Patent Publication Number: US-7907081-B2

Title: Millimeter wave imaging system

Description:
FIELD OF THE INVENTION 
     The present invention relates in general to imaging systems operative in the millimeter wave region. In particular the present invention relates to ellipsoidal shaped antennae reflector of active and or passive imaging systems in the range of frequencies starting in X band and including the terahertz region. 
     BACKGROUND OF THE INVENTION 
     Passive and active millimeter-wave imaging systems for a variety of applications are known. A comprehensive review of architectures of passive millimeter-wave (MMW) imaging systems is given for example in a paper by Alan H Lettington et al. 2003, J. Opt. A: Pure Appl. Opt. 5, S103-S110. The paper includes sources of radiation, atmospheric transmission, various types of available imaging system and a brief summary of exemplary applications. Specific issues related to detection capabilities provided by active imaging systems and a comparison between imaging with focal plan array antennae versus scanning an image by a single pixel are discussed for example in a paper of E. N. Grossman and A. J. Miller, 2003, Proceedings of SPIE, Vol. 50277, pp 62-70. Typically such systems consist of components such as lenses for optical beam forming and employ mechanical beam steering. However MMW lenses are somewhat impractical in cases in which the required range of detection, or the range to the target to be imaged, exceed a few meters. Therefore, an improved converging optics is called for. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a scheme of an active millimeter wave imaging system according to the present invention; 
         FIG. 2  is a presentation of a spheroid in a Cartesian coordinate system; 
         FIG. 3  is a side view of a spheroidal reflector according to a preferred embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PRESENT INVENTION 
     The structural aspects of an active and or passive imaging systems of the invention accommodated to a frequency range starting from X band and including the terahertz region, and the method of its operation are hereinafter described. Reference is made to  FIG. 1  in which an active imaging system (AIS)  20  operative in the millimeter wave range has a receiving antenna with ellipsoidal reflector  22 . One, or more arrays of detectors, as with array  24 , disposed at a focus of ellipsoid  25  adjacent to reflector  22 . Ellipsoid  25  has two foci located on its major axis, the first focus near reflector  22  and a second focus in the far side of the ellipsoid at a distance from the reflector. Signals received in detectors of array  24  are detected and transferred to an imaging processor, not shown, disposed in main imaging system unit  26 . A transmitter of millimeter waves and/or sub-millimeter waves, and an array or arrays of transmitters  28  illuminate a segment of the ellipsoidal shaped field of view of the receiving antenna. Rays  32  designate the illuminating beam. The transmitter, or transmitters are such disposed that a significant region around the second focus of the spheroid is substantially homogeneously illuminated. Any ray of the illuminating beam reflected from an object within a first region  34  centered at the second focus of the ellipsoid that is distant from the receiving antenna, and further impinging on reflector  22  is again reflected into a second region, not shown, which is centered at the first focus of ellipsoid  25  adjacent to reflector  22 . Such a reflected radiation impinges on detectors of array  24 , generating an electric signal that is further detected and transferred to the imaging processor. Images of such illuminated objects, as is  FIG. 38 , are displayed over a display of operator interface unit  40 . 
     The detection of the reflected radiation is either coherent or incoherent as in the prior art. At a time in which efficient detectors in the terahertz region, such as manufactured by employing nanotechnology techniques, will become available, active and passive imaging system operative in this frequency region will be similarly configured employing an ellipsoidal shaped receiving antenna reflector, according to the present invention. (Except for avoiding the illuminating transmitters in configurations of the passive imaging systems.) 
     Reflector of the Receiving Antenna 
     Design rules for manufacturing spheroidal reflectors according to the present invention are hereinafter described with reference to  FIG. 2 . In the figure, a general ellipsoid is shown in a Cartesian coordinate system. The surface of ellipsoid  50  the three major axes of which are designated by  52 ,  54 ,  56  are of lengths c, b and a respectively, is represented by equation 1: 
     
       
         
           
             
               
                 
                   
                     
                       
                         x 
                         2 
                       
                       
                         c 
                         2 
                       
                     
                     + 
                     
                       
                         y 
                         2 
                       
                       
                         b 
                         2 
                       
                     
                     + 
                     
                       
                         z 
                         2 
                       
                       
                         a 
                         2 
                       
                     
                   
                   = 
                   1. 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Any ray of electromagnetic radiation, such as ray  58 , emerging from focus  60  is reflected to pass through focus  62 . Rotating an ellipse such as ellipse  64 , around one of its axes, such as axis  56 , creates a three dimensional body called a spheroid. The lengths of the axes of this spheroid are b, b, a respectively. Ellipse  66  becomes by such rotation a circle, the radius of which is of a length b. The eccentricity of ellipse  64 , designated by the letter “e”, is represented by equation 2: 
     
       
         
           
             
               
                 
                   e 
                   = 
                   
                     
                       
                         
                           
                             a 
                             2 
                           
                           - 
                           
                             b 
                             2 
                           
                         
                       
                       
                         a 
                         2 
                       
                     
                     = 
                     
                       
                         
                           1 
                           - 
                           
                             
                               b 
                               2 
                             
                             
                               a 
                               2 
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     This spheroid has two foci:  60  and  62 , and its focal length  68  is denoted hereinafter by “f”. The present invention concerns cases in which the length b of the minor axis of the spheroid, is considerably smaller than the length a of the major axis. 
     Detection range “L” is the distance from the AIS to a detectable target. An approximation of this range is made by considering major axis a to be equal to about one half of the detection range, as is represented by equation 3: 
     
       
         
           
             
               
                 
                   a 
                   ≈ 
                   
                     
                       L 
                       2 
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     For given values of the spheroid axes&#39; lengths a and b, a general radius R and a deformation factor q exist to fulfill the relationships as in equation 4: 
     
       
         
           
             
               
                 
                   
                     a 
                     = 
                     
                       R 
                       q 
                     
                   
                   , 
                   
                     b 
                     = 
                     
                       R 
                       
                         q 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     where q&gt;0, and q&lt;&lt;1. 
     The eccentricity of the spheroid is then represented by equation 5: 
     
       
         
           
             
               
                 
                   
                     e 
                     = 
                     
                       
                         
                           1 
                           - 
                           q 
                         
                       
                       ≈ 
                       
                         1 
                         - 
                         
                           q 
                           2 
                         
                         - 
                         
                           
                             q 
                             2 
                           
                           8 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     and the focal length is represented by equation 6: 
     
       
         
           
             
               
                 
                   f 
                   = 
                   
                     
                       
                         a 
                         ⁡ 
                         
                           ( 
                           
                             1 
                             - 
                             e 
                           
                           ) 
                         
                       
                       ≈ 
                       
                         
                           R 
                           q 
                         
                         ⁢ 
                         
                           ( 
                           
                             1 
                             - 
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   q 
                                   2 
                                 
                                 - 
                                 
                                   
                                     q 
                                     2 
                                   
                                   8 
                                 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         R 
                         2 
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             
                               q 
                               4 
                             
                           
                           ) 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Substituting a and b with R and q respectively, result in equations with R and q whose solutions for given values of the focal length f and the detection range L are provided in equation 7: 
     
       
         
           
             
               
                 
                   q 
                   = 
                   
                     
                       2 
                       ⁢ 
                       
                         { 
                         
                           
                             
                               1 
                               + 
                               
                                 
                                   4 
                                   ⁢ 
                                   f 
                                 
                                 L 
                               
                             
                           
                           - 
                           1 
                         
                         } 
                       
                     
                     ≈ 
                     
                       
                         
                           4 
                           ⁢ 
                           f 
                         
                         L 
                       
                       ⁢ 
                       
                         ( 
                         
                           1 
                           - 
                           
                             f 
                             L 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     and in equation 8: 
     
       
         
           
             
               
                 
                   R 
                   = 
                   
                     
                       Lq 
                       2 
                     
                     = 
                     
                       2 
                       ⁢ 
                       f 
                       ⁢ 
                       
                         
                           { 
                           
                             1 
                             - 
                             
                               f 
                               L 
                             
                           
                           } 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     The minor axis of the spheroid is represented by equation 9:
 
 b =√{square root over ( fL (1− f/L ))}  (9)
 
     As a result, the spheroid is completely defined for given values of a focal length f and a detection range L. 
     Reference is now made to  FIG. 3  showing a side view of a reflector of a receiving antenna according to a preferred embodiment of the present invention. Diameter  80  of the spheroidally shaped reflector  82  is denoted by “D”. A parameter p is defined by the ratio of the focal length  84 , denoted by “f” and D: p=f/D. The depth  86  of the reflector is denoted by “d” and aspect angle  88  by which reflector  82  is seen from the focus  90 , is denoted by “φ”. The depth of the reflector d and the aspect angle φ, are represented by the equations 10 and 11, respectively: 
     
       
         
           
             
               
                 
                   d 
                   ≈ 
                   
                     
                       f 
                       
                         16 
                         ⁢ 
                         
                           p 
                           2 
                         
                       
                     
                     ⁡ 
                     
                       [ 
                       
                         1 
                         + 
                         
                           
                             f 
                             L 
                           
                           ⁢ 
                           
                             ( 
                             
                               1 
                               + 
                               
                                 1 
                                 
                                   4 
                                   ⁢ 
                                   
                                     p 
                                     2 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                     tg 
                     ⁡ 
                     
                       ( 
                       
                         ϕ 
                         / 
                         2 
                       
                       ) 
                     
                   
                   ≈ 
                   
                     
                       
                         D 
                         
                           4 
                           ⁢ 
                           f 
                         
                       
                       ⁡ 
                       
                         [ 
                         
                           1 
                           + 
                           
                             
                               ( 
                               
                                 f 
                                 / 
                                 L 
                               
                               ) 
                             
                             2 
                           
                         
                         ] 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     Physical Features of the Reflector of the Receiving Antenna 
     In a case in which a conical feed having an angular radiation pattern given by E feed (θ)=cos n  θ, is disposed at focus  90 , where “E feed ” denotes the magnitude of the electric field at the plane of the feed, as a function of the angle “θ”, measured relative to the axis of the reflector (similarly to the angle φ), the radial pattern of the electric field across a plan of the aperture of the reflector is depicted in equation 12: 
                           E   appert     ⁡     (   r   )         1   +       (     r   /   R     )     2         =         [     1   -       (     r   /   R     )     2       ]     n         [     1   +       (     r   /   R     )     2       ]       n   +   1           ,           (   12   )               
“E appert ” is the magnitude of the electric field and “R” is given by equation 8.
 
     Fitting a Gaussian beam to this radiation pattern at the edge of the reflector, for a value of “r” given by r=D/2 results in a waist diameter of the beam represented by equation 13: 
     
       
         
           
             
               
                 
                   
                     w 
                     = 
                     
                       
                         0.35 
                         ⁢ 
                         D 
                       
                       
                         
                           ( 
                           
                             
                               
                                 ( 
                                 
                                   n 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 
                                   log 
                                   10 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     1 
                                     + 
                                     
                                       
                                         ( 
                                         
                                           
                                             D 
                                             / 
                                             2 
                                           
                                           ⁢ 
                                           R 
                                         
                                         ) 
                                       
                                       2 
                                     
                                   
                                   ) 
                                 
                               
                             
                             - 
                             
                               n 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   log 
                                   10 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       
                                         ( 
                                         
                                           
                                             D 
                                             / 
                                             2 
                                           
                                           ⁢ 
                                           R 
                                         
                                         ) 
                                       
                                       2 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     where D is the diameter of the reflector, R is given by equation 8, and n is an integer whose values are n=1, 2, . . . . The minimal waist diameter w 0  is represented by the equation 14: 
     
       
         
           
             
               
                 
                   
                     
                       w 
                       0 
                     
                     = 
                     
                       w 
                       
                         
                           1 
                           + 
                           
                             
                               ( 
                               
                                 π 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   w 
                                   2 
                                 
                                 ⁢ 
                                 
                                   q 
                                   / 
                                   2 
                                 
                                 ⁢ 
                                 λ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 R 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     where w is the maximal waist diameter as is given by equation 13, q and R are as defined in equations 7 and 8 respectively, and λ is the wavelength of the imaging system. The range z 0  to the minimal spot which is the point in which the waist diameter reaches its minimal value is given by equation 15: 
     
       
         
           
             
               
                 
                   
                     z 
                     0 
                   
                   = 
                   
                     
                       
                         
                           
                             ( 
                             
                               π 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   w 
                                   2 
                                 
                                 / 
                                 2 
                               
                               ⁢ 
                               λ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               L 
                             
                             ) 
                           
                           2 
                         
                         ⁢ 
                         L 
                       
                       
                         1 
                         + 
                         
                           
                             ( 
                             
                               π 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   w 
                                   2 
                                 
                                 / 
                                 2 
                               
                               ⁢ 
                               λ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               L 
                             
                             ) 
                           
                           2 
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     Therefore the beam width according to the present invention at any range z from the reflector is given by equation 16: 
     
       
         
           
             
               
                 
                   
                     w 
                     ⁡ 
                     
                       ( 
                       z 
                       ) 
                     
                   
                   = 
                   
                     
                       w 
                       
                         
                           1 
                           + 
                           
                             
                               ( 
                               
                                 π 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   
                                     w 
                                     2 
                                   
                                   / 
                                   2 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 λ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 L 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         1 
                         + 
                         
                           
                             { 
                             
                               
                                 λ 
                                 / 
                                 π 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   w 
                                   2 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     
                                       z 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           1 
                                           + 
                                           
                                             
                                               ( 
                                               
                                                 π 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 
                                                   
                                                     w 
                                                     2 
                                                   
                                                   / 
                                                   2 
                                                 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 λ 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 L 
                                               
                                               ) 
                                             
                                             2 
                                           
                                         
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         
                                           ( 
                                           
                                             π 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               
                                                 w 
                                                 2 
                                               
                                               / 
                                               2 
                                             
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             λ 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             L 
                                           
                                           ) 
                                         
                                         2 
                                       
                                       ⁢ 
                                       L 
                                     
                                   
                                   ] 
                                 
                               
                             
                             } 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     The minimal waist diameter results a minimal resolvable spot by the imaging system at the range z 0  that closely equals the detection range L. The depth of the field of an imaging system of the invention is defined by means of equation 16, as the difference between the two “z” values in which the beam widths equal for example twice its minimal value, which is the waist diameter. 
     Example 1 
     The physical features of the receiving antennae such as minimal waist diameter, range to the minimal spot and depth of field, derived by employing the approximate equations according to the present invention were evaluated by comparing them to sizes of same parameters computed by employing physical optics (PO) techniques such as is implemented by the program GRASP9 of the TICRA company of Copenhagen Denmark. Table 1 below summarizes some exemplary cases in which the minimal waist diameters were computed according to equation 14 and the depths of field were computed by employing equation 16 and solving for the points in which the beam widths equal twice the waist diameter. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Parameters of exemplary reflectors of receiving antennae. 
               
            
           
           
               
               
               
               
            
               
                 frequency [GHz] 
                 220 
                 640 
                 1500 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                 focal Length [m] 
                 0.2 
                 0.05 
                 0.01 
               
               
                 reflector depth [m] 
                 0.08 
                 0.02 
                 0.06 
               
               
                 minimal waist diameter [m] 
                 0.058 
                 0.04 
                 0.025 
               
               
                 depth of field [m] 
                 3.9 
                 5.3 
                 4.9 
               
               
                   
               
            
           
         
       
     
     The corresponding values derived by employing GRASP9 agree up to some tens of percents with the sizes computed according to the invention such as shown in table 1. The ranges to the minimal spot were about the same according to both the approximate equation 15 of the invention and the numerical results of the GRASP9. The minimal waist diameters and the depths of field as a function of frequency according to the invention follow the actual results derived by means of GRASP9. 
     Example 2 
     An active imaging system for imaging targets at a detection range of 20 meters according to a preferred embodiment of the present invention, includes a receiving antenna with a spheroidal reflector. The focal length of the receiving antenna is 0.35 meter, which, jointly with the detection range determines the values of the major and minor axes of the spheroid, according to the aforementioned equations 3 and 9, to be of 10 and 2.62 meters respectively. The diameter, of the reflector is 0.6 meter and the depth of the reflector according to equation 10 is about 0.14 meter. 
     A transmitter radiating energy at a frequency of 100 GHz is disposed aside the reflector such that it substantially homogenously illuminates a region of a few meters around the second focus. A planar, rectangular detector array is disposed at the first focus (which is located at a distance of 0.35 meter from the reflector&#39;s apogee). The transmitter, detector array and the connection between the detector array and an imaging processor are as in the prior art. Radiation reflected from targets within a range of a few meters around the second focus of the spheroidal reflector (distanced from the reflector by about 20 meters) and further converged by the reflector of the receiving antenna, impinges the detector array. Images of targets such as of concealed objects under clothing are generated and displayed over a screen of the operator interface unit of the AIS. Spatial resolution of the images received is consistent with the computed minimal waist diameter of 0.084 meters, according to equation 14. The computed depth of field according to equation 16 of 3.7 meters, equals about half of its measured value which is 7 meters.