E-11                                8.5932E-142 8.5350E-03    1.5387E-03           9.7529E-05                  -8.0871E-06                         -1.8211E-06                                7.8755E-073 1.9156E-03    -1.1891E-03           -8.9141E-04                  5.0152E-04                         -1.1451E-04                                9.0080E-065 -5.6232E-03    -2.0760E-03           2.4941E-04                  9.7952E-05                         5.5174E-06                                -7.5037E-066 -6.2186E-02    2.4896E-04           6.7076E-03                  -5.2346E-04                         -4.7997E-04                                7.1999E-05__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 1FIELD: 36.0°  f/1.70STOP: 0.00 after surface 4. DIA: 2.5333__________________________________________________________________________EFL:   2.75018   FVD:      20.0004          ENP:             9.81765BFL:   0.805822   BRL:      19.1946          EXP:             -2.14066__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 2FIELD: 26.5°  f/2.10STOP: 0.00 after surface 4. DIA: 2.5447__________________________________________________________________________EFL:   4.00022   FVD:      20.0005          ENP:             9.19297BFL:   0.625972   BRL:      19.3746          EXP:             -3.67391__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 3FIELD: 18.0°  f/2.50STOP: 0.00 after surface 4. DIA: 2.5489__________________________________________________________________________EFL:   5.49945   FVD:      20.0002          ENP:             8.56414BFL:   1.02967   BRL:      18.9706          EXP:             -4.67093__________________________________________________________________________ 
    
     
                                           TABLE 3__________________________________________________________________________SN.   RADIUS   THICKNESS          GLASS CLR. AP.__________________________________________________________________________1a 16.9962   2.50844          SK5   9.062  3.1866   space 1      5.303  2.8898   3.21633          FK5   4.544ac   7.1808   space 2      3.195a 3.2207   1.14834          SK5   2.976  -3.7108   1.44272          STYRENE                2.947a 6.5050            2.80__________________________________________________________________________CONICS SURF. CONST. - k__________________________________________________________________________4 -1.0000E+00__________________________________________________________________________ZOOM THICKNESSESEFL   space 1  space 2__________________________________________________________________________3.8   6.595  0.0004.9   4.885  1.0936.5   3.163  1.6907.0   2.763  1.630__________________________________________________________________________EVEN POLYNOMIAL ASPHERESSN  AD    AE     AF     AG     AH     AI__________________________________________________________________________1 7.7828E-05   1.1677E-05          -8.8761E-08                 -1.3523E-08                        4.3159E-10                               0.0000E+004 1.0506E-02   -8.6755E-04          1.3016E-03                 3.3806E-04                        -3.8492E-04                               8.8656E-055 3.1087E-04   -3.4019E-04          5.3088E-04                 2.4463E-05                        -1.3487E-04                               3.6458E-057 1.0152E-02   4.4352E-04          3.2070E-04                 1.6785E-04                        2.4794E-05                               -1.1762E-05__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 1FIELD: 36.0°  f/2.60STOP: 0.00 after surface 5. DIA: 2.2449__________________________________________________________________________EFL:   3.80511  FVD:     18.3342         ENP:            6.16736BFL:   3.42291  BRL:     14.9113         EXP:            -1.41523__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 2FIELD: 27.0°  f/2.80STOP: 0.00 after surface 5. DIA: 2.3083__________________________________________________________________________EFL:   4.89981  FVD:     18.2984         ENP:            6.45515BFL:   4.00483  BRL:     14.2935         EXP:            -1.41523__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 3FIELD: 23.0°  f/2.80STOP: 0.00 after surface 5. DIA: 2.8031__________________________________________________________________________EFL:   6.50269  FVD:     18.2978         ENP:            6.61304BFL:   5.12847  BRL:     13.1693         EXP:            -1.41523__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 4FIELD: 19.0°  f/2.80STOP: 0.00 after surface 5. DIA: 2.9893__________________________________________________________________________EFL:   6.99986  FVD:     18.2987         ENP:            6.51301BFL:   5.58981  BRL:     12.7089         EXP:            -1.41523__________________________________________________________________________ 
    
     
                                           TABLE 4__________________________________________________________________________SN.   RADIUS   THICKNESS          GLASS              CLR. AP.__________________________________________________________________________1a 10.6067   2.94248          SK5 8.782  2.8047   space 1    4.813  2.7400   3.99513          FCD1              4.284ac   8.6000   space 2    2.865a 5.2500   2.53200          SK5 2.346  diffractive   0.00100          ******              2.727  surface         2.72__________________________________________________________________________CONICS SURF. CONST. - k__________________________________________________________________________4 -1.0000E+00__________________________________________________________________________ZOOM THICKNESSESEFL   space 1  space 2__________________________________________________________________________3.8   6.123  0.0004.9   4.485  1.2226.5   2.736  1.988__________________________________________________________________________EVEN POLYNOMIAL ASPHERESSN  AD     AE    AF    AG     AH     AI__________________________________________________________________________1 1.5125E-04    6.0816E-06          1.3344E-07                -1.1696E-10                       -1.8824E-11                              0.0000E+004 9.1629E-03    1.4308E-03          3.3106E-04                1.5987E-04                       2.5427E-06                              7.5641E-065 -6.5630E-03    2.1341E-03          8.2484E-04                -3.0732E-04                       -2.7287E-04                              6.4936E-05__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 1FIELD: 32.0°  f/2.80STOP: 0.00 after surface 4. DIA: 1.8602__________________________________________________________________________EFL:   3.82615  FVD:     18.3068         ENP:            6.94170BFL:   3.61318  BRL:     14.6936         EXP:            -1.61675__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 2FIELD: 23.0°  f/2.80STOP: 1.22 after surface 4. DIA: 1.9765__________________________________________________________________________EFL:   4.91587  FVD:     18.2807         ENP:            7.44774BFL:   4.00305  BRL:     14.2776         EXP:            -1.61675__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 3FIELD: 19.0°  f/2.80STOP: 1.99 after surface 4. DIA: 2.3125__________________________________________________________________________EFL:   6.48543  FVD:     18.2817         ENP:            7.89910BFL:   4.98707  BRL:     13.2946         EXP:            -1.61675__________________________________________________________________________ 
    
     
                                           TABLE 5__________________________________________________________________________SN.   RADIUS   THICKNESS          GLASS              CLR. AP.__________________________________________________________________________1a 11.3121   0.92031          SK5 6.642a 2.5168   space 1    4.573  2.5779   2.73342          KF5 3.104ac   9.3302   space 2    2.465a 6.0273   1.00000          SK5 2.686  diffractive   0.02057          ******              2.717  surface         2.71__________________________________________________________________________CONICS SURF. CONST. - k__________________________________________________________________________4  -1.0000E+00__________________________________________________________________________ZOOM THICKNESSESEFL   space 1  space 2__________________________________________________________________________2.8   7.504  0.0633.5   5.926  1.3904.7   4.170  2.291__________________________________________________________________________EVEN POLYNOMIAL ASPHERESSN  AD     AE     AF     AG     AH     AI__________________________________________________________________________1 1.6978E-03    2.8210E-04           -3.7877E-05                  1.2685E-07                         1.1266E-07                                -2.2722E-092 7.7378E-04    -3.8418E-04           5.0744E-04                  -1.2590E-04                         4.5972E-06                                6.1899E-084 1.3014E-02    2.1291E-02           -6.3545E-02                  8.1041E-02                         -4.4352E-02                                8.8687E-035 -1.9676E-03    -5.8404E-03           1.0048E-02                  -8.2147E-03                         3.3279E-03                                -5.2434E-04__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 1FIELD: 36.0°  f/2.60STOP: 0.00 after surface 5. DIA: 1.9529__________________________________________________________________________EFL:   2.76018  FVD:     16.5538         ENP:            4.42462BFL:   4.31250  BRL:     12.2413         EXP:            -.699053__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 2FIELD: 27.0°  f/2.80STOP: 0.00 after surface 5. DIA: 2.1003__________________________________________________________________________EFL:   3.54444  FVD:     16.5542         ENP:            4.19785BFL:   4.56401  BRL:     11.9902         EXP:            -2.31176__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 3FIELD: 23.0°  f/2.80STOP: 0.00 after surface 5. DIA: 2.4543__________________________________________________________________________EFL:   4.70592  FVD:     16.5547         ENP:            3.87829BFL:   5.41942  BRL:     11.1353         EXP:            -3.77642__________________________________________________________________________ 
    
     
                                           TABLE 6__________________________________________________________________________SN.   RADIUS   THICKNESS          GLASS CLR. AP.__________________________________________________________________________1  12.7245   3.00000          ACRYLIC                11.102a 404.1860   space 1      9.193a -45.1943   2.57119          SK5   9.004  3.5966   space 2      5.355  3.1880   3.27368          FK5   3.806ac   6.8115   space 3      2.907a 3.4793   1.14834          SK5   3.068  -4.0125   1.52903          STYRENE                3.039a 10.9772           2.93__________________________________________________________________________CONICS SURF. CONST. - k__________________________________________________________________________6 -1.0000E+00__________________________________________________________________________ZOOM THICKNESSESEFL   space 1  space 2      space 3__________________________________________________________________________4.0   0.274  7.981      0.0385.5   1.305  5.580      0.7598.0   2.386  3.179      0.8969.0   3.297  2.727      0.104__________________________________________________________________________EVEN POLYNOMIAL ASPHERESSN  AD    AE     AF     AG     AH     AI__________________________________________________________________________2 6.1059E-05   2.9993E-06          -1.6302E-08                 -1.0399E-09                        -1.7818E-11                               4.5793E-133 2.4601E-04   9.2334E-06          -8.4630E-08                 -1.2976E-08                        -2.9683E-10                               2.3802E-116 8.3243E-03   -2.0301E-03          1.1581E-03                 3.7123E-04                        -3.7992E-04                               8.1376E-057 5.0383E-04   1.3227E-04          -2.5209E-05                 -1.8024E-05                        2.1934E-06                               5.0602E-069 7.7885E-03   4.4442E-04          1.1285E-04                 2.6862E-05                        -3.7025E-06                               -1.7560E-06__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 1FIELD: 29.0°  f/2.60STOP: 0.00 after surface 6. DIA: 2.2609__________________________________________________________________________EFL:   3.99978  FVD:     23.5006         ENP:            10.4532BFL:   3.68488  BRL:     19.8157         EXP:            -1.57165__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 2FIELD: 23.0°  f/2.80STOP: 0.00 after surface 6. DIA: 2.3814__________________________________________________________________________EFL:   5.50059  FVD:     23.4999         ENP:            11.9398BFL:   4.33332  BRL:     19.1666         EXP:            -2.23994__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 3FIELD: 15.0°  f/2.80STOP: 0.00 after surface 6. DIA: 2.7787__________________________________________________________________________EFL:   8.00048  FVD:     23.5004         ENP:            13.3951BFL:   5.51748  BRL:     17.9829         EXP:            -2.38151__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 4FIELD: 13.0°  f/2.80STOP: 0.00 after surface 6. DIA: 2.8669__________________________________________________________________________EFL:   9.00135  FVD:     23.4998         ENP:            15.3327BFL:   5.84972  BRL:     17.6500         EXP:            -1.62798__________________________________________________________________________ 
    
     
                                           TABLE 7__________________________________________________________________________SN.   RADIUS   THICKNESS          GLASS CLR. AP.__________________________________________________________________________1a 6.2798   3.81301          ACRYLIC                10.532a 2.3184   Space 1      4.623a -8.6346   2.28707          FK5   2.704a -2.5287   Space 2      3.045a 4.4628   1.42354          SF2   4.686  2.3232   3.76900          FK5   4.187a -2.4592           4.46__________________________________________________________________________EVEN POLYNOMIAL ASPHERESSN  AD     AE     AF     AG     AH     AI__________________________________________________________________________1 -1.2527E-03    -7.9555E-07           1.4713E-06                  5.5037E-08                         1.5157E-09                                -9.3093E-122 -1.2812E-02    -8.1660E-05           -2.8414E-04                  -1.1018E-05                         1.6584E-05                                6.2920E-063 -6.9214E-03    -1.1828E-02           -2.6848E-03                  1.3200E-03                         8.4427E-04                                -2.8703E-044 5.8279E-03    -5.1619E-03           -5.5055E-04                  7.3209E-04                         2.3819E-04                                -1.1639E-045 -2.1316E-03    6.1825E-04           9.9131E-07                  -4.8820E-06                         -1.5303E-06                                2.2678E-077 2.9516E-02    -1.6791E-03           -1.9826E-04                  3.9826E-05                         2.0340E-05                                -2.2356E-06__________________________________________________________________________ZOOM THICKNESSESEFL   Space 1  Space 2__________________________________________________________________________2.75   5.053  0.3235.50   0.450  4.926__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 1FIELD: 38.0°  f/1.70STOP: 1.14 after surface 3. DIA: 2.3232__________________________________________________________________________EFL:   2.75008  FVD:     18.0732         ENP:            8.64115BFL:   1.40448  BRL:     16.6687         EXP:            -47.9927__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 2FIELD: 18.0°  f/2.50STOP: 1.14 after surface 3. DIA: 2.1085__________________________________________________________________________EFL:   5.50013  FVD:     18.0731         ENP:            4.82781BFL:   1.40448  BRL:     16.6686         EXP:            8.17937__________________________________________________________________________ 
    
     
                                           TABLE 8__________________________________________________________________________SN.   RADIUS   THICKNESS          GLASS CLR. AP.__________________________________________________________________________1  8.4213   4.14796          POLYCARB                12.312ac   2.5363   Space 1      5.893a 6.4257   5.50000          ACRYLIC                4.764  -5.3740   Space 2      5.035a 4.9351   2.62000          ACRYLIC                4.596ac   -2.6931   0.02000      4.617ac   -2.4850   1.45000          POLYCARB                4.558a 14.9612           4.52__________________________________________________________________________CONICS SURF. CONST. - k__________________________________________________________________________2 -1.0000E+006 -1.0000E+007 -1.0000E+00__________________________________________________________________________EVEN POLYNOMIAL ASPHERESSN.   AD     AE     AF     AG     AH     AI__________________________________________________________________________2  4.7387E-03     2.0774E-04            4.0578E-05                   -1.7764E-06                          -2.9975E-07                                 6.5544E-083  -4.9014E-04     -7.3601E-05            -1.6738E-07                   -9.2270E-07                          -1.8249E-07                                 6.9122E-085  -1.6121E-03     8.8969E-05            -4.9125E-05                   -5.4489E-06                          1.2664E-07                                 -2.1226E-086  -1.7529E-03     4.6796E-05            3.3765E-05                   4.3332E-06                          7.0086E-08                                 2.8772E-087  1.7980E-03     2.3259E-04            1.4868E-05                   1.5478E-06                          6.0858E-07                                 5.8231E-088  4.7626E-03     -2.8658E-04            2.9452E-05                   1.0259E-05                          -7.7642E-08                                 -3.8091E-07__________________________________________________________________________ZOOM THICKNESSESEFL   Space 1  Space 2__________________________________________________________________________4.0   7.844  0.3848.0   2.847  5.380__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 1FIELD: 34.5°  f/1.80STOP: 3.63 after surface 3. DIA: 4.0816__________________________________________________________________________EFL:   3.99991  FVD:     25.0803         ENP:            9.45134BFL:   3.11468  BRL:     21.9656         EXP:            -3.57716__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 2FIELD: 18.9°  f/2.30STOP: 3.63 after surface 3. DIA: 4.6708__________________________________________________________________________EFL:   7.99984  FVD:     25.0803         ENP:            7.89693BFL:   3.11493  BRL:     21.9654         EXP:            -7.75983__________________________________________________________________________ 
    
     
                                           TABLE 9__________________________________________________________________________SN.   RADIUS   THICKNESS          GLASS CLR. AP.__________________________________________________________________________1a 15.7205   7.27585          STYRENE                18.382  3.2659   Space 1      6.433a 6.2738   4.20811          ACRYLIC                4.564a -5.3778   Space 2      4.445a 3.6080   1.44262          ACRYLIC                4.826a 5.4227   1.16042      5.087a -5.4227   1.44262          ACRYLIC                5.148a -3.6080           5.05__________________________________________________________________________EVEN POLYNOMIAL ASPHERESSN.   AD     AE     AF     AG     AH     AI__________________________________________________________________________1  1.0654E-04     -1.6347E-06            4.8346E-08                   -4.1311E-10                          -6.4586E-13                                 2.5285E-143  -1.6510E-03     2.2595E-04            -8.7853E-05                   3.8498E-06                          9.6269E-07                                 -7.2923E-084  -1.1892E-03     -1.9645E-04            1.1723E-04                   -9.3873E-06                          -2.5734E-06                                 2.9434E-075  -3.8633E-03     -4.5747E-04            2.0174E-05                   -3.2030E-06                          -1.0994E-06                                 -9.8583E-086  -1.4714E-03     -1.6908E-04            -7.8496E-05                   -6.8306E-06                          -2.5379E-07                                 1.0984E-077  -1.4714E-03     1.6908E-04            7.8496E-05                   6.8306E-06                          2.5379E-07                                 -1.0984E-078  3.8633E-03     4.5747E-04            -2.0174E-05                   3.2030E-06                          1.0994E-06                                 9.8583E-08__________________________________________________________________________ZOOM THICKNESSESEFL   Space 1  Space 2__________________________________________________________________________4.0   6.974  2.0418.0   2.269  6.746__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 1FIELD: 38.0°  f/1.80STOP: 1.73 after surface 4. DIA: 2.8883__________________________________________________________________________EFL:   4.00007  FVD:     26.3094         ENP:            12.6909BFL:   1.76484  BRL:     24.5446         EXP:            -4.73970__________________________________________________________________________SYSTEM FIRST ORDER PROPERTIES, POS 2FIELD: 18.0°  f/2.50STOP: 1.75 after surface 4. DIA: 3.3551__________________________________________________________________________EFL:   7.99927  FVD:     26.3093         ENP:            11.7544BFL:   1.76473  BRL:     24.5446         EXP:            -22.6580__________________________________________________________________________ 
    
     
                       TABLE 10______________________________________MATERIAL         N.sub.⊖                    V.sub.⊖______________________________________ACRYLIC          1.4935  57.3FK5              1.4891  70.2SK5              1.5914  61.0FC5              1.4891  70.2FCD1             1.4984  81.2POLYCARB         1.5901  29.6STYRENE          1.5949  30.7SF2              1.6522  33.6______________________________________ 
    
     
                       TABLE 11______________________________________Example  Φ.sub.U1         Φ.sub.U1S                Φ.sub.U1S /Φ.sub.U1                       φ.sub.U2                             Φ.sub.U2S                                  Φ.sub.U2S /Φ.sub.U2                                         Φ.sub.U3______________________________________1      -.133  -.211  1.59   .146  .179 1.23   .1182      -.138  -.197  1.43   .184  .091 0.49   .0783      -.141  -.185  1.31   .126  .169 1.34   .1194      -.133  -.211  1.59   .146  .182 1.25   .1135      -.175  -.235  1.34   .155  .189 1.22   .1116      -.181  -.165  0.91   .106  .153 1.44   .1307      -.092  -.213  2.32   .154  --   --     .2168      -.120  -.233  1.94   .143  .076 0.53   .0269      -.115  -.180  1.57   .150  .079 0.53   .096______________________________________ 
    
     
                                           TABLE 12__________________________________________________________________________UNIT 1          UNIT 2     UNIT 3EXAMPLE M.sub.w    M.sub.t       M.sub.t /M.sub.w           M.sub.w              M.sub.t                  M.sub.t /M.sub.w                      M.sub.w                         M.sub.t                            M.sub.t /M.sub.w__________________________________________________________________________1               -1.29              -3.62                  2.81                      .39                         .24                            .622               -.74              -1.53                  2.07                      .51                         .50                            .983               -1.88              -20.70                  11.01                      .28                         .048                            .174               -1.33              -3.86                  2.90                      .38                         .22                            .585               -1.08              -2.43                  2.25                      .45                         .34                            .766     -.32    -.39       1.22           -2.12              22.40                  -10.57                      .22                         -.039                            -.187               -.71              -1.42                  2.00                      .36                         .36                            1.008               -.70              -1.40                  2.00                      .33                         .33                            1.009               -.71              -1.42                  2.00                      .63                         .63                            1.00__________________________________________________________________________ 
    
     
                       TABLE 13______________________________________EXAMPLE f.sub.1 f.sub.2                  f.sub.3                       f.sub.min                            |f.sub.1 |/f.sub.min                                  f.sub.2 /f.sub.min                                        |f.sub.3 |/                                        f.sub.min______________________________________1       -7.50   6.83   8.47 3.80 1.97  1.80  2.222       -7.25   5.43   12.80                       2.75 2.64  1.97  4.653       -7.11   7.93   8.40 3.80 1.87  2.09  2.204       -7.50   6.86   8.85 3.82 1.96  1.80  2.315       -5.70   6.43   9.00 2.76 2.07  2.33  3.266       -5.52   9.45   7.69 4.00 1.38  2.36  1.927       -10.90  6.51   4.63 2.75 3.96  2.37  1.688       -8.33   7.01   38.46                       4.00 2.08  1.75  9.639       -8.66   6.66   10.40                       4.00 2.17  1.67  2.60______________________________________ 
    
     
                       TABLE 14______________________________________EXAMPLE T.sub.1 /f.sub.min            T.sub.2 /f.sub.min                     T.sub.3 /f.sub.min                            T.sub.4 /f.sub.min                                   T.sub.5 /min______________________________________1       .77      .81      .662       1.60     1.49     1.393       .66      .85      .30    .384       .77      .81      .665       .33      .99      .366       .75      .64      .82    .29    .387       1.38     .83      .52    1.378       1.04     1.37     .66    .369       1.82     1.05     .36    .36______________________________________