Abstract:
A multiple aperture imaging system, that includes: a plurality of imaging elements for capturing light; an optical relay assembly for phasing the captured light; a means for diverting the captured light within the multiple aperture imaging system to produce a plurality of images; and an imaging sensor capable of receiving the captured light from each of the plurality of imaging elements.

Description:
FIELD OF THE INVENTION 
   The present invention relates generally to a system and method using multiple imaging elements to capture images. Specifically, the present invention relates to a multiple aperture imaging system combined with an optical relay assembly and optics for diverting captured light. 
   BACKGROUND OF THE INVENTION 
   Some factors that greatly impact the utility of an imaging system include resolution, signal-to-noise ratio (SNR), field of view (FOV), and the number of images that the imaging system can capture. Resolution determines the highest amount of image detail that can be captured in a scene and is fundamentally limited by the aperture size of the optical system (see  Introduction to Fourier Optics  by Joseph Goodman, McGraw-Hill, second edition, 1996). One calculation of aperture size employs a modulation transfer function (MTF). The MTF for an incoherent diffraction-limited optical system is essentially the aperture&#39;s MTF, which is calculated by autocorrelating the aperture function. For a clear circular aperture of diameter D, the incoherent aperture MTF is given by:
 
                   MTF   incoherent     ⁡     (   ρ   )       =       2   π     ⁡     [         cos     -   1       ⁡     (     ρ   n     )       -       ρ   n     ⁢       1   -     ρ   n   2             ]         ⁢     
     ⁢       for   ⁢           ⁢   0     ≤     ρ   n     ≤   1             (     Equation   ⁢           ⁢   1     )             
 MTF incoherent (ρ)=0 for ρ n &gt;1  (Equation 2)
 
where 
               ρ   n     =     ρ     ρ   c               (     Equation   ⁢           ⁢   3     )                 ρ     c   ⁡     (   incoherent   )         =       1     λ   ⁡     (     f   ⁢   #     )         =     D     λ   ⁢           ⁢   f                 (     Equation   ⁢           ⁢   4     )             
 
where ƒ is the focal length of the optical system, ƒ#≡ƒ/D, λ is the wavelength of the electromagnetic wave, and ρ is the radial spatial frequency. For coherent imaging systems with circular apertures, the MTF is simply the aperture function:
 
MTF coherent (ρ)=1 for 0≦ρ n ≦1  (Equation 5)
 
MTF coherent (ρ)=0 for ρ n &gt;1  (Equation 6)
 
where 
               ρ     c   ⁡     (   coherent   )         =       1     2   ⁢     λ   ⁡     (     f   ⁢   #     )           =     D     2   ⁢   λ   ⁢           ⁢   f                 (     Equation   ⁢           ⁢   7     )             
 
Note that for both coherent and incoherent imaging systems there is a distinct spatial frequency cutoff, ρ c , which is proportional to the aperture size and defines the highest spatial resolution that can be imaged with the optical system. An imaging system with a larger aperture size, therefore, will capture images at higher resolution than an imaging system with a smaller aperture size.
 
   Sparse apertures (also termed diluted apertures) use a reduced aperture area to synthesize the optical performance of a filled aperture. An optical system employing sparse apertures can combine the light captured by smaller apertures to capture a higher spatial resolution than possible from any of the individual apertures. This concept is very appealing in technology areas where a filled aperture is too large or heavy for the intended application. Sparse aperture concepts have been used to design large astronomical telescopes, such as the multiple mirror telescope in Arizona, as well as small endoscopic probes (see U.S. Pat. No. 5,919,128 by Fitch issued Jul. 6, 1999, titled “SPARSE APERTURE ENDOSCOPE”). Prior art sparse aperture systems that use multiple apertures to improve the resolution of the images have not had the versatility to take advantage of other benefits that can be obtained from multiple aperture systems. 
     FIG. 1   a  illustrates a traditional Cassegrain telescope  10 .  FIG. 1   b  illustrates a prior art sparse aperture telescope  12  created by removing parts of the primary mirror of the Cassegrain telescope  10  in  FIG. 1   a .  FIG. 1   c  illustrates a prior art sparse aperture telescope  14  created by using multiple afocal telescopes  16  that relay light into a combiner telescope  18  using an optical relay system  20  to precisely ensure that the light from each telescope arrives at a detector  21  simultaneously. 
   In general, a signal, measurable in the number of photons that reach the detector  21 , from a scene being imaged by an optical system, is 
             signal   =           A   detector     ⁢     π   ⁡     (     1   -   ɛ     )       ⁢     t   int         4   ⁢       (     f   ⁢   #     )     2     ⁢   hc       ⁢       ∫     λ   min       λ   max       ⁢         L   scene     ⁡     (   λ   )       ⁢     τ   optics     ⁢   λ   ⁢           ⁢     ⅆ   λ     ⁢           ⁢     (   photons   )                   (     Equation   ⁢           ⁢   8     )             
 
where A detector  is the area of the detector, ε is the fraction of the optical aperture area obscured, t int  is the integration time of the imaging system, h=6.63×10 −34  (j−s), c=3×10 8  (m/s), λ min  and λ max  define the spectral bandpass, L scene  is the spectral radiance from the scene, and τ optics , is the transmittance of the optics. Random noise, for example photon noise, arising from elements adds uncertainty to the signal level of the scene. Consequently random noise is quantified by the standard deviation of its statistical distribution, σ. The signal-to-noise ratio (SNR) is the ratio of the signal level to the noise level, i.e. 
               SNR   ≡     signal   noise       =     signal   σ             (     Equation   ⁢           ⁢   9     )             
 
If the photon noise from the scene is the dominant noise source, then the SNR is given by: 
             SNR   =       signal   σ     =       signal     signal       =     signal                 (     Equation   ⁢           ⁢   10     )             
 
because the photon noise follows a Poisson distribution of the signal, i.e. the variance of the noise equals the mean signal. If the SNR is not sufficient, then increasing the signal level from the scene relative to the noise will increase the SNR and improve the image quality. Increasing the integration time will increase the signal level, but this can introduce motion blur in the image if the imaging system moves relative to the scene or an object. Multiple short-exposure images of the same scene can be acquired by a single camera and summed together to increase the signal level without introducing motion blur. However, if the camera can only acquire one image at a time, there will be a time difference between the multiple images, which could introduce unwanted image artifacts.
 
   The field of view (FOV) of an imaging system determines the area of the scene that can be acquired in a single image.  FIG. 2  illustrates an image capture system, such as a camera, including an imaging element  22  having a focal length f, wherein the focal length is a property of the imaging element  22 , and an imaging sensor  24 . A scene  26  at a distance d o  in front of the camera will be properly focused at the imaging sensor  24  at a distance d i  behind the imaging element  22 , if the relationship between d o , d i , and f is 
                 1     d   o       +     1     d   i         =     1   f             (     Equation   ⁢           ⁢   11     )             
 
The field of view (FOV) describes the angle subtended by the imaging sensor  24 , given by 
             FOV   =     2   *       tan     -   1       ⁡     (       L   sensor       2   ⁢     d   i         )                 (     Equation   ⁢           ⁢   12     )             
 
where L sensor  is the length of the imaging sensor  24 . The length of the scene  26  captured by the imaging sensor  24  is given by: 
                 L   scene     =           d   o       d   i       ⁢     L   sensor       =       (         d   o     f     -   1     )     ⁢     L   sensor           ⁢     
     ⁢         If   ⁢           ⁢     d   o       ⪢   f   ⪢     L   sensor       ,   then             (     Equation   ⁢           ⁢   13     )                 L   scene     ≅         d   o     f     ⁢     L   sensor       ≅       d   o     ⁢   FOV             (     Equation   ⁢           ⁢   14     )             
 
Increasing the size of the imaging sensor  24  will increase the FOV and the area of the scene  26  imaged, but there are usually limitations to the size of imaging sensor  24  that can be used, due to manufacturing constraints and the image quality of the optical system off-axis. The FOV is usually increased by increasing d o  or by decreasing f, both of which decrease the scale of the image and reduce the resolution. The FOV, therefore, generally involves a trade between resolution and the area of the scene  26  imaged.
 
   The field of regard is the area in the scene  26  within which the image capture system can acquire an image. The field of regard is generally larger than the FOV and is determined by the image capture system&#39;s capability to view certain areas of the scene. A single imaging sensor  24  may take a long time to acquire multiple images within the field of regard. 
   There is a need, therefore, for a multiple aperture image capture system that can improve the resolution, produce a higher signal image, image a larger FOV, and/or improve the number of images acquired per unit time. 
   SUMMARY OF THE INVENTION 
   The aforementioned need is met, according to the present invention, by providing a multiple aperture imaging system, that includes: a plurality of imaging elements for capturing light; an optical relay assembly for phasing the captured light; a means for diverting the captured light within the multiple aperture imaging system to produce a plurality of images; and an imaging sensor capable of receiving the captured light from each of the plurality of imaging elements. 
   Advantageous Effect of the Invention 
   This invention allows the versatility of producing a high-resolution image or capturing multiple simultaneous images within the field of regard, which can be used to improve the collection efficiency of the image capture system, form a higher signal image, and/or form a higher field of view image than possible from individual imaging elements within the multiple aperture imaging system. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1   a  illustrates a prior art Cassegrain telescope; 
       FIG. 1   b  illustrates a prior art sparse aperture telescope utilizing a modified primary mirror of the Cassegrain telescope shown in  FIG. 1   a  to simulate a conventional telescope; 
       FIG. 1   c  illustrates a prior art sparse aperture telescope utilizing multiple afocal telescopes and a combiner telescope with an optical relay system to simulate a conventional telescope; 
       FIG. 2  is a schematic diagram of a prior art imaging system useful in describing the background of the present invention; 
       FIG. 3  illustrates a three-aperture system that synthesizes a larger aperture; 
       FIG. 4  illustrates the multiple aperture imaging system for a three-aperture configuration when it is configured to collect high-resolution images; 
       FIG. 5  illustrates the multiple aperture imaging system for a three-aperture configuration when it is configured to collect multiple simultaneous images within the filed of regard of the imaging system; 
       FIG. 6  illustrates the multiple aperture imaging system for a three-aperture configuration when it is configured to collect high-signal images; and 
       FIG. 7  illustrates the multiple aperture imaging system for a three-aperture configuration when it is configured to collect high-FOV images. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   In a method for imaging using multiple apertures, the present invention employs multiple imaging elements, each comprised of an optical system and a detector. The information collected by each imaging element can be combined to form an image with higher resolution than possible with any individual imaging element within the multiple aperture imaging system, or be used to capture multiple simultaneous images within the field of regard. These multiple, simultaneously captured images can be used to improve the collection efficiency of the image collection system; can be combined to form an image with a higher signal than possible with each individual imaging element; or can be combined to form an image with a higher field of view than possible with each individual imaging element. 
   The method disclosed in the present invention can be applied to a multiple aperture system with any number of apertures, but, for simplicity, the three-aperture configuration shown in  FIG. 3  will be used to describe the invention. Referring to  FIG. 3 , the image capture system is comprised of three apertures  28 , each with a diameter d and separated by a distance s. The diffraction-limited resolution of each aperture  28  is proportional to the diameter d, but if the electromagnetic wavefront propagating from each aperture  28  is coherently combined or synthesized, then a higher resolution can be captured, as if collected by a single aperture  30  of diameter d+s. This requires the electromagnetic wavefront propagating from each aperture  28  to be properly phased and coherently combined to form a high-resolution image. 
   The electromagnetic wavefront can be described more generally as a wave function with amplitude a(x,y,z) and phase φ(x,y,z). Referring to  FIG. 2 , an image I(x,y) recorded on the imaging sensor  24  a distance d i  from the aperture of the imaging element  22  only represents the intensity of the electromagnetic wavefront, given by: 
                     I   ⁡     (     x   ,   y   ,     d   i       )       =     |       a   ⁡     (     x   ,   y   ,     d   i       )       ⁢     ⅇ     -     ⅈϕ   ⁡     (     x   ,   y   ,     d   i       )             ⁢     |   2                   =       a   2     ⁡     (     x   ,   y   ,     d   i       )                     (     Equation   ⁢           ⁢   15     )             
 
   If the imaging element  22  is replaced with N multiple smaller apertures, then the wavefront from each aperture must be properly combined to maintain the resolution such that the multiple apertures can coherently sum to form an image 
               I   ⁡     (     x   ,   y   ,     z   2       )       =              ∑     n   =   1     N     ⁢         a   n     ⁡     (     x   ,   y   ,     z   2       )       ⁢     ⅇ       -   ⅈ     ⁢           ⁢       ϕ   n     ⁡     (     x   ,   y   ,     z   2       )                    2             (     Equation   ⁢           ⁢   16     )             
 
Simply imaging the wavefronts and summing the images from each aperture will not generate a high-resolution image, because the electromagnetic wavefronts are not properly summed; only the intensity values of the images are summed. However, summing the individual images can generate an image with a higher signal-to-noise ratio of the scene, at a resolution of a single aperture, than would be acquired by any single imaging element.
 
     FIG. 4  illustrates the invention for a three aperture imaging system  31  that is configured to collect high-resolution images. The electromagnetic radiation from the object in the FOV  32  within the field of regard  34  is received by the imaging system  31  comprised of a plurality of multiple imaging elements  36 . The imaging elements  36  can be lenses, telescopes, or other means for forming an image. Each imaging element  36  has a corresponding fold mirror  38 , a steering mirror  40 , and an imaging sensor  42 . When the present invention is configured to collect high-resolution images, the multiple imaging elements  36  are used as the apertures for a sparse aperture system. The steering mirrors  40  and the imaging sensors  42  are not used when the present invention is in this configuration. Captured light from each imaging element  36  is diverted, using a fold mirror  38  or other means, into an optical relay assembly  44 . The optical relay assembly  44  coherently sums the wavefronts from each multiple imaging element  36 . If the wavefronts are not properly summed, then the resolution corresponding to an aperture  30  for synthesizing, as shown in  FIG. 3 , will not be achieved. In one embodiment, the optical relay assembly  44  uses an optical delay path with associated active optics, as shown in U.S. Pat. No. 5,905,591, by Duncan et al. issued May 18, 1999, titled “MULTI-APERTURE IMAGING SYSTEM.” The resulting wavefront from the optical relay assembly  44  is imaged by the combiner  46 , which produces the proper wavefront to be imaged by the combiner imaging sensor  48 . The combiner  46  can be a lens, telescope, or any means for forming an image. The combiner imaging sensor  48  can be any number and type of imaging capture elements, for example, photographic film, charge-coupled devices, CMOS devices, or a spectrometer. The image acquired by the combiner imaging sensor  48  is processed by an image processor  50  to enhance the image data. Enhancement of the image data can include using a conventional Wiener filter for correcting any residual wavefront errors. A final image  52  will have a higher resolution than possible from any of the individual imaging elements  36  within the multiple aperture imaging system  31 . Other means for diverting captured light of each imaging element  36  can include at least one steering mirror, a prism, a beam combiner, a spatial light modulator, and a grating (not shown herein, but well understood by those skilled in the art). Specifically a steering mirror may be used to point each imaging element  36  to one or more points in a scene. 
     FIG. 5  shows that if the fold mirror  38 , or other means for diverting captured light of each imaging element  36 , is not placed in front of the steering mirror  40 , then each imaging element  36  will acquire an independent image on each imaging sensor  42 . The imaging sensors  42  can be any number and type of imaging capture elements, for example, photographic film, charge-coupled devices, CMOS devices, or a spectrometer. The plurality of images can be acquired in several ways to improve the utility of the image collection, depending on which area of the scene is imaged by each imaging element  36 . In one embodiment, pointing the imaging elements  36  is accomplished by using a steering mirror  40  associated with each imaging element  36 , but pointing of the imaging elements  36  can also be accomplished by changing the pointing geometry of each imaging element  36 . The optical relay assembly  44 , the combiner  46 , and the combiner imaging sensor  48  are not used when the present invention is configured to acquire separate images from each imaging element  36 .  FIG. 5  illustrates the present invention configured such that each imaging element images a different part of the scene within the field of regard  34 , thus simultaneously acquiring multiple images  54  of multiple objects. 
     FIG. 6  shows that when each imaging element  36  images the same location within the field of view of the scene  32 , the invention can be used to collect a higher signal-to-noise ratio (SNR) for the image than any individual captured image from a single imaging element  36 . The images  54  from each imaging sensor  42  are spatially registered and summed in an image processor  50  to form a single image  56 . 
     FIG. 7  illustrates that when each imaging element  36  is configured to point to adjacent scenes  32  in a field of regard  34 , the present invention can be used to collect high FOV images. In one embodiment, images  54  from each imaging sensor  42  are captured such that there is a common area in the scene that overlaps between adjacent images. An image processor  50  spatially registers the images in the overlap regions to properly align them before they are mosaicked together to form a single image  58 . Single image  58  has the resolution of a single imaging element, but also encompasses a larger area of the scene than possible with a single imaging element. 
   In summary, a multiple aperture imaging system has been invented that uses multiple imaging elements to form an image with higher resolution than possible with each individual imaging element, form an image with a higher SNR than possible with each individual imaging element, or form an image with a higher field of view than possible with each imaging individual element. 
   The invention has been described with reference to one embodiment. However, it is understood that a person of ordinary skill in the art can effect variations and modifications without departing from the scope of the invention. 
   PARTS LIST 
   
       
         10  Cassegrain telescope 
         12  sparse aperture telescope created by removing part of the primary mirror of Cassegrain telescope 
         14  sparse aperture telescope created by using multiple afocal telescopes 
         16  afocal telescopes 
         18  combiner telescope 
         20  optical relay system 
         21  detector 
         22  imaging element 
         24  imaging sensor 
         26  scene 
         28  single aperture of a multiple aperture imaging system 
         30  aperture 
         31  three aperture imaging system 
         32  field of view of the scene 
         34  field of regard 
         36  imaging element 
         38  fold mirror 
         40  steering mirror 
         42  imaging sensor 
         44  optical relay assembly 
         46  combiner 
         48  combiner imaging sensor 
         50  image processor 
         52  high-resolution image 
         54  images from imaging elements 
         56  high SNR image 
         58  high FOV image