Abstract:
An all-reflective zoom optical system is disclosed. The system comprises a plurality of curved relay mirrors successively reflecting electromagnetic radiation received by the system to generate a real image with electromagnetic radiation on a focal surface that is fixed across the zoom range. Further, the entrance aperture also is constant for any zoom position. The curved relay mirrors are movable in relationship to each other in mutually parallel tracks to effect the magnification. The system further includes a primary and secondary mirror for collecting and reflecting incoming electromagnetic radiation to the curved relay mirrors.

Description:
BACKGROUND OF THE INVENTION 
     Some earth-orbiting satellites contain optical imaging systems for tracking earth-bound targets. Generally, these systems generate real images that are converted into electrical signals and transmitted to the ground. 
     Depending upon the satellite&#39;s angle of inclination in relationship to the earth, the distance between the satellite and an earthbound target will vary. As a result, the image size of fixed sized objects will also change. A similar effect arises in scanning telescopic systems in aircraft. Here, as the telescope scans the terrain over which the aircraft is passing, depending on the telescope&#39;s angle inclination, the changing distance between the telescope and the various targets affect the relative image sizes. 
     The solution to maintaining image size independent of the distance between the satellite and the target is to use a zoom optical system that can increase magnification in response to the satellite&#39;s angle of inclination relative to the earth. One problem that arises, however, is the fact that traditional zoom optical systems have utilized refractive optical elements. Optical glass is the preferred material for refractive lenses, but this is restricted in wavelength from 500 to 950 nm. A few materials are available for wavelengths outside of the range but these have severe limitations in size and durability. One of the major defects of refractive optics is chromatic aberration which becomes more serious as the wavelength band increases. If this is a problem for a particular application, one has to use several lenses made of different materials which increases the weight of the optics. The weight of refractive optics is a problem in any event because refractive lenses are not lightweight as in the case of mirrors. Refractive optics are also much more susceptible to thermal effects than reflective optics, and controlling to thermal environment in space or airborne systems is not an easy task. A final problem in refractive optics relative to reflective optics is that they are subject to the deleterious effects of radiation because the light has to go through the material of which the lens is made, and the optical characteristic of materials are more sensitive to radiation effects than their physical characteristics. 
     SUMMARY OF THE INVENTION 
     An all-reflective zoom optical system solves the above-identified problems. Such a system comprises a plurality of curved relay mirrors successively reflecting electromagnetic radiation received by the system to generate a real image with the electromagnetic radiation at a focal surface. These curved relay mirrors are movable in relationship to each other in order to effect magnification. 
     In a particular embodiment of this invention, the focal surface remains fixed as the curved relay mirrors move in relationship to each other in order to change the magnification. Further, the entrance aperture is constant across the zoom range. Also in the embodiment of the invention, the optical system further comprises a primary mirror for collecting and reflecting received electromagnetic radiation and a secondary mirror for receiving the electromagnetic radiation from the primary and reflecting the electromagnetic radiation to the curved relay mirrors. 
     In other embodiments, the curved relay mirrors comprise a first relay mirror, a second relay mirror receiving the electromagnetic radiation from the first relay mirror, a third relay mirror receiving the electromagnetic radiation from the second relay mirror, and a fourth relay mirror receiving the electromagnetic radiation from the third relay mirror and reflecting the electromagnetic radiation onto the focal surface. The first and fourth relay mirrors have aspheric curvatures with only bilateral symmetry. The second relay mirror has a convex curvature. Of the mirrors, only the second and the third relay mirrors move to effect the magnification. Further, these mirrors move in parallel tracks. The third relay mirror has a spherical curvature. Finally, the focal surface has an aspheric curvature with only bilateral symmetry. 
     According to a different aspect of the invention, the system comprises relay mirrors successively reflecting electromagnetic radiation received by the system to generate a real image at a fixed focal surface. These relay mirrors are removable in relationship to each other in order to effect the magnification. 
     According to another aspect of the invention, a reflective zoom optical system comprises a primary mirror for collecting electromagnetic radiation, a stationary secondary mirror co-axial with the primary mirror for receiving the electromagnetic radiation from the primary mirror and a plurality of curved relay mirrors positioned behind the primary mirror for receiving and successively reflecting the electromagnetic radiation. These curved relay mirrors are movable in relationship to each other in order to effect magnification. 
     According to a particular embodiment of the invention, the curved relay mirrors generate a real image at an focal surface. Still further, the focal surface remains fixed as the curved relay mirrors move in relationship to each other producing the change in magnification. 
     The above and other features of the invention including various novel details of construction and combinations of parts will now be more particularly described with reference to the accompanying drawings and pointed out in the claims. It will be understood that the particular all-reflective zoom optical imaging system embodying the invention shown by way of illustration and not as a limitation of the invention. The principles and features of this invention may be employed and varied in numerous embodiments without departing from the scope of the invention. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a side view of the first embodiment of the zoom optical reflective system at an intermediate zoom position; 
     FIG. 2 is a side view of the first embodiment of the inventive system showing three exemplary zoom positions; 
     FIG. 3 is a side view of the relay mirrors of the first embodiment at the three zoom positions; 
     FIG. 4 is a graph illustrating focal length as a function of mirror motion for the second and third relay mirror in the first embodiment; 
     FIG. 5 is a side view of the second embodiment of the inventive zoom optical reflective system at an intermediate zoom position; 
     FIG. 6 is a top view of the second embodiment of the zoom optical reflective system at an intermediate zoom position; 
     FIG. 7 is a side view of the relay mirrors of the second embodiment at the three exemplary zoom positions; 
     FIG. 8 is a graph illustrating focal length as a function of mirror motion for the second, third, and fourth relay mirrors in the second embodiment; 
     FIG. 9 is a side view of the third embodiment of the inventive zoom optical reflective system at an intermediate zoom position; 
     FIG. 10 is a top view of the third embodiment of the zoom optical reflective system at the intermediate zoom position; 
     FIG. 11 is a side view of the second embodiment showing the three exemplary zoom positions simultaneously; and 
     FIG. 12 is a graph illustrating focal length as a function of mirror motion for first and second relay mirrors in the third embodiment. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     A first embodiment of an all-reflective zoom optical system constructed according to principles of the present invention is generally illustrated in FIGS. 1 through 4. Here, a primary mirror  105  receives light entering the optical system through an entrance aperture. The light reflected from the primary mirror  105  is focused towards a secondary mirror  110  co-axial and in front of the primary mirror  105 . The primary and secondary mirrors  105 ,  110  yield a Cassegrain front end, although a Gregorian would also be possible. 
     The secondary mirror  110  reflects the light axially through an aperture  115  formed in the primary mirror to fold mirror  120 , which reflects the light laterally parallel to the back of the primary mirror. A first relay mirror RM 1  is positioned to receive the light. The first relay mirror RM 1  is constrained to have a positive curvature because of the natural aperture growth after an image when the pupil image is virtual, and the large amount of field curvature due to the Petzval sum and astigmatism. 
     A second relay mirror RM 2  receives and reflects light from the first relay mirror RM 1 . This second relay mirror RM 2  is aspheric and convex. A third relay mirror RM 3  receives light reflected from the second relay mirror RM 2 . These second and third relay mirrors RM 2 , RM 3  are movable along mutually parallel straight tracks  150 ,  152  to provide the zoom function. The curvature of the third relay mirror RM 3  is spherical. An aspheric fourth relay mirror RM 4  reflects light from the third relay mirror RM 3  onto an stationary focal surface FS where a detector assembly  160  such as charged-coupled device, for example, converts the resulting real image into an electrical signal. The stationary focal surface is very important in view of the difficulties associated with moving the detector assembly during zooming. The curvature of the focal surface FS is also aspheric with only bilaterally symmetry. As demonstrated by the following tables, however, the curvature of the focal surface is small. This feature is advantageous because focal plane detectors are expensive and difficult to make. With a relatively flat focal surface, it is possible to construct the detector assembly from several flat sections butted together. 
     Although the focal surface FS does not change or move as zoom progresses, the line of sight changes by several tenths of a degree. Also, the entrance aperture is constant across the zoom range. This is important because the angular resolution is directly proportional to the size of the entrance pupil, and since the primary mirror is the largest and most expensive part of the system, this mirror should be utilized to the fullest extent possible. 
     As illustrated by FIG. 2, only the second and third relay mirrors RM 2 , RM 3  are moved to yield the zoom function. This eases the mechanical requirements because any motions of optical elements must be extremely precise. This is especially true for the larger mirrors, such as the primary  105 , secondary  110 , and first relay mirror RM 1 . These being fixed in relationship to each other makes their mounting straight forward. Further, since the tracks  150 ,  152  on which the second and third relay mirrors RM 2 , RM 3  move are straight and mutually parallel, the mechanisms for affecting the motion of these mirrors are considerably simplified. 
     Specifically, FIG. 2 shows three possible positions of the second and third relay mirrors RM 2 , RM 3  for f-stops of 5.7, 8.5, and 11.4. FIG. 3 shows only the four relay mirrors at the three f-stop positions. Specifically, if the second and third relay mirrors are at positions RM 2   a  and RM 3   a , the effective f-stop is 5.7. Positions RM 2   b  and RM 3   b  yield an f-stop of 8.5, and RM 2   c  and RM 3   c  give an f-stop of 11.4. 
     The following Tables I and II describe the curvature of the mirrors of a first embodiment system having a normalized focal length of 100-200 lens units, a field of view of 2.2-1.1 degrees, and an entrance aperture of 17.5 lens units. 
     
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE I 
               
               
                   
               
               
                 Description 
                 Radius 
                 Thickness 
                 Index 
                 Tilt 
                 Decenter 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Primary 
                 −47.744 
                 −17.2644 
                 −1.0 
                 — 
                 — 
               
               
                 Secondary 
                 −19.3672 
                 20.7774 
                 +1.0 
                 0.005170 
                 0.042333 
               
               
                 Fold Mirror 
                 (infinite) 
                 −5.5419 
                 −1.0 
                 −0.7854* 
                 — 
               
               
                 RM1 
                 7.0472 
                 3.4674 
                 +1.0 
                 −0.15532 
                 0.6082 
               
               
                 RM2 
                 4.3304 
                 −4.4973 
                 −1.0 
                 0.10449 
                 0.23653 
               
               
                 RM3 
                 16.1565 
                 12.7995 
                 +1.0 
                 0.073625 
                 −1.21610 
               
               
                 RM4 
                 −21.2053 
                 9.9083 
                 −1.0 
                 0.13569 
                 0.68968 
               
               
                 FS 
                 35.4484 
                 — 
                 — 
                 −0.056379 
                 — 
               
               
                   
               
               
                 *Axis tilt of 1.5708 radius  
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE II 
               
             
             
               
                   
               
               
                 ASPHERIC SURFACES 
               
             
          
           
               
                   
                 Conic Constant 
                 A4 
                 A6 
               
               
                   
                   
               
             
          
           
               
                 Primary 
                 −0.884204 
                 0.141753E-6 
                 −0.738707E-11 
               
               
                 Secondary 
                 −6.87123 
                 −0.524331E-4 
                 0.519850E-6 
               
               
                 RM3 
                 −4.93398 
                 0.111101E-3 
                 −0.716056E-6 
               
               
                   
               
             
          
         
       
     
     The first and fourth relay mirrors RM 1 , RM 4  and the focal surface FS have complex aspheric curvatures such that they only have bilateral symmetry. Thus, the following equation and variable list in Table III define the surface curvature (Z) as the sag, depth from a flat plane for the first and fourth relay mirrors RM 1 , RM 4 , and the focal surface FS.              Z   =       {       α   -   β           (     1   -       C   z        α       )       1   /   2       +       (     1   -       C   z        β       )       1   /   2           }     +                     U   4            α   2          (       α   2     -     β   2       )         +       U   6            α   3          (       α   3     -     β   3       )         +       U   8            α   4          (       α   4     -     β   4       )         +                   A   1          y   3       +       A   2          x   2        y     +                   A   3          y   4       +       A   4          x   2          y   2       +       A   5          x   4       +                   A   6          y   5       +       A   7          x   2          y   3       +       A   8          x   4        y     +                   A   9          y   6       +       A   10          x   2          y   4       +       A   11          x   4          y   2       +       A   12          x   6       +                   A   13          y   7       +       A   14          x   2          y   5       +       A   15          x   4          y   3       +       A   16          x   6        y     +                   A   17          y   8       +       A   18          x   2          y   6       +       A   19          x   4          y   4       +       A   20          x   6          y   2       +       A   21          x   8       +                   A   22          y   9       +       A   23          x   2          y   7       +       A   24          x   4          y   5       +       A   25          x   6          y   3       +       A   26          x   8        y     +                   A   27          y   10       +       A   28          x   2          y   8       +       A   29          x   4          y   6       +       A   30          x   6          y   4       +       A   31          x   8          y   2       +       A   32          x   10                   α   =           C   x          (     x   -     x   0       )       2     +         C   y          (     y   -     y   0       )       2                   β   =         C   x          x   0   2       =       C   y          y   0   2                     γ   =     1   /         C   x   2     +     C   y   2                                        
     
       
         
               
             
               
               
               
               
             
           
               
                 TABLE III 
               
               
                   
               
               
                 VARIABLE LIST 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 RM1 
                 CX = 1.41917194E−1 
                 CY = 1.41824485E−1 
                 CZ = −9.30309262E−4 
               
               
                   
                 X0 = 0.00000000000 
                 Y0 = 0.445660962 
               
               
                   
                 U4 = 5.4787809E−4 
                 U6 = 9.33809254E−6 
                 U8 = 0.00000000 
               
               
                   
                 U10 = 0.0000000 
                 A1 = −3.08178439E−4 
                 A2 = 6.03435251E−5 
               
               
                   
                 A3 = 1.9955499E−5 
                 A4 = −1.39060583E−5 
                 A5 = 2.42786600E−6 
               
               
                   
                 A6 = 0.0000000 
                 A7 = 0.00000000 
                 A8 = 0.00000000 
               
               
                   
                 A9 = −2.9945348E−7 
                 A1 = 1.33395986E−4 
                 A11 = 9.32324104E−6 
               
               
                   
                 A12 = −1.6926475E−5 
                 A13 = 4.61743259E−6 
                 A14 = 0.00000000 
               
               
                   
                 A15 = 0.0000000 
                 A16 = 0.00000000 
                 A17 = 6.98827096E−5 
               
               
                   
                 A18 = −3.3252476E−6 
                 A19 = −5.81910633E−7 
                 A20 = 2.16719860E−7 
               
               
                   
                 A21 = 0.00000000 
                 A22 = 0.00000000 
                 A23 = 0.0000000 
               
               
                   
                 A24 = 5.2686499E−7 
                 A25 = 2.16014672E−7 
                 A26 = 0.0000000 
               
               
                   
                 A27 = 0.00000000 
                 A28 = 0.00000000 
                 A29 = 0.0000000 
               
               
                   
                 A30 = 0.00000000 
                 A31 = 0.00000000 
                 A30 = 0.0000000 
               
               
                 RM4 
                 CX = −5.0317739E−2 
                 CY = −4.43746207E−2 
                 CZ = −2.83395355E−4 
               
               
                   
                 X0 = 0.00000000 
                 Y0 = 0.330973591 
               
               
                   
                 U4 = 5.4659765E−5 
                 U6 = 7.92740345E−7 
                 U8 = 0.000000000 
               
               
                   
                 U10 = 0.00000000 
                 A1 = 8.29030409E−4 
                 A2 = 9.43869569E−5 
               
               
                   
                 A3 = 8.0814757E−6 
                 A4 = −1.72817754E−7 
                 A5 = −5.1817582AE−8 
               
               
                   
                 A6 = 0.00000000 
                 A7 = 0.000000000 
                 A8 = 0.000000000 
               
               
                   
                 A9 = 7.4436903E−5 
                 A10 = −4.01938503E−5 
                 A11 = 9.71503596E−6 
               
               
                   
                 A12 = 1.5981259E−6 
                 A13 = 2.73891567E−8 
                 A14 = 0.000000000 
               
               
                   
                 A15 = 0.00000000 
                 A16 = 0.000000000 
                 A17 = −4.40484774E−5 
               
               
                   
                 A18 = 1.1386030E−6 
                 A19 = 9.21649842E−7 
                 A20 = −6.4074787E−10 
               
               
                   
                 A21 = 0.00000000 
                 A22 = 0.000000000 
                 A23 = 0.000000000 
               
               
                   
                 A24 = 3.3804981E−7 
                 A25 = −2.2291977E−11 
                 A26 = 0.000000000 
               
               
                   
                 A27 = 0.00000000 
                 A28 = 0.000000000 
                 A29 = 0.000000000 
               
               
                   
                 A30 = 0.00000000 
                 A31 = 0.000000000 
                 A32 = 0.000000000 
               
               
                 FS 
                 CX = 2.8213747E−2 
                 CY = 2.82137427E−2 
                 CZ = 9.88486234E−2 
               
               
                   
                 X0 = 0.00000000 
                 Y0 = 0.295266260 
               
               
                   
                 U4 = 0.00000000 
                 U6 = 0.000000000 
                 U8 = 0.000000000 
               
               
                   
                 U10 = 0.00000000 
                 A1 = 0.000000000 
                 A2 = 0.000000000 
               
               
                   
                 A3 = 0.00000000 
                 A4 = 0.000000000 
                 A5 = 0.000000000 
               
               
                   
                 A6 = 0.00000000 
                 A7 = 0.000000000 
                 A8 = 0.000000000 
               
               
                   
                 A9 = 3.19680393E−3 
                 A10 = 0.000000000 
                 A11 = 0.000000000 
               
               
                   
                 A12 = 0.00000000 
                 A13 = 0.000000000 
                 A14 = 0.000000000 
               
               
                   
                 A15 = 0.00000000 
                 A16 = 0.000000000 
                 A17 = −4.89804420E−2 
               
               
                   
                 A18 = −1.31987997E−2 
                 A19 = 0.000000000 
                 A20 = 0.000000000 
               
               
                   
                 A21 = 0.00000000 
                 A22 = 0.000000000 
                 A23 = 0.000000000 
               
               
                   
                 A24 = 1.56793790E−4 
                 A25 = 0.000000000 
                 A26 = 0.000000000 
               
               
                   
                 A27 = 0.00000000 
                 A28 = 0.000000000 
                 A29 = 0.000000000 
               
               
                   
                 A30 = 0.00000000 
                 A31 = 0.000000000 
                 A32 = 0.000000000 
               
               
                   
               
             
          
         
       
     
     FIG. 4 shows the focal length of the system as a function of mirror motion of the second and third relay mirrors RM 2 , RM 3  in the normalized scale of the lens units. 
     In some applications, the relay mirrors RM 1 , RM 2 , RM 3 , RM 4  shown in FIG. 3 could be retrofitted into a existing conventional Cassegrain front-end optical system. In this situation, the curvatures may require adjustments to optimize the resulting system. 
     A second embodiment of an all-reflective zoom optical system is generally shown in FIGS. 5 and 6, which illustrate a side and top views, respectively. This system is generally similar to the first embodiment except that the fourth relay mirror is not stationary. Here, a primary mirror  205  receives light entering the optical system through an entrance aperture. The curvature of the primary mirror  205  is close to parabolic. 
     The light the primary mirror  205  collects is reflected and focused toward a secondary mirror  210  coaxial and in front of the primary mirror  205 . This secondary mirror  210  is convex with an essentially hyperbolic curvature. 
     The light reflecting off the secondary mirror  210  is reflected axially through an aperture  215  formed in the primary mirror  205  to a first relay mirror RM 1 ′ positioned behind the primary mirror  205 . This first relay mirror RM 1 ′ has a concave spherical curvature and is stationary. 
     A second relay mirror RM 2 ′ receives the light from the first relay mirror RM 1 ′. This second relay mirror RM 2 ′ is aspheric and concave. Its curvature is close to hyperbolic. The third relay mirror RM 3 ′, which receives light from the second relay mirror RM 2 ′, is convex with an oblate spheroid curvature. 
     Finally, a fourth relay RM 4 ′ having a concave curvature receives light from the third relay RM 3 ′ and reflects it onto an focal surface FS, which is stationary as zoom progresses. The fourth relay mirror RM 4 ′ has a simple spherical curvature. 
     The second, third, and fourth relay mirrors RM 2 ′, RM 3 ′, and RM 4 ′ are movable to provide the zoom function. As the telescopic system is zoomed through its range, each of second through fourth relay mirrors moves varying amounts, but each of the mirrors move along mutually parallel tracks  250 ,  252 ,  254 . FIG. 7 shows the relay mirror positions for f-stops of 8.42, 10.0, and 11.42, respectively. This movement yields a zoom range of 1.4:1, which will maintain a constant ground sample distance with obliquities to 45°. 
     Specifically, if the second, third, and fourth relay mirrors are at positions RM 2 ′ a , RM 3 ′ a , and RM 4 ′ a  the effective f-stop is 8.42. Positions RM 2 ′ b , RM 3   b , RM 4 ′ b  yield an f-stop of 10.0, and RM 2 ′ c , RM 3 ′ c , RM 4 ′ c  give an f-stop of 11.42. 
     The focal surface FS is curved both spherically and aspherically. Again, although the focal surface does not change as zoom progresses, the line of sight changes by several tenths of a degree. Further, the entrance aperture remains constant across the zoom range so that angular resolution is maintained. 
     The following TABLES IV and V summarize the mirror curvatures for a system having a focal length of 100.0 lens units at an f-stop of 8.4 and a field of view of +/−0.022 radians. 
     
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE IV 
               
               
                   
               
               
                 De- 
                   
                   
                   
                   
                   
               
               
                 scrip- 
               
               
                 tion 
                 Radius 
                 Thickness 
                 Index 
                 Tilt 
                 Decenter 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Primary 
                 −49.9878 
                 −20.0855 
                 −1.0 
                 — 
                 — 
               
               
                 Second- 
                 −12.5504 
                 −30.0771 
                 +1.0 
                 −0.48488E−3 
                 — 
               
               
                 ary 
               
               
                 RM1′ 
                 −13.9143 
                 −5.1942 
                 −1.0 
                   0.29298E−1 
                 −0.1889E−2 
               
               
                 RM2′ 
                 23.9055 
                 2.9336 
                 +1.0 
                   0.89274E−2 
                 −0.87549 
               
               
                 RM3′ 
                 8.8092 
                 −6.7346 
                 −1.0 
                 −0.30791E−2 
                 −0.65879 
               
               
                 RM4′ 
                 10.2646 
                 7.2463 
                 +1.0 
                 −0.63802E−1 
                 −0.89448E−1 
               
               
                 FS 
                 14.1270 
                 — 
                 — 
                 — 
                 −0.11651 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE V 
               
             
             
               
                   
               
               
                 Aspheric Surfaces 
               
             
          
           
               
                   
                 Conic Constant 
                 A4 
                 A6 
               
               
                   
                   
               
             
          
           
               
                 Primary 
                 −1.00016 
                 0.284771E−7 
                 0.164556E−10 
               
               
                 Secondary 
                 −1.03499 
                 0.107770E−3 
                 −0.421084E−6 
               
               
                 RM1′ 
                 −38.8240 
                 0.282942E−3 
                 −0.640832E−5 
               
               
                 RM3′ 
                 5.88226 
                 −.794994E−3 
                 −0.550291E−4 
               
               
                 IS 
                 −0.794994E−3 
                 0.464797E−3 
                 −0.74795E−4 
               
               
                   
               
             
          
         
       
     
     FIG. 8 is a graph of the focal length of the system as a function of mirror movement of the second RM 2 ′, third RM 3 ′, and fourth RM 4 ′ relay mirrors in the normalized scale of lens units. 
     Turning now to FIGS. 9 and 10, a side and top view, respectively, of third embodiment of the inventive system is shown. This third embodiment of the inventive system is shown. This third embodiment maintains the Cassegrain front end including a primary mirror  305  and a secondary mirror  310 , but instead of four relay mirrors, only two aspheric relay mirrors are used. Specifically, a first relay mirror RM 1 ″ receives the light from the secondary mirror  310  through an aperture  315  of the primary mirror  305 . This first relay mirror RM 1 ″ is concave with a general aspheric curvature. A second relay mirror RM 2 ″ receives the light reflected by the first relay mirror RM 1 ″ and directs it to a fixed focal surface FS. The second relay mirrors RM 2 ″ also has a general aspheric curvature. In comparison with the second embodiment system, the two mirror relay is substantially longer. 
     FIG. 11 shows the two mirror relay section of the third embodiment at three possible zoom settings i.e. f-stops of 8.4, 10.0, and 11.42. Specifically, RM 1 ″ a  and RM 2 ″ a  are the positions of the first and second relay mirrors for an f-stop of 8.42; RM 1 ″ b  and RM 2 ″ b  correspond to an f-stop of 10.0 and RM 1 ″ c  and RM 2 ″ c  correspond to an f-stop of 11.42. Here again, the focal surface FS is fixed for all zoom positions. 
     Tables VI and VII set forth the lens curvatures in a normalized scale of 100.0 lens units at an f-stop of 8.3 with a maximum field of view of +/−0.023 radians. 
     
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE VI 
               
               
                   
               
               
                 Description 
                 Radius 
                 Thickness 
                 Index 
                 Tilt 
                 Decenter 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Primary 
                 −55.5476 
                 −19.7256 
                 −1.0 
                 — 
                 — 
               
               
                 Secondary 
                 −25.9706 
                 +37.1403 
                 +1.0 
                 −0.014967 
                 −2.3823 
               
               
                 RM1″ 
                 −19.7006 
                 −10.6741 
                 −1.0 
                 −0.044252 
                 −1.9499 
               
               
                 RM2″ 
                 +171.3684 
                 +12.7803 
                 +1.0 
                 −0.041896 
                 −4.9959 
               
               
                 FS 
                 +13.9632 
                 — 
                 — 
                 — 
                 — 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE VII 
               
             
             
               
                   
               
               
                 Aspheric Surfaces 
               
             
          
           
               
                   
                 Conic Constant 
                 A4 
                 A6 
               
               
                   
                   
               
             
          
           
               
                 Primary 
                 −1.13701 
                 −0.146316E−6 
                 −0.491552E−11 
               
               
                 Secondary 
                 −2.92913 
                 0.639009E−5 
                 −0.457040E−7 
               
               
                 RM1″ 
                 −3.25903 
                 −0.423483E−4 
                 0.106308E−6 
               
               
                 RM2″ 
                 −0.939589 
                 0.110288E−3 
                 −0.247716E−5 
               
               
                 FS 
                 0.0 
                 −0.319432E−3 
                 0.143885E−4 
               
               
                   
               
             
          
         
       
     
     FIG. 12 is a graph of the system focal length as a function of mirror movement of the first RM 1 ″ and second RM 2 ″ relay mirrors in the normalized scale of lens units for the third embodiment. 
     Those skilled in the art will know or be able to ascertain using no more than routine experimentation, many equivalents to the specific embodiments of the invention described herein. These and all other equivalents are intended to be encompassed by the followed claims.