Abstract:
A system and method for obtaining an image of an object out of line of sight, the method comprising directing a chaotic light beam at a first area containing the object; measuring the light from the chaotic light beam at a plurality of instances in time; using a photon detector, detecting light from a second area over a plurality of instances in time; the photon detector not being in the line of sight with the first area but in line-of-sight with a second area; using a processor, correlating the information received by the photon detector with the measurement of light from the chaotic light beam at specific instances in time; and producing an image of the object. The system for imaging information comprising a spatial receiver, a chaotic photon light source for producing light; the light comprising a first beam adapted to be directed at a first predetermined area containing an object, and a second beam which is received by the spatial receiver and measured at specific intervals in time; at least one processor operatively connected to the spatial receiver, the spatial receiver operating to transmit spatial information correlated to specific intervals of time to the processor; and a first receiver operatively connected to the at least one processor and operative to detect the influence of the object on the first portion of the light beam; the first receiver not being in the line of sight with the first predetermined area and adapted to detect light from a second predetermined area spaced from and coplanar with the first predetermined area, the at least one processor operating to correlate the outputs of the first receiver with spatial information derived from the spatial receiver at correlating intervals of time to create an image of the object.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims priority of U.S. patent application Ser. No. 12/819,602 entitled “Method and System for LIDAR Utilizing Quantum Properties,” filed Jun. 21, 2010 (ARL 09-35) which in turn claim priority of application Ser. No. 12/330,401 (U.S. Pat. No. 7,812,303; ARL07-33) entitled “Method and System for Creating an Image Using Quantum Properties of Light Based Upon Spatial Information From a Second Light Beam Which Does not Illuminate the Subject,” filed Dec. 8, 2008, which claims priority to U.S. Provisional Patent Application Ser. No. 60/993,792 filed Dec. 6, 2007. This application claims priority to U.S. patent application Ser. No. 12/837,668 (ARL 07-33D) entitled “Method and System for Creating an Image Using The Quantum Properties of Sound or Quantum Particles,” filed Jul. 16, 2010, which is a divisional application of U.S. Pat. No. 7,812,303, all of which are incorporated by reference herein. The present application and U.S. patent application Ser. No. 12/819,602 also claim priority of U.S. patent application Ser. No. 12/343,384 filed Dec. 23, 2008, entitled “Method and System for Quantum Imaging Using Entangled Photons Pairs,” now U.S. Pat. No. 7,847,234, issued Dec. 7, 2010 (ALR 09-15), and U.S. patent application Ser. No. 10/900,351, filed on Jul. 28, 2004, now U.S. Pat. No. 7,536,012 (ALR 03-92), which in turn claims priority to U.S. Provisional Application No. 60/493,107, filed Aug. 6, 2003, all of which are incorporated herein by reference. 
     
    
     GOVERNMENT INTEREST 
       [0002]    The invention described herein may be manufactured, used, and/or licensed by or for the United States Government. 
     
    
     BACKGROUND OF THE INVENTION 
       [0003]    One surprising consequence of quantum mechanics is the nonlocal correlation of a multi-particle system measured by joint-detection of distant particle detectors. In two publications by R. Meyers, K. S. Deacon, Y. H. Shih, entitled “Ghost Imaging Experiment by Measuring Reflected Photons,” Phys. Rev. A, Rapid Comm., Vol. 77, 041801 (R) (2008) and “A new Two-photon Ghost Imaging Experiment with Distortion Study,” J. Mod. Opt., 54: 16, 2381-2392 (2007), both of which are hereby incorporated by reference, “ghost imaging” of remote objects by measuring reflected photons is reported. 
         [0004]    “Ghost imaging” is a technique that allows a camera or image capture device to produce an image of an object which the camera or device does not directly receive; hence the terminology “ghost.” Early demonstrations of ghost imaging were based on the quantum nature of light; using quantum correlations between photon pairs to build an image of the unseen object. Generally speaking, “ghost imaging” comprises the characteristics of nonlocal multiphoton interference and imaging resolution that differs from that of classical imaging. Using correlated photons from photon pairs, a camera constructs an image using recorded pixels from photons that hit simultaneously at the object and the camera&#39;s image plane. 
         [0005]    Two types of “ghost imaging” has been used experimentally since 1995; Type I uses entangled photon pairs as the light source and Type II uses a chaotic thermal light. Klyshko diagrams are shown for Type I and II sources are shown in  FIGS. 2 and 3  respectfully. 
         [0006]    Conventional line-of-sight imaging (graphically depicted in  FIG. 1 ) lacks the ability to image target objects hidden by obstacles such as terrain, vegetation, buildings, and caves that place limitations on sensor positioning and field of view. Experiments have been performed proving that Ghost Imaging has abilities beyond those of classical imaging; including imaging through obscurants and turbulence. 
         [0007]      FIG. 4  is a schematic diagram of an experimental optical device by Pittman, et al., as described in Pittman, et al. “Optical Imaging by Means of Two-photon Quantum Entanglement: Physical Review A, Vol. 52, No. 5, November 1995, hereby incorporated by reference, and hereinafter referred to as Pittman, et al. As described in Pittman, et al., signal and idler beams emerging from the SPDC crystal are sent in different directions so that coincidence detections may be performed between two distant photon counting detectors. An aperture placed in front of one of the detectors, for example, the letters UMBC, is illuminated by the signal beam through a convex lens. By placing the other detector at a distance prescribed by a “two-photon Gaussian thin lens equation” and scanning it in the transverse plane of the idler beam, a sharp magnified image of this aperture is observed in the coincidence counting rate, even though both detector&#39;s single counting rates remain constant. 
         [0008]    The Pittman, et al. experimental setup is shown in  FIG. 4 . In the experiment a 2-mm-diameter beam from the 351.1-nm line of an argon ion laser is used to pump a nonlinear beta barium borate (BBO) (β-BaB 2 0 4 ) crystal that is cut at a degenerate type-II phase-matching angle to produce pairs of orthogonally polarized signal (e-ray plane of the BBO) and idler (o-ray plane of the BBO) photons. The pairs emerge from the crystal nearly collinearly, with ω s =ω i =ω p/2 . The pump is then separated from the slowly expanding down-conversion beam by a UV grade fused silica dispersion prism and the remaining signal and idler beams are sent in different directions by a polarization beam-splitting Thompson prism. The reflected signal beam passes through a convex lens with a 400-mm focal length and illuminates the (UMBC) aperture. Behind the aperture is the detector package D 1 , which consists of a 25-mm focal length collection lens in whose focal spot is a 0.8-mm-diam dry ice cooled avalanche photodiode. The transmitted idler beam is met by detector package D 2 , which consists of a 0.5-mm-diameter multimode fiber whose output is mated with another dry ice cooled avalanche photodiode. Both detectors are preceded by 83-nm-bandwidth spectral filters centered at the degenerate wavelength 702.2 nm. The input tip of the fiber is scanned in the transverse plane by two orthogonal encoder drivers, and the output pulses of each detector, which are operating in the Geiger mode, are sent to a coincidence counting circuit with a 1.8-ns acceptance window. By recording the coincident counts as a function of the fiber tip&#39;s transverse plane coordinate, an image of the UMBC aperture is seen as described further in Pittman, et al. The aperture containing the UMBC that was inserted in the signal beam (about 3.5×7 mm) is shown in the upper right, and the observed image (reportedly measured 7×14 mm) is shown beneath the aperture. Pittman, et al. demonstrated the viability of ghost imaging, it did not provide a viable solution for non-line-of-sight imaging, Current Ghost Imaging methods are based on having the object being imaged in the line-of-sight or field of view of the bucket detector. 
       SUMMARY OF PRESENT INVENTION 
       [0009]    The present invention is directed to obtaining an image of an object that is not in the direct line of sight or field of view of the viewer, which may be for example, a bucket detector. When a photon detector is aimed nearby the object but not at the object then a Ghost Image of part or the entirety of the object is generated. The photon detector detects photons from a first area which have been scattered by a process such as multiple scattering into a second area such that the detector measures photons while aimed at the second area. In addition, photons from the target area may scatter and induce fluorescence in the second area such that a ghost image can also be formed from the fluorescent photons. 
         [0010]    A preferred embodiment of the present invention enables imaging of an object or subject area when without the object or subject area being in the field of view of the bucket detector. This creates the possibility of imaging around corners; imaging of concealed objects, imaging of objects not in the line-of-sight to the detector, remote sensing, microscopic sensing, spectroscopy, identification of hidden or concealed objects, remote biometrics, design of new sensors and image processing methods, design of new types of stealth technology, design of new types of communications devices. 
         [0011]    The present invention demonstrates the ability to obtain an image of an object using a detector that is not in the direct line of sight or field of view of the image. By aiming a detector at a point nearby the object but not at the object then an image of part or the entirety of the object is generated. Thus, an image of object may be generated even in the presence of turbulence which might otherwise be disruptive to image generation or when a direct view of the object is not possible. 
         [0012]    Scattering of quantum particles such as photons off an object carries information of the object shape even when the quantum particles such as photons of light do not go directly to the receiver/detector, but may in turn be rescattered. The receiver/detector picks up quantum information on the object shape and its temporal relations to separately reference fields. The reference fields are recorded by an imager (CCD, digital cameras, video cameras, scanner, or camera, etc.) that looks at the light source but not the object. This technique may be utilized even when the detector was aimed at a region to the side of the object that was coplanar with the object. Experiments performed determined that Ghost Imaging has abilities beyond those of classical imaging, including imaging through obscurants and turbulence. Experiments have confirmed the potential to generate ghost images of objects when the “bucket” detector used in ghost imaging is significantly occluded. 
         [0013]    A preferred method comprises obtaining an image of an object out of line of sight comprising directing a chaotic light beam at a first area containing the object; measuring the light from the chaotic light beam at a plurality of instances in time; using a photon detector, detecting light from a second area over a plurality of instances in time; the photon detector not being in the line of sight with the first area but in line-of-sight with a second area; using a processor, correlating the information received by the photon detector with the measurement of light from the chaotic light beam at specific instances in time; and producing an image of the object. 
         [0014]    A preferred embodiment comprises a system for imaging information comprising a spatial receiver, a chaotic photon light source for producing light; the light comprising a first beam adapted to be directed at a first predetermined area containing an object, and a second beam which is received by the spatial receiver and measured at specific intervals in time; at least one processor operatively connected to the spatial receiver, the spatial receiver operating to transmit spatial information correlated to specific intervals of time to the processor; a first receiver operatively connected to the at least one processor and operative to detect the influence of the object on the first portion of the light beam; the first receiver not being in the line of sight with the first predetermined area and adapted to detect light from a second predetermined area spaced from and coplanar with the first predetermined area, and the at least one processor operating to correlate the outputs of the first receiver with spatial information derived from the spatial receiver at correlating intervals of time to create an image of the object. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]    The present invention can best be understood when reading the following specification with reference to the accompanying drawings, which are incorporated in and form a part of the specification, illustrate alternate embodiments of the present invention, and together with the description, serve to explain the principles of the invention. In the drawings: 
           [0016]      FIG. 1  is a graphical illustration of “Classical Imaging.” 
           [0017]      FIG. 2  is a Klyshko diagram for Type-I Ghost Imaging. 
           [0018]      FIG. 3  is a Klyshko diagram for Type-II Ghost Imaging. 
           [0019]      FIG. 4  is a schematic diagram of an optical device by Pittman, et al., as described in “Optical Imaging by Means of Two-photon Quantum Entanglement: Physical Review A, Vol. 52, No. 5, November 1995. 
           [0020]      FIG. 5A  is a schematic illustration of a quantum ghost imaging system comprising an arbitrary random, spatially correlated light source  12  in an air medium as the source of the illuminating light. 
           [0021]      FIG. 5B  is an illustration of the actual ghost image display on a monitor using the system of  FIG. 5A . 
           [0022]      FIGS. 6A through 6F  are a set of images depicting the results of a reflection ghost imaging experiment wherein the light path to the bucket detector passes through an obscuring medium. In this example the location of the obscuring medium is in the vicinity of position  15  of  FIG. 5A . 
           [0023]      FIG. 6A  is an instantaneous image of the spatially varying intensity of light source  12  collected on the detector  22  (using the target ARL) of  FIG. 5A . 
           [0024]      FIG. 6B  is an averaged image of the light source  12  obtained from detector  22  on averaging of 100 such images according to  FIG. 6A . 
           [0025]      FIG. 6C  is a G (2)  image of the object obtained by correlation to photon ghost imaging from signals  17  and  23  of  FIG. 5A . 
           [0026]      FIG. 6D  is an instantaneous image of the light source; object reflection. 
           [0027]      FIG. 6E  is an averaged image of the source. 
           [0028]      FIG. 6F  is the G (2)  image of object reflection. 
           [0029]      FIG. 7  is an illustrative schematic indicating that a quantum ghost image can be generated if there are phase aberrations in a path, using either transmitted or reflected photons. 
           [0030]      FIG. 8  is a perspective schematic view of quantum ghost imaging according to  FIG. 7  with a partially transparent mask encoding the letters “ARL.” 
           [0031]      FIG. 9  is a perspective schematic view of quantum ghost imaging generated with a correlated photons of a light emitting diode (LED) incoherent light source. 
           [0032]      FIG. 10  is schematic depiction of an experimental set-up for quantum imaging “absent-line-of-sight.” 
           [0033]      FIG. 11  is an illustration of an “ARL” target of  FIG. 10  printed in white and illustrating the approximate location  31  where the bucket detector  16  was aimed. 
           [0034]      FIG. 12  is an illustration of a ghost image computed using only the per frame photon counts integrated insider of the white box  31  (shown in  FIGS. 10 and 11 ) using 10,000 frames and the G (2)  ghost image was computed using compressive imaging methods. 
           [0035]      FIG. 13  is an illustration of result of ensemble integration of all the reference field measurements for 10,000 frames. 
       
    
    
       [0036]    A more complete appreciation of the invention will be readily obtained by reference to the following Description of the Preferred Embodiments and the accompanying drawings in which like numerals in different figures represent the same structures or elements. The representations in each of the figures are diagrammatic and no attempt is made to indicate actual scales or precise ratios. Proportional relationships are shown as approximates. 
       DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0037]    The present invention now will be described more fully hereinafter with reference to the accompanying drawings, in which embodiments of the invention are shown. However, this invention should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. In the drawings, the thickness of layers and regions may be exaggerated for clarity. Like numbers refer to like elements throughout. As used herein the term “and/or” includes any and all combinations of one or more of the associated listed items. 
         [0038]    As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
         [0039]    It will also be understood that when an element is referred to as being “connected” or “coupled” to another element, it can be directly connected or coupled to the other element or intervening elements may be present. In contrast, when an element is referred to as being “directly connected” or “directly coupled” to another element, there are no intervening elements present. 
         [0040]    It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. For example, when referring first and second locations, these terms are only used to distinguish one location, element, component, region, layer or section from another location, elements, component, region, layer or section. Thus, a first location, element, component, region, layer or section discussed below could be termed a second location, element, component, region, layer or section without departing from the teachings of the present invention. 
         [0041]    As used herein the terminology target path, object path, target beam, or object beam refers to the beam or path directed to the target or object space and or area. The terminology reference path or beam relates to the photon path or beam which is detected and/or measured by the CCD, camera, etc. (e.g. element  22 ). The terminology is not intended to limit the scope of the invention inasmuch as other terminology could be used to similarly describe similar operating systems. 
         [0042]    Embodiments of the present invention are described herein with reference to cross-section illustrations that are schematic illustrations of idealized embodiments of the present invention. As such, variations from the shapes of the illustrations as a result, for example, of manufacturing techniques and/or tolerances, are to be expected. Thus, embodiments of the present invention should not be construed as limited to the particular shapes of regions illustrated herein but are to include deviations in shapes that result, for example, from manufacturing. The regions illustrated in the figures are schematic in nature and their shapes are not intended to illustrate the precise shape of a region of a device and are not intended to limit the scope of the present invention. 
         [0043]    Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
         [0044]    A ghost image is the result of a convolution between the aperture function (amplitude distribution function) of the object A({right arrow over (ρ)} o ) and a δ-function like second-order correlation function G (2) ({right arrow over (ρ)} o ,{right arrow over (ρ)} i ) 
         [0000]        F ({right arrow over (ρ)} i )=∫ obj   d{right arrow over (ρ)}   o   A ({right arrow over (ρ)} o ) G   (2) ({right arrow over (ρ)} o ,{right arrow over (ρ)} i ).  (1)
 
         [0000]    where G (2) ({right arrow over (ρ)} o ,{right arrow over (ρ)} i )≅δ({right arrow over (ρ)} o     −   −{right arrow over (ρ)} i /m), {right arrow over (ρ)} o  and {right arrow over (ρ)} i  are 2D vectors of the transverse coordinate in the object plane and the image plane, respectively, and m is the magnification factor. The term δ function as used herein relates to the Dirac delta function which is a mathematical construct representing an infinitely sharp peak bounding unit area expressed as δ(x), that has the value zero everywhere except at x=0 where its value is infinitely large in such a way that its total integral is 1. The δ function characterizes the perfect point-to-point relationship between the object plane and the image plane. If the image comes with a constant background, as in this experiment, the second-order correlation function G (2) ({right arrow over (ρ)} o ,{right arrow over (ρ)} i ) in Eq. (1) must be composed of two parts 
         [0000]        G   (2) ({right arrow over (ρ)} o ,{right arrow over (ρ)} i )= G   0 +δ({right arrow over (ρ)} o −{right arrow over (ρ)} i   /m ).  (2)
 
         [0000]    where G 0  is a constant. The value of G 0  determines the visibility of the image. One may immediately connect Eq. (2) with the G (2)  function of thermal radiation 
         [0000]        G   (2)   =G   11   (1)   G   22   (1)   +|G   12   (1) | 2 .  (3)
 
         [0000]    where G 11   (1) G 22   (1) ˜G o  is a constant, and |G 12   (1) | 2 ˜δ({right arrow over (ρ)} 1 −{right arrow over (ρ)} 2 ) represents a nonlocal position-to-position correlation. Although the second-order correlation function G (2)  is formally written in terms of G (1) s as shown in equation (3), the physics are completely different. As we know, G 12   (1)  is usually measured by one photodetector representing the first-order coherence of the field, i.e., the ability of observing first-order interference. Here, in Eq. (3), G 12   (1)  is measured by two independent photodetectors at distant space-time points and represents a nonlocal EPR correlation. 
         [0045]    Differing from the phenomenological classical theory of intensity-intensity correlation, the quantum theory of joint photodetection, known conventionally as Glauber&#39;s theory and published in Glauber, R. J., “The Quantum Theory of Optical Coherence,” Phys. Rev. 130, 2529-2539 (1963) (hereby incorporated by reference); and Glauber, R. J. “Coherent and Incoherent States of the Radiation Field,” Phys. Rev. 131, 2766 (1963) (hereby incorporated by reference) dips into the physical origin of the phenomenon. The theory gives the probability of a specified joint photodetection event 
         [0000]        G   (2)   =Tr[{circumflex over (ρ)}E   (−) ({right arrow over (ρ)} 1 ) E   (−) ({right arrow over (ρ)} 2 ) E   (+) ({right arrow over (ρ)} 2 ) E   (+) ({right arrow over (ρ)} 1 )]  (4)
 
         [0000]    and leaves room for us to identify the superposed probability amplitudes. In Eq. (4), E (−)  and E (+)  are the negative and positive-frequency field operators at space-time coordinates of the photodetection event and {circumflex over (ρ)} represents the density operator describing the radiation. In Eq. (4), we have simplified the calculation to 2D. 
         [0046]    In the photon counting regime, it is reasonable to model the thermal light in terms of single photon states for joint detection, 
         [0000]    
       
         
           
             
               
                 
                   
                     
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         [0000]    where |ε|&lt;&lt;1. Basically, one models the state of thermal radiation, which results in a joint-detection event, as a statistical mixture of two photons with equal probability of having any transverse momentum {right arrow over (κ)} and {right arrow over (κ)}′. 
         [0047]    Assuming a large number of atoms that are ready for two-level atomic transition. At most times, the atoms are in their ground state. There is, however, a small chance for each atom to be excited to a higher energy level and later release a photon during an atomic transition from the higher energy level E 2 (ΔE 2 ≠0) back to the ground state E 1 . It is reasonable to assume that each atomic transition excites the field into the following state: 
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         [0000]    where |ε|&lt;&lt;1 is the probability amplitude for the atomic transition. Within the atomic transition, f(k, s)=         ψ k,s |ψ          is the probability amplitude for the radiation field to be in the single-photon state of wave number k and polarization s:|ψ k,s   †           =|1 k,s           ={circumflex over (α)} k,s |0&gt;. 
         [0048]    For this simplified two-level system, the density matrix that characterizes the state of the radiation field excited by a large number of possible atomic transitions is thus 
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                                    
                                   
                                      
                                     
                                       
                                         - 
                                         ω 
                                       
                                        
                                       
                                           
                                       
                                        
                                       
                                         t 
                                         
                                           0 
                                            
                                           j 
                                         
                                       
                                     
                                   
                                    
                                   
                                     
                                       a 
                                       ^ 
                                     
                                     
                                       k 
                                       , 
                                       s 
                                     
                                     † 
                                   
                                    
                                   
                                      
                                     0 
                                     〉 
                                   
                                 
                               
                             
                             ] 
                           
                           + 
                           
                             
                               ε 
                               2 
                             
                              
                             
                               [ 
                               … 
                               ] 
                             
                           
                         
                         } 
                       
                       + 
                       
                         
                           ε 
                           
                             * 
                             2 
                           
                         
                          
                         
                           [ 
                           … 
                           ] 
                         
                       
                     
                   
                 
                 } 
               
               . 
             
              
             
                
             
              
             
                 
             
             × 
             
               { 
               
                 
                    
                   0 
                   〉 
                 
                 + 
                 
                   
                     ε 
                     * 
                   
                    
                   
                     ⌈ 
                     
                       
                         ∑ 
                         
                           t 
                           
                             0 
                              
                             k 
                           
                         
                       
                        
                       
                         
                           ∑ 
                           
                             
                               k 
                               ′ 
                             
                             , 
                             
                               s 
                               ′ 
                             
                           
                         
                          
                         
                           
                             f 
                              
                             
                               ( 
                               
                                 
                                   k 
                                   ′ 
                                 
                                 , 
                                 
                                   s 
                                   ′ 
                                 
                               
                               ) 
                             
                           
                            
                           
                              
                             
                               ω 
                                
                               
                                   
                               
                                
                               
                                 t 
                                 
                                   0 
                                    
                                   k 
                                 
                               
                             
                           
                            
                           
                             〈 
                             0 
                              
                           
                            
                           
                             
                               a 
                               ^ 
                             
                             
                               
                                 k 
                                 ′ 
                               
                               , 
                               
                                 s 
                                 ′ 
                               
                             
                           
                         
                       
                     
                     ⌉ 
                   
                 
               
             
           
         
       
     
         [0000]    where e −iωt     0j    is a random phase factor associated with the state |ψ          of the jth atomic transition. Summing over t 0j  and t 0k  by taking all possible values, we find the approximation to the fourth order of |ε|, 
         [0000]    
       
         
           
             
               ρ 
               ^ 
             
             ≃ 
             
               
                 
                    
                   0 
                   〉 
                 
                  
                 
                   〈 
                   0 
                    
                 
               
               + 
               
                 
                   
                      
                     ε 
                      
                   
                   2 
                 
                  
                 
                   
                     ∑ 
                     
                       k 
                       , 
                       s 
                     
                   
                    
                   
                     
                       
                          
                         
                           f 
                            
                           
                             ( 
                             
                               k 
                               , 
                               s 
                             
                             ) 
                           
                         
                          
                       
                       2 
                     
                      
                     
                        
                       
                         l 
                         
                           k 
                           , 
                           s 
                         
                       
                       〉 
                     
                      
                     
                       〈 
                       
                         l 
                         
                           k 
                           , 
                           s 
                         
                       
                        
                     
                   
                 
               
               + 
               
                 
                   
                      
                     ε 
                      
                   
                   4 
                 
                  
                 
                   
                     ∑ 
                     
                       k 
                       , 
                       s 
                     
                   
                    
                   
                     
                       ∑ 
                       
                         
                           k 
                           ′ 
                         
                         , 
                         
                           s 
                           ′ 
                         
                       
                     
                      
                     
                       
                         
                            
                           
                             f 
                              
                             
                               ( 
                               
                                 k 
                                 , 
                                 s 
                               
                               ) 
                             
                           
                            
                         
                         2 
                       
                        
                       
                         
                            
                           
                             f 
                              
                             
                               ( 
                               
                                 
                                   k 
                                   ′ 
                                 
                                 , 
                                 
                                   s 
                                   ′ 
                                 
                               
                               ) 
                             
                           
                            
                         
                         2 
                       
                        
                       
                          
                         
                           
                             l 
                             
                               k 
                               , 
                               s 
                             
                           
                            
                           
                             l 
                             
                               
                                 k 
                                 ′ 
                               
                               , 
                               
                                 s 
                                 ′ 
                               
                             
                           
                         
                         〉 
                       
                        
                       
                         
                           〈 
                           
                             
                               l 
                               
                                 k 
                                 , 
                                 s 
                               
                             
                              
                             
                               l 
                               
                                 
                                   k 
                                   ′ 
                                 
                                 , 
                                 
                                   s 
                                   ′ 
                                 
                               
                             
                           
                            
                         
                         . 
                       
                     
                   
                 
               
             
           
         
       
     
         [0000]    The second-order transverse spatial correlation function is thus 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       G 
                       
                         ( 
                         2 
                         ) 
                       
                     
                      
                     
                       ( 
                       
                         
                           
                             ρ 
                             → 
                           
                           1 
                         
                         , 
                         
                           
                             ρ 
                             → 
                           
                           2 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         
                           κ 
                           → 
                         
                         , 
                         
                           
                             κ 
                             → 
                           
                           ′ 
                         
                       
                     
                      
                     
                       
                         
                            
                           
                             
                               〈 
                               0 
                                
                             
                              
                             
                               
                                 E 
                                 2 
                                 
                                   ( 
                                   + 
                                   ) 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     ρ 
                                     → 
                                   
                                   2 
                                 
                                 ) 
                               
                             
                              
                             
                               
                                 E 
                                 1 
                                 
                                   ( 
                                   + 
                                   ) 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     ρ 
                                     → 
                                   
                                   1 
                                 
                                 ) 
                               
                             
                              
                             
                                
                               
                                 
                                   l 
                                   
                                     κ 
                                     → 
                                   
                                 
                                  
                                 
                                   l 
                                   
                                     
                                       κ 
                                       → 
                                     
                                     ′ 
                                   
                                 
                               
                               〉 
                             
                           
                            
                         
                         2 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0049]    The electric field operator, in terms of the transverse mode and coordinates, can be written as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         E 
                         j 
                         
                           ( 
                           + 
                           ) 
                         
                       
                        
                       
                         ( 
                         
                           
                             ρ 
                             → 
                           
                           j 
                         
                         ) 
                       
                     
                     ∝ 
                     
                       
                         ∑ 
                         
                           κ 
                           → 
                         
                       
                        
                       
                         
                           
                             g 
                             j 
                           
                            
                           
                             ( 
                             
                               
                                 κ 
                                 → 
                               
                               ; 
                               
                                 
                                   ρ 
                                   → 
                                 
                                 j 
                               
                             
                             ) 
                           
                         
                          
                         
                           
                             a 
                             ^ 
                           
                            
                           
                             ( 
                             
                               κ 
                               → 
                             
                             ) 
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where â{right arrow over (κ)} is the annihilation operator for the mode corresponding to {right arrow over (κ)} and g j ({right arrow over (ρ)} j ; {right arrow over (κ)}) is the Green&#39;s function associated with the propagation of the field from the source to the jth detector. Substituting the field operators into Eq. (6), we obtain 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       G 
                       
                         ( 
                         2 
                         ) 
                       
                     
                      
                     
                       ( 
                       
                         
                           
                             ρ 
                             → 
                           
                           1 
                         
                         , 
                         
                           
                             ρ 
                             → 
                           
                           2 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         
                           κ 
                           → 
                         
                         , 
                         
                           
                             κ 
                             → 
                           
                           ′ 
                         
                       
                     
                      
                     
                       
                         
                            
                           
                             
                               
                                 
                                   g 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       κ 
                                       → 
                                     
                                     ; 
                                     
                                       
                                         ρ 
                                         → 
                                       
                                       2 
                                     
                                   
                                   ) 
                                 
                               
                                
                               
                                 
                                   g 
                                   1 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         κ 
                                         → 
                                       
                                       ′ 
                                     
                                     ; 
                                     
                                       
                                         ρ 
                                         → 
                                       
                                       1 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 
                                   g 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         κ 
                                         → 
                                       
                                       ′ 
                                     
                                     ; 
                                     
                                       
                                         ρ 
                                         → 
                                       
                                       2 
                                     
                                   
                                   ) 
                                 
                               
                                
                               
                                 
                                   g 
                                   1 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       κ 
                                       → 
                                     
                                     ; 
                                     
                                       
                                         ρ 
                                         → 
                                       
                                       1 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                            
                         
                         2 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Eq. (8) indicates a two-photon superposition. The superposition happens between two different yet indistinguishable Feynman alternatives that lead to a joint photodetection: (1) photon {right arrow over (κ)} and photon {right arrow over (κ)}′ are annihilated at {right arrow over (ρ)} 2  and {right arrow over (ρ)} 1 , respectively, and (2) photon {right arrow over (κ)}′ and photon {right arrow over (κ)} are annihilated at {right arrow over (ρ)} 2  and {right arrow over (ρ)} 1 , respectively. The interference phenomenon is not, as in classical optics, due to the superposition of electromagnetic fields at a local point of space time. It is due to the superposition of g 2 ({right arrow over (κ)}; {right arrow over (ρ)} 2 )g 1 ({right arrow over (κ)}′; {right arrow over (ρ)} 1 ) and g 2 ({right arrow over (κ)}′; {right arrow over (ρ)} 2 )g 1 ({right arrow over (κ)}; {right arrow over (ρ)} 1 ) the so-called two-photon amplitudes. 
         [0050]    Completing the normal square of Eq. (8), it is easy to find that the sum of the normal square terms corresponding to the constant of G 0  in Eq. (2): Σ {right arrow over (κ)} |g 1 ({right arrow over (κ)}; {right arrow over (ρ)} 1 )| 2 Σ {right arrow over (κ)}′ |g 2 ({right arrow over (κ)}′; {right arrow over (ρ)} 2 )| 2 =G 11   (1) G 22   (1) , and the cross term |Σ {right arrow over (κ)} g 1 *({right arrow over (κ)}; {right arrow over (ρ)} 1 )g 2 ({right arrow over (κ)}; {right arrow over (ρ)} 2 )| 2 =|G 12   (1) ({right arrow over (ρ)} 1 , {right arrow over (ρ)} 2 )| 2  gives the δ function of position-position correlation 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                          
                         
                           ∫ 
                           
                             
                                
                               
                                 κ 
                                 → 
                               
                             
                              
                             
                               
                                 g 
                                 1 
                                 * 
                               
                                
                               
                                 ( 
                                 
                                   
                                     κ 
                                     → 
                                   
                                   ; 
                                   
                                     
                                       ρ 
                                       → 
                                     
                                     1 
                                   
                                 
                                 ) 
                               
                             
                              
                             
                               
                                 g 
                                 2 
                               
                                
                               
                                 ( 
                                 
                                   
                                     κ 
                                     → 
                                   
                                   ; 
                                   
                                     
                                       ρ 
                                       → 
                                     
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                          
                       
                       2 
                     
                     ≃ 
                     
                       
                          
                         
                           δ 
                            
                           
                             ( 
                             
                               
                                 
                                   ρ 
                                   → 
                                 
                                 o 
                               
                               + 
                               
                                 
                                   ρ 
                                   → 
                                 
                                 i 
                               
                             
                             ) 
                           
                         
                          
                       
                       2 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         g 
                         1 
                       
                        
                       
                         ( 
                         
                           
                             κ 
                             → 
                           
                           ; 
                           
                             
                               ρ 
                               → 
                             
                             o 
                           
                         
                         ) 
                       
                     
                     ∝ 
                     
                       
                         Ψ 
                          
                         
                           ( 
                           
                             
                               κ 
                               → 
                             
                             , 
                             
                               
                                 - 
                                 
                                   c 
                                   ω 
                                 
                               
                                
                               
                                 d 
                                 A 
                               
                             
                           
                           ) 
                         
                       
                        
                       
                          
                         
                            
                            
                           
                               
                           
                            
                           
                             
                               κ 
                               → 
                             
                             · 
                             
                               
                                 ρ 
                                 → 
                               
                               o 
                             
                           
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     
                       
                         g 
                         2 
                       
                        
                       
                         ( 
                         
                           
                             κ 
                             → 
                           
                           ; 
                           
                             
                               ρ 
                               → 
                             
                             i 
                           
                         
                         ) 
                       
                     
                     ∝ 
                     
                       
                         Ψ 
                          
                         
                           ( 
                           
                             
                               κ 
                               → 
                             
                             , 
                             
                               
                                 - 
                                 
                                   c 
                                   ω 
                                 
                               
                                
                               
                                 d 
                                 B 
                               
                             
                           
                           ) 
                         
                       
                        
                       
                          
                         
                            
                            
                           
                               
                           
                            
                           
                             
                               κ 
                               → 
                             
                             · 
                             
                               
                                 ρ 
                                 → 
                               
                               i 
                             
                           
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   where 
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0000]    are the Green&#39;s functions propagated from the radiation source to the transverse planes of d A  and d B =d A . In Eq. (10), ψ(ωd/c) is a phase factor representing the optical transfer function of the linear system under the Fresnel near-field paraxial approximation, ω is the frequency of the radiation field, and c is the speed of light. 
         [0051]    Substituting this δ function together with the constant G 0  into Eq. (1), an equal sized lensless image of A({right arrow over (ρ)} 0 ) is observed in the joint detection between the CCD array and the photon counting detector D 1 . The visibility of the image is determined by the value of G 0 . 
         [0052]    The ghost images are thus successfully interpreted as the result of two-photon interference. The two-photon interference results in a point-point correlation between the object plane and the image plane and yields a ghost image of the object by means of joint photodetection. 
         [0053]    As shown in  FIG. 5A , and disclosed in more detail in U.S. Pat. No. 7,812,303, a quantum ghost imaging system comprising an arbitrary random, spatially correlated light source  12  in an air medium as the source of the illuminating light. Radiation from a chaotic pseudothermal source  12  is divided into two paths by a nonpolarizing beam splitter  28 , which divides the light into paths  13  and  21 . In path A, an object  14  is illuminated by the light source at a distance of d A . The object  14  receives a light source output  13  and reflects light along 15. The reflected light output  15 , reflected from the surface of the object, is collected by a “bucket” detector  16  and integrated for some exposure time. The bucket detector  16  is simulated by using a large area silicon photodiode for collecting the randomly scattered and reflected photons from the object  14 . The integrated values of the intensity are transmitted via interconnection  17  to the two-photon correlation computation subsystem  18 . In path B, a second spatially addressable detector  22  is deployed. Output  21  is collected by a spatially addressable detector  22  that is observing the source  12  for the same exposure time at  16 . The detector  22  includes a two-dimensional (2D) photon counting CCD array, cooled for single-photon detection, and may optionally include a lens. A triggering pulse from a computer is used to synchronize the measurements at 16 and 22 for two-photon joint detection. The time window is preferably chosen to match the coherent time of the radiation to simplify computation. The light intensity is also preferably chosen for each element of the detector  22  working at a single-photon level within the period of detector element response time. The chaotic light  12  is simulated by transmitting a laser beam first through a lens to widen the beam and then through a phase screen made from rotating ground glass. The detector  22  is placed at any given distance d B . As shown in  FIG. 5A , d A =d B . It can be appreciated, however, that the present invention is operative when d B  does not equal d A . The detector  22  faces the light source instead of facing the object  14 . The spatially addressable intensity values are transmitted via interconnection  23  to the two-photon correlation computation subsystem  18 . The two-photon correlation computation subsystem  18  comprises a voltage output recorder, coincidence circuit and CDCD output recorder. Subsystem  18  computes the two-photon correlation quantum ghost image in accordance with Eq. 3 utilizing the input values from interconnections  17  and  23 . 
         [0054]    Additionally, electronic circuitry components of the computer relative to the detectors  16  and  22  comprise a coincidence circuit which provides detection coordination between detectors  16  and  22 . A photon registration history for detector  16  is also provided, which provides a temporal log for the integrated values  17  transmitted to the computer  18 A. The second spatially addressable detector  22  is provided with spatially addressable output that is subsequently fed to the computer and onto a display (not shown). For the optical bench schematic of FIG.  5 A, the actual ghost image display on a monitor is provided in  FIG. 5B  and is discernable as the original toy figure. It can be appreciated that the image quality shown in  FIG. 5B  is improved by increasing photon flux along path  15 . 
         [0055]    To confirm the ability to generate a ghost image of an object through an obscuring medium, an obscuring medium of frosted glass is inserted along the optical path  15  of  FIG. 5A .  FIG. 6A  is an instantaneous image of the light source  12  collected on the detector  22  (using the target ARL).  FIG. 6B  is an averaged image of the light source  12  obtained from detector  22  on averaging of 100 such images according to  FIG. 6A .  FIG. 6C  is a G (2)  image of the object obtained by correlation to photon ghost imaging from signals  17  and  23 . The instantaneous image of the obscured reflection object  14  is provided in  FIG. 6D  while the averaged image of the obscured reflection object  14  is provided in  FIG. 6E . 
         [0056]      FIGS. 7 and 8  depict an inventive ghost imaging system in which the object is a semi-opaque mask  14 ′ providing a transmissive photon output  46  to reach the bucket detector  16 . In  FIG. 8 , the mask  14 ′ is a stencil of the letters “ARL”. The detector  22  in this regime of  FIGS. 7 and 8  is a two-dimensional charge couple device array that provides two-dimensional speckle data as the spatially addressable intensity values  23  to the computer  18 A with gated electrical values being communicated to the computer  18 A with gated exposure start and stop triggers being communicated to the detectors  16  and  22 . The object  14 ′ is located a distance d′ A  from the bucket detector  16 . 
         [0057]    In accordance with a preferred embodiment, as depicted in  FIG. 8 , the laser source  12  in conjunction with the rotating phase screen diffuser  40 , emits light uncorrelated in space and time. Thus, the speckle images  23  are random distributions in space and time. The beam splitter  28  essentially “halves” the intensity of the initial speckle image from diffuser  40  and splits it into two different paths ( 21  and  13 ) as shown in  FIG. 8 . Spatially correlated means that correlations are present at any given instant of time between the two paths  13 ,  21 . There will be a point to point correlation between the speckle images on each path, although paths are spatially distinct. The coincidence detection by the processor  18  is temporal; i.e. correlated at specific time intervals. “Correlation” or “Correlated,” as used in the present application, means a logical or natural association between two or more paths; i.e., an interdependence, relationship, interrelationship, correspondence, or linkage. For example, the present invention may be used in conjunction with sunlight, an incoherent light source, whereby a first and second plurality of photons are emitted from the sun at the same time. If the first detector is located on the earth (ground) receives the first plurality of photons, and the second detector located in space (such as in a satellite orbiting the earth) receives a second plurality of photons, the time intervals need to be synchronized; i.e., a first plurality of photons which strikes the ground object is correlated with a second plurality of photons detected in space at synchronized timing intervals. It can be readily appreciated by those skilled in the art that if the detected samples from the first and second plurality of photons are not part of the correlation, it will not contribute to the G (2)  image as mathematically described in the above equations. Further, coincidence has to do with two measurements at the same or approximately the same time. For example, when a coincidence occurs, one must compensate for the media involved to take into account the variation in particle velocity between different media. 
         [0058]    In  FIG. 8 , the mask  14 ′ is a stencil of the letters “ARL”. The detector  22  in this regime of  FIGS. 7 and 8  is a two-dimensional charge couple device array that provides two-dimensional speckle data as the spatially addressable intensity values  23  to the computer  18 A with gated electrical values being communicated to the computer  18 A with gated exposure start and stop triggers being communicated to the detectors  16  and  22 . The object  14 ′ is located a distance d′ A  from the bucket detector  16 . 
         [0059]    In accordance with the embodiment depicted in  FIG. 8 , the laser source  12  in conjunction with the rotating phase screen diffuser  40 , emits light uncorrelated in space and time. Thus, the speckle images  23  are random distributions in space and time. The beam splitter  28  essentially “halves” the intensity of the initial speckle image from diffuser  40  and splits it into two different paths ( 21  and  13 ) as shown in  FIG. 8 . Spatially correlated means that correlations are present at any given instant of time between the two paths  13 ,  21 . There will be a point to point correlation between the speckle images on each path, although paths are spatially distinct. The coincidence detection by the processor  18  is temporal; i.e. correlated at specific time intervals. “Correlation” or “Correlated,” as used in the present application, means a logical or natural association between two or more paths; i.e., an interdependence, relationship, interrelationship, correspondence, or linkage. For example, the present invention may be used in conjunction with sunlight, an incoherent light source, whereby a first and second plurality of photons are emitted from the sun at the same time. If the first detector is located on the earth (ground) receives the first plurality of photons, and the second detector located in space (such as in a satellite orbiting the earth) receives a second plurality of photons, the time intervals need to be synchronized; i.e., a first plurality of photons which strikes the ground object is correlated with a second plurality of photons detected in space at synchronized timing intervals. It can be readily appreciated by those skilled in the art that if the detected samples from the first and second plurality of photons are not part of the correlation, it will not contribute to the G (2)  image as mathematically described in the above equations. Further, coincidence has to do with two measurements at the same or approximately the same time. For example, when a coincidence occurs, one must compensate for the media involved to take into account the variation in particle velocity between different media. 
         [0060]      FIG. 9  is a perspective schematic of a reflective ghost imaging scheme according to the present invention using light emitting diodes as a representative incoherent light source in a field setting and insensitive to transmission through obscuring medium. Similarly, solar radiation as a light source, as described in further detail in U.S. Pat. No. 7,812,303, hereby incorporated by reference. 
         [0061]    A preferred embodiment of the present invention may utilize a light source emitting radiation that is one of an entangled, thermal, or chaotic light source. The photons from the light source may be divided into two paths: one path for the object to be imaged, and the other path in which images of the entangled, thermal, or chaotic light are measured independent of interaction with the objects. Any or all paths may pass through an obscuring medium. The measurements of the entangled, thermal, or chaotic light may then stored for future processing. In U.S. Pat. No. 7,812,303, the light in the object path is collected into a bucket detector and measured. The measurements of the bucket detector are then stored for future processing. A process for solving for the G (2)  Glauber coherence between the two paths is provided to reconstruct the image. The G (2)  Glauber coherence between the two paths is used to generate a correlation two-photon ghost image. 
       Non-Line-of-Sight-Ghost-Imaging 
       [0062]      FIG. 10  is schematic depiction of an experimental set-up for quantum imaging “absent-line-of-sight,” including photon probability paths from the illuminated target. During this experiment, only the photons that were measured in the white outlined area  31  were used. The white outlined area contained no spatial patterns about the “ARL” target because only photon counts were measured by a non-resolving single pixel bucket detector  16 . The “ARL was not in the line-of-sight of the bucket detector  16 . The photon counts inside the white outlined area  31  were used as the “bucket” measurements. Computing the G (2)  correlations using the bucket measurements and the coincidentally measured reference frames produced the Ghost image of ARL in  FIG. 12 . This experiment was conducted under conditions of extreme turbulence in all of the paths for both the reference and the target (as shown in  FIG. 10 ). However, the technique can be utilized with or without turbulence. Compressive Imaging (CI) methods were used to compute the G (2)  ghost image; however, similar images could be produced using direct Glauber G (2)  computations. As explained in detail above, the G (2)  image of the object is obtained by correlation to photon ghost imaging from signals produced by bucket detector  16  and imager  22 . The imager  22  may be a CCD, digital camera, video camera, scanner, or the like. Similarly, the detector  16  may comprise a bucket detector or CCD, digital camera, video camera, scanner, or the like which is configured to count photons (i.e., record energy imparted by photons). The two-photon correlation computation subsystem  18  comprises a voltage output recorder, coincidence circuit and CDCD output recorder. Subsystem  18  computes the two-photon correlation quantum ghost image in accordance with Eq. 3 utilizing the input values from elements  16  and  22 . 
         [0063]    In the preferred embodiment depicted schematically in  FIG. 10 , a “Ghost Image” an object is obtained that is not in the direct line of sight or field of view of the viewer, which may be for example, a bucket detector  16 . When a bucket detector is aimed nearby the object at location  31 , then a “Ghost Image” of part or the entirety of the object is generated, even in the presence of turbulence which might otherwise be disruptive to image generation. Scattering of quantum particles such as photons off the object, such as the location depicted in the oval  31 , carries information of the object shape even when the quantum particles such as photons of light do not go directly to the bucket detector  16 . The bucket detector  16  picks up quantum information on the object shape and its temporal relations to separate reference fields. The reference fields are recorded by an imager  22  (CCD, or camera, etc.) that looks at the light source  12  but not the object.  FIG. 13  is the result of ensemble integration of all the reference field measurements for 10,000 frames. The embodiment of  FIG. 10  comprises the computer  18 A which functions in a manner described with respect to  FIG. 8  above. However, in  FIG. 8  the target  14  is a mask. In the embodiment of  FIG. 10 , the target  14 ′ appears on a piece of paper on which the letters ARL are printed. The paper was approximately 1.7 m from the detector  16 . 
         [0064]      FIG. 11  is a low resolution average image “ARL” bucket target area for 10,000 frames. The non-line-of-sight “bucketing” area  31  was located within the box outlined in white. All of the frames were imaged through high levels of turbulence. As depicted in  FIG. 11 , the invention was observed to work even when the bucket detector  16  was aimed at a region to the side of the ARL (shown as area  31  in  FIG. 11 ) that was coplanar with the object, i.e., the ARL appeared on a piece of paper and the bucket detector was directed to the paper at the location labeled  31  in  FIG. 11 . 
         [0065]    In connection with  FIG. 11 , the ARL target was produced using a 10 point bold Arial font colored white, with black background, actual printed size. The ARL target was printed in white using an Arial 10 point font bold capital letters. To obtain a perspective as to scale, given that a single font is 0.3527 mm, the height was approximately 3.527 mm. The measured distance from the beginning of the A to the end of the letter “L” is approximately 9 mm. The width of the rectangle  31  was approximately 1.25 mm and the height was approximately 1.75 mm. The rectangle  31  was approximately 2 mm from the upright portion of the “L.” 
         [0066]    The paper  14 ′ in  FIG. 11  is translucent with an approximate weight of 20 pounds per 500 basis ream with a brightness value of 92 on a TAPPI Brightness scale of 1 to 100. The paper in  FIG. 11  was mounted on white cardboard backing. The paper  14 ′ was semi-shiny to visible light laser illumination and had a thickness of 0.097 mm. 
         [0067]    Translucent objects allow the light to enter the material, where it is scattered around in a manner that depends on the physical properties of the material like the absorption coefficient (a) and the scattering coefficient (s), as described further in “Acquisition of Subsurface Scattering Objects,” a Diploma Thesis by Christian Fuchs, Max-Planck-Institut für Informatik, Saarbrücken, Germany (date appearing on thesis is Feb. 9, 2006). Accordingly light may enter the material for subsurface scattering, including single scattering as described further in “Acquisition of Subsurface Scattering Objects,” hereby incorporated by reference. Moreover, concepts relating to a general bidirectional surface scattering distribution function (BSSRDF), relating to light transport, is described further in “A Practical Model for Subsurface Light Transport,” hereby incorporated by reference. 
         [0068]    The image of ARL, like any other object, may be generated even in the presence of turbulence which might otherwise be disruptive to image generation. A description of the effect of turbulence and compression of images may be found in Meyers, et al, “Ghost Imaging Experiments at ARL,” Quantum Communications and Quantum Imaging VIII, Proc. Of SPIE Vol. 7815, 781501 (2010), and R. Meyers, K. Deacon, and Y. Shih, “Turbulence-free ghost imaging,” App. Phys. Lett, 98, 111115 (2011), both of which are hereby incorporated by reference. Scattering of quantum particles such as photons off the object (in this case “ARL”) carries information of the object shape even when the quantum particles such as photons of light do not go directly to the bucket detector  16 . The bucket detector  16  picks up quantum information on the object shape and its temporal relations to separate reference fields. The reference fields are recorded by an imager  22  (CCD, or camera, etc.) that looks at the light source but not the object. The preferred embodiment depicted in  FIG. 10  was observed to work when the bucket detector was aimed at the region  31  in  FIG. 11 , which is to the side of the object (ARL) that was coplanar with the object (ARL). 
         [0069]    It is noted that where the bucket detector  16  is referenced herein, a camera may be used the output of which can be converted to nonspatial output in a manner similar to a bucket detector without departing from the scope of the present invention. 
         [0070]    When a detector  16  is aimed nearby the object but not at the object then a Ghost Image of part or the entirety of the object is generated. The object is generated even in the presence of turbulence which might otherwise be disruptive to image generation. Scattering of quantum particles such as photons off the object carries information of the object shape even when the quantum particles such as photons of light do not go directly to the bucket detector. The detector  16  picks up quantum information on the object shape and its temporal relations to separately referenced fields are recorded by an imager  22  (CCD, or camera, etc.) that “looks” at the light source but not the object. The invention was observed to work even when the bucket detector was aimed at a region to the side of the object that was coplanar with the object. 
         [0071]    Patent documents and publications mentioned in the specification are indicative of the levels of those skilled in the art to which the invention pertains. These documents and publications are incorporated herein by reference to the same extent as if each individual document or publication was specifically and individually incorporated herein by reference. 
         [0072]    The preferred embodiments of the present invention may be used for active and passive illumination and determination of 3D structure from single views to mitigate enemy cover, concealment, and camouflage. Further potential applications include persistent surveillance applications, stealthier, and more robust situational awareness for urban warfare, UAV and robotic surveillance, persistent surveillance, and IED surveillance. Improved medical imaging will result since bone will be less effective in shielding soft tissue from imaging detectors. 
         [0073]    As used herein the terminology processor includes a computer, microprocessor, multiprocessor, central processing unit, CPU, controller, mainframe, signal processing circuitry, or a plurality of computers, processors, microprocessors, multiprocessors, controller, CPUs, or mainframes or combinations thereof and/or equivalents thereof. 
         [0074]    As used herein, the terminology “object” may include visual information, an image, printed matter, subject, a plurality of objects, material, surface, wall, poster, paper, picture, or anything similar. 
         [0075]    As used herein the terminology “diffuse reflection” means reflection of light, sound, or radio waves from a surface in all directions. Diffuse reflection is the reflection of light from a surface such that an incident ray is reflected at many different angles, rather than at one precise angle, as is the case for specular reflection. If a surface is completely nonspecular, the reflected light will be evenly spread over the hemisphere surrounding the surface (2×π steradians). 
         [0076]    As used herein the terminology “CCD” means charge-coupled device, a high-speed semiconductor used chiefly in image detection. Digital cameras, video cameras, and optical scanners all use CCD arrays. 
         [0077]    As used herein the terminology “nonspatial photon detector” means a detector (such as a bucket detector) of photons that has no spatial resolution. 
         [0078]    As used herein the terminology “spatial light detector” or “spatial receiver” means a detector or receiver capable of resolving spatial information from the light or quantum particles received. 
         [0079]    Although various preferred embodiments of the present invention have been described herein in detail to provide for complete and clear disclosure, it will be appreciated by those skilled in the art that variations may be made thereto without departing from the spirit of the invention. 
         [0080]    It should be emphasized that the above-described embodiments are merely possible examples of implementations. Many variations and modifications may be made to the above-described embodiments. All such modifications and variations are intended to be included herein within the scope of the disclosure and protected by the following claims.