Abstract:
A ground penetrating radar system includes a cart configured to be movable along the ground. A computer is mechanically coupled to the cart. A radar electronics module is mechanically coupled to the cart and electrically coupled to the computer. A first antenna array is mechanically coupled to the cart, electrically coupled to the radar electronics module, and oriented to radiate into the ground and receive radiation from the ground. A second antenna array is mechanically coupled to the cart, electrically coupled to the radar electronics module, and oriented to radiate into the ground and receive radiation from the ground. A movement detector, which is configured to detect movement of the cart, is coupled to the computer. The computer is configured to trigger the radar electronics module when the computer detects that the cart has moved a predefined distance. The system uses nearfield beam forming, which is accomplished through fully coherent signal processing and synthetic aperture reception and processing, to image buried objects in three dimensions. The system displays a plan, or top, view and a side view of the area being scanned to provide a three dimensional perspective on a two dimensional computer screen.

Description:
The invention was made with Government Support under Federal Contract Numbers DAAB07-98-C-G014 and DAAB15-00-C-1009 awarded by the United States Army. The Government has certain rights in the invention. 
    
    
     FIELD OF THE INVENTION 
     In general, the invention relates to the field of radar systems. More particularly, the invention relates to the field of ground penetrating radar systems. 
     BACKGROUND OF THE INVENTION 
     There are numerous applications in which it is useful to view images of underground objects or objects embedded in the ground or in a material such as concrete, that would not otherwise be visible. For example, it is helpful to utility workers to see images of pipes, cables and conduits that are underground where they are about to dig a hole or a trench. It would be even more helpful if the workers could see a three-dimensional image, so that if an imaged object is deep in the ground below the depth they intend to work, they need not be concerned with the object. 
     Similarly, a system that would allow workers to see images in three dimensions beneath the surface of the ground would be useful in the field of mine detection. This field has become increasingly important as populations have been moving back into previously war-torn areas of the earth. Frequently, when a war ends, civilians move back into a mined area before the authorities can mount a demining operation. Many civilians are injured or killed by such mines even after a war is over. During a war, demining operations help clear a mine field before foot soldiers or vehicles cross it. 
     In such demining operations, it is useful to know accurately not only the surface coordinates of a buried mine, but also the depth at which the mine is buried. It is also important that the equipment used for demining is mobile and that it is capable of exploring a large amount of territory in a short period of time, while maintaining an accurate and detailed record of the objects detected. Such information allows personnel to make intelligent decisions regarding the methods and equipment that are necessary to remove the detected mines. 
     SUMMARY OF THE INVENTION 
     The invention is a ground penetrating radar system mounted on a cart to achieve the desired mobility. The system uses two offset banks of interleaved transmit and receive antennas to achieve the desired accuracy. The receive and transmit antennas are properly oriented with respect to each other to reduce cross coupling and maximize desired subsurface echoes. The system uses nearfield beam forming, which is accomplished through fully coherent signal processing and synthetic aperture reception and processing, to image buried objects in three dimensions. The system displays a plan, or top, view and a side view of the area being scanned to provide a three dimensional perspective on a two dimensional computer screen. 
     In general, in one aspect, the invention features a ground penetrating radar system which includes a cart configured to be movable along the ground. A computer is mechanically coupled to the cart. A radar electronics module is mechanically coupled to the cart and electrically coupled to the computer. A first antenna array is mechanically coupled to the cart, electrically coupled to the radar electronics module, and oriented to radiate into the ground and receive radiation from the ground. A second antenna array is mechanically coupled to the cart, electrically coupled to the radar electronics module, and oriented to radiate into the ground and receive radiation from the ground. A movement detector, which is configured to detect movement of the cart, is coupled to the computer. The computer is configured to trigger the radar electronics module when the computer detects that the cart has moved a predefined distance. 
     Implementations of the invention may include one or more of the following. The radar electronics module may include a first radar electronics module electrically coupled to the first antenna array and a second radar electronics module electrically coupled to the second antenna array. The first antenna array may be configured to radiate and receive radiation from a first series of points along a first set of curves parallel to the direction of movement of the cart. The second antenna array may be configured to radiate and receive radiation from a second series of points along a second set of curves parallel to the direction of movement of the cart. The first set of curves may be interleaved with the second set of curves. 
     In general, in another aspect, the invention features a ground penetrating radar system including a first bank of receive antennas arranged along a first axis, a first bank of transmit antennas arranged along a second axis substantially parallel to the first axis and horizontally displaced from the first axis, a second bank of receive antennas arranged along a third axis substantially parallel to the first axis and horizontally displaced from the first axis, and a second bank of transmit antennas arranged along a fourth axis substantially parallel to the first axis and horizontally displaced from the first axis. A first radar electronics module is coupled to the first bank of transmit antennas and the first bank of receive antennas. A second radar electronics module is coupled to the second bank of transmit antennas and the second bank of receive antennas. The transmit antennas in the first bank of transmit antennas are interleaved with the receive antennas in the first bank of receive antennas and the transmit antennas in the second bank of transmit antennas are interleaved with the receive antennas in the second bank of receive antennas. The receive antennas in the first bank of transmit antennas are offset along the first axis from the receive antennas in the second bank of transmit antennas. 
     Implementations of the invention may include one or more of the following. The first bank of transmit antennas may be offset along the second axis with respect to the second bank of transmit antennas. The banks of receive antennas may alternate with the banks of transmit antennas. Each transmit antenna may be adjacent to at least one receive antenna. Each transmit antenna may be oriented to minimize electromagnetic coupling to at least one of its adjacent receive antennas. Each transmit antenna may include at least one spiral arm of conductive material. Each receive antenna may include at least one spiral arm of conductive material. A tangent to the inside of the spiral arm at the edge of a transmit antenna may be substantially perpendicular to a tangent to the inside of the spiral arm at the edge of a receive antenna adjacent to the transmit antenna. Each transmit antenna may include two spiral arms of conductive material. Each receive antenna may include two spiral arms of conductive material. 
     The transmit antennas and the receive antennas may have faces with centers. Two adjacent first bank receive antennas from the first bank of receive antennas and a first bank transmit antenna from the first bank of transmit antennas interleaved between the two adjacent first bank receive antennas may be positioned such that lines between the centers of the faces of the two adjacent first bank receive antennas and the interleaved first bank transmit antenna form a first triangle having sides of approximately the same length. Two adjacent second bank receive antennas from the second bank of receive antennas and a second bank transmit antenna from the second bank of transmit antennas interleaved between the two adjacent second bank receive antennas may be positioned such that lines between the centers of the faces of the two adjacent second bank receive antennas and the interleaved second bank transmit antenna form a second triangle having sides of approximately the same length. A vertex of the first triangle may be displaced in the direction of the first axis relative to a corresponding vertex of the second triangle by an amount substantially equal to one-half the distance from the center of one side of the first triangle to the center of another side of the first triangle. 
     The third axis may be horizontally displaced from the first axis by an amount substantially equal to eight times the distance from the center of one side of the first triangle to the center of another side of the first triangle. The transmit antennas may not be required to be in contact with the ground when in operation. The receive antennas may not be required to be in contact with the ground when in operation. 
     In general, in another aspect, the invention features a ground penetrating radar system including a digital module. The digital module includes a direct digital synthesizer configured to generate a digital IF reference signal. A digital to analog converter is coupled to the direct digital synthesizer and is configured to convert the digital IF reference signal to an analog IF transmit signal. An analog to digital converter is configured to convert an analog IF receive signal to a digital IF receive signal. A digital down converter is configured to digitally mix the digital IF receive signal with the digital IF reference signal to produce an in-phase product and the digital IF reference signal shifted in phase by ninety degrees to produce a quadrature product. The ground penetrating radar system includes an RF module coupled to the digital module. The RF module includes an up-converter configured to convert the analog IF transmit signal into a transmit signal and a down-converter configured to convert a receive signal into an analog IF receive signal. The system includes a transmit antenna array coupled to the up-converter for radiating the transmit signal and a receive antenna array coupled to the down-converter for receiving the receive signal. 
     Implementations of the invention may include one or more of the following. The transmit antenna array may include a plurality of transmit antennas. The receive antenna array may include a plurality of receive antennas. The system may include a digital signal processor. The system may include a transmit switch for applying the transmit signal to one of the plurality of transmit antennas. The transmit switch may be controlled by the digital signal processor. The system may include a receiver switch for receiving the receive signal from one of the plurality of receive antennas. The receiver switch may be controlled by the digital signal processor. The digital signal processor may control the direct digital synthesizer, the digital down converter, the up-converter and the down-converter. The transmit signal may be a stepped-frequency transmit signal. The receive signal may be a stepped-frequency receive signal. The system may include a computer coupled to a processor through an extensible network. The processor may be configured to communicate with the digital signal processor. The extensible network may be a local area network, e.g., ETHERNET network. 
     In general, in another aspect, the invention features a ground penetrating radar system including a digital module configured to generate an analog IF transmit signal and to receive an analog IF receive signal. The system includes an RF module, which includes a triple-heterodyne up-converter for converting an analog IF transmit signal into a stepped-frequency transmit signal. The RF module also includes a triple-heterodyne frequency converter for converting a stepped-frequency receive signal into an analog IF receive signal. The system includes a transmit antenna coupled to the up-converter for radiating the stepped-frequency transmit signal and a receive antenna coupled to the down-converter for receiving the stepped-frequency receive signal. 
     Implementations of the invention may include one or more of the following. The triple-heterodyne up-converter may include a first up-converter configured to mix the analog IF transmit signal with a signal from a first local oscillator to produce a first intermediate signal and an aliased first intermediate signal. The triple-heterodyne up-converter may include a first filter coupled to the first up-converter for substantially rejecting the aliased first intermediate signal. The triple-heterodyne up-converter may include a second up-converter coupled to the first filter configured to mix the first intermediate signal with a signal from a second local oscillator to produce a second intermediate signal and an aliased second intermediate signal. The triple-heterodyne up-converter may include a second filter coupled to the second up-converter for substantially rejecting the aliased second intermediate signal. The triple-heterodyne up-converter may include a down-converter coupled to the second filter configured to mix the second intermediate signal with a stepped frequency signal to produce the stepped-frequency transmit signal and an aliased stepped-frequency transmit signal. The stepped-frequency transmit signal may have substantially no frequency components in the pass bands of the first filter or the second filter. The triple-heterodyne up-converter may include a third filter coupled to the down-converter for substantially rejecting the aliased stepped-frequency transmit signal. 
     The triple-heterodyne up converter may include an up-converter configured to mix the stepped-frequency receive signal with a stepped-frequency signal to produce a first intermediate signal and an aliased first intermediate signal. The triple-heterodyne up-converter may include a first filter coupled to the first up-converter for substantially rejecting the aliased first intermediate signal. The triple-heterodyne up-converter may include a first down-converter coupled to the first filter configured to mix the first intermediate signal with a signal from a first local oscillator to produce a second intermediate signal and an aliased second intermediate signal. The triple-heterodyne up-converter may include a second filter coupled to the first down-converter for substantially rejecting the aliased second intermediate signal. The triple-heterodyne up-converter may include a second down-converter coupled to the second filter configured to mix the second intermediate signal with a second local oscillator to produce the analog IF receive signal and an aliased analog IF receive signal. The triple-heterodyne up-converter may include a third filter coupled to the second down-converter for substantially rejecting the aliased analog IF receive signal. 
     In general, in another aspect, the invention features a ground penetrating radar system including a transmitter, a receiver, an array of transmit antennas, an array of receive antennas interleaved with the array of transmit antennas, a transmit switch configured to selectively couple the transmitter to one of the array of transmit antennas and a receive switch configured to selectively couple the receiver to one of the array of receive antennas. The array of transmit antennas is arranged in one or more rows. The array of receive antennas is arranged in one or more rows. Each row is parallel to, adjacent to and offset from one of the rows of transmit antennas, so that each receive antenna in a row except one is adjacent to two transmit antennas, and each transmit antenna in a row except one is adjacent to two receive antennas. The transmit switch and the receive switch are configured to couple the transmitter and receiver, respectively, to a first transmit antenna and a first adjacent receive antenna, and subsequently to the first transmit antenna and a second adjacent receive antenna. 
     In general, in another aspect, the invention features a method for collecting and displaying data from a ground penetrating radar system, which includes a plurality of transmit antennas and a plurality of receive antennas. Each transmit antenna, except one, has two adjacent receive antennas. The system is mounted on a movable cart. The method includes collecting raw data. Collecting raw data includes (a) selecting a first of the plurality of transmit antennas. Collecting raw data further includes (b) selecting a first receive antenna that is adjacent to the selected transmit antenna. Collecting raw data further includes (c) collecting data using the selected transmit antenna and the selected receive antenna to produce raw data. The raw data collected at spatial location (x m , y n ) is denoted by {tilde over (Ψ)} mnp  where the indices m, n are used to denote position in a grid of spatial locations where data has been collected, and p is an index ranging from 1 to P corresponding to the frequency f p  at which the data was collected. Collecting raw data includes (d) repeating step (c) for both receive antennas adjacent to the selected transmit antenna. Collecting raw data further includes (e) repeating steps b, c and d for all transmit antennas. Collecting raw data further includes repeating steps a, b, c, d, and e each time the cart moves to a new location. The method further includes preconditioning the raw data to produce preconditioned data, analyzing the preconditioned data, and displaying images of the analyzed data. 
     Implementations of the invention may include one or more of the following. Preconditioning the raw data to produce preconditioned data may include (g) removing a constant frequency component and a system travel time delay, (h) removing a transmit-antenna to receive-antenna coupling effect, (i) prewhitening, and (j) repeating steps (g), (h) and (i) for each spatial location of the raw data. 
     Removing a constant frequency component and a system travel time delay may include applying the following equation:            Ψ   ^     mnp     =       (         Ψ   ~     mnp     -       1   P            ∑     p   =   1     P                       Ψ   ~     mnp           )            exp        (          ·   2          π   ·     f   p     ·   τ       )       .                              
     Removing the transmit-antenna to receive-antenna coupling effect may include applying the following equation: 
     
       
         Ψ mnp ={circumflex over (Ψ)} mnp −{circumflex over (Ψ)} mñp   
       
     
     where {circumflex over (Ψ)} mñp  is an in track reference scan. 
     Removing the transmit-antenna to receive-antenna coupling effect may include applying the following equation:          Ψ   mnp     =         Ψ   ^     mnp     -       1       N   2     -     N   1     +   1       ·       ∑     n   =     N   1         N   2                         Ψ   ^     mnp                                  
     where N 1  and N 2  define a region to be imaged. 
     Removing the transmit-antenna to receive-antenna coupling effect may include applying the following equation:          Ψ   mnp     =       ∑     q   =     -   Q       Q                       a   q     ·       Ψ   ^       m   ,     n   +   q     ,   p                                  
     where a q  are digital filter coefficients chosen to reject low frequency spatial energy. 
     Removing the transmit-antenna to receive-antenna coupling effect may include applying the following equation: 
     
       
         Ψ mnp ={circumflex over (Ψ)} mnp −{circumflex over (Ψ)} {tilde over (m)}np   
       
     
     where {circumflex over (Ψ)} {tilde over (m)}np  is a cross line reference scan. 
     Prewhitening may include applying the following equation: 
     
       
         γ mnp   =b   p ·Ψ mnp   
       
     
     where b p  are frequency dependent weights. 
     Analyzing the preconditioned data may include applying the following equation:          I   mnp     =       1       (       2      U     +   1     )          (       2      V     +   1     )        P       ·       ∑     u   =     -   U       U                       ∑     v   =     -   V       V                       ∑     p   =     P   1         P   2                         γ       m   +   u     ,     n   +   v     ,   p            exp        (          ·   2          π   ·     f   p     ·     τ   uvw         )                                        
     where 
     I mnw  is the complex image value at spatial location (x F,m , y F,n , z w ); 
     U is the SAR array size in the cross-track direction; 
     V is SAR array size in the along track direction; 
     (f P     1   , f P     2   ) is the frequency processing band; 
     τ uvw  is the travel time from source (u, v) in the SAR array down to a focal point at depth z w  and back up to receiver (u, v) in the SAR array;            x     F   ,   m       =         3      d     4     +         (     m   -   1     )        d     4         ;                          
     y F,m =0.933013d+(n−1)dy; 
     d=5.52 inches; and 
     dy=scan spacing. 
     The transmit antennas and the receive antennas may be in contact with the ground and the following equation may apply:          τ   uvw     =       1     c   g            [         (       x     s   ,   u       -     x     r   ,   u         )     2     +       (       y     s   ,   v       -     y     r   ,   v         )     2     +     z   w   2       ]                              
     where (x s,u , y s,v ) and (x r,u , y r,v ) are the location of the transmit and receive antennas and c g  is the speed of light in the ground. 
     Displaying images of the analyzed data may include computing a plan view image of the analyzed data, computing a side view image of the analyzed data, and displaying the plan view image and the side view image. 
     Computing a plan view image of the analyzed data may include applying the following equation: 
     
       
         PlanView mn =max w   |I   mnw | 2   
       
     
     where 
     max w  is the maximum value across all w (depths). 
     Computing a side view image of the analyzed data may include applying the following equation: 
     
       
         SideView nw =max m   |I   mnw | 2   
       
     
     where 
     max w  is the maximum value across all w (depths). 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     FIG. 1 is a perspective view of a ground penetrating radar system according to the present invention. 
     FIG. 2 is a block diagram of a ground penetrating radar system. 
     FIG. 3 illustrates the grid of radar data collected by a ground penetrating radar system. 
     FIG. 4 illustrates the geometry of antenna arrays incorporated in the ground penetrating radar system. 
     FIG. 5 illustrates the switching among the antennas within the antenna arrays. 
     FIG. 6 illustrates the configuration of the antennas. 
     FIG. 7 illustrates the relative orientation of a transmit antenna and a receive antenna. 
     FIG. 8 is a block diagram of the electronics in a ground penetrating radar system. 
     FIG. 9 is a block diagram of a digital module. 
     FIG. 10 is a block diagram of an embodiment of the signal synthesis and analysis module within a digital module. 
     FIG. 11 is a block diagram of a digital down-converter. 
     FIG. 12A is a block diagram of an embodiment of the signal synthesis and analysis module within a digital module. 
     FIG. 12B is a block diagram of a field programmable gate array. 
     FIG. 13 is a block diagram of the RF module. 
     FIG. 14 is a frequency plan for a preferred embodiment of the ground penetrating radar system. 
     FIG. 15 illustrates a stepped-frequency signal. 
     FIG. 16 is a block diagram of the first stage in a triple-heterodyne frequency up-converter and the last stage in a triple-heterodyne frequency converter. 
     FIG. 17 is a block diagram of a middle stage in a triple-heterodyne frequency up-converter and the middle stage in a triple-heterodyne down-converter. 
     FIG. 18 illustrates the last stage in a triple-heterodyne frequency up-converter and the first stage in a triple-heterodyne frequency converter. 
     FIG. 19 is a block diagram of amplifiers and filters in the triple-heterodyne up-converter and the triple-heterodyne frequency converter. 
     FIG. 20 is a block diagram of a local oscillator. 
     FIG. 21 is a block diagram of the transmit switch and the receive switch. 
     FIG. 22 illustrates the grid of points collected by movement of the ground penetrating radar system along the ground. 
     FIG. 23 is a block diagram of the raw data collection processing. 
     FIG. 24 is a block diagram of the raw data analysis processing. 
     FIG. 25 illustrates the geometry of depth focusing. 
     FIG. 26 illustrates the geometry of collection of points midway between a transmit antenna and a receive antenna. 
     FIG. 27 illustrates the geometry of synthetic aperture radar processing. 
     FIG. 28 illustrates a volume of collected data and a top view and a side view of that data. 
     FIG. 29 illustrates images of data prior to processing. 
     FIG. 30 illustrates images of data after processing. 
     FIG. 31 illustrates a physical block diagram of the processing performed in the ground penetrating radar system. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In the following detailed description and in the several figures of the drawings, like elements are identified with like reference numerals. 
     As shown in the drawings for purposes of illustration, the invention is embodied in a novel ground penetrating radar system. A system according to the invention includes interleaved antenna arrays of properly oriented spiral transmit and receive antennas. Switching among the antennas allows samples to be efficiently taken with high spatial density. A digital frequency synthesizer and digital down converter allow fast and accurate measurements. Triple heterodyne up and down conversion reduces the likelihood that mixing products will interfere with the measurements. The system is extensible because of a local area network, e.g., ETHERNET, interconnection between system components. The system uses advanced processing and spatial filtering techniques to improve the quality of the images produced. 
     A ground penetrating radar system  102 , illustrated in FIG. 1, includes a cart  104  that can be moved along the ground. In the preferred embodiment, the cart  104  has four all terrain wheels  106  that give the cart  104  mobility over all types of terrain. Other techniques for providing mobility, such as tracks or skids, are within the scope of the invention. 
     In an preferred embodiment, the cart  104  is a lightweight, compact design fabricated out of aluminum tubing. Four inch square, thin wall tubing is used for the frame. All joints are welded and the frame is painted with polyurethane paint. Mount points for all major system components are built into the frame with easy access to each mount for individual component removal without tools. In other embodiments, the cart is fabricated out of other metals, such as steel, or other materials, such as light-weight composites. 
     The system  102  includes a computer  108  mechanically coupled to the cart  104 . In the preferred embodiment illustrated in FIG. 1, the computer  108  is a laptop computer, having its own display, memory, long term storage and other peripherals, that rests on or is secured to the cart  104 . In other embodiments, the computer is a desktop-type computer. 
     A radar electronics module  110 ,  112  is mechanically coupled to the cart  104  and electrically coupled to the computer  108 . In a preferred embodiment, the radar electronics module  110 ,  112  includes two 25 inch wide, 12 inch long, 2.5 inch high black anodized aluminum enclosures  110 ,  112 , each containing two separate compartments for a digital circuit board and an analog (or RF) printed circuit board (both described in detail below). The circuit board compartments are separated by an aluminum plate, which physically and electrically isolates the boards. The barrier plate eliminates any potential for EMI and RFI noise between the two boards. The radar module enclosure cavities are accessible by removing the top cover plate. 
     A first (or front) antenna array  114  is mechanically coupled to the cart  104  and electrically coupled to the radar electronics module  110 ,  112 . The first antenna array  114  is oriented to radiate into the ground and receive radiation from the ground. A second (or back) antenna array  116  is mechanically coupled to the cart  104  and electrically coupled to the radar electronics module  110 ,  112 . The second antenna array  116  is oriented to radiate into the ground and receive radiation from the ground. 
     The two antenna arrays  114  and  116  are coupled to the cart  104  by an antenna framework  118 . The antenna arrays  114  and  116  and the antenna framework  118  can be removed from the cart  104  for diagnostics and transport. The height of the antenna arrays  114  and  116  above the ground may be adjusted by a machine screw jack  120  to be, in a preferred embodiment, between six inches and twenty inches. A drill motor  122  drives the machine screw jack  120  to raise and lower the antenna arrays. The drill motor  122  could be replaced by any type of motor that has sufficient power to raise and lower the antenna arrays. The antenna framework  118  offsets the antenna banks (in a preferred embodiment by 24 inches) from the cart  104  frame to eliminate any possibility of target shadowing by the frame. 
     A movement detector  202 , shown in FIG. 2, coupled to the computer detects movement of the cart  104 . In the preferred embodiment, the movement detector  202  is an optical encoder mounted on the front right wheel of the cart  104 . 
     The computer  108  triggers the radar electronics module  110 ,  112  when the computer  108  detects that the cart  104  has moved a predefined distance. In this way, data can be acquired at prescribed intervals measured by the motion detector  202 . 
     In a preferred embodiment, the radar electronics module  110 ,  112  includes two electronics modules. A first radar electronics module  110  is coupled to the first antenna array  114 . A second radar electronics module  112  is coupled to the second antenna array  116 . 
     The first antenna array  114  radiates and receives radiation from a first series of points, e.g.  302  shown in FIG. 3, along a first set of curves  304  parallel to the direction of movement  306  of the cart  104 . In FIG. 3, the open circles represent the locations of the centers of the transmit and receive antennas when they take a radar sample, as described below. The closed, or filled, circles represent the location of the samples. In a preferred embodiment, the curves in the first set of curves  304  are approximately d/2, or 2.76 inches, apart. 
     Similarly, the second antenna array  116  radiates and receives radiation from a second series of points, e.g.  308 , along a second set of curves  310  parallel to the direction of movement  306  of the cart  104 . Note that in FIG. 3, the second antenna array  116  is shown a large distance behind the first antenna array  114 . Actually, the two arrays are preferably arranged in much closer proximity to each other, as shown in FIGS. 1 and 2 and as discussed below in the discussion of FIG.  4 . In a preferred embodiment, the curves in the second set of curves  310  are approximately d/2, or 2.76 inches, apart. The first set of curves  304  is interleaved with the second set of curves  310 . The result is a set of curves including the first set of curves  304  and the second set of curves  310 , with the curves being approximately d/4, or 1.38, inches apart. 
     The parameter d in FIG. 3 denotes the outside diameter of an antenna. In a preferred embodiment, d=5.515 inches. The individual transmit and receive antennas are of the log spiral type and were designed to operate over the band 800-4000 MHz but actually radiate well down to 500 MHz. The antenna cavity is nine inches tall and is filled with radar absorbing material to minimize reflections from the top of the antenna. The transmit and receive antennas have different windings in order to minimize cross coupling during the simultaneous transmission and reception required by a stepped-frequency radar. 
     The first antenna array  114  includes a first bank of receive antennas  402  arranged along a first axis  404  and a first bank of transmit antennas  406  arranged along a second axis  408  substantially parallel to the first axis and horizontally displaced from the first axis, as shown in FIG.  4 . The second antenna array  116  includes a second bank of receive antennas  410  arranged along a third axis  412  substantially parallel to the first axis  404  and horizontally displaced from the first axis  404  and a second bank of transmit antennas  414  arranged along a fourth axis  416  substantially parallel to the first axis  404  and horizontally displaced from the first axis  404 . 
     In a preferred embodiment, the first radar electronics module  110  is coupled to the first bank of receive antennas  402  and the first bank of transmit antennas  406 . The second radar electronics module  112  is coupled to the second bank of receive antennas  410  and the second bank of transmit antennas  414 . 
     As can be seen in FIG. 4, the receive antennas in the first bank of receive antennas  402  are interleaved with the transmit antennas in the first bank of transmit antennas  406 . Similarly, the receive antennas in the second bank of receive antennas  410  are interleaved with the transmit antennas in the second bank of transmit antennas  414 . 
     Further, the receive antennas in the first bank of receive antennas  402  are offset along the first axis  404  from the receive antennas in the second bank of receive antennas. Similarly, the first bank of transmit antennas  406  is offset with respect to the second bank of transmit antennas  414 . The banks of transmit antennas  406 ,  414  alternate with the banks of receive antennas  402 ,  410 . 
     Each receive antenna, e.g.  418 , is adjacent to at least one transmit antenna, e.g.  420 ,  422 . Each receive antenna, e.g.  418 , is oriented to minimize electromagnetic coupling with at least one of its adjacent transmit antennas, e.g.  420 ,  422 . 
     The close spacing of the curves  304  and  310 , shown in FIG. 3, is accomplished through the interleaving of the transmit and receive banks of antennas, as discussed above, and by sharing the transmit and receive antennas within the same bank. Each transmit antenna transmits to its two adjacent receive antennas, as shown in FIG.  5 . The transmit/receive sequence for the first antenna array is TX 0 -RX 0 , TX 0 -RX 1 , TX 1 -RX 1 , TX 1 -RX 2 , . . . , TX 6 -RX 6 . The transmit/receive sequence for the second antenna array is similar. Each time a transmitter/receiver pair (such as TX 0 -RX 0 ) is energized, a sample of radar data is taken. By moving the cart in the cart movement direction  306  and taking samples at regular distance intervals (measured by the movement detector  202 ), an array of data may be acquired. Further, samples at a number of frequencies are taken at each sample location. 
     The data structure produced by this process is a complex array of numbers of the form y(m,n,p) where m is the cross-track index (m=1,2, . . . ,26), n is the row or scan index and p is the frequency index. The quantity y(m,n,p) is the complex frequency response of the ground at the location (m,n). It is the quantity measured by the stepped-frequency radar. The Fourier transform of y(m,n,p) is the equivalent time domain response of the radar at location (m,n). 
     Each transmit antenna  602 , illustrated in FIG. 6, includes at least one spiral arm  604  of conductive material. Similarly, each receive antenna, e.g.  606 , includes at least one spiral arm  608  of conductive material. 
     The transmit antenna  602  and one of its adjacent receive antennas  606  are oriented so that a tangent  702  to the inside of the spiral arm  604  at the edge of a transmit antenna  602  is substantially perpendicular to a tangent  704  to the inside of the spiral arm  608  at the edge of a receive antenna  606  adjacent to the transmit antenna. This orientation minimizes electromagnetic cross coupling between the transmit antenna  602  and the receive antenna  606 . 
     In a preferred embodiment, each transmit antenna, e.g.  602 , includes two spiral arms  604 ,  610  of conductive material and each receive antenna  606  includes two spiral arms  608 ,  612  of conductive material. 
     As shown in FIG. 4, the transmit antennas, e.g.  424  and  426 , and the receive antennas, e.g.  428 , have faces. Each of the faces has a center. Two adjacent first bank receive antennas  424 ,  426  from the first bank of receive antennas  402  and a first bank transmit antenna  428  from the first bank of transmit antennas  406  interleaved between the two adjacent first bank receive antennas  424 ,  426  are positioned such that lines between the centers of the faces of the two adjacent first bank receive antennas  424 ,  426  and the interleaved first bank transmit antenna  428  form a first triangle  430  having sides of approximately the same length. 
     Two adjacent second bank receive antennas  432 ,  434  from the second bank of receive antennas  410  and a second bank transmit antenna  436  from the second bank of transmit antennas  414  interleaved between the two adjacent second bank receive antennas  432 ,  434  are positioned such that lines between the centers of the faces of the two adjacent second bank receive antennas  432 ,  434  and the interleaved second bank transmit antenna  436  form a second triangle  438  having sides of approximately the same length. 
     A vertex  440  of the first triangle  430  is displaced in the direction of the first axis  404  relative to a corresponding vertex  442  of the second triangle  438  by an amount substantially equal to one-half the distance from the center of one side of the first triangle  432  to the center of another side of the first triangle  432 . 
     In a preferred embodiment, the third axis  412  is horizontally displaced from the first axis  404  by an amount substantially equal to eight times the distance from the center of one side of the first triangle  432  to the center of another side of the first triangle  432 . 
     In a preferred embodiment, neither the transmit antennas, e.g.  420 , nor the receive antennas, e.g.  422 , are required to be in contact with the ground when in operation. 
     In a preferred embodiment, the ground penetrating radar system operates in a continuous wave mode. The first and second radar electronics modules  110 ,  112  generate a frequency-stepped radar signal and receive and analyze the return signal. 
     The first and second radar electronics modules  110 ,  112  in the ground penetrating radar system each include a digital module  802 ,  804  coupled to the computer  108 , and an RF module  806 ,  808  coupled to the digital module  802 ,  804 , as shown in FIG.  8 . The digital module  802 ,  804  generates an IF signal, which in the preferred embodiment has a frequency of 10.7 MHz. The RF module  806 ,  808 , under the control of the digital module  802 ,  804 , converts the IF signal to a stepped-frequency signal, RFTX, which is provided to a transmit switch  810 . The transmit switch  810 ,  812  provides the RFTX signal to one transmit antenna in its respective first or second antenna array  114 ,  116  which radiates a signal into the ground. 
     A stepped frequency return signal is received by the antenna array  114 ,  116  and routed to a receiver switch  814 ,  816 . The receiver switch  814 ,  816  selects a receive antenna from which to receive the returned signal and routes the signal to the RF module  806 ,  808 . The RF module  806 ,  808 , under the control of the digital module  802 ,  804 , converts the stepped frequency return signal into a receive IF signal, which in the preferred embodiment has a frequency of 10.7 MHz. The digital module  802 ,  804  demodulates the IF signal and provides the result to the computer  108  for storage and processing. 
     The digital module  802 ,  804 , illustrated in more detail in FIG. 9, includes an extensible network interface  902 , which in the preferred embodiment is a local area network, e.g., ETHERNET, interface, and a point-to-point communication interface  904 , which in the preferred embodiment is an RS-232 interface. Both the extensible network interface  902  and the point-to-point communication interface  904  allow communication between the computer  108  and a processor  906  within the digital module  802 ,  804  for communicating configuration commands and data from the computer  108  to the digital module  802 ,  804  and for communicating status and collected and processed data from the digital module  802 ,  804  to the computer  108 . Data and program code for the processor  906  are stored within the digital module on a memory  910 . A signal synthesis and analysis module  908  synthesizes the transmit IF signal, controls the transmitter switch  810 ,  812 , controls the up- and down-conversion performed in the RF module  806 ,  808 , demodulates the receive IF signal, and controls the receiver switch  814 ,  816 . 
     The signal synthesis and analysis module  908 , shown in more detail in FIG. 10, includes a direct digital synthesizer  1002 , which generates a digital IF reference signal  1004 . A digital to analog converter  1006  converts the digital IF signal to an analog IF transmit signal  1008 . In a preferred embodiment, the analog IF transmit signal  1008  is a 10.7 MHz IF signal. In a preferred embodiment, the direct digital synthesizer  1002  and the digital to analog converter  1006  are incorporated into a single module  1010 , such as the AD7008 manufactured by Analog Devices. The AD7008 includes a 10-bit analog to digital converter. 
     The digital IF reference signal  1004  provides a stable and accurate reference for both the transmit and receive paths of the apparatus. As will be seen, the digital IF reference signal  1004  is used in the down conversion process without the necessity of applying delays. 
     The signal synthesis and analysis module  908  also includes an analog to digital converter  1012  which digitizes the analog IF receive signal  1014  to produce a digital IF receive signal  1016 . The digital IF receive signal  1016  is routed to a digital down converter  1018  which digitally mixes the digital IF receive signal  1016  with the digital IF reference signal  1004  from the direct digital synthesizer  1002  through a programmable logic device (PLD)  1020 . The PLD  1020  provides control logic and interfacing for the direct digital synthesizer  1002  and the digital down converter  1018  and a digital signal processor (DSP)  1022 . The DSP  1022  controls the direct digital synthesizer  1002 , the digital down converter  1018 , and the other peripherals in the system. The PLD also receives an Out of Range signal from the analog to digital converter  1012 , which it communicates to the DSP  1022 . The DSP  1022  reacts by changing the gain in the receive chain, as discussed below. 
     The digital down converter  1018  digitally mixes  1102  the digital IF reference signal  1004  with the digital IF receive signal  1016  to produce an in-phase product  1104 , as shown in FIG.  11 . The in-phase product  1104  is then digitally filtered by a low pass filter  1106  to produce a filtered in phase component  1108  which is transferred to the DSP  1022  for processing and storage. 
     The digital down converter  1018  also digitally shifts the phase of the digital IF reference signal by ninety degrees  1110  and digitally mixes  1112  it with the digital IF receive signal  1016  to produce a quadrature product  1114 . The quadrature product  1114  is then digitally filtered through a low pass filter  1116  to produce a filtered quadrature component  1118  which is passed to the DSP  1022  for processing and storage. 
     In a preferred embodiment, the low pass filters  1106  and  1116  perform their functions by integrating a moving window of input data. In one embodiment, the window is  128  signals wide. 
     Returning to FIG. 10, the signal synthesis and analysis module  908  includes a memory  1024  where the DSP  1022  and the PLD  1020  store data. The signal synthesis and analysis module  908  also includes a program memory  1026  where program code for the DSP  1022  is stored. 
     Another example embodiment of the digital module  908  is illustrated in FIG.  12 A. The DSP  1022 , the memory  1024  and the program memory  1026  remain in the same configuration as shown in FIG.  10 . The data and programs stored in the memory  1024  and the program memory  1026  may be different from the data and programs stored in the same elements in FIG. 10. A PLD  1202  provides a control logic interface between the DSP  1022  and a field programmable gate array (FPGA)  1204 . A memory  1206 , preferably a programmable read only memory (PROM), stores the FPGA boot program. A clock  1208 , preferably an 85.6 MHz clock, provides a clock signal to the FPGA, a digital to analog converter (DAC)  1210  and an analog to digital converter (ADC)  1212 . The FPGA  1204  is controlled by the PLD  1202 , which in turn is controlled by the DSP  1022 , through control lines  1214 . 
     The FPGA  1204  generates a digital IF reference signal  1216 . The DAC  1210  converts the digital IF reference signal  1216  to an analog signal which is isolated by transformer  1218  and provided as the analog IF transmit signal  1008 . 
     The analog IF receive signal  1014  is converted by the ADC  1212  to a digital receive signal  1220  which is provided to the FPGA  1204 . The ADC  1212  also produces an out of range signal  1222  if the analog IF receive signal  1014  exceeds the range of the ADC  1212 . 
     The FPGA  1204  produces received data  1224  which is transferred to the DSP  1022  for processing. 
     In one example embodiment of the FPGA, illustrated in FIG. 12B, the digital receive signal  1220  is provided to two digital mixers  1226  and  1228 . The first digital mixer  1226  mixes the digital receive signal  1220  with a digital cosine wave  1230  having a frequency, in one preferred embodiment, of 10.7 MHz. The output of the first digital mixer  1226  is the real component  1232  of the digital receive signal  1220 . The real component  1232  is filtered  1234 , preferably by summing a  128  sample moving window of data, to produce a filtered real component signal  1236  which is provided to a multiplexer  1238 . 
     The second digital mixer  1228  mixes the digital receive signal  1220  with a digital sine wave  1240  having a frequency, in one preferred embodiment, of 10.7 MHz. Preferably, the digital sine wave  1240  is identical to the digital cosine wave  1230  except that the digital sine wave  1240  is shifted ninety degrees in phase with respect to the digital cosine wave  1230 . The output of the first digital mixer  1228  is the imaginary component  1242  of the digital receive signal  1220 . The imaginary component  1242  is filtered  1244 , preferably by summing a  128  sample moving window of data, to produce a filtered imaginary component signal  1246  which is provided to the multiplexer  1238 . 
     The digital sine wave  1240  is also provided as the digital IF reference signal  1216 . 
     The multiplexer  1238  provides to the DSP  1022  either the filtered real component signal  1236  or the filtered imaginary component signal  1246 , depending on the select signal  1248 . 
     The RF module  806 ,  808 , shown in more detail in FIG. 13, includes a triple-heterodyne up-converter  1302  for converting the analog IF transmit signal  1008  into a stepped-frequency transmit signal  1304 . The RF module  806 ,  808  also includes a triple-heterodyne frequency converter  1306  for converting a stepped frequency receive signal  1308  into the analog IF receive signal  1014 . 
     The triple-heterodyne up-converter  1302  includes a first up-converter  1310 . The first up-converter  1310  includes a mixer  1602 , as shown in FIG. 16, which mixes the analog IF transmit signal  1008  (after it has been isolated by transformer  1604  and filtered by low pass filter  1606 ) with the signal from a first local oscillator  1312  to produce a first intermediate signal  1314  and an aliased first intermediate signal  1402 , as shown in FIG.  14 . These two signals are isolated by transformer  1608  and amplified by amplifiers  1610 ,  1612  and  1613 . A filter  1614 , having a pass band  1404 , shown in FIG. 14, substantially rejects the aliased first intermediate signal  1402 . In the preferred embodiment, the first local oscillator  1312  operates at a frequency of 122 MHz and when mixed with the 10.7 MHz IF produces mixing products at 111.3 MHz and 132.7 MHz. In the preferred embodiment, the filter  1614  has a center frequency of 139.75 MHz and passes the 132.7 MHz mixing product. 
     A second up-converter  1316  includes a mixer  1702 , as shown in FIG. 17, which mixes the first intermediate signal  1314  with the signal produced by the second local oscillator  1318  to produce a second intermediate signal  1320  and an aliased second intermediate signal  1406 , as shown in FIG. 14. A filter  1704  substantially rejects the aliased second intermediate signal  1406 . In the preferred embodiment, the second local oscillator  1318  operates at a frequency of 2275 MHz and when mixed with the first intermediate signal  1314  produces mixing products at 2142.3 MHz and 2407.7 MHz. In the preferred embodiment, the filter  1704  has a center frequency of 2450 MHz and passes the 2407.7 MHz product. 
     A down-converter  1322  includes a mixer  1802 , shown in FIG. 18, that mixes the second intermediate signal  1320  (after being amplified by amplifier  1804 ) with a stepped frequency signal  1324  generated by a synthesizer  1326  to produce the stepped-frequency transmit signal  1328  and an aliased stepped-frequency transmit signal (not shown in FIG.  14 ). The stepped-frequency transmit signal has substantially no frequency components in the pass bands of the first filter  1614  or the second filter  1704 . A third filter  1902 , shown in FIG. 19, substantially rejects the aliased stepped-frequency transmit signal (after it is amplified by amplifier  1904 ). Amplifier  1906  amplifies the output of the third filter  1902  to produce the stepped-frequency transmit signal  1304 . In the preferred embodiment, the third filter  1902  is a low pass filter with a 3 dB break point at 2000 MHz. 
     The synthesizer  1326  is controlled by the DSP  1022  through the LO Control and Configuration signals shown on FIG. 13 to produce a stepped-frequency signal  1324 , illustrated in FIG.  15 . The frequency of the stepped-frequency signal  1324  steps through a range of frequencies  1502  under the control of the DSP  1022 . In the preferred embodiment the range of frequencies  1502  is from 500 to 2000 MHz. In the preferred embodiment, when the stepped-frequency signal  1324  is mixed with the second intermediate signal  1322  the result is a preamplified stepped-frequency transmit signal  1328  ranging from 407.7 MHz to 1907.7 MHz. 
     The triple-heterodyne up-converter  1302  includes amplifiers and filters  1330  which amplify and filter the preamplified stepped-frequency transmit signal  1328  before it is sent to the transmit switch  810 ,  812  and then to the antenna array  114 ,  116  as stepped-frequency transmit signal  1304 . 
     The triple-heterodyne up converter  1306  includes an amplifier/filter  1332  that amplifies, using amplifier  1908 , and filters, using filter  1910 , the stepped-frequency receive signal  1308  to produce an amplified stepped-frequency received signal  1334 , as illustrated in FIG.  19 . 
     An up-converter  1336  uses mixer  1806  to mix the stepped-frequency receive signal  1334  (after amplification by amplifier  1808 ) with the stepped-frequency signal  1324  output of the synthesizer  1326  to produce a first intermediate signal  1338  and an aliased first intermediate signal  1410 , as shown in FIG. 14. A first filter  1810  substantially rejects the aliased first intermediate signal  1410  (after it has been amplified by amplifier  1812 ). 
     A first down-converter  1340  uses a mixer  1706  to mix the first intermediate signal  1338  with the signal produced by the second local oscillator  1318  to produce a second intermediate signal  1342  and an aliased second intermediate signal  1412 . A second filter  1708  substantially rejects the aliased second intermediate signal  1412  (after it is amplified by amplifier  1710 ). 
     A second down-converter  1344  uses a mixer  1616  to mix the second intermediate signal  1342  (after it is amplified by amplifier  1618 ) with the signal produced by the first local oscillator  1312  to produce the analog IF receive signal  1014  and an aliased analog IF receive signal (not shown). A third filter  1620  substantially rejects the aliased analog IF receive signal. An variable-gain amplifier  1622  between the mixer  1616  and the third filter  1620  allows the DSP to control the receive gain using gain control signals  1624 . A transformer  1626  isolates the mixer  1616  from the amplifier  1624 . An amplifier  1628  amplifies the output of the third filter  1620  and a transformer  1630  isolates the output of the amplifier  1628  from the output  1014 . 
     In a preferred embodiment, the second local oscillator, shown in detail in FIG. 17, is a phase locked loop including a phase locked loop (PLL) frequency synthesizer  1712 . In a preferred embodiment, PLL frequency synthesizer  1712  is a MC145202 manufactured by Motorola. 
     The PLL frequency synthesizer  1712  has an SDI input, a SCLK input and an SLD input from the DSP  1022 . The SDI input is the serial data line from the DSP  1022  that provides the configuration data for the PLL frequency synthesizer  1712 . Through the configuration data transferred through the SDI input, the DSP  1022  can specify the frequency at which the phase locked loop  1318  is to operate. In the preferred embodiment, the SDI signal is also used to transfer data into the local oscillator  1326 , as discussed below. 
     The SCLK is used to clock the transfer of serial data into the PLL frequency synthesizer  1712 . In the preferred embodiment, the SCLK signal is also used to clock the transfer of data into the LO, as described below. The SLD signal is activated when the SDI data is intended for the PLL frequency synthesizer  1712 . 
     The PLL frequency synthesizer  1712  provides a loop error signal  1716  as an input to the voltage controlled oscillator (“VCO”)  1714 . The frequency of the output  1718  of the VCO  1714  varies with the loop error signal  1716 . The VCO output is amplified by amplifier  1720  and provided as the output of local oscillator  1318  through amplifiers  1722  and  1724 . The output of amplifier  1720  is frequency divided by divider  1726  to produce an input to the PLL frequency synthesizer  1712 , thereby closing the phase locked loop. 
     In other embodiments, the phase locked loop  1318  is replaced by other apparatus for generating a stable frequency signal, such as a crystal. 
     The local oscillator  1326 , shown in more detail in FIG. 18, includes an LO synthesizer  1814 , which generates the stepped frequency signal  1324 . Amplifiers  1816  and  1818  amplify the stepped frequency signal  1324  for use by the down converter  1322  and the up converter  1336 . 
     The LO synthesizer  1814  is controlled by the DSP using control lines  1820  and produces a calibration signal PN  1822 , which is used by the DSP to calibrate the LO. 
     The LO synthesizer  1814 , illustrated in detail in FIG. 20, includes a digital to analog converter (DAC)  2002  which is provided a voltage reference  2004 . The level of the analog output of the DAC  2002  is determined by the SDI, SCLK and SLD inputs from the DSP. These signals were described above in the description of the phase locked loop  1318 . When the SLD signal enables the DAC  2002 , the SCLK signal clocks data in the SDI signal into the DAC  2002 . The data clocked into the DAC determines the level of its output. 
     The DAC output is amplified by an amplifier  2005  and used to drive a voltage controlled oscillator (VCO)  2006 . Thus, by selecting the data to store in the DAC  2002 , the DSP  1022  can control the frequency of the output of the VCO  2006 . In a preferred embodiment, the DSP  1022  controls the frequency of the output of the VCO  2006  to vary in steps, as shown in FIG. 15, from 1000 to 2000 MHz. An amplifier  2008  amplifies the output of the VCO  2006 . 
     The system generates the entire desired range of frequencies, which, in a preferred embodiment is from 500 to 2000 MHz, by using a series of switches. To generate the stepped frequency signal over the range from 500 to 1000 MHz, the DSP unasserts the SHI signal which causes an input switch  2010  to switch to its “lo” position and an output switch  2012  to switch to its “lo” position. This configuration of switches causes the amplified output of the VCO  2006  to be routed to a frequency divider  2104 , which divides the frequency of the signal by two. The result is filtered by low pass filter  2016  and provided as the stepped frequency signal  1324 . 
     The DSP  1022  can generate the higher range of frequencies (e.g., from 1000 to 2000 MHz) by asserting the SHI signal, which causes the input switch  2010  and the output switch  2012  to switch to their respective “HI” positions. Similarly, switch  2018  is also closed allowing the amplified output of the VCO  2006  to be filtered by a low pass filter and provided as the stepped frequency signal  1324 . 
     The output of the VCO  2006  is also used to generate a calibration signal PN for use by the DSP  1022 . To accomplish this, the output of the VCO  2006  is amplified by amplifier  2022  and its frequency is divided by  64  by using a series of dividers  2024 ,  2026 , and  2028 . A comparator  2030  squares the edges of the divided signal. Two PALs  2032  and  2034  provide a logic interface between the divided signal and the DSP  1022 . 
     The transmit switch  810 ,  812 , illustrated in FIG. 21, includes seven single-pole, single-throw switches  2102  with their common poles wired in parallel and connected to the stepped-frequency transmit signal  1304 . The other pole of each switch is connected to one of the transmit antennas. Therefore, when one of the switches  2102  is actuated, the stepped frequency transmit signal  1304  is connected to a respective transmit antenna. 
     The selection of which of the switches  2102  to close is controlled by the DSP  1022  through the transmitter switch control lines, which include control lines TXCTL 1 , TXCTL 2 , and TXCTL 3 . The binary combination of these control lines determine which of the transmitter switches  2102  will close. 
     The receiver switch  814 ,  816  also includes seven single-pole, single-throw switches  2104  with their common poles wired in parallel and connected to the stepped frequency received signal  1308 . The other pole of each switch is connected to one of the received antennas in the receive array. Therefore, when one of the switches  2104  is closed, the corresponding receive antenna provides the stepped frequency received signal  1308 . 
     The determination of which of the switches  2104  is to close is controlled by the DSP  1022  through the receive switch control signals, which includes three switch control signals RXCTL 1 , RXCTL 2 , and RXCTL 3 . The switch  2104  that is closed depends on the binary combination of those three control signals. 
     As discussed above, in a preferred embodiment, the system records data at  13  locations spaced 2.76 inches apart for each antenna array  114 ,  116 . Software in the computer  108  fuses this data into a grid of rows and columns of data, where each row includes data taken from 26 locations spaced 1.38 inches apart. The columns represent the data taken at different locations along the direction of cart movement  306  (see FIG.  3 ). 
     In general, the system records stepped-frequency radar data over an n row by m channel grid, as illustrated in FIG. 22, with the location of the individual points in the grid being expressed as (x m , y n ) where x m =m·dx, y n =n·dy, where dx is the space between points in the cross track direction (see FIG.  3 ), m is an index in the cross track direction, dy is the sampling interval in the in track direction, and n is an index in the in track direction. In the preferred embodiment, dx is 1.38 inches and dy is operator selectable, and is preferably selected to be 1.38 inches, producing a rectangular array. In the preferred embodiment, m varies from 1 to 26 and n varies from 1 to N, where N is the total number of scans that the system performs. 
     In the preferred embodiment, data channels m=1,3,5, . . . ,25 are recorded using the first antenna array  114  and data channels m=2,4,6, . . . ,26 are recorded using the second antenna array  116 . The cross track resolution when both antenna arrays are used is 1.38″. Individual images can be formed using either the first antenna array  114  alone or the second antenna array alone. For individual images of these two types, the cross track resolution is 2.76″. 
     The processing that the system performs includes collecting raw data and analyzing the raw data. Collecting the raw data, illustrated in FIG. 23, includes detecting movement of the cart to the next data collection position (block  2302 ). The system accomplishes this by monitoring the movement detector  202 . The system then selects one of the transmit antennas (block  2304 ) and determines if all of the transmit antennas have been processed (block  2306 ). If they have, the process terminates (block  2308 ) until the cart moves to the next data collection position (block  2302 ). 
     If the all of the transmit antennas have not yet been processed, the system selects a receive antenna adjacent to the selected transmit antenna (block  2310 ). The system then determines if both of the receive antennas adjacent to the selected transmit antenna have been processed (block  2312 ). If they have, the system selects the next transmit antenna (block  2314 ) and returns to the beginning of the loop (to block  2306 ). 
     Otherwise, the system collects data using the selected transmit antenna and the selected receive antenna (block  2316 ) to produce raw data  2318 , the raw data collected at spatial location (x m , y n ) being denoted by {tilde over (Ψ)} mnp  where the indices m, n are used to denote position in the grid of spatial locations where data has been collected, and p is an index ranging from 1 to P corresponding to the frequency f p  at which the data was collected. The frequency step of the system is df=(f P −f 1 )/(P−1). The unambiguous range of the radar is c/(2·df) where c denotes light speed in air. Each of the data points {tilde over (Ψ)} mnp  is a complex number. In a preferred embodiment, a user may specify f 1  and f p . 
     Once the data has been collected for the selected transmit antenna and the selected receive antenna, the system selects the next receive antenna (block  2320 ) and returns to the beginning of the data collection loop (block  2312 ). 
     Analyzing the raw data  2318 , as illustrated in FIG. 24, includes preconditioning the raw data  2318  to produce preconditioned data (block  2402 ), analyzing the preconditioned data (block  2404 ) and displaying images of the analyzed data (block  2406 ). 
     Preconditioning the raw data to produce preconditioned data includes removing a constant frequency component and a system travel time delay (block  2408 ), removing a transmit-antenna to receive-antenna coupling effect (block  2410 ) and prewhitening (block  2412 ) for each spatial location of the raw data. 
     In the preferred embodiment, removing the constant frequency component and the system travel time delay (block  2408 ) includes applying the following equation:            Ψ   ^     mnp     =       (         Ψ   ~     mnp     -       1   P            ∑     p   =   1     P                       Ψ   ~     mnp           )            exp        (          ·   2          π   ·     f   p     ·   τ       )       .                              
     Removing the transmit-antenna to receive-antenna coupling effect (block  2410 ) is performed to minimize the effects of ground bounce. In the preferred embodiment, this is accomplished by using a spatial high pass filter which acts in the in track direction. This changes the system from an absolute return system to a relative return system. 
     There are several techniques for implementing the spatial high pass filter. They include single row differencing, averaging techniques, Fourier techniques, and digital filtering. Single row differencing, which is the simplest method, includes applying the following equation: 
      Ψ mnp ={circumflex over (Ψ)} mnp −{circumflex over (Ψ)} mñp   
     where {circumflex over (Ψ)} mñp  is an in track reference scan. In a preferred embodiment, the user selects the in track reference scan. 
     Another technique, called average differencing, applies the following equation:          Ψ   mnp     =         Ψ   ^     mnp     -       1       N   2     -     N   1     +   1       ·       ∑     n   =     N   1         N   2                         Ψ   ^     mnp                                  
     where N 1  and N 2  define a region to be imaged. 
     A generalized technique for removing the transmit-antenna to receive-antenna coupling effect comprises applying the following equation:          Ψ   mnp     =       ∑     q   =     -   Q       Q                       a   q     ·       Ψ   ^       m   ,     n   +   q     ,   p                                  
     where a q  are digital filter coefficients chosen to reject low frequency spatial energy. 
     Removing the transmit-antenna to receive-antenna coupling effect may be accomplished by performing spatial filtering in the cross track direction by applying the following equation: 
     
       
         Ψ mnp ={circumflex over (Ψ)} mnp −{circumflex over (Ψ)} {tilde over (m)}np   
       
     
     where {circumflex over (Ψ)} {tilde over (m)}np is a cross line reference scan. 
     In the preferred embodiment, prewhitening (block  2442 ) includes applying the following equation: 
     
       
         γ mnp   =b   p ·Ψ mnp   
       
     
     where b p  are frequency dependent weights. 
     In the preferred embodiment, analyzing the preconditioned data (block  2404 ) includes depth focusing (block  2414 ) and synthetic aperture radar (SAR) processing (block  2416 ). 
     Depth focusing (block  2414 ) includes analyzing the preprocessed data to resolve a target in depth. The geometry of depth focusing (block  2414 ) is illustrated in FIG.  25 . To accomplish depth focusing (block  2414 ) the system measures the transfer function of the ground as a function of frequency. The Fourier transform of the transfer function yields the desired depth response function. The relevant equations are:                I        (     x   ,   y   ,   z     )       =                  ∫     f     m                 i                 n         f     m                 a                 x                Ψ        (   f   )            exp        (     2π                 f                 τ     )                          f                     =                Δ                 f          ∑     p   =   1       N   f                         Ψ   p          exp        (     2π                   f   p        τ     )                                          
     where I(x,y,z) is the complex image amplitude and the travel time from the source to the focal point and back again is as follows:          τ        (     x   ,   y   ,   z     )       =           R     s   ,   air       +     R     r   ,   air           c   air       +         R     s   ,   ground       +     R     r   ,   ground           c   ground                                
     In the preferred embodiment, depth focusing is performed at points, e.g. point  2202  in FIG. 22, directly beneath the points of tangency between the source and receive antennas, as illustrated in FIG.  26 . The complex amplitude of the image is formed using the following equation:          I        (       x   m     ,     y   n     ,   z     )       =     Δ                 f          ∑     p   =   1       N   f                         Ψ   mnp          exp        [     2π                   f   p            τ   mn          (       x   m     ,     y   n     ,   z     )         ]                                    
     SAR processing (block  2416 ), which can enhance the images eventually produced from the raw data, is accomplished by combining data from multiple locations using nearfield, delay and sum beamforming, as illustrated in FIG.  27 . The equation for SAR processing is shown below:                  I     n   ^            (       x   m     ,     y   n     ,   z     )       =                Δ                 f          ∑     u   =     -   U       U                       ∑     v   =     -   V       V                       ∑     p   =     P   1         P   2                       Δ                   Ψ       m   +   u     ,     n   +   v     ,   p   ,     n   ^                                            exp        (          ·   2          π   ·     f   p     ·       τ       m   +   u     ,     n   +   v              (       x   m     ,     y   n     ,   z     )           )                                    
     The phase weights in this equation do not depend on absolute sensor position and, in the preferred embodiment, they are precomputed and reused which greatly reduces the time required to perform SAR processing. 
     In the preferred embodiment, the size of the SAR array is ( 2 M s +1)( 2 N s +1). For M s =1 and N s =1, the array will contain 9 points. 
     SAR processing (block  2416 ) is an optional procedure which can be selected by the user to enhance the images produced by the system. 
     Depth focusing (block  2414 ) and SAR processing (block  2416 ) can be accomplished in one step by applying the following equation:          I   mnp     =       1       (       2      U     +   1     )          (       2      V     +   1     )        P       ·       ∑     u   =     -   U       U                       ∑     v   =     -   V       V                       ∑     p   =     P   1         P   2                         γ       m   +   u     ,     n   +   v     ,   p            exp        (          ·   2          π   ·     f   p     ·     τ   uvw         )                                        
     where 
     I mnw  is the complex image value at spatial location (x F,m , y F,n , z w ); 
     U is the SAR array size in the cross-track direction; 
     V is SAR array size in the along track direction; 
     (f P     1   , f P     2   ) is the frequency processing band; 
     τ uvw  is the travel time from source (u, v) in the SAR array down to a focal point at depth z w  and back up to receiver (u, v) in the SAR array;            x     F   ,   m       =         3      d     4     +         (     m   -   1     )        d     4         ;                          
     y F,m =0.933013d+(n−1)dy, preferably; 
     d=5.52 inches, preferably; and 
     dy=scan spacing. 
     The system can operate with the transmit antennas and the receive antennas in contact with the ground. In that case:          τ   uvw     =       1     c   g            [         (       x     s   ,   u       -     x     r   ,   u         )     2     +       (       y     s   ,   v       -     y     r   ,   v         )     2     +     z   w   2       ]                              
     where (x s,u , y s,v ) and (x r,u , y r,v ) are the location of the transmit and receive antennas and c g  is the speed of light in the ground. 
     The preprocessing of the data (block  2402 ) and the analysis of the preprocessed data (block  2404 ) produces a block of data representing a three dimensional volume  2802  as illustrated in FIG.  28 . The invention allows the display of a plan view of the analyzed data and a side view of the analyzed data. 
     Displaying images of the analyzed data (block  2406 ) includes computing a plan view image of the analyzed data, computing a side view image of the analyzed data (block  2418 ) and displaying the plan view image and the side view image (block  2420 ). 
     In the preferred embodiment, computing the plan view image of the analyzed data includes applying the following equation: 
     
       
         PlanView mn =max w   |I   mnw | 2   
       
     
     where 
     max w  is the maximum value across all w (depths). 
     In the preferred embodiment, computing the side view image of the analyzed data includes applying the following equation: 
     
       
         SideView nw =max m   |I   mnw | 2   
       
     
     where 
     max w  is the maximum value across all w (depths). 
     In other embodiments, the plan view image and the side view image are computed using other rendering techniques such as averaging or displaying only image values that fall within defined ranges. Any method or technique for presenting a side view and a plan view fall within the scope of the invention. 
     The results of removing the transmit-antenna to receive-antenna coupling effects (block  2410 ) and SAR processing (block  2416 ) are illustrated in FIGS. 29 and 30. FIG. 29 shows the data without removing the transmit-antenna to receive-antenna coupling effects (block  2410 ) and SAR processing (block  2416 ). FIG. 30 shows the same data after difference referencing using the first data row (block  2410 ) and after SAR processing (block  2416 ). A mine is visible at about channel  7  and Y-Range 1.5 in the plan view and at a depth of about 6 and a Y-Range of about 1.5 in the side view. 
     A physical description of a preferred embodiment of the processing performed by the ground penetrating radar is illustrated in FIG.  31 . 
     The GPSAR program  3102  resides on the computer  108  and provides user control of the ground penetrating radar data acquisition. It accepts a file name, dy (the in track distance between grid points) and array offset (the distance the two antenna arrays are offset from each other). 
     The ENCODER program  3104  resides on the computer  108  and triggers the system to take data based on a signal from the movement detector  202 . It also receives the scan data and stores it as raw binary data  3106 . 
     The RADARBIN.C program  3108  resides on the computer  108  and converts the raw binary data  3106  to ASCII data sorted by scan  3110 . 
     The MGPRVOL.F program  3112  resides on the computer  108  and computes a volumetric image  3114  from the ASCII data  3110 . 
     The GPRIMAGE.C program  3116  renders a plan view  3118  and a side view  3120  from the volumetric image  3114 . 
     The HTML User Interface  3122  is a web browser such as Netscape Navigator or Microsoft Explorer. 
     The programs stored in the memory  908  for the processor  906  in the digital modules control the configuration of their respective components and accept as inputs the start frequency, stop frequency, number of frequency steps in the scan, and the dwell time at each scan step. These programs also provide a local area network, e.g., ETHERNET, interface to the computer  108  and serve up a web page that can be accessed from the computer  108  through the HTML user interface  3122 . These programs also collect data from the DSP  1022 . 
     The programs stored in the program memory  1026  for the DSP  1022  control the digital module  802 ,  804 , the RF module  806 ,  808 , and the TX and RX switches  810 ,  812 ,  814 , and  816 . 
     While some of the components have been described as being implemented in hardware and others in software or firmware, it will be apparent to persons of ordinary skill in the art that some of the hardware portions could be implemented in software or firmware and that some of the software or firmware portions could be implemented in hardware. The software or firmware portions of the system may be written in machine language, assembly language or a higher order language, including such languages as C++, FORTRAN, JAVA or PEARL. 
     Although several specific embodiments of the invention have been described and illustrated, the invention is not to be limited to the specific forms or arrangements of the parts steps so described and illustrated. The invention is limited only by the claims.