Abstract:
An apparatus having double focuses and utilizing a chromatic aberration senses the positions observed in the direction perpendicular to a common optical axis of first and second objects separated from each other by a very small distance on the order of several microns to several tens of microns, such as the distance between a mask and a wafer in an X-ray exposure system. The apparatus is provided with a lens system for imaging the marks of the two objects in an identical plane by axial spherical visible light having two different wavelengths, and is also provided with a filter for cancelling blurring caused by chromatic aberration. The images of the respective marks are optically processed. Thus, the positional relationship observed in the direction perpendicular to a common optical axis of the two objects can be sensed by a single lens and thereby the small distance between the objects can be accurately set.

Description:
RELATED APPLICATION 
     This is a continuation-in-part of U.S. application Ser. No. 179,566 filed Apr. 8, 1988 now abandoned. 
    
    
     BACKGROUND OF THE INVENTION 
     This invention relates to an apparatus having double focuses and utilizing a chromatic aberration for accurately sensing the positions observed in the direction perpendicular to a common optical axis of first and second objects separated from each other by a very short distance. 
     When a single objective lens is used to view the alignment marks of two spaced objects such as a mask and wafer for the purpose of proximity exposure, the gap between the two objects must be made small in order to improve resolving power. In general, if the settable gap is on the order of 10 microns, resolution must be reduced, thus making it impossible to detect the clear image necessary for highly accurate alignment. 
     Recently, however, detection systems have been proposed in which alignment can be achieved with great precision upon setting a gap of sufficient size between a mask and wafer, e.g., a gap of 10 microns or more. Two examples of such systems can be mentioned. The first is a detecting optical system that relies upon a double focal point lens utilizing the principle of double refraction (see &#34;X-Ray Exposure Devices&#34; in Precision Machines, 1985, vol. 51, No. 12, pp. 34-38). The second is a detecting optical system using rhombic detection (see the specification of Japanese Patent Application Laid-Open No. 61-100930). 
     Both of these conventional systems make possible highly precise detection by obtaining a clear image, despite a gap size of 10 microns or more. However, since polarized light is employed in the first optical system, the amount of optical information taken in is reduced to a fraction, often a very small fraction. The result is very low resolving power. In the second optical system, the angle between the object plane and the optic axis is not a right angle. Consequently, the area whose image is formed is reduced depending upon the angle and is narrowed to a fraction of the real field of view. 
     Here a detailed explanation of the relationship between resolving power and gap is in order. The resolving power and focal depth of a single objective lens are defined by the following Rayleigh equations: 
     
         Resolving power =0.61 ×λ/NA                   (1) 
    
     
         Focal depth =λ/2n (1-cos α)                   (2) 
    
     where 
     λ: wavelength used, 
     NA: numerical aperture, 
     n : refractive index of medium, 
     λ: angular aperture. 
     It will be appreciated from Eqs. (1) and (2) that resolving power and focal depth are mutually contradictory in the sense that increasing one decreases the other. In other words, if an attempt is made to raise resolving power, focal depth is reduced. For example, letting NA =0.40, λ=436 nm, n =1 (air), we obtain a resolving power of 0.67 μm and a focal depth of 2.6 μm (range). If an attempt is made to observe a mask and wafer simultaneously at this resolving power, the gap required would be less than 2.6 μm. This is a value which is not feasible in view of mask flatness, wafer flatness, the flatness of a process layer formed on the upper surface of the wafer, and an error involved in measuring the gap. The smallest gap presently obtainable in view of the foregoing is about 10 μm. 
     In order to set a gap of 10 μm, the required focal depth would be 10 μm or more. Accordingly, from Eq. (1), resolving power would be less than 1.1 μm in such case. 
     Thus, in order to realize highly precise alignment, it is necessary that the alignment marks of the mask and wafer be sensed with greater clarity by raising the resolving power of the objective lens in the detecting optical system. On the other hand, the focal depth must be increased in order to set the gap between the mask and wafer to a usable range (no less than about 10 μm). It is obvious from Eqs. (1) and (2), however, that both of these requirements cannot be satisfied simultaneously. 
     SUMMARY OF THE INVENTION 
     Accordingly, an object of the present invention is to provide an apparatus for sensing the positions of two spaced objects, wherein it is possible to obtain a depth of focus greater than a settable gap between the two objects upon assuring a sufficient resolving power for, e.g., highly precise alignment, while resolving power and focal depth abide by the foregoing Rayleigh equations. 
     According to the present invention, the foregoing object is attained by providing an apparatus having double focuses and utilizing a chromatic aberration for sensing the relative positions observed in the direction perpendicular to a common optical axis of first and second objects separated from each other by a small distance in the direction of the optical axis, the apparatus comprising: 
     a lens system for imaging a mark each of the first and second objects being accompanied by chromatic aberrations due to said small distance with first and second sets of lights having respective different wavelengths; a relative arrangement of the first and second objects and an objective lens in such a manner that the image plane of said first object occupied by the light of the first set of wavelengths is formed in a plane identical to the image plane of said second object occupied by the light of the second set of wavelengths; a filter means having first and second filter elements for cancelling the lights of the first and second sets of wavelengths respectively so as to cancel the image blur of the second object formed on the image plane of the second object due to the chromatic aberration caused by the light of the first set of wavelengths and the image blur of the first object formed on the image plane of the first object due to the chromatic aberration caused by the light of the second set of wavelengths. In particular, said chromatic aberration is an axial spherical chromatic aberration in the optical axis. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIGS. 1 through 3 are graphs illustrating the principle of the present invention; 
     FIG. 4 is a schematic view illustrating an example of alignment marks of a mask and wafer; 
     FIG. 5 is a schematic view illustrating how a superimposed mask and wafer appear on the screen of an image pick-up device; 
     FIG. 6 is a schematic view illustrating one example of a filter; 
     FIG. 7 is a schematic view illustrating a lens system embodying the present invention; and 
     FIGS. 8 through 10 are graphs showing aberration curves in accordance with first through third embodiments of the invention. 
    
    
     DETAILED DESCRIPTION 
     The principle of the invention will be explained before proceeding with a description of preferred embodiments. 
     In an actual optical system, an objective lens is accompanied by other lenses such as an eyepiece and relay lens to provide an image having a certain magnification. In order to explain the basic approach of the present invention, however, the discussion will be limited solely to a single objective lens. In addition, to simplify the discussion of the optical properties, a thin lens system will be dealt with and only paraxial formulae for a thin lens will be used. Initial Conditions: 
     (1) wavelengths used: α, β(nm), where α&lt;β 
     (2) objective lens: N.A. =NA; magnification =10×; diameter d; angular aperture θ; refractive indices for wavelengths 60 , β=R.sub.α, R.sub.β, respectively; focal points for wavelengths α, β=F.sub.α, F.sub.β, respectively 
     (3) distance (object distance) from principal point A to object =S 
     (4) distance (image distance) from principal point A to image plane =S&#34;.sub.α (for wavelength α); distance (image distance) from principal point A to image plane =S&#34;.sub.β (for wavelength β). 
     FIG. 1 illustrates the initial settings for the aforementioned conditions (1) through (4). 
     From conditions (1) and (2), the resolving powers and focal depths are as shown in Table 1, in accordance with the aforementioned Raleigh equations. 
     
                       TABLE 1______________________________________Wavelength    α     β______________________________________Resolving power         0.61 × α/NA                     0.61 × β/NAFocal depth   α/2(1 - cos α)                     β/2(1 - cos α)______________________________________ 
    
     The lens position is referred to as the principal point, and this position is shown at A on the optical axis. 
     The object is situated on the left side of the lens at a position M located at a distance S from the principal point. Images for the respective wavelengths can be formed at points B and C on the side of the lens opposite the object. 
     The refractive index of the objective lens differs depending upon the wavelength; the shorter the wavelength, the higher the refractive index and, hence, the closer the focal point is to the lens. Accordingly, since the wavelengths are related by α&lt;β, the image for wavelength α is formed at point B, and the image for wavelength β is formed at point C. Let S&#34;.sub.α, S&#34;.sub.β represent the distances of the respective images from the principal point. 
     Since the image planes are located at B and C in FIG. 1, let us consider forming the images in such a manner that the image planes occupy an identical arbitrary position on the optic axis. In order to simplify the development of the equations, it will be assumed that point C is moved to make it coincide with point B. 
     To bring point C into coincidence with point B, the position of the object should be moved leftward from M away from the principal point A, as is obvious from the arrangement shown in FIG. 1. FIG. 2 shows the result of such movement, with the new object position being designated M&#39;. 
     The distance δ covered by movement of the object from point M to point M&#39; in FIG. 2 is found. From Gauss&#39; theorem, we have ##EQU1## Solving this equation for δ gives us ##EQU2## Magnification m is expressed by a value satisfying the following equation: ##EQU3## 
     It is readily apparent from the foregoing that in order to make the imaging point C based on wavelength β coincide with the point B, the position of the object should be moved from M to M&#39; over a distance α. This movement of the object is accompanied by a change in magnification, with the magnification of the image for the object at M&#39; being mX. 
     Next, let us consider a case where objects are placed at both M and M&#39; and the images of the objects are formed at point B by simultaneously irradiating them with light of the two wavelengths α and β. 
     In order to facilitate a more detailed discussion of the invention, it will be assumed that a mask is placed at point M, a wafer at point M&#39;, and the picture plane of a TV camera at the imaging point B. This state can be realized by supplementing FIG. 2 with the images of the mask (at point M) and wafer (at point M&#39;) with regard to the wavelength α. The result is shown in FIG. 3. 
     FIG. 3 differs from FIGS. 1 and 2 in that a new point D appears on the left side of point B. This point is that at which the image of the wafer (point M&#39;) is formed for wavelength α. Letting Sd represent the distance of this point from the principal point A, we find Sd as follows: ##EQU4## Therefore, ##EQU5## 
     The foregoing demonstrates that the image planes corresponding to the mask (point M) can be obtained at points B and C, and that the image planes corresponding to the wafer (point M&#39;) can be obtained at points D and B. In other words, it will be understood that the image planes for the two objects, namely the mask and the wafer, will coincide at the point B in FIG. 3. It should be noted that whereas the images at point B are in focus, the images of the wafer and mask at the respective points D and C appear blurred due to axial spherical chromatic aberration. 
     What actually appears on the image pick-up device for the state shown in FIG. 3 will now be considered. 
     Examples of the alignment marks for a mask and wafer are as shown in FIG. 4, in which the alignment marks are imagined to be rectangular and the shorter side of the mask mark is assumed to be greater than the shorter side of the wafer mark. 
     With the mask and wafer of FIG. 4 superimposed, the patterns which appear on the picture tube screen along with blurring caused by axial spherical chromatic aberration are illustrated in FIG. 5. For the sake of convenience, the color associated with wavelength α is indicated by the solid lines, and the color associated with wavelength β is indicated by the broken lines. 
     The chromatic aberrations of magnification associated with the mask and wafer shall be denoted by Zm and Zw and are obtained by using the following equations: ##EQU6## where h represents the length of the short side of the rectangular marks. In actuality, the blurring expressed by Eqs. (6) and (7) is determined geometrically in FIG. 3. 
     A filter of the kind shown in FIG. 6 may be used to remove the blurred portions of FIG. 5. The filter illustrated in FIG. 6 is composed of two coated surfaces. One is a coated surface which passes only the light of wavelength α, while the other is a coated surface which passes only the light of wavelength β. The design of the filter is decided in accordance with the state of the patterns shown in FIG. 5, and the boundaries of the coated surfaces are situated intermediate those of the mask marks and wafer marks. 
     Accordingly, if FIGS. 5 and 6 are superimposed, it will be apparent that, as regards the wafer marks, the axial spherical chromatic aberration due to wavelength α is cut by the filter so that a focused, clear image can be seen by virtue of wavelength β. Similarly, with regard to the mask mark, blurring due to wavelength β is cut by the filter and a focused, clear image is obtained by virtue of wavelength α. The mask and wafer marks are thus imaged on the screen of the image pick-up device. The resolving power and depth of focus of each image abide by the Rayleigh equations (1) and (2), and it is possible for the gap between the marks to be set freely without being constrained by Eq. (1). 
     An example of actual calculation based on Eqs. (3) through (7) will now be set forth. 
     Initial Conditions: 
     (1) wavelengths used: α=436 nm; β=587 (nm) 
     (2) objective lens: NA =0.4; magnification n =10×; diameter d =10 mm; angular aperture =23.6; refractive indices R.sub.α =1.52669, R.sub.β =1.51472; glass material: BK7; focal points F.sub.α =12.5, F.sub.β =12.741 
     (3) S =13.75 
     (4) S&#34;.sub.α =137.5; S&#34;.sub.β =173.6146 
     
         ______________________________________Resolving Power and Depth of Focus       Resolving PowerWavelength (nm)       (μm)       Depth of Focus (μm)______________________________________436         0.66          2.7587         0.895         3.7______________________________________ 
    
     Magnification Error: 
     wafer image magnification=9.792× 
     mask image magnification=10× 
     Wafer-Mask Gap: δ=0.292 mm 
     Chromatic Difference of Magnification: 
     Mask: Zm =7.71 μm 
     Wafer: Zw =7.56 μm, where h =40 μm 
     Magnification error is a factor which must be taken into consideration in terms of processing the images picked up by a detecting system based on this chromatic difference of magnification. Since reduction takes place owing to the magnification of 9.792× with regard to the wafer in the calculations exemplified above, it is required that the scaling constant for the wafer be increased at a ratio of 10:9.792 for a mask magnification of 10×. As for the filter, design should conform to the shapes or positions of the alignment masks. 
     It should be noted that chromatic difference of magnification for two-colored light (blue and yellow) naturally occurs in the principal plane of the objective lens. However, since the amount of this chromatic difference of magnification does not have an appreciable effect upon the gist of the invention, the present discussion will proceed neglecting such aberration. 
     A specific embodiment of lens design will now be described. 
     The overall arrangement of a lens system is illustrated in FIG. 7, in which a relay lens, field lens and objective lens are used in combination. The most important lens is the objective lens which, in the illustrated embodiment, is basically designed based on the system described in the specification of Japanese Patent Publication No. 43-15237. The present lens system is designed so as to employ two types of light beams, namely a g line (wavelength: 435.84 nm) and e line (wavelength: 546.07 nm). 
     Embodiment 1 
     Object-to-Object Distance =Axial spherical Chromatic Aberration =40 μm 
     The objective lens specifications are shown in Table 2. 
     Data relating to lens curvature, center thickness, refractive index, glass material and stop for each of the lens system elements Nos. 1 through 17 are shown in Table 3. Also, the relationship between glass material and the refractive indices of the g and e lines are illustrated in Table 4. The Seidel&#39;s variable for the lens systems thus designed and arranged are indicated in Table 5. 
     It will be appreciated from the foregoing that these aberration values are very low and are fully corrected. 
     FIG. 8 illustrates the aberration curves. These curves also clearly show that the aberrations are well corrected. 
     
                       TABLE 2______________________________________Objective Lens Specifications______________________________________Total optical path diameter                 488.135Focal length          -1.830Rear focal point      -0.731Front focal point     275.496Entrance pupil        275.496Entrance diameter     1.464Entrance magnification                 -0.234Exit pupil            *****Exit magnification    *****Object distance       -1.000Magnification (reciprocal)                 -0.666660D-02Image distance        1.2202______________________________________ 
    
     
                       TABLE 3______________________________________Data for Embodiment 1Lens      Center    Refractive                            GlassNo.  curvature thickness index   material                                    Stop______________________________________1    0.000     273.6350                  0.002    21.133    1.2000    1.52621 BK7     0.003    -15.748   0.7000    1.72933 SF15    0.004    -35.884   35.2621                   0.005    29.857    1.0000    1.52621 BK7     0.006    -29.857   155.8808                  0.007    0.000     -1.3458                   3.138    12.174    2.5600    1.51989 K1      0.009    -8.533    1.2000    1.72944 LAK8    0.0010   -73.985   6.0800                    0.0011   16.084    2.1600    1.58490 BAF3    0.0012   -7.966    0.7440    1.75805 LAF8    0.0013   -20.060   0.4160                    0.0014   7.433     2.0000    1.80839 LASF01  0.0015   -33.638   4.8000    1.76190 SF10    0.0016   14.808    1.9387                    0.0017   0.000     -0.7185                   0.00______________________________________ 
    
     
                       TABLE 4______________________________________Relationship between glass materialand refractive index            Refractive index                  g-line   e-lineNo.    Glass material  (435.84) (546.07)______________________________________2      BK7             1.52621  1.518253      SF15            1.72933  1.704435      BK7             1.52621  1.518258      K1              1.51989  1.511739      LAK8            1.72944  1.7161511     LF1             1.59026  1.5762912     LAF8            1.75805  1.7394514     LASF01          1.80839  1.7901315     SF10            1.76190  1.73429______________________________________ 
    
     
                                           TABLE 5__________________________________________________________________________Seidel&#39;s variable in Embodiment 1                 Image                 surface    Surface     Comatic     curvature   Petzval    Aberra-     Aberra-           Astig-                 Aberra-                       Distor-                             Aberra-No. tion  tion  matism                 tion  tion  tion__________________________________________________________________________1   0.00000     0.00000           0.00000                 0.00000                       0.00000                             0.000002   -0.00020     0.00194           -0.01899                 0.04884                       0.47842                             0.029863   0.00050     0.00272           0.01489                 0.02383                       0.13042                             0.008944   0.00046     -0.00490           -0.05167                 -0.07318                       -0.77169                             -0.021515   0.00000     0.00009           -0.00362                 -0.02475                       -1.05363                             -0.021136   0.00000     0.00008           0.00247                 -0.01866                       0.57849                             -0.021137   0.00000     0.00000           0.00000                 0.00000                       0.00000                             0.000008   -0.34045     0.10352           -0.03148                 -0.08289                       0.02521                             -0.051429   0.86166     0.12558           0.01830                 0.03540                       0.00516                             -0.0171010  -0.04013     -0.03615           -0.03256                 -0.04299                       -0.03873                             -0.0104311  0.00226     -0.00388           0.00667                 -0.03532                       0.06071                             -0.0419912  0.48235     -0.07057           0.01032                 0.02460                       -0.00360                             0.0142813  -0.67360     -0.03619           -0.00194                 -0.04128                       -0.00222                             -0.0393314  0.02401     -0.04631           -0.08933                 -0.02072                       -0.03997                             -0.1100515  -0.07025     0.01118           -0.00178                 -0.00257                       -0.00041                             -0.0007916  -0.36922     -0.04973           -0.00670                 -0.04674                       -0.00630                             -0.0534417  0.00000     0.00000           0.00000                 0.00000                       0.00000                             0.00000SUM -0.12353     -0.00295           -0.00675                 -0.26064                       -0.54478                             -0.25389__________________________________________________________________________ *Three-dimensional variables when total system focal length is normalized to 1 mm. 
    
     Embodiment 2 
     Object-to-Object Distance=Axial spherical Chromatic Aberration=50 μm 
     The objective lens specifications are shown in Table 6. 
     Data relating to lens curvature, center thickness, refractive index, glass material and stop for each of the lens system elements Nos. 1 through 17 are shown in Table 7. The Seidel&#39;s variable for the lens systems thus designed and arranged are indicated in Table 8. 
     It will be appreciated from the foregoing that these aberration values are very low and are fully corrected. 
     FIG. 9 illustrates the aberration curves. These curves also show that the aberrations are well corrected. 
     
                       TABLE 6______________________________________Objective lens Specifications______________________________________Total optical path diameter                 487.722Focal length          -1.830Rear focal point      -0.731Front focal point     275.496Entrance pupil        275.496Entrance diameter     1.464Entrance magnification                 -0.235Exit pupil            *****Exit magnification    *****Object distance       -1.000Magnification (reciprocal)                 -0.666660D-02Image distance        1.1917______________________________________ 
    
     
                       TABLE 7______________________________________Data for Embodiment 2Lens      Center    Refractive                            GlassNo.  curvature thickness index   material                                    Stop______________________________________1    0.000     273.5390                  0.002    21.133    1.2000    1.52621 BK7     0.003    -15.748   0.7000    1.72933 SF15    0.004    -35.884   35.2621                   0.005    29.857    1.0000    1.52621 BK7     0.006    -29.857   155.4240                  0.007    0.000     -1.3015                   3.088    12.175    2.5600    1.51989 K1      0.009    -8.449    1.2000    1.72944 LAK8    0.0010   -69.688   6.0800                    0.0011   16.591    2.1600    1.59861 BAF3    0.0012   -7.842    0.7440    1.75805 LAF8    0.0013   -20.385   0.4160                    0.0014   7.434     2.0000    1.80839 LASF01  0.0015   -33.597   4.8000    1.76190 SF10    0.0016   14.455    1.9387                    0.0017   0.000     -0.7470                   0.00______________________________________ 
    
     
                                           TABLE 8__________________________________________________________________________Seidel&#39;s variable in Embodiment 2                 Image                 surface    Surface     Comatic     curvature   Petzval    Aberra-     Aberra-           Astig-                 Aberra-                       Distor-                             Aberra-No. tion  tion  matism                 tion  tion  tion__________________________________________________________________________1   0.00000     0.00000           0.00000                 0.00000                       0.00000                             0.000002   -0.00020     0.00194           -0.01904                 0.04889                       0.47953                             0.029853   0.00050     0.00271           0.01482                 0.02376                       0.12966                             0.008944   -0.00046     -0.00489           -0.05153                 -0.07304                       -0.76913                             -0.021515   0.00000     0.00009           -0.00362                 -0.02475                       -1.05301                             -0.021136   0.00000     0.00008           0.00247                 -0.01866                       0.57858                             -0.021137   0.00000     0.00000           0.00000                 0.00000                       0.00000                             0.000008   -0.33712     0.10348           -0.03176                 -0.08317                       0.02553                             -0.051419   0.87226     0.12550           0.01806                 0.03532                       0.00508                             -0.0172710  -0.04319     -0.03781           -0.03309                 -0.04416                       -0.03866                             -0.0110711  0.00225     -0.00470           0.00868                 -0.03262                       0.06017                             -0.0413012  0.45516     -0.06912           0.01050                 0.02373                       -0.00360                             0.0132413  -0.66730     -0.03585           -0.00193                 -0.04063                       -0.00218                             -0.0387014  0.02287     -0.04550           -0.09054                 -0.01949                       -0.03878                             -0.1100315  - 0.06960     0.01124           -0.00181                 -0.00261                       -0.00042                             -0.0007916  -0.36058     -0.04975           -0.00686                 -0.04788                       -0.00660                             -0.0547417  0.00000     0.00000           0.00000                 0.00000                       0.00000                             0.00000SUM -0.12514     -0.00291           -0.00459                 -0.25733                       -0.54223                             -0.25274__________________________________________________________________________ *Three-dimensional variables when total system focal length is normalized to 1 mm. 
    
     Embodiment 3 
     Object-to-Object Distance =Axial spherical Chromatic Aberration =60 μ m 
     The objective lens specifications are shown in Table 9. 
     Data relating to lens curvature, center thickness, refractive index, glass material and stop for each of the lens system elements Nos 1 through 17 are shown in Table 10. The Seidel&#39;s variable for the lens systems thus designed and arranged are indicated in Table 11. 
     It will be appreciated from the foregoing that these aberration values are very low and are fully corrected. 
     FIG. 10 illustrates the aberration curves. These curves also show that the aberrations are well corrected. 
     
                       TABLE 9______________________________________Objective Lens Specifications______________________________________Total optical path diameter                 488.294Focal length          -1.830Rear focal point      -0.660Front focal point     275.503Entrance pupil        275.503Entrance diameter     1.464Entrance magnification                 -0.234Exit pupil            *****Exit magnification    *****Object distance       -1.000Magnification (reciprocal)                 -0.666660D-02Image distance        1.2906______________________________________ 
    
     
                       TABLE 10______________________________________Data for Embodiment 3Lens      Center    Refractive                            GlassNo.  curvature thickness index   material                                    Stop______________________________________1    0.000     273.5390                  0.002    21.133    1.2000    1.52621 BK7     0.003    -15.748   0.7000    1.72933 SF15    0.004    -35.884   35.2621                   0.005    29.857    1.0000    1.52621 BK7     0.006    -29.857   156.0190                  0.007    0.000     -1.3244                   3.138    12.242    2.5600    1.51989 K1      0.009    -8.507    1.2000    1.72944 LAK8    0.0010   -69.688   6.0800                    0.0011   16.229    2.1600    1.59026 LF1     0.0012   -7.936    0.7440    1.75805 LAF8    0.0013   -20.134   0.4160                    0.0014   7.461     2.0000    1.80839 LASF01  0.0015   -33.556   4.8000    1.76190 SF10    0.0016   14.777    1.9387                    0.0017   0.000     -0.6481                   0.00______________________________________ 
    
     
                                           TABLE 11__________________________________________________________________________Seidel&#39;s variable in Embodiment 3                 Image                 surface    Surface     Comatic     curvature   Petzval    Aberra-     Aberra-           Astig-                 Aberra-                       Distor-                             Aberra-No. tion  tion  matism                 tion  tion  tion__________________________________________________________________________1   0.00000     0.00000           0.00000                 0.00000                       0.00000                             0.000002   -0.00020     0.00194           -0.01897                 0.04883                       0.47808                             0.029863   0.00050     0.00272           0.01492                 0.02386                       0.13065                             0.008944   -0.00046     -0.00490           -0.05172                 -0.07322                       -0.77246                             -0.021515   0.00000     0.00009           -0.00362                 -0.02475                       -1.05382                             -0.021136   0.00000     0.00008           0.00247                 -0.01866                       0.57847                             -0.021137   0.00000     0.00000           0.00000                 0.00000                       0.00000                             0.000008   -0.33667     0.10299           -0.03150                 -0.08264                       0.02528                             -0.051139   0.86881     0.12554           0.01814                 0.03529                       0.00510                             -0.0171510  -0.03240     -0.03149           -0.03060                 -0.03994                       -0.03882                             -0.0093411  0.00158     -0.00258           0.00422                 -0.03764                       0.06144                             -0.0418512  0.48553     -0.07137           0.01049                 0.02433                       -0.00358                             0.0138413  -0.68198     -0.03585           -0.00188                 -0.04107                       -0.00216                             -0.0391914  0.02626     -0.04793           -0.08748                 -0.02217                       -0.04046                             -0.1096515  - 0.07038     0.01081           -0.00166                 -0.00239                       -0.00037                             -0.0007316  -0.38561     -0.05233           -0.00710                 -0.04645                       -0.00630                             -0.0535517  0.00000     0.00000           0.00000                 0.00000                       0.00000                             0.00000SUM -0.12502     -0.00261           -0.00934                 -0.26139                       -0.54470                             -0.25205__________________________________________________________________________ *Three-dimensional variables when total system focal length is normalized to 1 mm.