Abstract:
New families of two mirror unobscured telescopes with compact Schiefspiegler, eccentric pupil Cassegrain geometries, incorporating aspheres, tilted and decentered secondaries, and tilted decentered focal surfaces. These variables allow control of focal surface tilt. All embodiments, from f/5 to f/16, are totally reflecting, fully baffled systems, with wide diffraction limited FOVs and unobscured aperture MTFs. Systems optimized with the focal plane normal to the gut ray are well suited for visual and general use. They can incorporate a variable iris for f/number control and allow focusing along the gut ray with minimal field tilt. Systems optimized with a fixed focal plane tilt are well suited for high resolution, wide field collimators and IR scene generators. Any light reflected at focus can be trapped, eliminating Narcissus or “cats eye” effects. Additionally, this reflection can be used to provide a uniform “background” irradiance field.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to Provisional Application Ser. No. 61/350,102, filed on Jun. 1, 2011, entitled “All Reflective 2 Mirror Unobscured Wide Field Visual Telescope and Collimator Designs”, owned by the Applicant hereof and hereby expressly incorporated by reference herein. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     (Technical Field) 
     The presently claimed invention relates to optics and more particularly to two mirror unobscured telescope designs of compact “Schiefspiegler”, off axis Cassegrain geometry, incorporating aspheres, tilted and decentered secondary, and tilted focal surfaces, which serve as fast, high resolution, moderately wide field telescopes/collimators. The tilted focal surfaces allow for new unique and desirable properties of the unobscured systems. 
     2. Background Art 
     Since the popularization of affordable amateur telescopes, there has been an ongoing argument between the reflector owners and the refractor owners, over which system is better. Reflecting telescopes have no color aberrations, but the central obscuration from the secondary causes loss of light as well as diffraction effects which degrade the image. The central obscuration in the pupil causes a reduction of the Strehl ratio of a point image and a decrease in mid spatial frequencies in the Optical Modulation Transfer Function (MTF). In addition, the secondary mirror support, or “spider”, gives rise to the familiar “star” shaped diffraction pattern about bright stars. Refracting telescopes have no central obscurations but suffer from color aberrations, which can usually be only partially corrected using two lens elements. These color effects are not present in reflecting telescopes. Further, two element refractor apertures are smaller than reflectors for the same price, affording less light gathering power, or with more lens elements get much more expensive, heavier, and start having problems with unwanted reflections and stray light. 
     More complicated optical systems, such as the many variations of Schmidt-Cassegrains with refractive correctors, can, like refractors, only be optimized in a particular region of the spectrum and often suffer from compromises made in surface figure complexity to lessen the cost of the optical system. 
     Unobscured all reflecting telescopes designs suffer from neither MTF degradation nor color aberrations. Still, very few unobscured system designs have been produced in any quantity due to other issues. The designs in the literature are typically of small aperture, high f/number, and are often complicated in alignment and mounting. 
     The problem with prior art centered two mirror visual optical systems is the secondary and spider support: 
     occult light—reducing system throughput; 
     produce diffraction effects, which causes the focus of the system to be broader, thus lowering the MTF of the system; and 
     produce opto-mechanical mounting problems due to the conflicting requirements of simultaneously mounting the secondary mirror to tolerances while minimizing the shadow cast by the secondary holder and spider. 
     The problems with prior art one and two mirror eccentric pupil or off axis designs for visual use are: 
     they have troubling focal plane tilt; 
     they are hard to baffle properly, and 
     they have smaller usable fields of view than their equivalent diameter centered optical systems. 
     For collimator use, prior art designs are centered systems which have obscuring optics which: 
     occult light and thereby underfill the optical system they are used in conjunction with; 
     reflections from the target retical produce reflections which can cause narcissus effects in the system under test; and 
     the reflecting area of the target retical can produce background signals of unknown and or uncontrolled amplitude. 
     For collimator use current eccentric pupil systems are limited in usable field of view and may have reflections from the target retical which are uncontrolled, possibly resulting in narcissus effects or providing a nominal field background which is radiometrically uncontrolled. 
     The problems with three and more mirror unobscured optical systems are their complexity and difficulty of alignment. 
     There are currently four prior art systems that attempt to provide a solution to the existing problems. These include the Schiefspiegler telescope, an unobscured, tilted field Newtonian telescope, a notionally, eccentric pupil Cassegrain telescope or Ritchey-Chre´tien, (R-C), designs. The shortcomings of these devices are many. The Schiefspeigler telescope is too “slow” due to a high f/number and low throughput and too small a working field of view. The unobscured Newtonian device is also similarly “slow”. The eccentric pupil Cassegrain (or R-C) tilted field of view and non-gut ray centered focus “walk” or focus remains on the geometric axis of symmetry while shifting from the gut ray. The three or more mirror systems are more costly to build and difficult to align. 
     Conventional wisdom in optical system design is to avoid tilts and decenters, except on an “individually compensating basis” so as to allow the entire system to be simply modeled using classical aberration theory. Modeling this system using classical aberration theory would be just so “messy” that optical designers have avoided doing it—hence we have not seen this design before. An expert, who is also an amateur astronomer, who has looked into midsized, reasonably fast, unobscured designs for amateur telescope, has proposed that this would require 3 or more mirror elements. 
     Quoting from the conclusion of a recent review article, “The World of Unobstructed Reflecting Telescopes” by José Sasián: “The known designs cover very well the span of small (3 to 5 inches) and medium apertures (6 to 8 inches) with great practicality and transportability. However, for larger apertures (10 inches or more), there is a need for very compact and moderately fast designs, (f/8 to f/15). These designs will probably require three mirrors and a double-curvature surface like the large Tri-Schiefspiegler discussed in section . . . . ” 
     The prior art approaches (other than the Schiefspeigler, where it hardly matters due to the very high f/number) do not even attempt to control the tilt of the focal plane of the system. For visual use the tilted focal plane, when brought to focus in the eye, causes the image at one side to be out of focus in one direction, while at the other side, it is out of focus in the other direction. Additionally, baffling against stray light becomes a serious issue for low f/number Cassegrain systems. The incidence angle of the gut ray to the focal plane surface causes problems for the prior art system when used visually. As the f/numbers are reduced, or as power and field of view of an eyepiece increase, the focal surface of the image in the eye diverges from the retina.  FIG. 1  shows the large angle, (9.5 degrees), which the focal surface makes with respect to the gut ray of a nominally 10″ aperture, f/7 eccentric pupil Cassegrain which can also be baffled. If the system is compressed radially, to lessen this angle to the focal surface, the baffling will fail. Thus, for low f/number systems, the off axis Cassegrain has a necessarily large angle at the focal surface if the stray light is suppressed. 
     The nine 9.5 degree incidence angle of the gut ray to the focal plane surface causes problems for the system when used visually. As the f/numbers are reduced, or as power and field of view of an eyepiece increase, the focal surface of the image in the eye diverges from the retina.  FIG. 2  shows an “ideal” paraxial optical model of a f/7 Off Axis Cassegrain with 9.6 degree focal surface tilt. Assuming a 1″ efl eyepiece and a 9.6 degree image tilt in eye at 70×1″ efl eye, (70×), the image tilt on the back of the eye is 9.6 degrees. This situation worsens with increase in power. With a ½″ efl eyepiece, (140×), as shown in  FIG. 3 , things are a factor of 2 worse, with the image tilt on the back of the eye now 19.2 degrees. 
     A modest image tilt is not a particularly vexing problem for imaging systems with film or a CCD, (Charge Coupled Device), electronic imaging array at the focal lane. Linear distortion is a small problem. On the other hand, visual imaging with an eyepiece may be a serious problem, especially at system f/numbers of f/8 or less. This would also be a problem with the off axis Newtonian Telescopes at lower f/numbers although the baffling requirement becomes more severe for the Cassegrain. 
     Control of the tilt of the focal plane allows the system to be used for lower f/number, a wider field of view, higher resolution and better MTF. For visual and imaging optics this allows much better focusing properties and the ability to aperture the unobscured pupil with an iris. For collimating and IR scene generating optics, the tilt of the focal plane allows reflections from the target reticle to be controlled eliminating Narcissus and allowing the field over the reflective portion of the retical to be illuminated with a constant irradiance. 
     SUMMARY OF THE INVENTION 
     Disclosure of the Invention  
     A described above, there are no unobscured telescope designs which incorporate control of the tilt of the focal plane with the wide field of view of the best centered two mirror designs, such as Cassegrain or R-C designs. To overcome the shortcomings of the prior art and to solve the problems described above, the presently claimed invention is disclosed. 
     The first of the new two mirror telescope called “nCUB” designs, n for normal incidence field of view (FOV), C for conic optical surfaces, U for unobscured entrance pupil and B for baffled, provide “conventional fields of view” with no central obscuration and control of the focal plane surface, normal to the gut ray field point, providing superior visual performance to the tilted focal plane of more conventional unobscured or eccentric pupil one or two mirror systems. 
     Alternately, the “tCUB” family of designs, t for tilted, C for conic optical surfaces, U for unobscured entrance pupil and B for baffled, provide for control of the tilt of the focal surface for control of reflections from that surface for use in collimators, and IR scene generators. Additionally this design technique can be used for optical systems for “covert use” which do not want a “cats eye” reflection to be produced at the focal plane, and reflected back out of the system in a manner which might allow detection of the optical device. In addition by controlling the tilt of the focal plane retical, reflections of a standard brightness or color temperature background may be provided in the reflecting areas of the retical instead of having these areas of unknown or uncontrolled background amplitude. 
     Other objects, advantages and novel features, and further scope of applicability of the presently claimed invention will be set forth in part in the detailed description to follow, taken in conjunction with the accompanying drawings, and in part will become apparent to those skilled in the art upon examination of the following, or may be learned by practice of the claimed invention. The objects and advantages of the claimed invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated into and form a part of the specification, illustrate several embodiments of the presently claimed invention and, together with the description, serve to explain the principles of the claimed invention. The drawings are only for the purpose of illustrating a preferred embodiment of the claimed invention and are not to be construed as limiting the claimed invention. In the drawings: 
         FIG. 1  is Prior Art—Drawing of baffled off axis—eccentric pupil Cassegrain—10″ diameter f/7 optical system—showing focal plane tilt. 
         FIG. 2  is Prior Art—Screen dump of ZEMAX modeling of effect of focal plane tilt on visual use of an eyepiece at 70× 
         FIG. 3  is Prior Art—Screen dump of ZEMAX modeling of effect of focal plane tilt on visual use of an eyepiece at 140× 
         FIG. 4  is drawing for detailed description of optical system geometry 
         FIG. 5  is drawing for detailed description of primary mirror geometry 
         FIG. 6  is drawing for detailed description of secondary mirror geometry 
         FIG. 7  is drawing for detailed description of focal plane geometry 
         FIG. 8  is drawing for detailed description of iris and gut ray geometry 
         FIG. 9  is drawing for detailed description of system baffling geometry 
         FIG. 10  is drawing for detailed description of nCUB focusing geometry 
         FIG. 11  drawing for detailed description of tCUB stray light suppression 
         FIG. 12  is table of mirror radii and thickness for nCUB systems f/5-f/16 
         FIG. 13  is table of conic constants, decenters and tilts for nCUB f/5-f/16 
         FIG. 14  is table of mirror radii and thickness for tCUB systems f/5-f/16 
         FIG. 15  is table of conic constants, decenters and tilts for tCUB f/5-f/16 
         FIG. 16  is ZEMAX screen dump—f/5 nCUB optics and properties 
         FIG. 17  is ZEMAX screen dump—f/6 nCUB optics and properties 
         FIG. 18  is ZEMAX screen dump—f/7 nCUB optics and properties 
         FIG. 19  is ZEMAX screen dump—f/8 nCUB optics and properties 
         FIG. 20  is ZEMAX screen dump—f/9 nCUB optics and properties 
         FIG. 21  is ZEMAX screen dump —f/10 nCUB optics and properties 
         FIG. 22  is ZEMAX screen dump—f/10.7 nCUB optics and properties 
         FIG. 23  is ZEMAX screen dump—f/12 nCUB optics and properties 
         FIG. 24  is ZEMAX screen dump—f/14 nCUB optics and properties 
         FIG. 25  is ZEMAX screen dump—f/16 nCUB optics and properties 
         FIG. 26  is ZEMAX screen dump—f/7 system at infinite object distance 
         FIG. 27  is ZEMAX screen dump—f/7 system at 2640′ object distance 
         FIG. 28  is ZEMAX screen dump—f/7 system at 1000′ object distance 
         FIG. 29  is ZEMAX screen dump—f/7 system at 417′ object distance 
         FIG. 30  is ZEMAX screen dump—f/5 tCUB optics and properties 
         FIG. 31  is ZEMAX screen dump—f/5 tCUB stray light control 
         FIG. 32  is ZEMAX screen dump—f/6 tCUB optics and properties 
         FIG. 33  is ZEMAX screen dump—f/6 tCUB stray light control 
         FIG. 34  is ZEMAX screen dump—f/7 tCUB optics and properties 
         FIG. 35  is ZEMAX screen dump—f/7 tCUB stray light control 
         FIG. 36  is ZEMAX screen dump—f/8 tCUB optics and properties 
         FIG. 37  is ZEMAX screen dump—f/8 tCUB stray light control 
         FIG. 38  is ZEMAX screen dump—f/9 tCUB optics and properties 
         FIG. 39  is ZEMAX screen dump—f/9 tCUB stray light control 
         FIG. 40  is ZEMAX screen dump—f/10 tCUB optics and properties 
         FIG. 41  is ZEMAX screen dump—f/10 tCUB stray light control 
         FIG. 42  is ZEMAX screen dump—f/10.7 tCUB optics and properties 
         FIG. 43  is ZEMAX screen dump—f/10.7 tCUB stray light control 
         FIG. 44  is ZEMAX screen dump—f/12 tCUB optics and properties 
         FIG. 45  is ZEMAX screen dump—f/12 tCUB stray light control 
         FIG. 46  is ZEMAX screen dump—f/14 tCUB optics and properties 
         FIG. 47  is ZEMAX screen dump—f/14 tCUB stray light control 
         FIG. 48  is ZEMAX screen dump—f/16 tCUB optics and properties 
         FIG. 49  is ZEMAX screen dump—f/16 tCUB stray light control 
         FIG. 50  is ZEMAX screen dump—f/7 tUBA optics and properties 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Best Modes for Carrying out the Invention 
     The presently claimed invention is based upon the general layout of a two mirror eccentric pupil unobscured Cassegrain optical system, consisting of a concave primary mirror and a convex secondary mirror. 
     As shown in  FIG. 4 , ray of light  10  from the center of object surface  00 , goes through center of the entrance pupil  02 , of the telescope, reflects off of the center of primary mirror  04 , reflects again off of the center of secondary mirror  06 , and forms a portion of the image at the center focal plane surface  08 . This ray which reflects at or traverses the center of all these surfaces is commonly referred to as the gut ray  10 . The centers of all optical surfaces  00 ,  02 ,  04 ,  06 ,  08  lie in a plane  20 , which is the plane of mirror symmetry for the system. All three ray vector paths of gut ray  10  lie completely in the plane of mirror symmetry for system  20 , as well. 
     As shown in  FIG. 5 , primary mirror  04 , is an off axis section of a rotationally symmetric aspheric concave mirror  12 , referred to as a parent mirror. The section or primary mirror  04  which is used does not contain the axis of symmetry  14  of the primary mirror&#39;s rotationally surface figure. The axis of symmetry of parent mirror is parallel to gut ray  10 , incident on primary mirror  04  and both vectors lie in plane of mirror symmetry  20 . The primary center offset, Op  16 , is the perpendicular distance from the center of convex primary mirror  04  to the axis of symmetry of the parent mirror surface  12 . If parent mirror surface  12  is a conic, it may be defined mathematically about axis of symmetry  14  by the vertex radius Rp and conic constant Kp, then the surface of primary mirror  04  that is being used is fully defined by offset Op  16 , diameter of the mirror Dp  18  and the parent surface vertex radius Rp and conic constant Kp. 
     A standard formula for a conic optical mirror surface (“sag”), Z(r) about its axis of symmetry in terms of c=1/Rs (the vertex radius), and k=conic constant Ks is:
 
 Z ( r )=( c*r^ 2)/(1+sqr(1−((1 +k )* c^ 2* r^ 2)))
 
     More complex parent mirror surfaces may be polynomial surfaces of rotation about the vertex axis or even torroidal surfaces, which are once again defined about the vertex axis, but may have only mirror symmetry about the plane of symmetry for optical system  20 . For simplicity, this disclosure will be described in the conic form, but the geometry of the primary and secondary surfaces can be generalized into both rotationally symmetric polynomial surfaces and further to torroidal surfaces symmetric about the plane of mirror symmetry for system  20 , and this disclosure is intended to include these other embodiments 
     As shown in  FIG. 6 , secondary mirror  06 , is an off axis section of a rotationally symmetric aspheric convex parent mirror  22 , and is similar to the situation of the primary mirror  04  described previously. Section of secondary mirror  06  which is used does not contain the axis of symmetry  24  of the secondary mirror&#39;s rotationally symmetric surface. The perpendicular offset distance of the center of the mirror from the axis of symmetry is defined as Os  26  and the diameter of the secondary mirror is defined as Ds  28 . As with the primary mirror, if parent mirror surface  22  is defined by the vertex radius Rs and conic constant Ks, then the surface of the secondary mirror  06  is fully defined by offset Os  26 , diameter Ds  28 , radius Rs and conic constant Ks of parent mirror surface  22 . 
     Still referring to  FIG. 6 , the vertex of the convex secondary parent mirror  22  is displaced from the primary mirror vertex axis  14 , distances parallel  30  and perpendicular  32  to the primary vertex  14 . Both vectors  30  and  32  lie in mirror symmetry plane of system  20 . The axis of symmetry of secondary mirror  24  is tilted with respect to the axis of symmetry of primary mirror  14 , such that the two axes are in the same plane, but tilted by an angle Theta S  32 . 
     As shown in  FIG. 7 , focal plane  08 , is a circular plane surface centered on the gut ray  10 . The axis of focal plane  08  is situated with respect to the vertex axis of secondary mirror  24  by a distance along the vertex axis  36  and a distance perpendicular to it  38 . Again, both vectors  36  and  38 , lie in the mirror symmetry plane of the system  20 . As with the previous embodiments of the surfaces, the axis normal the center of focal plane  40  is tilted with respect to the axis of symmetry of secondary  24 , such that the two axes are in the same plane, but tilted by an angle Theta F  42 . The angle between focal surface normal  40  and gut ray  10  at incidence of focal surface  08  strikes an angle Gamma F  44 . Note that Gamma F may be zero, i.e., the gut ray  10  may be perpendicular to the focal surface  08 . 
     As shown in  FIG. 8 , the surface spacings along the gut ray are defined as: 1/ the distance from object surface  00  to entrance pupil center  02 , So-e  52 , 2/ the distance from the center of entry pupil center  02  to the center of the primary  04 , Se-p  54  and, 3/ the distance from the center of the primary mirror  04  to the center of secondary mirror  06 , Sp-s  56  and 4/the distance from the center of secondary mirror  06  to the center of focal plane  08 , Ss-f  58 . An iris  50 , preferably of an adjustable and variable diameter, may be positioned at entrance pupil  02  and centered about gut ray  10 , to vary the f/number of the system. The angle between incident gut ray  10  and the surface normal at the center of primary mirror  04  is Gamma P  48  and the angle between incident gut ray  10  and the surface normal at the center of secondary mirror  06  is Gamma S  46 . 
     As shown in  FIG. 9 , baffling is accomplished by circular stop  62 , or iris  50 , at entrance pupil  02 , and a pair of flat obscuring baffles  64  and  66 , perpendicular to the plane of the symmetry of mirror system  20 . First baffle  64 , arranged just outside the overlap of the bundle of light flowing between entrance pupil  02  and primary mirror  04  and the bundle of light between the primary mirror  04  and secondary mirror  06 . Second baffle  66 , is arranged just outside the overlap of the bundle of light flowing between the between the primary mirror  04  and secondary mirror  06  and the bundle of light flowing between secondary mirror  06  and focal surface  08 . In a well baffled system, an arbitrary ray  68  entering through the circular stop  62 , or iris  50 , which can just get passed two baffles  64  and  66  will not impinge on focal surface  08 . 
       FIGS. 10 and 11  show the difference in angle of the normal to the focal plane, relative to the gut ray incident at focus, Gamma F  44  between the nCUB, (Gamma F is zero), and related visual and photographic systems and the tCUB, (Gamma F is non zero), and related collimator and scene generator systems. 
     As shown in  FIG. 10 , for the visible and photographic, nCUB, systems, the tilt of focal plane  08  to gut ray  10  is configured so the angle, Gamma F  44  is equal to zero. With the focal surface perpendicular to the incident gut ray, focusing along gut ray  10  is simple, as an arbitrary focal plane surface  70  corresponding to a nearer object distance  52 , than the normal “infinite conjugate” focal plane  08  remains perpendicular and centered to extended gut ray  10  without lateral image walk. In addition, the action of an iris  50  is symmetric about gut ray  10  at an arbitrary focus position  70 . 
     As shown in  FIG. 11  for the tCUB IR collimator, for scene generators and the like, the tilt of focal plane  44 , Gamma F is non zero and a predetermined fixed angle. The optical system geometry not only allows reticle  72  to be imaged “perfectly” to the collimator output, but also allows light from a system being tested  80 , reflecting from a reticle  72  at the focal surface to be diverted to a baffle  74  and eliminated. This can be used to prevent narcissus and “cats eye” reflections from going back out the entrance pupil of the optical system. In the case of an IR scene generator, baffle  74  can be a uniform emitting surface maintained at a low temperature to provide a uniform background irradiance in between the higher emittance apertures in the reticle. 
     The basic elements for the disclosed embodiments are: two mirrors and the geometry of their surfaces and the placement of the mirrors with respect to each other, the positions of the object planes and entrance pupil, and the tilt and position of the focal plane; baffles to control stray light; focus of the normal focal plane along the gut ray of the system as in the nCUB; or tilt of a reticle at the focal plane and the baffling of the stray light reflected from it, the use of a low temperature emitting the surface to create a uniform background in the reflected area of the reticle as in the tCUB; and optionally an iris to control the f/number or speed of the system. 
     INDUSTRIAL APPLICABILITY  
     The claimed invention is further illustrated by the following non-limiting examples. 
       FIGS. 12 through 14  show the variation of several relevant geometric factors for the nCUB family of telescopes from f/5 to f/16. Again, all are scaled to an aperture of 10 inches. All optical analysis for the nCUB optical systems are shown for a single visible wavelength of 0.55 um, all tCUB for an infrared wavelength of 1.0 um. Since there are no color effects, other than diffraction, all aberrations are purely geometric and because of this, the performance of any sized system at any wavelength can be found by the appropriate scaling. 
     Note that in ZEMAX the decenter and tilt the secondary is measured with respect to the vertex axis of the decentered primary mirror, and the tilt and decenter of the focal plane may be measured relative to the vertex axis of the decentered secondary mirror. 
     EXAMPLE I 
     nCUB Visual Telescopes 
     For systems which have been optimized for a focal surfaces orthogonal to the axis of the gut ray, disclosed is a family of nCUB optical systems from f/5 to f/16. These systems are described by the optical prescription parameters from ZEMAX, which are shown in  FIGS. 12 and 13 .  FIG. 12  shows spreadsheet compilations and plots of mirror radii and spacings.  FIG. 13  shows spreadsheet compilations and plots of conic constants, decenters and tilts. 
       FIGS. 16 through 25  are printouts of ZEMAX screen dumps for nCUB optical systems from f/5 through f/16. The printouts give a complete description of the optical device in terms of surfaces, surface vertex radius, thicknesses between surfaces, conic constants of the surfaces, tilts and decenters. There is a line drawing of the optical system as well as a field performance “map” and wavefront error plot versus field plot, field curvature/distortion plot, and “FFT Diffraction Ensquared Energy Half Width plot, which gives theoretical spot sizes for different field points. ZEMAX is a professional Optical design software which is a product of ZEMAX Development Corporation, 3001 112 th  Ave NE, Suite 202, Bellevue, Wash. 98004-8017. 
     A list of the parameters used in the detailed description of the device and their nominally corresponding ZEMAX parameter values follow: 
     
       
         
               
               
               
             
           
               
                   
                   
               
               
                   
                 Detailed Device Parameter 
                 Corresponding ZEMAX Parameter 
               
               
                   
                   
               
             
             
               
                   
                 Object Surface 00 
                 Surface # OBJ 
               
               
                   
                 Entrance Pupil Surface 02 
                 Surface # 1 
               
               
                   
                 Primary Mirror 04 
                 Surface # 4 
               
               
                   
                 Secondary Mirror 06 
                 Surface # 6 
               
               
                   
                 Focal Plane 08 
                 Surface # 10 
               
               
                   
                 Spacings o-e 52 
                 Surface OBJ thickness 
               
               
                   
                 Spacing e-p 54 
                 Surface 1 thickness 
               
               
                   
                 Vertex spacing p-s 30 
                 Surface 4 thickness 
               
               
                   
                 Vertex spacing s-f 36 
                 Surface 8 thickness 
               
               
                   
                 Primary: Rp 
                 Surface 4 radius 
               
               
                   
                 Secondary Rs 
                 Surface 8 radius 
               
               
                   
                 Primary Kp 
                 Surface 4 conic 
               
               
                   
                 Secondary Ks 
                 Surface 8 conic 
               
               
                   
                 Primary Offset Op 16 
                 Surface 3 decenter 
               
               
                   
                 Secondary Offset Os 26 
                 Surface 5 decenter 
               
               
                   
                 Focus Offset Of 38 
                 Surface 9 decenter 
               
               
                   
                 Tilt Theta S 32 
                 Surface 5 tilt about x 
               
               
                   
                 Tilt Theta F 42 
                 Surface 9 tilt about x 
               
               
                   
                   
               
             
          
         
       
     
       FIGS. 26-29  show the reasonable focusing properties of an example 10″ diameter f/7 nCUB telescope using the same style ZEMAX screen dumps, used to describe the nCUB systems prior. Note that the focal plane  70  remains perpendicular to the gut ray  10  over a range of focus down to 417′ with the center of the object field staying in the center of the focal plane  08  with reasonable field performance. The focusing performance of other f/number nCUB systems is expected to be similarly well behaved. 
     EXAMPLE II 
     tCUB Collimator Telescopes 
     For systems which have been optimized for a focal surface tilted to the axis of the gut ray, for collimator use, disclosed is a family of tCUB optical systems, also from f/5 to f/16. These systems are described optical prescription parameters from ZEMAX which are shown in  FIGS. 14-15 .  FIG. 14  shows spreadsheet compilations and plots of mirror radii and spacings.  FIG. 15  shows spreadsheet compilations and plots of conic constants, decenters and tilts. 
       FIGS. 30 through 49  are printouts of ZEMAX screen dumps for tCUB optical systems from f/5 through f/16. The first of each two printout pages for each f/number are similar to the printouts for the nCUB, prior, and give a complete description of the optical device in terms of surfaces, surface vertex radius, thicknesses between surfaces, conic constants of the surfaces, tilts and decenters. The second page for each f/number shows how stray light from the test optic  80  is eliminated after reflection from a retical  72  at the tilted focal plane  08  surface and absorbed by a stop  74 . 
     EXAMPLE III 
     nUBA Telescopes 
     The nUBA systems are analogs of the nCUB systems, except that they have 16 th  order aspheric (A) primary and secondary mirror surface descriptions in place of the conic (C) formula for hyperbolas which are used for the CUB systems. Since the conic mathematical description is nominally equivalent to a 4 th  order aspheric, the higher order aspheric terms allow a slightly better optical system at the expense of increased complexity and cost.  FIG. 50  is a ZEMAX screen dump for an 10″ f/7 example of a nUBA. Note that the performance is only slightly better than that of the nCUB. 
     EXAMPLE IV 
     tUBA Systems 
     As with the nUBA systems, the tUBA systems are analogs of the tCUB systems, except that they have 16 th  order aspheric (A) primary and secondary mirror surface descriptions in place of the conic (C) formula for hyperbolas which are used for the CUB systems. 
     EXAMPLE V 
     Torroidal Systems 
     As with the nCUB, tCUB systems and the nUBA and TUBA systems, there are analogs these systems, which would use generic aspheric torroidal surfaces. These analogs will have similar properties to the systems described earlier. As in the shift to higher order aspheric surfaces, this would add some performance at the cost of complexity and testing. 
     CONCLUSION 
     Tilting and decentering the secondary of the off axis two mirror system allows control of the tilt and position of the focal surface. By optimizing the tilt and decenter of the secondary in addition to other optical variables, one can control the tilt of the focal surface relative to the gut ray in these two mirror—off axis Cassegrain—Schiefspiegler geometry telescopes, while at the same time optimizing the image over a reasonably wide FOV. Being an all mirror system, there is no color aberrations, and the aberrations in general scale with aperture for a given f/number system. 
     Although the claimed invention has been described in detail with particular reference to these preferred embodiments, other embodiments can achieve the same results. Variations and modifications of the presently claimed invention will be obvious to those skilled in the art and it is intended to cover all such modifications and equivalents. The entire disclosures of all references, applications, patents, and publications cited above, are hereby incorporated by reference.