Abstract:
An endoscope relay optics design that reduces the number of air surfaces while maintaining high levels of correction. A lens assembly for incorporation into an optical transfer system (where two such assemblies define an optical transfer module for transferring an image between successive image planes) is of unitary construction. The assembly comprises five elements including a central rod-like element of high index material, a pair of negative elements of relatively low index, high dispersion material cemented to opposite ends of the central element, and a pair of positive end elements of high index, low dispersion material cemented to the negative elements. The powers of the elements are determined by requiring the Petzval sum to assume a desired low value, with index difference being the primary contributor to the correction. The two exposed surfaces are flat or mildly concave and include an aspheric component to correct spherical aberration.

Description:
CROSS REFERENCE TO RELATED CASES 
     This application is a continuation-in-part of copending U.S. Application, Ser. No. 191,926 filed May 9, 1988 now U.S. Pat. No. 4,946,267. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to relay optics, and more specifically to endoscope relay optics. 
     BACKGROUND OF THE INVENTION 
     U.S. Pat. No. 4,575,195, which is hereby incorporated by reference, discloses a series of endoscope relay optics characterized by the Petzval sum being corrected to a desired degree primarily by index difference, thereby avoiding any spaced high powered elements or sharply bent elements. Spherical aberration is corrected by providing aspheric surfaces on the exposed surfaces of negative plastic elements glued to positive glass elements. The design of the lenses discussed in the patent is very flexible and allows a high degree of correction so that the image quality at the eyepiece of the endoscope is high. 
     However, quality usually has its price, and the price in this case is a relatively large number of glass-air and plastic-air interfaces for most of the embodiments. Thus, while the lenses themselves are readily manufacturable in the sense of having relatively gentle surfaces, the cost of coating the large number of interfaces can be considerable. 
     SUMMARY OF THE INVENTION 
     The present invention provides an endoscope relay optics design that reduces the number of air surfaces while maintaining substantially the levels of correction that characterize the prior art endoscope optics referred to above. 
     A lens assembly for incorporation into an optical transfer system (where two such assemblies define an optical transfer module for transferring an image between successive image planes) is of unitary construction. For one set of examples, the assembly comprises five elements including a central rod-like element of high index, low dispersion material (typically having convex or flat surfaces), a pair of negative elements of relatively low index, high dispersion material cemented to opposite ends of the central element, and a pair of positive end elements of high index, low dispersion material cemented to the negative elements. The powers of the elements are determined by requiring the Petzval sum to assume a desired low value, with index difference being the primary contribution to the correction. The lenses are of symmetric configuration to correct coma, distortion, and lateral color, and the dispersions of the material are choses to correct chromatic aberration. 
     In some examples, the two exposed surfaces are flat (but not abutting adjacent assemblies) or mildly curved and include an aspheric component to correct spherical aberration. In other examples, the exposed surfaces do not include aspheric components. Rather, aspherics are located along the interfaces between the positive end elements, and their abutting negative elements. In a limiting case, where the end surfaces are flat, they abut the flat end surfaces of the adjacent lens assemblies, whereupon the flat faces can be cemented, or adjacent end elements can be made unitary. In a further limiting case, the negative elements and the central element can be formed of the same material, and can thus be unitary. 
     The present invention thus achieves a high level of optical correction and improved manufacturability due to the absence of steep curves and the small number of air interfaces. 
     A further understanding of the nature and advantages of the present invention may be realized by reference to the remaining portions of the specification and the attached drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is an optical schematic of an endoscope showing transfer assemblies; 
     FIGS. 2A-L are optical schematics of various examples of five-element transfer assemblies according to the present invention; 
     FIG. 3 is an optical schematic of a limiting case of the assembly of FIG. 2L; 
     FIGS. 4A-C are optical schematics of other limiting cases; and 
     FIG. 5 is an optical schematic of a paired doublet assembly. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1 is an optical schematic of an endoscope 5 in which the relay optics of the present invention may be incorporated. The system comprises an objective 10 for forming an image in a first image plane 12, a relay system 15 for transmitting an image in plane 12 to a second image plane 17, and an eyepiece 18 for viewing the transmitted image. Objective 10 and transfer system 15 occupy a relatively small diameter barrel which is typically surrounded by an annular fiberoptics bundle. A typical diameter of the lenses is about 2.5 mm. 
     In use, the endoscope is inserted within a body cavity or the like by a physician for viewing of internal body regions. Objective 10 forms an image of the region to be viewed at first image plane 12, which image is transmitted by relay system 15 to second image plane 17 proximate eyepiece 18 for direct viewing by the physician or communication to a television camera. In some of the examples to be discussed below, relay system 15 comprises a plurality of cemented five-element assemblies 20. Assemblies 20 are arranged in pairs, with each pair providing a transfer module (i.e. a module which transfers an image from one plane at the front of the module to a second plane at the rear of the module). In certain limiting cases, the entire relay system can be a single cemented assembly. 
     FIGS. 2A-L are optical schematics of various examples of assemblies 20 illustrating the detailed design and construction thereof. A portion of a neighboring assembly is shown in phantom. Assemblies 20 are preferably identical and symmetric from end to end. Each assembly 20 includes a central rod-like element 22, first and second negative elements 25 separated by and cemented to central element 22, and first and second positive end elements 27 separated by the central and negative elements and cemented to the negative elements. 
     The geometric characteristics of assembly 20 are defined by an entrance pupil plane 30a, a front surface 30b, a first cemented surface 30c, a second cemented surface 30d, a third cemented surface 30e, a fourth cemented surface 30f, a rear surface 30g, and an image plane 30h. It will be appreciated that entrance pupil plane 30a and image plane 30h would properly be referred to as an image plane and an exit pupil plane for the other assembly in the module. 
     The geometrical and optical parameters for the examples of FIGS. 2A-L are set forth in Appendices 1A-L, and utilize the nomenclature wherein surfaces designated A-H correspond to plane 30a, surfaces 30b-g, and plane 30h. Units are in millimeters, it being understood that the actual lenses are much smaller. Although the values in the appendices provide an assembly length of about 200 mm, and a diameter of 30-35 mm, the actual lenses would be on the order of 10-15 times smaller. 
     For the examples of FIGS. 2A-K, each of front and rear surfaces 30b and 30g has an aspheric component. For the assembly of FIG. 2L, each of first and fourth cemented surfaces 30c and 30f has an aspheric component. The aspheric components in both instances are characterized by the conic constant k (equal to minus the square of the eccentricity) and aspheric coefficients AD, AE, AF, and AG. For a surface having a base radius R (curvature c=1/R) and tangent to the x-y plane at the origin, the distance z from the x-y plane of a point (x,y) on the surface is given by the following equation: ##EQU1## where ρ 2  =x 2  +y 2 . 
     Table 1 summarizes the general configuration of the elements of the assemblies of FIGS. 2A-L. The element surfaces that are formed with aspherics are denoted by asterisks. 
     The general method of designing five-element assembly 20 may be outlined as follows. First, with the general configuration in mind, reasonable indices of refraction are determined from a choice of suitable materials. For example, the assembly of FIG. 2A has negative elements 25 are formed of a flint glass having a relatively low index of refraction and high dispersion. End elements 27 are formed of a crown glass having low dispersion and high index. Central element 22 is preferably also formed of a crown glass having a high index and low dispersion. As the optical power of the central element is modest, this preference is not strong. The central element provides strength for the cemented assembly. 
     Having determined the indices of refraction, and further imposing the requirement that the assembly be symmetric, the powers of the individual elements are determined by requiring the Petzval sum to be reduced to a predetermined desired level and further requiring a given overall power. At this point, the choice of materials may be refined so that the dispersions can be chosen to correct chromatic aberration. Spherical aberration, coma, and astigmatism are not yet corrected. However, the provision of an aspheric surface on end elements 27 corrects spherical aberration, it being noted that with glass molding, it is no more difficult to provide an aspheric surface than a spherical surface. The stop location with respect to cemented surfaces 30c and 30d, together with the distribution between those surfaces is now chosen to correct astigmatism, while coma and distortion are corrected by utilizing a symmetric configuration with two identical axially aligned assemblies defining the transfer module. 
     The advantages of the design of assembly 20 may be seen. First, while each transfer module comprises ten elements, there are only three different elements, namely two identical central elements, four identical negative elements, and four identical end elements. Furthermore, as described above, the elements may be molded glass. Steep surfaces as are characteristic of sharply bent elements are avoided, and assembly of the overall system is simple. 
     The above examples also illustrate the flexibility of the design. The examples of FIGS. 2A and 2G have the lowest Petzval sum, at the expense of lower speed. Conversely, the example of FIG. 2I is considerably faster, but with a higher Petzval sum. Additionally, the examples of FIGS. 2E-F and 2J-L, which are constrained to have flat surfaces are generally slower with higher Petzval sums. The examples of FIGS. 2C and 2I illustrate the use of polycarbonate plastic rather than flint glass for the negative elements, while the example of FIG. 2D illustrates the use of very high index material for the end elements. Moreover, for the examples of FIGS. 2F and 2K, where there is no power at the surfaces of the central element, the central element can have high dispersion, thereby adding to the flexibility of the design. 
     FIG. 3 is an optical schematic of a transfer module 40 that represents a limiting case of the example of FIG. 2L. The lens parameters are set forth in Appendix 2. The example of FIG. 2L, like all the preceding examples with flat end faces, has the flat faces slightly spaced from the pupil and image planes. With slight modification, the flat end faces can be constrained to lie in the pupil and image planes so that adjacent end faces abut and can be cemented. Alternatively, the two abutting end elements can be formed as a unitary element. Transfer module 40 can be thought of as including a pair of assemblies, with adjacent assemblies sharing a common element. The first assembly includes a central rod-like element 42, negative elements 45, a positive plano-convex front element 47 and the front half of a convex-convex element 48. The geometry is characterized by a front surface 50a (which is also the first image surface), cemented surfaces 50b, 50c, 50d and 50e, and a pupil plane 50f which bisects convex element 48. 
     FIGS. 4A and 4B are optical schematics, each of an assembly 60 where the limiting case relative to the examples of FIGS. 2A-L is that the central element and the negative elements are the same material, and thus define a unitary negative rod-like element 62, to which are cemented positive end elements 67. The geometry is characterized by a pupil plane 70a, a front surface 70b (slightly concave in FIG. 4A and flat in FIG. 4B), cemented surfaces 70c and 70d, a rear surface 70e, and an image plane 70f. 
     FIG. 4C shows a transfer module 80 that represents the limiting case where the flat end faces coincide with the pupil and image planes so that adjacent positive elements merge into unitary elements. Assembly 80 includes a central rod-like element 82 to which are cemented a positive plano-convex front element 87 and the front half of a convex-convex element 88. The geometry is characterized by a flat front surface 80a (which is also the first image surface), cemented surfaces 80b and 80c, and a pupil plane which bisects convex element 88. The lens parameters for the assemblies of FIGS. 4A-C are set forth in Appendices 3A-C. 
     FIG. 5 shows a paired doublet transfer assembly 90. The optical parameters are set forth in Appendix 4. 
     In conclusion, it can be seen that the present invention provides design for relay optics that is characterized by high levels of correction, manufacturability, and flexibility. While the above gives a description of the preferred embodiments of the invention, various modifications, alternative constructions and equivalents may be employed without departing from the spirit of the invention. Therefore, the above description and illustrations should not be taken as limiting the scope of the invention which is defined by the appended claims. 
     
                                           TABLE 1__________________________________________________________________________FIG(s).  End Elements            Negative Elements                       Central Element__________________________________________________________________________2A-D,2G-I  concave*-convex            concave-concave                       convex2E     plano*-convex            concave-concave                       convex2F     plano*-convex            plano-concave                       flat2J     convex*-convex            concave-concave                       convex2K     concave*-convex            plano-concave                       flat2L     plano-convex*            concave*-concave                       convex__________________________________________________________________________ 
    
     
         __________________________________________________________________________APPENDIX 1A(PETZVAL SUM = 0.22)__________________________________________________________________________SURFACE RADIUS THICKNESS                MEDIUM  INDEX   ABBE NO.__________________________________________________________________________A     --         1.000  AirB     -63.111         10.602 Schott LAF21                        1.792   47.23C     -15.873         5.506  Schott LF6                        1.570   42.56D      30.551        165.602 Schott LAF21                        1.792   47.23E     -30.551         5.506  Schott LF6                        1.570   42.56F      15.873         10.602 Schott LAF21                        1.792   47.23G      63.111         1.000  AirH     --__________________________________________________________________________ CONICSURF  CONSTANT        AD      AE      AF      AG__________________________________________________________________________B     1.516E + 01        -3.126E-06                -5.248E-09                        -1.507E-11                                0.000E + 00G     1.516E + 01         3.126E-06                 5.248E-09                         1.507E-11                                0.000E + 00__________________________________________________________________________BF    F/NBR  OID     T-MAG   REF OBJ HT                                REF AP HT__________________________________________________________________________1.008 4.00   399.643 -1.000  12.5    12.5__________________________________________________________________________WAVL NBR    1   2          3   4         5WAVELENGTH  0.5461           0.4800     0.6438                          0.0000    0.0000SPECTRAL WT 1.0000           1.0000     1.0000                          1.0000    1.0000__________________________________________________________________________ 
    
     
         __________________________________________________________________________APPENDIX 1B(PETZVAL SUM = 0.71)__________________________________________________________________________SURFACE RADIUS THICKNESS                MEDIUM   INDEX   ABBE NO.__________________________________________________________________________A     --         1.000  AirB      110.974         13.985 Schott LASFN30                         1.807   46.13C     -21.284         3.006  Schott LF7                         1.578   41.22D      37.398        164.099 Schott LAF21                         1.792   47.23E     -37.398         3.000  Schott LF7                         1.578   41.22F      21.284         13.985 Schott LASFN30                         1.807   46.13G      110.974         1.000  AirH     --__________________________________________________________________________ CONICSURF  CONSTANT        AD      AE       AF      AG__________________________________________________________________________B     1.849E + 01        -3.019E-06                -3.764E-09                         -6.490E-12                                 0.000E + 00G     1.849E + 01         3.019E-06                 3.764E-09                          6.490E-12                                 0.000E + 00__________________________________________________________________________BF    F/NBR  OID     T-MAG    REF OBJ HT                                 REF AP HT__________________________________________________________________________1.017 3.33   400.156 -1.000   15.0    15.0__________________________________________________________________________WAVL NBR    1   2          3   4          5WAVELENGTH  0.5461           0.4800     0.6438                          0.0000     0.0000SPECTRAL WT 1.0000           1.0000     1.0000                          1.0000     1.0000__________________________________________________________________________ 
    
     
         __________________________________________________________________________APPENDIX 1C(PETZVAL SUM = 0.80)__________________________________________________________________________SURFACE RADIUS THICKNESS                MEDIUM  INDEX   ABBE NO.__________________________________________________________________________A     --        1.000   AirB     -128.871         11.396 Schott LASF3                        1.813   40.36C      -21.742         4.000  Polycarbonate                        1.590   29.62D       46.858        167.394 Schott SF57                        1.855   23.64E      -46.858         4.000  Polycarbonate                        1.590   29.62F       21.742         11.396 Schott LASF3                        1.813   40.36G      128.872         1.000  AirH     --__________________________________________________________________________ CONICSURF  CONSTANT        AD      AE      AF      AG__________________________________________________________________________B     2.385E + 01        -2.563E-06                -2.859E-09                        -4.520E-12                                0.000E + 00C     2.385E + 01         2.563E-06                 2.859E-09                         4.520E-12                                0.000E + 00__________________________________________________________________________BF    F/NBR  OID     T-MAG   REF OBJ HT                                REF AP HT__________________________________________________________________________1.022 3.33   400.351 -1.000  15.0    15.0__________________________________________________________________________WAVL NBR    1   2          3   4         5WAVELENGTH  0.5461           0.4800     0.6438                          0.0000    0.0000SPECTRAL WT 1.0000           1.0000     1.0000                          1.0000    1.0000__________________________________________________________________________ 
    
     
         __________________________________________________________________________APPENDIX 1D(PETZVAL SUM = 0.60)__________________________________________________________________________SURFACE RADIUS THICKNESS                MEDIUM   INDEX   ABBE NO.__________________________________________________________________________A     --         1.000  AirB     -109.876         14.212 Schott LASFN31                         1.886   40.76C      -23.049         3.000  Schott F5                         1.607   37.76D       35.968        163.663 Schott LAF21                         1.792   47.23E      -35.968         3.000  Schott F5                         1.607   37.76F       23.049         14.212 Schott LASFN31                         1.886   40.76G      109.876         1.000  AirH     --__________________________________________________________________________ CONICSURF  CONSTANT        AD      AE       AF      AG__________________________________________________________________________B     1.868E + 01        -2.400E-06                -2.307E-09                         -3.133E-12                                 0.000E + 00C     1.868E + 01         2.400E-06                 2.307E-09                          3.133E-12                                 0.000E + 00__________________________________________________________________________BF    F/NBR  OD      T-MAG    REF OBJ HT                                 REF AP HT__________________________________________________________________________1.006 3.33   400.180 -1.000   15.0    15.0__________________________________________________________________________WAVL NBR    1   2          3   4          5WAVELENGTH  0.5461           0.4800     0.6438                          0.0000     0.0000SPECTRAL WT 1.0000           1.0000     1.0000                          1.0000     1.0000__________________________________________________________________________ 
    
     
         __________________________________________________________________________APPENDIX 1E(PETZVAL SUM = 1.33)__________________________________________________________________________SURFACE RADIUS THICKNESS                MEDIUM  INDEX   ABBE NO.__________________________________________________________________________A     --         1.000  AirB     Flat         12.327 Schott LAFN24                        1.761   47.57C     -24.819         3.000  Schott LF7                        1.578   41.22D      79.030        166.990 Schott LAK10                        1.723   50.17E     -79.030         3.000  Schott LF7                        1.578   41.22F      24.819         12.327 Schott LAFN24                        1.761   47.57G     Flat         1.000  AirH     --__________________________________________________________________________ CONICSURF  CONSTANT        AD      AE      AF      AG__________________________________________________________________________B     0.000E + 00        -2.490E-06                -2.162E-09                        -1.722E-12                                0.000E + 00G     0.000E + 00         2.490E-06                 2.162E-09                         1.722E-12                                0.000E + 00__________________________________________________________________________BF    F/NBR  OID     T-MAG   REF OBJ HT                                REF AP HT__________________________________________________________________________1.0448 3.33   399.3333                -1.000  15.0    15.0__________________________________________________________________________WAVL NBR    1   2          3   4         5WAVELENGTH  0.5461           0.4800     0.6438                          0.0000    0.0000SPECTRAL WT 1.0000           1.0000     1.0000                          1.0000    1.0000__________________________________________________________________________ 
    
     
         __________________________________________________________________________APPENDIX 1F(PETZVAL SUM = 1.34)__________________________________________________________________________SURFACE RADIUS THICKNESS                MEDIUM   INDEX   ABBE NO.__________________________________________________________________________A     --         1.000  AirB     Flat         10.188 Schott LASFN30                         1.807   46.13C     -27.271         3.000  Schott TIF3                         1.551   41.89D     Flat        172.759 Schott SF6                         1.813   25.24E     Flat         3.000  Schott TIF3                         1.551   41.89F      27.271         10.188 Schott LASFN30                         1.807   46.13G     Flat         1.000  AirH     --__________________________________________________________________________ CONICSURF  CONSTANT        AD      AE       AF      AG__________________________________________________________________________B     0.000E + 00        -2.693E-06                -1.757E-09                         -9.843E-13                                 0.000E + 00G     0.000E + 00         2.693E-06                 1.757E-09                          9.843E-13                                 0.000E + 00__________________________________________________________________________BF    F/NBR  OID     T-MAG    REF OBJ HT                                 REF AP HT__________________________________________________________________________1.0588 3.33   402.3318                -1.000   15.0    15.0__________________________________________________________________________WAVL NBR    1   2          3   4          5WAVELENGTH  0.5461           0.4800     0.6438                          0.0000     0.0000SPECTRAL WT 1.0000           1.0000     1.0000                          1.0000     1.0000__________________________________________________________________________ 
    
     
         __________________________________________________________________________APPENDIX 1G(PETZVAL SUM = 0.23)__________________________________________________________________________SURFACE RADIUS THICKNESS                MEDIUM  INDEX   ABBE NO.__________________________________________________________________________A     --         2.000  AirB     -65.414         11.211 Schott LAF21                        1.792   47.23C     -15.949         3.000  Schott LF7                        1.578   41.22D      28.884        167.568 Schott LAF25                        1.789   41.04E     -28.884         3.000  Schott LF7                        1.579   41.22F      15.949         11.211 Schott LAF21                        1.792   47.23G      65.414         2.000  AirH     --__________________________________________________________________________ CONICSURF  CONSTANT        AD      AE      AF      AG__________________________________________________________________________B     1.687E + 01        -2.983E-06                -4.188E-09                        -7.958E-12                                0.000E + 00G     1.687E + 01         2.982E-06                 4.188E-09                         7.958E-12                                0.000E + 00__________________________________________________________________________BF    F/NBR  OID     T-MAG   REF OBJ HT                                REF AP HT__________________________________________________________________________2.003 4.00   400     -1.000  10.2    10.2__________________________________________________________________________WAVL NBR    1   2          3   4         5WAVELENGTH  0.5461           0.4800     0.6438                          0.0000    0.0000SPECTRAL WT 1.0000           1.0000     1.0000                          1.0000    1.0000__________________________________________________________________________ 
    
     
         __________________________________________________________________________APPENDIX 1H(PETZVAL SUM = 0.23)__________________________________________________________________________SURFACE RADIUS THICKNESS                MEDIUM   INDEX   ABBE NO.__________________________________________________________________________A     --         1.000  AirB     -117.681         14.879 Schott LASFN30                         1.807   46.13C      -22.026         3.000  Schott LF7                         1.578   41.22D       37.521        162.605 Schott LAF21                         1.792   47.23E      -37.521         3.000  Schott LF7                         1.578   41.22F       22.026         14.879 Schott LASFN30                         1.807G      117.681         1.000  AirH     --__________________________________________________________________________ CONICSURF  CONSTANT        AD      AE       AF      AG__________________________________________________________________________B     2.453E + 01        -2.427E-06                -2.820E-09                         -4.759E-12                                 0.000E + 00G     2.453E + 01         2.427E-06                 2.820E-09                          4.759E-12                                 0.000E + 00__________________________________________________________________________BF    F/NBR  OID     T-MAG    REF OBJ HT                                 REF AP HT__________________________________________________________________________1.000 2.78   400     -1.000   15.05   15.05__________________________________________________________________________WAVL NBR    1   2          3   4          5WAVELENGTH  0.5461           0.4800     0.6438                          0.0000     0.0000SPECTRAL WT 1.0000           1.0000     1.0000                          1.0000     1.0000__________________________________________________________________________ 
    
     
         __________________________________________________________________________APPENDIX 1I(PETZVAL SUM = 0.77)__________________________________________________________________________SURFACE RADIUS THICKNESS                MEDIUM   INDEX   ABBE NO.__________________________________________________________________________A     --         2.000  AirB     -125.497         15.740 Schott LASF3                         1.813   40.36C      -22.623         4.000  Polycarbonate                         1.590   29.62D       43.034        157.900 Schott SF57                         1.855   23.64E      -43.034         4.000  Polycarbonate                         1.590   29.62F       22.623        15.740  Schott LASF3                         1.813   40.36G      125.497         2.000  AirH     --__________________________________________________________________________ CONICSURF  CONSTANT        AD      AE       AF      AG__________________________________________________________________________B     3.323E + 01        -1.722E-06                -1.307E-09                         -1.208E-12                                 0.000E + 00G     3.323E + 01         2.722E-06                 1.307E-09                          1.208E-12                                 0.000E + 00__________________________________________________________________________BF    F/NBR  OID     T-MAG    REF OBJ HT                                 REF AP HT__________________________________________________________________________2.000 2.27   400     -1.000   17.3    17.3__________________________________________________________________________WAVL NBR    1   2          3   4          5WAVELENGTH  0.5461           0.4800     0.6438                          0.0000     0.0000SPECTRAL WT 1.0000           l 0000     l 0000                          1.0000     1.0000__________________________________________________________________________ 
    
     
                                           APPENDIX 1J__________________________________________________________________________ (PETZVAL SUM = 1.22)__________________________________________________________________________SURFACE  RADIUS THICKNESS                   MEDIUM  INDEX   ABBE NO.__________________________________________________________________________A        --           1.000   AirB        885.300           9.615   Schott LAFN24                           1.761   47.57C        -25.732           3.000   Schott LLF1                           1.551   45.47D        31.395           173.016 Schott BK7                           1.519   63.96E        -31.395           3.000   Schott LLF1                           1.551   45.47F        25.732           9.615   Schott LAFN24                           1.761   47.57G        -885.300           1.000   AirH        --__________________________________________________________________________    CONICSURF     CONSTANT           AD      AE      AF      AG__________________________________________________________________________B        0.000E + 00           -2.648E - 06                   -2.041E - 09                           -1.831E - 12                                   0.000E + 00G        0.000E + 00            2.648E - 06                    2.041E - 09                            1.831E - 12                                   0.000E + 00__________________________________________________________________________BF       F/NBR  OID     T-MAG   REF OBJ HT                                   REF AP HT__________________________________________________________________________1.000    4.00   400     -1.000  15.2    15.2__________________________________________________________________________WAVL NBR 1      2       3       4       5__________________________________________________________________________WAVELENGTH    0.5461 0.4800  0.6438  0.0000  0.0000SPECTRAL WT    1.0000 1.0000  1.0000  1.0000  1.0000__________________________________________________________________________ 
    
     
                                           APPENDIX 1K__________________________________________________________________________ (PETZVAL SUM = 1.29)__________________________________________________________________________SURFACE  RADIUS THICKNESS                   MEDIUM   INDEX   ABBE NO.__________________________________________________________________________A        --           1.000   AirB        -2053.907           9.025   Schott LASFN30                            1.807   46.13C        -24.212           3.046   Schott LF6                            1.570   42.56D        flat           174.460 Schott SF6                            1.813   25.24E        flat           3.046   Schott LF6                            1.570   42.56F        24.212           9.025   Schott LASFN30                            1.807   46.13G        2053.907           1.000   AirH        --__________________________________________________________________________    CONICSURF     CONSTANT           AD      AE       AF      AG__________________________________________________________________________B        0.000E + 00           -3.396E - 06                   -2.846E - 09                            -2.902E - 12                                    0.000E + 00G        0.000E + 00            3.396E - 06                    2.846E - 09                             2.902E - 12                                    0.000E + 00__________________________________________________________________________BF       F/NBR  OID     T-MAG    REF OBJ HT                                    REF AP HT__________________________________________________________________________1.000    3.33   400     -1.000   15.3    15.3__________________________________________________________________________WAVL NBR 1      2       3        4       5__________________________________________________________________________WAVELENGTH    0.5461 0.4800  0.6438   0.0000  0.0000SPECTRAL WT    1.0000 1.0000  1.0000   1.0000  1.0000__________________________________________________________________________ 
    
     
                                           APPENDIX 1L__________________________________________________________________________ (PETZVAL SUM = 1.32)__________________________________________________________________________SURFACE  RADIUS  THICKNESS                    MEDIUM  INDEX   ABBE NO.__________________________________________________________________________A        --            1.000   AirB        flat            12.331  Schott LAFN24                            1.761   47.57C        -23.080            3.000   Schott LF7                            1.578   41.22D        117.954            167.765 Schott LAK10                            1.723   50.17E        -117.954            3.000   Schott LF7                            1.578   41.22F        23.081            12.331  Schott LAFN24                            1.761   47.57G        flat            1.000   AirH        --__________________________________________________________________________    CONICSURF     CONSTANT            AD      AE      AF      AG__________________________________________________________________________C        -5.747E + 00             6.992E - 06                     1.247E - 09                            0.000E - 12                                    0.000E + 00F        -5.747E + 00            -6.992E - 06                    -1.247E - 09                            0.000E - 12                                    0.000E + 00__________________________________________________________________________BF       F/NBR   OID     T-MAG   REF OBJ HT                                    REF AP HT__________________________________________________________________________1.000    3.33    400     -1.000  15.5    15.5__________________________________________________________________________WAVL NBR 1       2       3       4       5__________________________________________________________________________WAVELENGTH    0.5461  0.4800  0.6438  0.0000  0.0000SPECTRAL WT    1.0000  1.0000  1.0000  1.0000  1.0000__________________________________________________________________________ 
    
     
                                           APPENDIX 2__________________________________________________________________________ (PETZVAL SUM = 1.33)__________________________________________________________________________SURFACE  RADIUS  THICKNESS                    MEDIUM  INDEX   ABBE NO.__________________________________________________________________________A        flat            14.312  Schott LAFN24                            1.761   47.57B        -23.358            3.000   Schott LF7                            1.578   41.22C        102.675            165.773 Schott LAK10                            1.723   50.17D        -102.675            3.000   Schott LF7                            1.578   41.22E        23.358            14.312  Schott LAFN24                            1.761   47.56F        --__________________________________________________________________________    CONICSURF     CONSTANT            AD      AE      AF      AG__________________________________________________________________________B        -5.748E + 00             6.755E - 06                     1.104E - 09                            0.000E - 12                                    0.000E + 00E        -5.748E + 00            -6.755E - 06                    -1.104E - 09                            0.000E - 12                                    0.000E + 00__________________________________________________________________________BF       F/NBR   OID     T-MAG   REF OBJ HT                                    REF AP HT__________________________________________________________________________0.000    3.33    400     -1.000  15.16   15.16__________________________________________________________________________WAVL NBR 1       2       3       4       5__________________________________________________________________________WAVELENGTH    0.5461  0.4800  0.6438  0.0000  0.0000SPECTRAL WT    1.0000  1.0000  1.0000  1.0000  1.0000__________________________________________________________________________ 
    
     
                                           APPENDIX 3A__________________________________________________________________________ (PETZVAL SUM = 1.19)__________________________________________________________________________SURFACE  RADIUS THICKNESS                   MEDIUM  INDEX   ABBE NO.__________________________________________________________________________A        --           1.000   AirB        -55947           10.692  Schott LAFN28                           1.777   49.33C        -24.770           177.057 Schott LF6                           1.570   42.56D        24.770           10.692  Schott LAFN28                           1.777   49.33E        55947           1.000   AirF        --__________________________________________________________________________    CONICSURF     CONSTANT           AD      AE      AF      AG__________________________________________________________________________B        0.000E + 00           -2.814E - 06                   -2.353E - 09                           -2.578E - 12                                   0.000E + 00E        0.000E + 00            2.814E - 06                    2.353E - 09                            2.578E - 12                                   0.000E + 00__________________________________________________________________________BF       F/NBR  OID     T-MAG   REF OBJ HT                                   REF AP HT__________________________________________________________________________1.000    3.57   400     -1.000  16.27   16.27__________________________________________________________________________WAVL NBR 1      2       3       4       5__________________________________________________________________________WAVELENGTH    0.5461 0.4800  0.6438  0.0000  0.0000SPECTRAL WT    1.0000 1.0000  1.0000  1.0000  1.0000__________________________________________________________________________ 
    
     
                                           APPENDIX 3B__________________________________________________________________________ (PETZVAL SUM = 1.18)__________________________________________________________________________SURFACE  RADIUS  THICKNESS                    MEDIUM   INDEX   ABBE NO.__________________________________________________________________________A        --            1.000   AirB        Flat            12.833  Schott LASFN30                             1.807   46.13C        -24.328            166.930 Schott F8                             1.599   38.91D        24.328            12.833  Schott LASFN30                             1.807   46.13E        Flat            1.000   AirH        --__________________________________________________________________________    CONICSURF     CONSTANT            AD      AE       AF      AG__________________________________________________________________________B        -6.183E + 01             5.836E - 06                     5.973E - 09                             0.00E - 12                                     0.000E + 00G        -6.183E + 01            -5.836E - 06                    -5.973E - 09                             0.00E - 00                                     0.000E + 00__________________________________________________________________________BF       F/NBR   OID     T-MAG    REF OBJ HT                                     REF AP HT__________________________________________________________________________1.000    3.33    400     -1.000   16.80   16.80__________________________________________________________________________WAVL NBR 1       2       3        4       5__________________________________________________________________________WAVELENGTH    0.5461  0.4800  0.6438   0.0000  0.0000SPECTRAL WT    1.0000  1.0000  1.0000   1.0000  1.0000__________________________________________________________________________ 
    
     
                                           APPENDIX 3C__________________________________________________________________________ (PETZVAL SUM = 1.19)__________________________________________________________________________SURFACE  RADIUS  THICKNESS                    MEDIUM    INDEX   ABBE NO.__________________________________________________________________________A        flat            14.597  Schott LASFN320                              1.807   46.13B        -24.138            171.710 Schott F8 1.599   38.91C        24.138            14.597  Schott LASFN30                              1.807   46.13D        flat__________________________________________________________________________    CONICSURF     CONSTANT            AD      AE        AF      AG__________________________________________________________________________B        -6.450E + 00             5.718E - 06                     4.678E - 10                              0.000E - 00                                      0.000E + 00C        -6.450E + 00            -5.718E - 06                    -4.678E - 10                              0.000E - 00                                      0.000E + 00__________________________________________________________________________BF       F/NBR   OID     T-MAG     REF OBJ HT                                      REF AP HT__________________________________________________________________________0.000    3.33    400     -1.000    16.52   16.52__________________________________________________________________________WAVL NBR 1       2       3         4       5__________________________________________________________________________WAVELENGTH    0.5461  0.4800  0.6438    0.0000  0.0000SPECTRAL WT    1.0000  1.0000  1.0000    1.0000  1.0000__________________________________________________________________________ 
    
     
                                           APPENDIX 4__________________________________________________________________________ (PETZVAL SUM = -0.28)__________________________________________________________________________SURFACE  RADIUS THICKNESS                   MEDIUM  INDEX   ABBE NO.__________________________________________________________________________A        --           0.600   AirB        142.090           142.090 Schott LASFN31                           1.886   40.76C        -27.780           2.874   Schott TIFN5                           1.598   35.24D        50.246           181.032 AirE        -50.246           2.874   Schott TIFN5                           1.598   35.24F        27.780           6.000   Schott LASFN31                           1.886   35.24G        -142.090           0.600   AirH        --__________________________________________________________________________    CONICSURF     CONSTANT           AD      AE      AF      AG__________________________________________________________________________B        0.000E + 00           -3.395E - 06                   -2.392E - 09                           -1.628E - 12                                   0.000E + 00G        0.000E + 00            3.395E - 06                    2.392E - 09                            1.628E - 12                                   0.000E + 00__________________________________________________________________________BF       F/NBR  OID     T-MAG   REF OBJ HT                                   REF AP HT__________________________________________________________________________0.600    7.14   399.958 -1.000  14.53   14.53__________________________________________________________________________WAVL NBR 1      2       3       4       5__________________________________________________________________________WAVELENGTH    0.5461 0.4800  0.6438  0.0000  0.0000SPECTRAL WT    1.0000 1.0000  1.0000  1.0000  1.0000__________________________________________________________________________