Abstract:
The present invention relates to an optical ocular system having imaging optics that map an image generated in an object plane such that a user can perceive the same in an image plane, wherein the imaging optics comprise a first lens having negative refractive power, and a deflection element having positive refractive power, which is connected downstream of the first lens, effecting a folding of the optical path by means of a single reflection, wherein the first lens and the object plane form a first optical group, and a displacement unit is provided, which can change the distance between the first optical group and the displacement element for the correction of spherical ametropia of the user.

Description:
PRIORITY CLAIM 
     The present application is a National Phase entry of PCT Application No. PCT/EP2008/002487, filed Mar. 28, 2008, which claims priority from German Application Number 102007015278.9-51, filed Mar. 29, 2007, the disclosures of which are hereby incorporated by reference herein in their entirety. 
     BACKGROUND OF THE INVENTION 
     The present invention relates to an optical ocular system having an imaging optic, which images an image generated in an object plane so that a user can perceive it in an image plane, the imaging optic comprising a first lens having negative refractive power and a deflection element downstream from the first lens having positive refractive power, which causes folding of the beam path using a single reflection. 
     Such an optical ocular system is described in, for example, EP 1 513 000 A1. The ocular system is used therein in an HMD device (head-mounted display device). However, the ocular system cited at the beginning can also be used in microscopes or telescopes. 
     It is disadvantageous that when using an HMD device, for example, the user, if he must wear spectacles because of spherical defective vision, also has to wear these spectacles when using the HMD device. Wearing the spectacles and wearing the HMD device in addition is frequently viewed as unpleasant, however. It is also difficult to place the HMD device in its intended form on the head when the user is still wearing spectacles. 
     SUMMARY OF THE INVENTION 
     Proceeding therefrom, it is the object of the invention to improve an optical ocular system of the type cited at the beginning so that it is better suitable for users having spherical defective vision. 
     The object of the invention is achieved in an optical ocular system of the type cited at the beginning in that the first lens and the object plane form a first optic group and a displacement unit is provided, which can change the spacing between the first optic group and the deflection element to correct spherical defective vision of the user. The user having spherical defective vision can thus use the optical ocular system without his spectacles, because the adaptation to the spherical defective vision can be realized using the displacement unit. It is particularly advantageous in this case that a spacing within the imaging optic is changed for this purpose, so that the user does not have to move himself relative to the optical ocular system, in order to be able to perceive the image sharply. 
     The displacement unit can be implemented so that it can displace the first optic group along the optical axis of the imaging optic. In particular, it can provide a displacement path of ±2 mm. A diopter range of ±3.5 can thus be covered. Displacement-related imaging errors are minimized by the displacement along the optical axis. 
     The spacing between the first lens and the object plane in an example embodiment is fixed and/or constant during the displacement of the first optic group. I.e., the optic group as a whole is displaced. 
     Both the boundary surface of the first lens facing toward the deflection element and also the boundary surface of the deflection element facing toward the first lens may each be curved convexly. Spatially, this is a very favorable variant, because no difficulties arise in regard to the mountings of first lens and deflection element, because the least spacing occurs between the vertices on the optical axis between both boundary surfaces. There is thus sufficient space for the mountings. 
     The deflection element is particularly implemented in one piece. No complex adjustment is thus necessary. In particular, the entry and exit faces of the deflection element have different curvatures. The face on which the reflection occurs is preferably implemented as a planar face (i.e., having an infinitely large curvature). 
     Of course, the deflection element can also be implemented in multiple pieces. In this case, it can be a 90° prism having a planar deflection face and a planar entry side and a planar exit side, for example. A planoconvex lens is attached on its planar side on each of the exit and entry sides. The planoconvex lenses may be cemented with, glued with, or joined by optical contact bonding to the prism, for example. Any other type of connection is also possible. 
     The two boundary surfaces of the first lens and the entry and exit faces of the deflection element may be curved aspherically, the aspheric faces being rotationally symmetric and centered on the optical axis of the imaging optic. 
     The boundary surface of the deflection element facing toward the first lens may be implemented as a diffractive surface. Color errors may thus be corrected outstandingly. 
     The deflection element can cause the folding of the beam path by 70°-110°. A deflection of 90° is preferred. 
     The ocular system can have an image element for generating the image in the object plane. For this purpose, the image element itself can be situated in the object plane. It is also possible, however, that imaging of the image element is performed in the object plane. 
     A self-illuminating or a non-self-illuminating display element can be provided as the image element. In particular, the display element can have a plurality of pixels controllable independently of one another, which may particularly be situated in lines and columns. The image element can be an LCD module, an LCoS module, or also an adjustable mirror matrix. 
     The first lens and the image element may be held in a single mounting. It is thus easily possible to keep the spacing between image element and lens constant. 
     Furthermore, the first lens and the image element may be connected to one another in a form-fit manner. This is possible using a corresponding mounting, for example. 
     The imaging optic and the image element form an eye module. Such an eye module can be provided twice, so that one eye module is provided for each eye of the user. Binocular embodiments may thus be implemented. 
     In particular, the spacing between the optic group and the deflection element can be changeable independently of one another in both eye modules. It is thus possible to compensate for different spherical visual defects of the two eyes of the user. 
     In the ocular system, the beam path in the eye module from the image plane up to the exit pupil of imaging optic can be essentially L-shaped, the eye modules being situated so that the spacing of the two optic groups is less than the spacing of the two deflection elements. However, it is also possible that the eye modules are situated so that the spacing of the two optic groups is greater than the spacing of the two deflection elements. 
     A vignetting mask, shutter or stop can be provided between the image element and the first lens. This stop functions to suppress or block undesired scattered light. The vignetting stop can particularly have a contour adapted to the contour of an imaging area of the image element. Thus, for example, it can have a rectangular transmissive area, if the imaging area is also rectangular. In particular, the transmissive area in the stop is somewhat larger than the imaging area of the imaging element. 
     Furthermore, a display device having an optical ocular system according to the invention (or a corresponding refinement) is provided, which also has a mounting module to be worn on the head, the imaging optic being fastened on the mounting module and the image imaged using the imaging optic being perceptible by a user wearing the display device. 
     Furthermore, the image element can be fastened on the mounting module. 
     The mounting module can be implemented as a spectacle-type framework, beanie, cap, strap, or in another way. 
     The ocular system according to the invention (including its refinements) can also be used in a microscope and a telescope, so that a corresponding microscope or telescope is provided. 
     It is understood that the above-mentioned features and the features to be explained hereafter are usable not only in the disclosed combinations, but rather also in other combinations or alone, without leaving the scope of the present invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention is explained in greater detail hereafter for exemplary purposes with reference to the drawings, which also disclose features essential to the invention. In the figures: 
         FIG. 1  shows a schematic top view of a display device having optical ocular system; 
         FIG. 2  shows a schematic enlarged view of the ocular system  1  from  FIG. 1 , and 
         FIG. 3  shows a further embodiment of a display device having optical ocular systems. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  shows an embodiment of the optical ocular system  1 ,  2  according to the invention, in which it is used in a binocular display device  3  to be worn on the head of a user. 
     The display device  3 , which can also be referred to as an HMD device (head-mounted display device), comprises a mounting module  4 , which is schematically shown in  FIG. 1  and comprises a housing  5  accommodating the two optical ocular systems  1 ,  2  and two lateral earpieces  6  and  7 . The mounting module  4  is thus implemented like spectacle frames, which the user can put on in the same way as spectacles. 
     As may be inferred from  FIG. 1 , the display device  3  contains a separate optical ocular system  1 ,  2  in each case for the right and left eyes of the user, which are implemented identically except for their configuration in the mounting module  4 . Therefore, only the optical ocular system  1  for the left eye of the user is described in detail in the following description. 
     The optical ocular system  1  is shown enlarged in  FIG. 2 . As may be inferred from  FIG. 2 , it comprises an image-generating element  8 , which generates an image to be shown in an object plane  9 . This is achieved here in that the image-generating area of the element  8  lies in the object plane  9 . The image-generating element can be a self-illuminating or a non-self-illuminating display. For example, it can be implemented as an LCD module, an LCoS module, or as an tilting mirror matrix. 
     A concave-convex lens  10  is downstream from the image-generating element  8 , which is positively connected to the image-generating element  8 . This is implemented in the example described here by a common mounting  17 , which is only schematically shown in  FIG. 2 . 
     The lens  10  is a deflection element  11  having a curved entry face F 5 , a planar deflection face F 6 , and a curved exit face F 7  downstream. The exit pupil of the optical ocular system  1  is identified by the reference numeral  15 . 
     In operation, the image generated using the image-generating element  8  is imaged via the lens  10 , which has negative refractive power, and the deflection element or deflection prism  11 , which has positive refractive power, in the exit pupil  15  as a virtual image, so that a user wearing the display device  3  can perceive the imaged image. The lens  10  forms an imaging optic  16  together with the deflection element  11 . 
     In order to be able to adapt the display device  3  to spherical defective vision of the user, a displacement unit  18  (which is only shown in  FIG. 2 ) is provided, which can displace the image-generating element  8  and the lens  10 , which together form a first optic group  19 , along the optical axis OA of the imaging optic  16  by ±2 mm, as indicated by the double arrow P 1 . Defective vision in the range of ±3.5 diopter can thus be corrected. 
     In the ocular system described here, the exit pupil  15  is 14 mm from the lens vertex of the exit face F 7  and has a size of 6 mm×10 mm. The diagonal of the image shown is shown at a field of vision angle of at least 30° and the deflection by the planar deflection face F 6  is preferably in the range of 70°-110°. The lens  10  and the deflection element  11  are preferably each formed from an optical plastic, so that the weight of the ocular system  1  is low. 
     A stop  20  can be provided between the image-generating element  8  and the lens  10 . The stop  20  is only shown in  FIG. 3  (as a dashed line) and preferably has a transmissive area (e.g., a recess) having the same contour as the imaging area of the image-generating element  8 . The transmissive area can be somewhat larger than the imaging area, in order to suppress undesired scattered light. In the example described here, the imaging area of the element  8  has a rectangular shape, so that the transmissive area of the shading stop  20  is also implemented as rectangular. 
     The entry and exit faces F 5 , F 7  and the two boundary faces F 3 , F 4  of the lens  10  are aspherical, rotationally-symmetric faces, which are centered to the optical axis OA of the imaging optic  16 . The material of the lens  10  is different from the material of the deflection element  11 , the material of the deflection element  11  having a lower dispersion than the material of the lens  10 . 
     In order to ensure outstanding color correction, the entry face F 5  is additionally also implemented as a diffractive face. The implementation of the entry face F 5  as a diffractive face provides the advantage that it is a face inside the imaging optic  16 , so that it can easily be protected from dirtying. 
     The diffractive face F 5  has a kinoform profile. In detail, the diffractive face F 5  comprises concentric rings having the lens vertex of the entry face F 5  as the center point. Each ring has an inner radius and an outer radius. The inner radius of the first ring is zero. The outer radius of the mth ring is the inner radius of the m+1th ring. The width of the rings becomes continuously smaller from the middle to the edge of the lens. The groove depth on the inner radius is zero, and it is d on the outer radius. Upon the transition from the mth ring to the m+1th ring, a step of the height d is thus provided. The diffractive face can be described using the following phase profile function φ: 
     
       
         
           
             φ 
             = 
             
               
                 
                   2 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   π 
                 
                 
                   λ 
                   0 
                 
               
               ⁢ 
               
                 
                   ∑ 
                   n 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   
                     C 
                     n 
                   
                   ⁢ 
                   
                     r 
                     
                       2 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       n 
                     
                   
                 
               
             
           
         
       
     
     In this equation, λ 0  stands for the reference wavelength and C n  are the coefficients of the phase polynomial. The radius r of the mth ring is calculated from 
     
       
         
           
             
               m 
               ⁢ 
               
                   
               
               ⁢ 
               
                 λ 
                 0 
               
             
             = 
             
               
                 ∑ 
                 n 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   C 
                   n 
                 
                 ⁢ 
                 
                   r 
                   
                     2 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     n 
                   
                 
               
             
           
         
       
       
         
           
             
               m 
               = 
               1 
             
             , 
             2 
             , 
             3 
             , 
             … 
           
         
       
     
     There are at most N rings, with 
     
       
         
           
             N 
             = 
             
               
                 1 
                 
                   λ 
                   0 
                 
               
               ⁢ 
               
                 
                   ∑ 
                   n 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   
                     C 
                     n 
                   
                   ⁢ 
                   
                     r 
                     max 
                     
                       2 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       n 
                     
                   
                 
               
             
           
         
       
     
     In this equation, r max  stands for half of the lens diameter. 
     The groove depth d on each ring is 
             d   =       λ   0         n   0     -   1             
with n 0  being the index of refraction of the material for λ 0 . In the embodiment described here, it has been shown that it was sufficient to describe the diffractive face using the coefficient C 1 . This is specified in following Table 3.
 
     The aspheric faces are described using the following formula (arrow height formula) 
               z   ⁡     (   h   )       =         ρ   ⁢           ⁢     h   2         1   +       1   -       (     1   +   K     )     ⁢     ρ   2     ⁢     h   2               +     A   ⁢           ⁢     h   4       +     Bh   6     +     Ch   8     +     Dh   10     +     Eh   12     +     Fh   14     +     Gh   16     +     Hh   18             
z arrow height
 
K eccentricity
 
ρ vertex curvature
 
h height
 
A, B, C, . . . H coefficients for higher-order terms
 
     The precise optical construction of the imaging optic  16  can be inferred from following Tables 1 through 4, Table 1 describing the lens  10  and the deflection element  11 . The aspheric faces are specified in greater detail in Table 2 and the diffractive face is specified in greater detail in Table 3. The materials used (see column “material” of the table) are characterized in Table 4. It is also specified in the column “face type” of Table 1 whether it is an aspheric and possibly a diffractive face. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                   
                 Spacing to the 
                   
               
               
                 Face 
                 Face type 
                 Radius [mm] 
                 next face [mm] 
                 Material 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                  9 
                   
                 Infinite 
                 0.000000 
                   
               
               
                 F1 
                   
                 Infinite 
                 0.900000 
                 NBK7_SCHOTT 
               
               
                 F2 
                   
                 Infinite 
                 3.038000 
               
               
                 F3 
                 Aspherical 
                 −6.44595 
                 3.800000 
                 PSTYR 
               
               
                 F4 
                 Aspherical 
                 −8.97318 
                 2.100000 
               
               
                 F5 
                 Aspherical, 
                 13.15788 
                 17.500000 
                 480R 
               
               
                   
                 diffractive 
               
               
                 F6 
                   
                 Infinite 
                 16.500000 
                 480R 
               
               
                 F7 
                 Aspherical 
                 −20.71599 
                 18.300000 
               
               
                 15 
                   
                 Infinite 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
             
             
               
                 Face 
                 K 
                 A 
                 B 
                 C 
               
               
                   
               
               
                 F3 
                 0.000000 
                 −0.110584E−02 
                 0.261827E−03 
                 −0.134534E−04 
               
               
                 F4 
                 0.000000 
                 0.405943E−04 
                 0.270194E−04 
                 −0.769285E−06 
               
               
                 F5 
                 0.000000 
                 −0.682894E−04 
                 −0.180150E−05 
                 0.168871E−07 
               
               
                 F7 
                 0.000000 
                 0.388888E−04 
                 −0.199410E−06 
                 0.239487E−08 
               
               
                   
               
             
          
           
               
                   
                 D 
                 E 
                 F 
                 G 
                 H 
               
               
                   
               
               
                 F3 
                 0.336914E−06 
                 −0.289232E−08 
                 −0.224721E−10 
                 0.669441E−13 
                 0.892241E−14 
               
               
                 F4 
                 0.771130E−08 
                 0.682475E−11 
                 −0.384074E−12 
               
               
                 F5 
                 −0.744599E−10 
                 0.475142E−13 
               
               
                 F7 
                 −0.174143E−10 
                 0.468155E−13 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                   
                   
                   
                 Order of 
                   
                   
                   
                   
               
               
                 Face 
                 C 1   
                 λ 0   
                 diffraction 
                 N 
                 R 1 [mm] 
                 R N [mm] 
                 d[mm] 
               
               
                   
               
             
             
               
                 F7 
                 −2.2919 × 10 −3   
                 546.07 
                 1 
                 599 
                 0.4881 
                 11.9465 
                 0.001 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
               
                 Material 
                 Short name 
                 n d   
                 v d   
                 ρ in g/cm 3   
               
               
                   
               
             
             
               
                 NBK7_SCHOTT 
                 NBK7_SCHOTT 
                 1.51680 
                 64.17 
                 2.51 
               
               
                 PMMA 
                 PMMA 
                 1.49178 
                 57.99 
                 1.19 
               
               
                 POLYSTYRENE 
                 POLY 
                 1.59250 
                 30.84 
                 1.10 
               
               
                 POLYCARBONATE 
                 PC 
                 1.58500 
                 30.00 
                 1.25 
               
               
                 TOPAZ 
                 TOPAZ 
                 1.53320 
                 56.72 
                 1.02 
               
               
                 ZEONEX E48R 
                 E48R 
                 1.52996 
                 56.24 
                 1.01 
               
               
                 ZEONEX 330R 
                 330R 
                 1.50904 
                 52.80 
                 1.01 
               
               
                 ZEONEX 480R 
                 480R 
                 1.52470 
                 56.24 
                 1.01 
               
               
                   
               
             
          
         
       
     
     In Table 4, n d  he is the index of refraction for 587.56 nm, ν d  is the corresponding Abbe number, and ρ is the density. 
     The focal width f 1  of the lens  10 , the focal width f 2  of the deflection element  11 , and the focal width f of the imaging optic  16  are specified in Table 5 for the example 1 described in connection with Tables 1-4 and the following examples 2-9 still to be described. In examples 1-6 and in example 9, f=19.7 mm, the diagonal field of vision is 32°. In example 7, f=21.0, and the diagonal field of vision is 30°. In example 8, f=25.4 and the diagonal field of vision is 25°. 
     
       
         
               
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 5 
               
             
             
               
                   
                   
               
               
                   
                 Partial focal widths 
               
             
          
           
               
                   
                 Focal width f 
                 f 1   
                 f 2   
               
               
                   
                 Imaging optic 16 
                 Lens 10 
                 Deflection element 11 
               
               
                   
                   
               
             
          
           
               
                 Example 1 
                 19.7 
                 −106.0 
                 22.5 
               
               
                 Example 2 
                 19.7 
                 −101.7 
                 22.5 
               
               
                 Example 3 
                 19.7 
                 −102.4 
                 22.4 
               
               
                 Example 4 
                 19.7 
                 −103.5 
                 22.4 
               
               
                 Example 5 
                 19.7 
                 −103.7 
                 22.3 
               
               
                 Example 6 
                 19.7 
                 −102.5 
                 22.3 
               
               
                 Example 7 
                 21.0 
                 −57.2 
                 22.8 
               
               
                 Example 8 
                 25.4 
                 −27.6 
                 25.1 
               
               
                 Example 9 
                 19.7 
                 −233.5 
                 23.2 
               
               
                   
               
             
          
         
       
     
     The focal width of the aspheric deflection element  11  varies only slightly and is in the range of the focal width of the imaging optic  16  made of deflection element  11  and lens  10 . The focal width of the lens  10  varies little if only different materials are used, the index of refraction and dispersion differences of the materials for the lens  10  being slight. The focal width of the lens  10  varies very strongly if the focal width of the imaging optic  16  and thus the field to be imaged is varied. 
     For the focal widths f, f 1 , and f 2 , the following relationship applies:
 
0.9 *f&lt;f   1 &lt;1.5 *f  and 1.0 *f&lt;|f   2 |&lt;13.0 *f  
 
     The optical data for eight further embodiments are specified hereafter in the same way as for the example already described, no diffractive face being provided in Example 9. 
     Example 2 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
               
             
             
               
                   
                   
                   
                 Spacing to the 
                   
               
               
                 Face 
                 Face type 
                 Radius [mm] 
                 next face [mm] 
                 Material 
               
               
                   
               
               
                  9 
                   
                 Infinite 
                 0.000000 
               
               
                 F1 
                   
                 Infinite 
                 0.900000 
                 NBK7_SCHOTT 
               
               
                 F2 
                   
                 Infinite 
                 3.123190 
               
               
                 F3 
                 Aspherical 
                 −6.31092 
                 3.700000 
                 PCARB 
               
               
                 F4 
                 Aspherical 
                 −8.58638 
                 2.100000 
               
               
                 F5 
                 Aspherical, 
                 13.42140 
                 17.500000 
                 480R 
               
               
                   
                 diffractive 
               
               
                 F6 
                   
                 Infinite 
                 16.500000 
                 480R 
               
               
                 F7 
                 Aspherical 
                 −20.70854 
                 18.300000 
               
               
                 15 
                   
                 Infinite 
               
               
                   
               
             
          
           
               
                 Face 
                 K 
                 A 
                 B 
                 C 
                 D 
               
               
                   
               
               
                 F3 
                 0.000000 
                 −0.105810E−02 
                 0.268979E−03 
                 −0.147703E−04 
                 0.372695E−06 
               
               
                 F4 
                 0.000000 
                 0.548035E−04 
                 0.260686E−04 
                 −0.771603E−06 
                 0.783687E−08 
               
               
                 F5 
                 0.000000 
                 −0.676831E−04 
                 −0.173704E−05 
                 0.172058E−07 
                 0.732592E−10 
               
               
                 F7 
                 0.000000 
                 0.362404E−04 
                 −0.186980E−06 
                 0.260500E−08 
                 −0.167321E−10 
               
               
                   
               
             
          
           
               
                   
                 E 
                 F 
                 G 
                 H 
                 J 
               
               
                   
               
               
                 F3 
                 −0.319554E−08 
                 −0.229890E−10 
                 0.129444E−12 
                 0.921098E−14 
                 0.190547E−16 
               
               
                 F4 
                 0.102057E−10 
                 −0.314121E−12 
               
               
                 F5 
                 0.533178E−13 
               
               
                 F7 
                 0.404917E−13 
               
               
                   
               
             
          
           
               
                   
                   
                   
                 Order of 
                   
                   
                   
                   
               
               
                 Face 
                 C 1   
                 λ 0   
                 diffraction 
                 N 
                 R 1 [mm] 
                 R N [mm] 
                 d[mm] 
               
               
                   
               
               
                 F7 
                 −2.2224 × 10 −3   
                 546.07 
                 1 
                 580 
                 0.4957 
                 11.9378 
                 0.001 
               
               
                   
               
             
          
         
       
     
     Example 3 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
               
             
             
               
                   
                   
                   
                 Spacing to the 
                   
               
               
                 Face 
                 Face type 
                 Radius [mm] 
                 next face [mm] 
                 Material 
               
               
                   
               
               
                  9 
                   
                 Infinite 
                 0.000000 
               
               
                 F1 
                   
                 Infinite 
                 0.900000 
                 NBK7_SCHOTT 
               
               
                 F2 
                   
                 Infinite 
                 3.120000 
               
               
                 F3 
                 Aspherical 
                 −6.37965 
                 3.700000 
                 PSTYR 
               
               
                 F4 
                 Aspherical 
                 −8.66726 
                 2.127559 
               
               
                 F5 
                 Aspherical, 
                 13.43253 
                 17.500000 
                 E48R 
               
               
                   
                 diffractive 
               
               
                 F6 
                   
                 Infinite 
                 16.500000 
                 E48R 
               
               
                 F7 
                 Aspherical 
                 −20.87079 
                 18.300000 
               
               
                 15 
                   
                 Infinite 
               
               
                   
               
             
          
           
               
                 Face 
                 K 
                 A 
                 B 
                 C 
                 D 
               
               
                   
               
               
                 F3 
                 0.000000 
                 −0.105700E−02 
                 0.270109E−03 
                 −0.148213E−04 
                 0.371356E−06 
               
               
                 F4 
                 0.000000 
                 0.550271E−04 
                 0.259918E−04 
                 −0.770428E−06 
                 0.781146E−08 
               
               
                 F5 
                 0.000000 
                 −0.674612E−04 
                 −0.173212E−05 
                 0.172212E−07 
                 −0.732963E−10 
               
               
                 F7 
                 0.000000 
                 0.360549E−04 
                 −0.187285E−06 
                 0.258817E−08 
                 −0.167328E−10 
               
               
                   
               
             
          
           
               
                   
                 E 
                 F 
                 G 
                 H 
                 J 
               
               
                   
               
               
                 F3 
                 −0.316610E−08 
                 −0.226518E−10 
                 0.162353E−12 
                 0.908005E−14 
                 −0.198492E−16 
               
               
                 F4 
                 0.969201E−11 
                 −0.314977E−12 
               
               
                 F5 
                 0.524624E−13 
               
               
                 F7 
                 0.414271E−13 
               
               
                   
               
             
          
           
               
                   
                   
                   
                 Order of 
                   
                   
                   
                   
               
               
                 Face 
                 C 1   
                 λ 0   
                 diffraction 
                 N 
                 R 1 [mm] 
                 R N [mm] 
                 d[mm] 
               
               
                   
               
               
                 F7 
                 −2.2188 × 10 −3   
                 546.07 
                 1 
                 579 
                 0.4961 
                 11.9374 
                 0.001 
               
               
                   
               
             
          
         
       
     
     Example 4 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
               
             
             
               
                   
                   
                   
                 Spacing to the 
                   
               
               
                 Face 
                 Face type 
                 Radius [mm] 
                 next face [mm] 
                 Material 
               
               
                   
               
               
                  9 
                   
                 Infinite 
                 0.000000 
               
               
                 F1 
                   
                 Infinite 
                 0.900000 
                 NBK7_SCHOTT 
               
               
                 F2 
                   
                 Infinite 
                 3.120000 
               
               
                 F3 
                 Aspherical 
                 −6.37840 
                 3.700000 
                 PCARB 
               
               
                 F4 
                 Aspherical 
                 −8.65554 
                 2.150248 
               
               
                 F5 
                 Aspherical, 
                 13.42553 
                 17.500000 
                 E48R 
               
               
                   
                 diffractive 
               
               
                 F6 
                   
                 Infinite 
                 16.500000 
                 E48R 
               
               
                 F7 
                 Aspherical 
                 −20.92638 
                 18.300000 
               
               
                 15 
                   
                 Infinite 
               
               
                   
               
             
          
           
               
                 Face 
                 K 
                 A 
                 B 
                 C 
                 D 
               
               
                   
               
               
                 F3 
                 0.000000 
                 −0.102859E−02 
                 0.268403E−03 
                 −0.148407E−04 
                 0.371361E−06 
               
               
                 F4 
                 0.000000 
                 0.390289E−04 
                 0.261050E−04 
                 −0.767730E−06 
                 0.780055E−08 
               
               
                 F5 
                 0.000000 
                 −0.675269E−04 
                 −0.173137E−05 
                 0.172109E−07 
                 −0.731766E−10 
               
               
                 F7 
                 0.000000 
                 0.362318E−04 
                 −0.185754E−06 
                 0.258608E−08 
                 −0.166517E−10 
               
               
                   
               
             
          
           
               
                   
                 E 
                 F 
                 G 
                 H 
                 J 
               
               
                   
               
               
                 F3 
                 −0.317289E−08 
                 −0.221025E−10 
                 0.169215E−12 
                 0.874111E−14 
                 −0.150746E−16 
               
               
                 F4 
                 0.918020E−11 
                 −0.317003E−12 
               
               
                 F5 
                 0.535132E−13 
               
               
                 F7 
                 0.444178E−13 
               
               
                   
               
             
          
           
               
                   
                   
                   
                 Order of 
                   
                   
                   
                   
               
               
                 Face 
                 C 1   
                 λ 0   
                 diffraction 
                 N 
                 R 1 [mm] 
                 R N [mm] 
                 d[mm] 
               
               
                   
               
               
                 F7 
                 −2.1824 × 10 −3   
                 546.07 
                 1 
                 570 
                 0.5002 
                 11.9424 
                 0.001 
               
               
                   
               
             
          
         
       
     
     Example 5 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
               
             
             
               
                   
                   
                   
                 Spacing to the 
                   
               
               
                 Face 
                 Face type 
                 Radius [mm] 
                 next face [mm] 
                 Material 
               
               
                   
               
               
                  9 
                   
                 Infinite 
                 0.000000 
               
               
                 F1 
                   
                 Infinite 
                 0.900000 
                 NBK7_SCHOTT 
               
               
                 F2 
                   
                 Infinite 
                 3.124979 
               
               
                 F3 
                 Aspherical 
                 −6.39073 
                 3.700000 
                 PSTYR 
               
               
                 F4 
                 Aspherical 
                 −8.66860 
                 2.100000 
               
               
                 F5 
                 Aspherical, 
                 13.43194 
                 17.500000 
                 TOPAZ 
               
               
                   
                 diffractive 
               
               
                 F6 
                   
                 Infinite 
                 16.500000 
                 TOPAZ 
               
               
                 F7 
                 Aspherical 
                 −21.01111 
                 18.300000 
               
               
                 15 
                   
                 Infinite 
               
               
                   
               
             
          
           
               
                 Face 
                 K 
                 A 
                 B 
                 C 
                 D 
               
               
                   
               
               
                 F3 
                 0.000000 
                 −0.113039E−02 
                 0.273295E−03 
                 −0.147757E−04 
                 0.370988E−06 
               
               
                 F4 
                 0.000000 
                 0.734150E−04 
                 0.258357E−04 
                 −0.771096E−06 
                 0.781671E−08 
               
               
                 F5 
                 0.000000 
                 −0.674430E−04 
                 −0.173202E−05 
                 0.172200E−07 
                 −0.732795E−10 
               
               
                 F7 
                 0.000000 
                 0.360408E−04 
                 −0.187399E−06 
                 0.258799E−08 
                 −0.167200E−10 
               
               
                   
               
             
          
           
               
                   
                 E 
                 F 
                 G 
                 H 
                 J 
               
               
                   
               
               
                 F3 
                 −0.319593E−08 
                 −0.239540E−10 
                 0.144448E−12 
                 0.956120E−14 
                 0.169992E−17 
               
               
                 F4 
                 0.973764E−11 
                 −0.314155E−12 
               
               
                 F5 
                 0.524923E−13 
               
               
                 F7 
                 0.413999E−13 
               
               
                   
               
             
          
           
               
                   
                   
                   
                 Order of 
                   
                   
                   
                   
               
               
                 Face 
                 C 1   
                 λ 0   
                 diffraction 
                 N 
                 R 1 [mm] 
                 R N [mm] 
                 d[mm] 
               
               
                   
               
               
                 F7 
                 −2.2154 × 10 −3   
                 546.07 
                 1 
                 579 
                 0.4965 
                 11.9463 
                 0.001 
               
               
                   
               
             
          
         
       
     
     Example 6 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
               
             
             
               
                   
                   
                   
                 Spacing to the 
                   
               
               
                 Face 
                 Face type 
                 Radius [mm] 
                 next face [mm] 
                 Material 
               
               
                   
               
               
                  9 
                   
                 Infinite 
                 0.000000 
               
               
                 F1 
                   
                 Infinite 
                 0.900000 
                 NBK7_SCHOTT 
               
               
                 F2 
                   
                 Infinite 
                 3.129602 
               
               
                 F3 
                 Aspherical 
                 −6.32866 
                 3.700000 
                 PCARB 
               
               
                 F4 
                 Aspherical 
                 −8.60206 
                 2.100000 
               
               
                 F5 
                 Aspherical, 
                 13.43205 
                 17.500000 
                 TOPAZ 
               
               
                   
                 diffractive 
               
               
                 F6 
                   
                 Infinite 
                 16.500000 
                 TOPAZ 
               
               
                 F7 
                 Aspherical 
                 −21.00964 
                 18.300000 
               
               
                 15 
                   
                 Infinite 
               
               
                   
               
             
          
           
               
                 Face 
                 K 
                 A 
                 B 
                 C 
                 D 
               
               
                   
               
               
                 F3 
                 0.000000 
                 −0.110810E−02 
                 0.272724E−03 
                 −0.147855E−04 
                 0.370907E−06 
               
               
                 F4 
                 0.000000 
                 0.718451E−04 
                 0.258913E−04 
                 −0.770928E−06 
                 0.781572E−08 
               
               
                 F5 
                 0.000000 
                 −0.674595E−04 
                 −0.173228E−05 
                 0.172177E−07 
                 −0.732712E−10 
               
               
                 F7 
                 0.000000 
                 0.360787E−04 
                 −0.186836E−06 
                 0.258799E−08 
                 −0.167306E−10 
               
               
                   
               
             
          
           
               
                   
                 E 
                 F 
                 G 
                 H 
                 J 
               
               
                   
               
               
                 F3 
                 −0.319437E−08 
                 −0.236943E−10 
                 0.148886E−12 
                 0.957053E−14 
                 0.245264E−17 
               
               
                 F4 
                 0.974128E−11 
                 −0.314425E−12 
               
               
                 F5 
                 0.524635E−13 
               
               
                 F7 
                 0.412770E−13 
               
               
                   
               
             
          
           
               
                   
                   
                   
                 Order of 
                   
                   
                   
                   
               
               
                 Face 
                 C 1   
                 λ 0   
                 diffraction 
                 N 
                 R 1 [mm] 
                 R N [mm] 
                 d[mm] 
               
               
                   
               
               
                 F7 
                 −2.2182 × 10 −3   
                 546.07 
                 1 
                 579 
                 0.4962 
                 11.9389 
                 0.001 
               
               
                   
               
             
          
         
       
     
     Example 7 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
               
             
             
               
                   
                   
                   
                 Spacing to the 
                   
               
               
                 Face 
                 Face type 
                 Radius [mm] 
                 next face [mm] 
                 Material 
               
               
                   
               
               
                  9 
                   
                 Infinite 
                 0.000000 
               
               
                 F1 
                   
                 Infinite 
                 0.900000 
                 NBK7_SCHOTT 
               
               
                 F2 
                   
                 Infinite 
                 3.524287 
               
               
                 F3 
                 Aspherical 
                 −6.21922 
                 3.700000 
                 PSTYR 
               
               
                 F4 
                 Aspherical 
                 −9.29975 
                 1.851370 
               
               
                 F5 
                 Aspherical, 
                 14.11834 
                 17.500000 
                 E48R 
               
               
                   
                 diffractive 
               
               
                 F6 
                   
                 Infinite 
                 16.500000 
                 E48R 
               
               
                 F7 
                 Aspherical 
                 −20.64291 
                 18.300000 
               
               
                 15 
                   
                 Infinite 
               
               
                   
               
             
          
           
               
                 Face 
                 K 
                 A 
                 B 
                 C 
                 D 
               
               
                   
               
               
                 F3 
                 0.000000 
                 −0.203782E−02 
                 0.285716E−03 
                 −0.139103E−04 
                 0.363895E−06 
               
               
                 F4 
                 0.000000 
                 −0.200704E−03 
                 0.310975E−04 
                 −0.794131E−06 
                 0.747524E−08 
               
               
                 F5 
                 0.000000 
                 −0.833537E−04 
                 −0.160281E−05 
                 0.174477E−07 
                 −0.766781E−10 
               
               
                 F7 
                 0.000000 
                 0.301837E−04 
                 −0.212268E−06 
                 0.264276E−08 
                 −0.155875E−10 
               
               
                   
               
             
          
           
               
                   
                 E 
                 F 
                 G 
                 H 
                 J 
               
               
                   
               
               
                 F3 
                 −0.344951E−08 
                 −0.287210E−10 
                 0.213991E−12 
                 0.866484E−14 
                 0.787728E−16 
               
               
                 F4 
                 0.801007E−11 
                 −0.346847E−12 
               
               
                 F5 
                 0.621673E−13 
               
               
                 F7 
                 0.336162E−13 
               
               
                   
               
             
          
           
               
                   
                   
                   
                 Order of 
                   
                   
                   
                   
               
               
                 Face 
                 C 1   
                 λ 0   
                 diffraction 
                 N 
                 R 1 [mm] 
                 R N [mm] 
                 d[mm] 
               
               
                   
               
               
                 F7 
                 −2.2507 × 10 −3   
                 546.07 
                 1 
                 588 
                 0.4926 
                 11.9440 
                 0.001 
               
               
                   
               
             
          
         
       
     
     Example 8 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
               
             
             
               
                   
                   
                   
                 Spacing to the 
                   
               
               
                 Face 
                 Face type 
                 Radius [mm] 
                 next face [mm] 
                 Material 
               
               
                   
               
               
                  9 
                   
                 Infinite 
                 0.000000 
               
               
                 F1 
                   
                 Infinite 
                 0.900000 
                 NBK7_SCHOTT 
               
               
                 F2 
                   
                 Infinite 
                 3.034584 
               
               
                 F3 
                 Aspherical 
                 −5.79408 
                 3.700000 
                 PSTYR 
               
               
                 F4 
                 Aspherical 
                 −11.092 
                 4.6047 
               
               
                 F5 
                 Aspherical, 
                 18.48583 
                 17.0 
                 E48R 
               
               
                   
                 diffractive 
               
               
                 F6 
                   
                 Infinite 
                 16.0 
                 E48R 
               
               
                 F7 
                 Aspherical 
                 −21.090 
                 18.300000 
               
               
                 15 
                   
                 Infinite 
               
               
                   
               
             
          
           
               
                 Face 
                 K 
                 A 
                 B 
                 C 
                 D 
               
               
                   
               
               
                 F3 
                 0.000000 
                 −0.294837E−03 
                 0.217886E−03 
                 −0.135366E−04 
                 0.417117E−06 
               
               
                 F4 
                 0.000000 
                 0.294642E−03 
                 0.155171E−04 
                 −0.763873E−06 
                 0.907407E−08 
               
               
                 F5 
                 0.000000 
                 −0.558147E−04 
                 −0.131968E−05 
                 0.161370E−07 
                 −0.676346E−10 
               
               
                 F7 
                 0.000000 
                 0.203916E−04 
                 −0.188128E−06 
                 0.229619E−08 
                 −0.166872E−10 
               
               
                   
               
             
          
           
               
                   
                 E 
                 F 
                 G 
                 H 
                 J 
               
               
                   
               
               
                 F3 
                 −0.323209E−08 
                 −0.629421E−10 
                 −0.810392E−12 
                 0.130009E−13 
                 0.118379E−14 
               
               
                 F4 
                 0.301720E−10 
                 −0.547672E−12 
               
               
                 F5 
                 0.123929E−12 
               
               
                 F7 
                 0.540813E−13 
               
               
                   
               
             
          
           
               
                   
                   
                   
                 Order of 
                   
                   
                   
                   
               
               
                 Face 
                 C 1   
                 λ 0   
                 diffraction 
                 N 
                 R 1 [mm] 
                 R N [mm] 
                 d[mm] 
               
               
                   
               
               
                 F7 
                 −1.6334 × 10 −3   
                 546.07 
                 1 
                 465 
                 0.5782 
                 12.4683 
                 0.001 
               
               
                   
               
             
          
         
       
     
     Example 9 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
               
             
             
               
                   
                   
                   
                 Spacing to the 
                   
               
               
                 Face 
                 Face type 
                 Radius [mm] 
                 next face [mm] 
                 Material 
               
               
                   
               
               
                  9 
                   
                 Infinite 
                 0.000000 
               
               
                 F1 
                   
                 Infinite 
                 0.900000 
                 NBK7_SCHOTT 
               
               
                 F2 
                   
                 Infinite 
                 3.607542 
               
               
                 F3 
                 Aspherical 
                 −6.46993 
                 3.700000 
                 PSTYR 
               
               
                 F4 
                 Aspherical 
                 −8.23353 
                 2.100000 
               
               
                 F5 
                 Aspherical 
                 12.82389 
                 17.500000 
                 480R 
               
               
                 F6 
                   
                 Infinite 
                 16.500000 
                 480R 
               
               
                 F7 
                 Aspherical 
                 −21.79411 
                 18.300000 
               
               
                 15 
                   
                 Infinite 
               
               
                   
               
             
          
           
               
                 Face 
                 K 
                 A 
                 B 
                 C 
                 D 
               
               
                   
               
               
                 F3 
                 0.000000 
                 −0.101416E−02 
                 0.240311E−03 
                 −0.133574E−04 
                 0.354515E−06 
               
               
                 F4 
                 0.000000 
                 −0.127675E−03 
                 0.344968E−04 
                 −0.917430E−06 
                 0.766501E−08 
               
               
                 F5 
                 0.000000 
                 −0.444101E−04 
                 −0.202281E−05 
                 0.173608E−07 
                 −0.689916E−10 
               
               
                 F7 
                 0.000000 
                 0.401394E−04 
                 −0.245898E−06 
                 0.247065E−08 
                 −0.168386E−10 
               
               
                   
               
             
          
           
               
                   
                 E 
                 F 
                 G 
                 H 
                 J 
               
               
                   
               
               
                 F3 
                 −0.318319E−08 
                 −0.328007E−10 
                 0.196918E−12 
                 0.133085E−13 
                 −0.658499E−16 
               
               
                 F4 
                 0.356150E−10 
                 −0.530855E−12 
               
               
                 F5 
                 −0.110641E−13 
               
               
                 F7 
                 0.437093E−13