Abstract:
Various embodiments provide an optical system including a plurality of mirrors, each mirror having a rotational axis of symmetry; and a detector configured to detect an image formed by the plurality of mirrors. The plurality of mirrors are configured to scan an object space along a first direction. The plurality of mirrors are configured and arranged so that a focal length of the plurality of mirrors along the first direction is greater than a focal length of the plurality of mirrors in a second direction perpendicular to the first direction so as to obtain a ratio of anamorphism greater than approximately 1.5.

Description:
BACKGROUND 
     This disclosure pertains to optical imagers and in particular to an anamorphic relayed imager having multiple rotationally symmetric powered mirrors. 
     Demand for imaging systems that provide wide area surveillance is increasing. Wide area surveillance can be performed at an elevated position relative to ground surface. Wide area surveillance can be used in various applications such as, for example, on an unmanned aerial vehicle (UAV) platform, an aircraft, or a satellite for target recognition. Wide area surveillance can be performed at various wavelength ranges depending on the desired application. The wavelength ranges of interest include short wavelength infrared radiation (SWIR) in the wavelength range between approximately 1 μm and 3 μm, mid wavelength infrared radiation (MWIR) in the wavelength range between approximately 3 μm and 5 μm, and long wavelength infrared radiation (LWIR) in the wavelength range between approximately 8 μm and 12 μm. 
     Imaging systems use an image sensing device for sensing radiation collected by a series of imaging optics including one or more lenses, one or more mirrors, or both. Typically, the image sensing device is a focal plane array (FPA), which includes an array or matrix of radiation sensing pixels, positioned at a focal plane of the optics. 
     Conventional FPAs generally include square pixels such that when used with conventional optical systems, a square ground sample distance (GSD) or footprint is projected when viewing an object at or near nadir from an elevated position, i.e., when viewing nearly straight down at an angle of approximately 0 deg. relative to nadir direction from a viewing platform (e.g., a UAV, a satellite, etc.). However, when viewing at an angle that is extremely off-nadir (e.g., approaching the local horizon), the square angular subtense of the square FPA pixel becomes elongated in the elevation direction to an extreme rectangular GSD or footprint. This effectively reduces the resolution of the EPA sensor in that direction. For example, when viewing at an elevation angle of approximately 45 deg. from nadir direction, the elevation GSD is double the elevation GSD when viewing at nadir direction (assuming a flat earth surface). When viewing at an elevation angle of approximately 60 deg. from nadir direction, the elevation GSD is quadruple the elevation GSD when viewing at nadir direction (assuming a flat earth). 
     In order to limit the impact on resolution for viewing at greater angles from the nadir direction, a focal length of the imaging optics is approximately doubled in the along-scan (A-S) or elevation direction relative to a focal length in the cross-scan (C-S) direction perpendicular to the A-S direction. In this way, the angular subtense of the FPA square pixel is halved (divided by two) in the A-S direction. As a result, a smaller GSD can be maintained at large viewing angles from nadir direction. The difference in focal length between a plane in the imaging optics in the A-S direction and a plane in the imaging optics in the C-S direction is termed anamorphism. Most conventional optical systems have little or no anamorphism. 
     Conventional optical systems that exhibit any useful degree of anamorphism do so by using cylindrical surfaces on mirrors, lenses, such as in cinematographic recording systems (e.g., CINEMASCOPE, PANAVISION, etc.). However, such cylindrical surfaces are difficult to make and test. 
     Currently, there are no practical optical systems useful in an aerospace environment which achieve (and thus employ) such anamorphism to maintain good ground resolution. By practical optical system, it is meant an optical system with a relatively large FOV (FOV greater than about 3 deg.) to be useful, an optical system that maintains good image quality over the entire FOV, an optical system that is all-reflective and present essentially no-sensing wavelength restrictions, or an optical system that provides 100% cold-shielding and thus allow the use of cold IR FPAs, or any combination of two or more thereof. 
     Therefore there is a need for anamorphic imaging systems that provide one or more of the above features. 
     SUMMARY 
     One or more embodiments of the present disclosure provide an optical system including a plurality of mirrors, each mirror having a rotational axis of symmetry; and a detector configured to detect an image formed by the plurality of mirrors. The plurality of mirrors are configured to scan an object space along a first direction. The plurality of mirrors are configured and arranged so that a focal length of the plurality of mirrors along the first direction is greater than a focal length of the plurality of mirrors in a second direction perpendicular to the first direction so as to obtain a ratio of anamorphism greater than approximately 1.5. 
     These and other features and characteristics of the present disclosure, as well as the methods of operation and functions of the related elements of structure and the combination of parts and economies of manufacture, will become more apparent upon consideration of the following description and the appended claims with reference to the accompanying drawings, all of which form a part of this specification, wherein like reference numerals designate corresponding parts in the various figures. In one embodiment of this disclosure, the structural components illustrated herein are drawn to scale. It is to be expressly understood, however, that the drawings are for the purpose of illustration and description only and are not intended as a definition of the limits of the inventive concept. As used in the specification and in the claims, the singular form of “a”, “an”, and “the” include plural referents unless the context clearly dictates otherwise. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the accompanying drawings: 
         FIG. 1A  is a lateral view of an optical system having anamorphism showing a ray-tracing simulation on the optical system, according to one embodiment; 
         FIG. 1B  is a top view of the optical system shown in  FIG. 1A ; 
         FIG. 2  depicts a relative position of mirrors of the optical system shown in  FIGS. 1A and 1B , according to one embodiment; and 
         FIG. 3  depicts a schematic representation of an image grid of 0.5 deg. by 0.5 deg. squares GSD in object space obtained using the optical system shown in  FIGS. 1A ,  1 B and  2 , according to one embodiment. 
     
    
    
     DETAILED DESCRIPTION 
       FIGS. 1A and 1B  show a ray-tracing simulation on an optical system having anamorphism, according to one embodiment.  FIG. 1A  is a lateral view of the optical system and  FIG. 1B  is a top view of the optical system. Optical system  10  includes imaging optics  11  having mirrors  12 ,  13 ,  14 ,  15 , and  16 , and radiation detector or sensor  18  (e.g., FPA). In the embodiment shown in  FIG. 1A , five mirrors are provided. However, any number of mirrors greater than three can be used. Mirrors  12 ,  13 ,  14 ,  15  and  16  can be attached to an optical bench structure to maintain a relative position between the various mirrors. 
     Radiation from an object at far field is collected by series of mirrors  12 ,  13 ,  14 ,  15  and  16  and directed onto detector or sensor  18 . In one embodiment, first mirror  12  has a positive power, second mirror  13  has a negative power, third mirror  14  has a positive power, fourth mirror  15  has a negative power, and fifth mirror  16  has a positive power. Rays emitted by the object at far field are received by first mirror  12  which directs the rays onto second mirror  13 . Second mirror  13  in turn reflects the rays towards third mirror  14  which directs the rays onto fourth mirror  15 . Rays received by fourth mirror  15  are directed onto fifth mirror  16  which forms an image of the object on detector  18 . 
     First mirror  12  and second mirror  13  cooperate to form an intermediate image IM 1 . A field stop may be located at a position of intermediate image IM 1 . First mirror  12  and second mirror  13  together function as or form multi-mirror reflective objective optical component  10 A that forms intermediate image IM 1 . Although objective optical component  10 A is shown having two mirrors, objective optical component  10 A may comprise two or more mirrors. 
     Third mirror  14 , fourth mirror  15  and fifth mirror  16  together function or form multi-mirror relay optical component  10 B that relays the intermediate image IM 1  to image IM 2  on detector  18 . Although relay optical component  10 B is shown having 3 mirrors, relay optical component  10 B can have one, two, three or more mirrors. 
     In one embodiment, a sum of the optical powers of all mirrors  12 ,  13 ,  14 ,  15  and  16  is substantially zero to satisfy the Petzval sum criterion. In one embodiment, a curvature of fifth mirror  16  can be selected so as to correct field curvature to achieve a substantially planar focal surface or near zero Petzval sum on detector  18 . For example, by providing a substantially planar focal surface or near zero Petzval sum on the detector this allows to minimize optical aberrations. 
     In one embodiment, mirrors  12 ,  13 ,  14 ,  15  and  16  are tilted and decentered relative to each other so as to achieve a desired ratio of anamorphism (e.g., approximately a 2 to 1 ratio anamorphism).  FIG. 2  depicts a relative position of mirrors  12 ,  13 ,  14 ,  15  and  16 , according to one embodiment. As shown in  FIG. 2 , mirrors  12 ,  13 ,  14 ,  15  and  16  are decentered and tilted relative to each other. The various axes of rotation and symmetry are indicated in  FIG. 2 . The term axis of symmetry is used herein to signify that a rotation or a spin of a mirror around its axis of symmetry does not change a ray path of reflected rays from the mirror from one position to another rotated position of the mirror. First or primary mirror  12  has axis of rotation PP, second or secondary mirror  13  has axis of rotation SS, third or tertiary mirror  14  has axis of rotation TT, fourth or quaternary mirror  15  has axis of rotation QQ, and fifth or quinternary mirror  16  has axis of rotation KK. As shown in  FIG. 2 , the axes of symmetry PP, SS, TT, QQ and KK are shifted relative to each other. Furthermore, in one embodiment, the axes PP, SS, TT, QQ and KK are also angled relative to each other. For example, as shown in  FIG. 2 , axes PP and TT form an angle relative to each other. Axes PP and SS form also an angle relative to each other. In addition, as shown in  FIG. 2 , although axis SS and axis TT appear to be nearly collinear, these two axes also form an angle relative to each other albeit very small. Similarly, axes QQ and KK also appear to be nearly collinear. However, these two axes also form an angle relative to each albeit very small. 
     In one embodiment, the relative position of the various mirrors including the de-centering of the mirrors (i.e., centers of symmetry of the various mirrors are spaced apart from each other) and the tilting of the mirrors (i.e., the angle between the axes of symmetry of the various mirrors) allows to achieve a desired ratio of anamorphism. 
     In one embodiment, mirrors  12 ,  13 ,  14 ,  15  and  16  are positioned, oriented and tilted to achieve an approximately 2 to 1 ratio of anamorphism. In an approximately 2 to 1 ratio of anamorphism, a focal length of imaging optics  11  in a first direction (A-S direction) is approximately twice the focal length of imaging optics  11  in a second direction (C-S direction) perpendicular to the first direction. 
     In one embodiment, with optical system  10  having a 12 cm aperture, a focal length of imaging optics  11  including mirrors  12 ,  13 ,  14 ,  15  and  16  in the A-S direction is approximately 47.6 cm for a speed of F/3.97. On the other hand, a focal length of imaging optics  11  in the C-S direction is approximately 24.75 cm. In this embodiment, a speed of optical system  10  is approximately F/2.06. The FOV of optical system  10  is 3 deg. in the A-S direction by 9 deg. in the C-S direction. 
     in one embodiment, an average 80% geometrical blur diameter containing 80% of rays is approximately 21.6 μm across the FOV. A resulting root mean square of wave front error (RMS WFE) (e.g., at the wavelength centered around 3 μm) averaged over the FOV is approximately 0.233 μm. In one embodiment, an RMS WFE value or range of values and/or the an average geometrical blur diameter define the image quality of an optical system at a certain radiation wavelength or in a certain range of radiation wavelengths. These values of the blur diameter and RMS WFE indicate a good image quality can be achieved using optical system  10 . 
     Optical system  10  has a real entrance pupil at AP and forms a reimaged stop  17  between mirror  16  and image plane IM 2  on detector  18 . A reimaged stop is an optical stop, real or virtual, that provides reduced amount of flare caused by ray diffraction at other optical elements (e.g., at mirrors  13 ,  14 ,  15  and/or  16 ). In one embodiment, a pupil magnification is about 3.0 times in the A-S plane (in the A-S direction) and about 1.5 times in the C-S plane (in the C-S direction). 
     In the process of creating a ratio of approximately 2 to 1 (e.g., 1.92) anamorphism, about √{square root over (2)} to 1 ratio anamorphism is achieved in the objective component  10 A (formed by first mirror  12  and second mirror  13 ) of imaging optics  11 , and about to 1 ratio anamorphism is achieved in the relay component  10 B (formed by third mirror  14 , fourth mirror  15  and fifth mirror  16 ). 
       FIG. 3  depicts a schematic representation of an image grid  30  of 0.5 deg. by 0.5 deg. squares GSD  32  in object space, according to one embodiment. As shown in  FIG. 3 , the whole image grid  30  is covered by a FOV of the optical system  10 . In one embodiment, the FOV of optical system  10  is approximately 9 deg. in the C-S direction and approximately 3 deg. in the A-S direction. In one embodiment, an effective focal length of optical system  10  in the A-S direction is approximately 47.62 cm and an effective focal length of optical system  10  in the C-S direction is approximately 24.75 cm. As a result, a ratio of approximately 2 to 1 anamorphism is achieved. Specifically, a 1.92 (47.62 cm/24.75 cm) anamorphism is achieved. In one embodiment, a 0.5 deg. GSD in object space provides an imaging resolution of approximately 0.416 cm in the A-S direction on detector (e.g., FPA) 18, and 0.5 deg. GSD in object space provides an imaging resolution of approximately 0.216 in the C-S direction on detector (e.g., FPA) 18. 
     A speed of optical system  10  in the A-S direction can be calculated by dividing the effective focal length in the A-S direction by a dimension (e.g., diameter) of the aperture AP. In the above example, by dividing the effective focal length of approximately 47.62 cm in the A-S direction by the aperture AP of about 12 cm, the speed of the optical system in the A-S direction is approximately F/3.97. Similarly, a speed of optical system  10  in the C-S direction can be calculated by dividing the effective focal length in the C-S direction by a dimension (e.g., diameter) of the aperture AP. In the above example, by dividing the effective focal length of approximately 24.75 cm in the C-S direction by the aperture AP of about 12 cm, the speed of the optical system in the C-S direction is approximately F/2.06. 
     A specific prescription for an embodiment of the optical system illustrated in  FIGS. 1A ,  1 B and  2  is given in TABLE 1. 
     
       
         
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE I 
               
               
                   
               
               
                 Surf. 
                 Decrip. 
                 Rd 
                 CC 
                 Ad 
                 Ae 
                 Af 
                 Ag 
                 Yd 
                 Alpha 
                 Thk 
                 Matl. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 Ent. Pupil 
                 inf. 
                   
                   
                   
                   
                   
                 28.864 
                 10.088 
                 96.3151 
                 Air 
               
               
                   
                 (AP) 
               
               
                 2 
                 Pint 
                 −93.0216 
                 −0.233173 
                 7.312E−08 
                 −2.528E−12 
                 −6.206E−16 
                 1.180E−19 
                 −19.8645 
                 −21.0098 
                 −44.3691 
                 Refl 
               
               
                 3 
                 Sec. 
                 −184.502  
                 27.9059 
                 −2.867E−06 
                 −1.485E−09 
                 1.157E−12 
                 7.284E−16 
                 0.4855 
                 −11.3941 
                 15.3406 
                 Refl 
               
               
                 4 
                 Int. image 
                 inf. 
                   
                   
                   
                   
                   
                   
                   
                 27.7325 
                 Air 
               
               
                   
                 (IM1) 
               
               
                 5 
                 Third 
                 −140.467  
                 4.910178 
                 9.090E−08 
                 −4.418E−11 
                 2.787E−15 
                 9.392E−18 
                 −11.4946 
                 −13.9364 
                 −43.1014 
                 Refl 
               
               
                 6 
                 Fourth 
                 −71.0819 
                 7.013669 
                 −2.153E−07 
                 1.513E−09 
                 −3.821E−12 
                 1.206E−14 
                 14.4209 
                 −4.7266 
                 44.1989 
                 Refl 
               
               
                 7 
                 Fifth 
                 −66.2402 
                 0.160633 
                 −1.628E−09 
                 −2.090E−11 
                 4.388E−14 
                 −3.501E−17 
                 13.5905 
                 −1.8471 
                 −45.0393 
                 Refl 
               
               
                 8 
                 Stop 
                 inf. 
                   
                   
                   
                   
                   
                 7.882 
                   
                 −15.2998 
                 Air 
               
               
                 9 
                 Image 
                 inf. 
                   
                   
                   
                   
                   
                 8.025 
                   
                 n/a 
                 n/a 
               
               
                   
                 (IM2) 
               
               
                   
               
             
          
         
       
     
     In Table 1 are listed the various optical surfaces of optical system  10  and their respective radii of curvature (Rd), conic constants (CC), aspheric coefficients (Ad), (Ae), (Af), (Ag), decenter (Yd), tilt Alpha, and thickness (Thk), and type of material (Mat1) when applicable. For example, surfaces  2 ,  3 ,  5 ,  6  and  7  correspond to first, second, third, fourth and fifth mirrors  12 ,  13 ,  14 ,  15  and  16 , respectively. Surfaces  4  and  9  correspond respectively to images IM 1  and IM 2 , respectively. Surface  1  corresponds to entrance pupil or aperture AP, and surface  8  corresponds to the reimaged stop  17 . 
     In this optical prescription, optical system  10  has an entrance pupil diameter of approximately 12 cm, a stop size of approximately 3.8 cm in the C-S direction by 7.8 cm in the A-S direction decentered by approximately 7.88 cm. Additionally, the average effective focal length in the A-S direction is approximately 47.74 cm and the average focal length in the C-S direction is approximately 24.48 cm. The average F-number in the A-S direction is approximately F/3.98 and the average F-number in the C-S direction is approximately F/2.04. The FOV in the A-S direction is about 3.0 deg. and 9.0 deg. in the C-S direction. Additionally, it can be shown by accurate raytracing that aberrations of all types, both monochromatic and polychromatic, are suitably small, so as to render the optical design image quality diffraction limited in the SWIR, MWIR and LWIR wavelength bands. 
     Although in the above embodiments optical system  10  is described as having approximately a 2 to 1 ratio of anamorphism, as it can be appreciated, optical system  10  can be designed and configured to achieve any desired ratio of anamorphism. For example, a 1.5 factor of anamorphism or greater can be achieved. 
     It should be appreciated that in one embodiment, the drawings herein are drawn to scale (e.g., in correct proportion). However, it should also be appreciated that other proportions of parts may be employed in other embodiments. 
     Although the inventive concept has been described in detail for the purpose of illustration based on various embodiments, it is to be understood that such detail is solely for that purpose and that the inventive concept is not limited to the disclosed embodiments, but, on the contrary, is intended to cover modifications and equivalent arrangements that are within the spirit and scope of the appended claims. For example, it is to be understood that the present disclosure contemplates that, to the extent possible, one or more features of any embodiment can be combined with one or more features of any other embodiment. 
     Furthermore, since numerous modifications and changes will readily occur to those with skill in the art, it is not desired to limit the inventive concept to the exact construction and operation described herein. Accordingly, all suitable modifications and equivalents should be considered as falling within the spirit and scope of the present disclosure.