Patent Publication Number: US-11378679-B2

Title: Sensor array imaging device

Description:
CROSS-REFERENCE 
     This application claims the benefit of U.S. Provisional Patent Application Ser. No. 62/543,128, filed on Aug. 9, 2017, which is hereby incorporated by reference to its entirety. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to systems that include sensor arrays to acquire data and means to process data to create one-dimensional, two-dimensional or three-dimensional images of scene content within a sensed field of view. In particular, the present invention relates to the forming of sensed images of scenes and objects in fields of view that may be near or far from sensor arrays, with the sensor array either held stationary or moving. 
     BACKGROUND 
     Sensor arrays have proven utility in both the transmission and reception of signals. On transmission, arrays can be used to conventionally form a “beam” in the far-field of the sensor array to concentrate transmitted signal energy in a region of interest, thereby creating a “field of view.” On receive, sensor arrays have been traditionally used to form one or more steered beams for estimation of the angle-of-arrival of signals reflected from scatterers within the far-field. A “scatterer” is a point within the field of view capable of reflecting transmitted signal energy back to the sensor array. Sensor arrays have been used to search for the existence of remote objects by sweeping a steered transmitted beam through a region of interest and searching for echoes from scatterers within the field of view. Traditionally, sensor arrays require means for beamforming and means for beam steering, conventionally provided by on-array analog signal processing circuitry. Operationally, sensor arrays traditionally require a sequence of steered beams, each requiring one or more pulses to be transmitted, to span the field of view being searched. Beam based searching of the sensor array&#39;s remote environment can be overly expensive in the time resources required to scan the search volume and overly expensive in the amount of power resources that must be consumed during multiple, swept beam transmissions. Moreover, due to limitations of conventional processing methods, traditional beamforming for array sensing is only physically possible in the “far-field” of the array, where the notion of a “far-field” traditionally represents a distance that is sufficiently far from the array that electromagnetic or acoustic wave fronts transmitted by the array are nearly planar within the vicinity of the down-range field of view. This far-field limitation of conventional, so called, “Fraunhofer plane-wave beamforming” is inherent in the performance of the processes used to form the beam. Conventional plane-wave processing creates transmit and receive Fraunhofer plane wave beams that exist only at far-field distances. 
     There is a need for means and methods of processing of sensor array data that provide scatterer localization in the traditional near-field of a sensor array and which also provide enhanced scatterer localization in the traditional far-field. An imaging based approach of processing of sensor array data, instead of a beam forming and beam steering approach, would satisfy such a need. An imaging based approach would provide an image of the contents of a sensor array&#39;s field of view, where pixel intensity and pixel position values within the field of view image would indicate both the position (range and angle) and strength of reflective scatterers within that field of view. 
     There is a need to replace beam based search procedures with image based search procedures. Data processing methods capable of producing images from a sensor array would provide more information about the exact nature (position/strength) of individual scatterers within the field of view being imaged. Traditional beam base search methods are only capable of identifying the ranges and rather coarse position angles of the scatterers within fields of view of limited size. 
     Further, there is a need for a means to more quickly search an extended field of view volume (i.e., a field of view larger than a single Fraunhofer plane wave beamwidth) with transmission of a single transmitted pulse from a stationary sensor array. This need requires a replacement of the swept beam or steered angle-of-arrival estimation approach of volume searching with array sensing. A single pulse approach to extended volume searching can be achieved if an image of the contents of an enlarged field of view can be formed by processing the data of the array with the echoes received from a single transmitted pulse. The speed of search can be increased if the field of view supported by a single pulse imaging method is larger than the traditional beamwidth of swept beam based search methods. 
     There is a need for a single pulse, “real,” sensor array imaging method that can be combined with “synthetic” array imaging processes. Imaging methods exist for a form of array sensing called, “synthetic arrays.” Synthetic arrays are commonly used in radar systems called, “synthetic aperture radars” (SARs). With synthetic array radars, many pulses are typically transmitted and collected to form a synthesized array as a single sensor element (antenna) is moved along a predetermined (flight) path. This single sensor element movement creates the “synthetic” array, but at a price of transmission/reception of many pulses. There is a need to increase the effectiveness of synthetic array imaging methods by reducing the number of pulses that are transmitted, and by reducing the amount of sensor movement required for synthetic aperture formation. There is a need for a means for form sensor array based imagery from a real, stationary, sensor array. 
     Moreover, real arrays in the form of digital arrays are becoming more common. A digital array removes analog hardware that has been used for on-array analog processing to form and steer beams. A digital array places multiple analog-to-digital converters closer to each array sensor element. Digital data is then transferred off-array for processing in computer software. With a digital array, sensor element data is directly acquired (without analog Fraunhofer beamforming analog processing circuitry) in digital format from each sensor element. Hence, a digital sensor array presents an opportunity for increased sophistication in off-array digital processing. 
     There is a need for a new means to form imagery with the transmission and reception of a single pulse from a stationary digital sensor array. There is also a need to form imagery with a digital sensor array with digital data gathered from both near or far from the sensor array. There is also a need to combine single pulse, stationary, digital sensor array methods with multiple pulse, moving sensor array, synthetic array operational concepts. Single pulse data collections gathered for image formations, which can be called “single pulse dwells,” can be extended to “multiple pulse dwells” as a digital sensor array is moved in SAR-like applications. There is a need to use image methods achievable with single pulses to improve the performance (e.g., the rate of image production) of SAR-like image methods that have traditionally required sensor movement. 
     SUMMARY 
     The disclosed technology relates to systems for forming imagery of enlarged fields of view with the transmission and reception of a single pulse from a digital sensor array. The disclosed technology relates to single pulse, stationary, and sensor array operations. In addition, the disclosed technology relates to multiple pulse, nonstationary, and sensor array operations. 
     One aspect of the disclosed technology relates to a system for producing sensed images. The system includes a sensor array which includes a plurality of sensor elements capable of transmitting waveform signals and receiving echoes. The system also includes an image display device and a processor. The processor receives sensor element echo data from the transmitted waveform of the sensor array, and performs a temporal discrete Fourier transform (DFT) on the recorded sensor element data. When a size of a field of view to be displayed is larger than a size of the sensor array, the processor performs zero padding to modify the sensor element data received from the sensor array to a size of the expanded field of view for storage in a sensor data buffer. When the size of a field of view to be displayed is not larger than a size of the sensor array, the processor stores the sensor element data to the sensor data buffer without zero padding. The system performs a spatial DFT on the sensor data buffer to result in a sensor wavenumber data buffer. The processor determines a first spatial reference point location of the sensor array. The processor determines a second spatial reference point location of the field of view. The processor generates a reference Fresnel field based on the transmitted waveform, based on the size of the expanded field of view, and based on the first and second spatial reference point locations to obtain reference Fresnel field data. The processor performs a spatial DFT on the reference Fresnel field data to form forward Huygens-Fresnel transfer data. The processor performs complex number conjugation of the forward Huygens-Fresnel transfer data to form inverse Huygens-Fresnel transfer data for storage in an inverse Huygens-Fresnel transfer data buffer. The processor multiplies each data element of the sensor wavenumber buffer with each corresponding data element of the inverse Huygens-Fresnel transfer data buffer and with corresponding element data of a filter matched to the transmitted waveform in the conventional pulse compression sense. The processor stores the multiplied data elements into a rectilinear spectrum data buffer. The processor performs Stolt mapping on the rectilinear spectrum data buffer to form nonuniformly sampled angular spectrum data for storage in an angular spectrum data buffer. The processor performs uniform resampling of nonuniformly sampled angular spectrum data. The processor performs spatial inverse DFT on uniformly resampled angular spectrum data to generate an image of the potentially expanded field of view illustrating contents of the field of view. The processor displays the image on the image display device. 
     In one embodiment, the sensor elements have a predefined spatial arrangement. 
     In one embodiment, the image of the field of view is one, two or three dimensional. 
     In one embodiment, the image of the field of view has a predefined data sample spacing. 
     In one embodiment, the predefined data sample spacing of the image of the field of view is proportional to, including possibly equal to, a predefined spacing between the sensor elements of the sensor array. 
     In one embodiment, a total number of pixels that span a cross-range extent in the azimuth dimension, the elevation dimension, or in both cross-range dimensions of a one-, two- or three-dimensional field of view is equal to a total number of the sensor elements in the sensor array. In one embodiment, the total number of pixels that span a cross-range extent of the field of view is less than, equal to, or is greater than a total number of the sensor elements in the sensor array. 
     In one embodiment, a total number of pixels that span a cross-range extent in the azimuth dimension, the elevation dimension, or in both cross-range dimensions of a one-, two- or three-dimensional, enlarged or expanded field of view is greater than a total number of the sensor elements in the sensor array. 
     In one embodiment, a total number of elements of the inverse Huygens-Fresnel transfer data buffer equals a total number of data samples (image pixels) that span a cross-range extent of the field of view. 
     In one embodiment, the processor generates one or more fields of views with distinct associated spatial reference points, distinct reference Fresnel fields, and distinct reference Fresnel field data buffers. 
     In one embodiment, the sensor array is a two-dimensional sensor array. 
     In one embodiment, the sensor array includes at least one of a multidimensional array and a conformal surface array. 
     In one embodiment, the processor integrates data from multiple sensor positions, obtained by moving one or more sensors arrays, or obtained by a system of distinct multiple sensor arrays, each either stationary or moving. 
     Another aspect of the disclosed technology relates to a system for producing a reference Fresnel field signal. The system includes a sensor array which includes a plurality of sensor elements. The sensor elements have a predefined spacing. The sensor elements may have a predefined waveform transmitted from the sensor array. The system includes a processor. The processor determines a spatial reference point for the sensor array. The processor determines a spatial reference point for a field of view to be imaged. The processor generates reference Fresnel field sample data based on the transmitted waveform to account for a space between the spatial reference points of the sensor array and the field of view. The processor generates a data buffer containing reference Fresnel field sample data. The reference Fresnel field sample data has reference Fresnel field data sample spacing which is proportional to, including possibly equal to, the predefined spacing of the sensor elements. A total number of Fresnel field data samples of the reference Fresnel field sample data is identical to a total number of cross-range data samples of a field of view. 
     In one embodiment, the spatial reference point of the sensor array identifies a nominal center point position of the sensor array. 
     In one embodiment, the spatial reference point for the field of view identifies a nominal center point position of the field of view. 
     An additional aspect of the disclosed technology relates to a system for producing an inverse Huygens-Fresnel transfer signal. The system includes a sensor array which includes a plurality of sensor elements. The sensor elements have a predefined spacing. The sensor elements may have a predefined waveform transmitted from the sensor array. The system includes a processor. The processor determines a spatial discrete Fourier transform of reference Fresnel field data to produce forward Huygens-Fresnel transfer data for a forward Huygens-Fresnel transfer buffer. The reference Fresnel field data has reference Fresnel field data sample spacing which is proportional to, including possibly equal to, the predefined spacing of the sensor elements. A total number of Fresnel field data samples of the reference Fresnel field sample data is identical to a total number of cross-range data samples of a field of view. The processor determines a complex conjugation of the forward Huygens-Fresnel transfer data to produce data for an inverse Huygens-Fresnel transfer buffer. 
     The invention accordingly comprises the several steps and the relation of one or more of such steps with respect to each of the others, and the apparatus embodying features of construction, combinations of elements and arrangement of parts that are adapted to affect such steps, all is exemplified in the following detailed disclosure, and the scope of the invention will be indicated in the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the invention, reference is made to the following description and accompanying drawings, in which: 
         FIG. 1A  illustrates a block diagram of a system according to one aspect of the disclosed technology. 
         FIG. 1B  illustrates a block diagram illustrating operation of the system of  FIG. 1A . 
         FIG. 1C  illustrates a uniform linear sensor array according to one aspect of the disclosed technology. 
         FIG. 1D  illustrates a nonuniform linear sensor array according to one aspect of the disclosed technology. 
         FIG. 1E  illustrates a planar sensor array according to one aspect of the disclosed technology. 
         FIG. 1F  illustrates a conformal sensor array according to one aspect of the disclosed technology. 
         FIG. 1G  illustrates definition of near-field and far-field of a sensor array according to one aspect of the disclosed technology. 
         FIG. 1H  illustrates the data collected by a swarm of twenty distinct sensor arrays, each with a planar array, according to one aspect of the disclosed technology. 
         FIG. 1I  illustrates the volumetric imagery of a set of nineteen distinct scatterers with data sensed and recorded by a swarm of twenty sensor arrays, each with a planar array, according to one aspect of the disclosed technology. 
         FIG. 2  illustrates Fraunhofer beamforming failure of the prior art to resolve scatterer position in azimuth with transmission of a single pulse waveform. 
         FIG. 3  illustrates a two-dimensional field of view image from the echo of a single pulse according to one aspect of the disclosed technology. 
         FIG. 4  illustrates a set of scatterers within an expanded field of view that produces the image of  FIG. 3  according to one aspect of the disclosed technology. 
         FIG. 5  illustrates a three-dimensional field of view image from the echo of a single pulse according to one aspect of the disclosed technology. 
         FIG. 6A  illustrates a two-dimensional field of view image of a line of point scatterers, and  FIG. 6B  illustrates the corresponding single pulse field of view image acquired with a stationary sensor array according to one aspect of the disclosed technology. 
         FIG. 7A  illustrates a multiple pulse dwell field of view image of the line of scatterers in  FIG. 6A , and  FIG. 7B  illustrates an extended multiple pulse dwell field of view image, both achieved with sensor array movement according to one aspect of the disclosed technology. 
         FIG. 8  illustrates an image (one-dimensional) of a field of view that is relatively near the sensor array according to one aspect of the disclosed technology. 
         FIG. 9  illustrates an image (one-dimensional) of a field of view that is relatively far from the sensor array according to one aspect of the disclosed technology. 
         FIG. 10  illustrates sensor array element spacing and field of view predefined data sample spacing according to one aspect of the disclosed technology. 
         FIGS. 11A-C  illustrate example sensor array data for near, midrange and far ranges according to one aspect of the disclosed technology. 
         FIGS. 12A-C  illustrate example zero-padded sensor array data for near, midrange and far ranges according to one aspect of the disclosed technology. 
         FIGS. 13A-C  illustrate sensor wavenumber data buffer contents for near-range, midrange and far-range fields of views according to one aspect of the disclosed technology. 
         FIG. 14  illustrates a reference Fresnel field according to one aspect of the disclosed technology. 
         FIG. 15A  illustrates an example reference Fresnel field presented in a two-dimensional format according to one aspect of the disclosed technology. 
         FIG. 15B  illustrates an example reference Fresnel field presented in a three-dimensional format according to one aspect of the disclosed technology. 
         FIG. 16  illustrates the definition of cross-range sizes of sensor array, zero-padded sensor array data buffer, expanded field of view, reference Fresnel field data buffer, forward Huygens-Fresnel transfer function and inverse Huygens-Fresnel transfer data buffer according to one aspect of the disclosed technology. 
         FIGS. 17A-C  illustrates example reference Fresnel field data buffer contents for near, midrange and far ranges according to one aspect of the disclosed technology. 
         FIG. 18  illustrates use of an omnidirectional signal transmission with multiple receive fields of view according to one aspect of the disclosed technology. 
         FIGS. 19A-C  illustrate inverse Huygens-Fresnel transfer data buffer contents for near-range, midrange and far-range fields of views according to one aspect of the disclosed technology. 
         FIGS. 20A-C  illustrate rectilinear spectrum data buffer contents for near-range, midrange and far-range fields of views according to one aspect of the disclosed technology. 
         FIGS. 21A-C  illustrate angular spectrum data buffer contents for near-range, midrange and far-range fields of views according to one aspect of the disclosed technology. 
         FIG. 22A  illustrates one possible format for expression of a rectilinear spectrum according to one aspect of the disclosed technology. 
         FIG. 22B  illustrates Stolt formatting of a rectilinear spectrum into a nonuniformly sampled angular spectrum according to one aspect of the disclosed technology. 
         FIG. 22C  illustrates uniform resampling of angular spectrum data according to one aspect of the disclosed technology. 
         FIGS. 23A-B  illustrates a flow diagram of example processes performed by the system of  FIG. 1A  according to one aspect of the disclosed technology. 
         FIG. 24  illustrates another flow diagram of example processes performed by the system of  FIG. 1A  according to one aspect of the disclosed technology. 
         FIG. 25  illustrates yet another flow diagram of example processes performed by the system of  FIG. 1A  according to one aspect of the disclosed technology. 
         FIGS. 26A-C  illustrate two-dimensional images for near-range, midrange and far-range fields of views according to one aspect of the disclosed technology. 
         FIG. 27  illustrates prior art technologies failure of discrete Fourier transform (DFT) based angle-of-arrival (AoA) estimate with near-field spherical waves. 
     
    
    
     DETAILED DESCRIPTION 
     In the following detailed description, numerous specific details are set forth by way of examples in order to provide a thorough understanding of the relevant teachings. However, it should be apparent to those skilled in the art that the present teachings may be practiced without such details. In other instances, well known methods, procedures, components, and/or circuitry have been described at a relatively high-level, without detail, in order to avoid unnecessarily obscuring aspects of the present teachings. 
     The present application relates to, but not limited to, a system that utilizes arrays of discrete sensors to collect data to support processing for the creation of images of the contents of the sensor array&#39;s field of view.  FIGS. 1A-1B  show an exemplary signal processing system  1  with a sensor array  10  to perform imaging with transmission of a single pulse signal, where the single pulse signal is transmitted simultaneously by all transmitter/receiver sensor elements of the sensor array  10 . A “single pulse” may be a waveform such as a continuous wave signal, a pulse waveform, a frequency modulated waveform, a composite pulse waveform formed with multiple subpulses, a phase modulated waveform, or one of many other waveform selection possibilities. 
     The sensor array  10  may include an array of sensor elements. Each sensor element may be an antenna element. Each antenna element may receive echo signals and provide descriptive digital data. The sensor array of sensor elements may be associated with a sensor array position reference point. The array position reference point may be a spatial point that describes a nominal position of the entire sensor array  10 . Conventional pulse compression methods such as matched filtering may be utilized by the system. 
     The sensor array  10  may include a digital sensor array that forms images representative of the scatterers of objects within a sensor array field of view by using the single pulse signal. A scatterer is part of an object or part of a scene that reflects the waveform transmitted by the sensor array  10 . An image is comprised of an array of data samples/pixels/voxels and is capable of describing scatterer echo strength (via sample/pixel/voxel amplitude values), scatterer phase (via complex sample/pixel/voxel phase values) and scatterer position (via sample/pixel/voxel position values within the field of view image). 
     The sensor elements of the sensor array  10  may have a predefined spacing. For example, there may exist a predefined physical spacing among the sensor elements as illustrated in  FIGS. 1C-1F . The sensor array  10  may be a one-dimensional linear sensor array as illustrated by  FIG. 1C . The predefined spatial arrangement of sensor elements may be uniform or nonuniform as illustrated respectively by  FIGS. 1C-1D  for the case of a linear array. The sensor array  10  may be a two-dimensional planar sensor array as illustrated by  FIG. 1E . The sensor array  10  may be a multidimensional conformal surface array as illustrated by  FIG. 1F . 
     In the context of the present invention, “near” means a field of view that may be at close distance, including adjacent to, the sensor array. In the context of the present invention, “far” means a field of view that may be at a larger distance. The boundary between “near” and “far” in the context of the present invention, as illustrated in  FIG. 1G , is defined as that distance from the sensor array  10  where the beam width of a traditionally formed Fraunhofer plane wave beam is the same size in the cross-range dimension as the cross-range size of the sensor array. 
     The down-range extent of the field of view of the sensor array  10  may be arbitrarily set or bounded by any finite value. The cross-range (azimuth, elevation, or both) extent of the field of view may be arbitrarily set or bounded by any finite value, but at a minimum, may be at least as large in the cross-range dimension(s) as the cross-range extent of the sensor array  10 . 
     The sensor array  10  may include, but not limited to, wireless communications antenna arrays, radar antenna arrays, seismic antenna arrays, sonar antenna arrays, acoustic antenna arrays and ultrasound antenna arrays. The sensor array  10  may perform one or more of the following: wireless communications sensing, microwave electromagnetic sensing, millimeter wave electromagnetic sensing, radio frequency electromagnetic sensing, lower frequency electromagnetic sensing, very low frequency acoustic sensing, low frequency acoustic sensing, and high/ultrasonic frequency acoustic sensing. Acoustic sensing may occur in air or water. 
     The system  1  may include a non-transitory computer readable medium  12 , a processor  15 , and an image display device  20  or an image processing computer  30 . The non-transitory computer readable medium  12  may include one or more of the following: a sensor data buffer  40 , a reference Fresnel field data buffer  70 , a rectilinear spectrum data buffer  80 , an angular spectrum data buffer  90 , an inverse Huygens-Fresnel transfer data buffer  92  and a sensor wavenumber data buffer  43 . The processor  15  may execute one or more of the following: spatial forward discrete Fourier transform  48 , reference point determinator  50 , a reference Fresnel field generator  60 , spatial inverse spatial discrete Fourier transform  62 , and Stolt format generator  64 . 
     The processor  15  may integrate data from multiple sensor array positions, obtained by moving a sensor array, or obtained by a system of distinct sensor arrays, either stationary or moving as illustrated in  FIG. 1H , where the two-dimensional sensor data array buffers are illustrated for a set of twenty sensor array positions.  FIG. 1I  illustrates the volumetric imagery produced with the multiple sensor array data of  FIG. 1H . 
     Contrary to traditional technology that produces conventional angle-of-arrival (AoA) parameter estimates or range (only) profiles (see  FIG. 2  for an example conventional range profile produced by a single Fraunhofer plane wave beam), the processor  15  may generate a field-of-view image with transmission of a signal waveform and reception of reflected signal echoes.  FIG. 3  provides an example field-of-view image produced with the same data set as conventionally used in  FIG. 2 . The field-of-view image may be displayed in the image display device  20  or the image processing computer  30 .  FIG. 3  illustrates a two-dimensional (down-range/cross-range) image from the echo of a single pulse with a one-dimensional sensor array.  FIG. 3  illustrates an image of a field of view that contains ten point scatterers as distributed in  FIG. 4 . Scatterers may be descriptive of the contents of the field of view, and may be viewed as localized elements of the scene contents that reflect part of the transmitted signal received from the sensor array  10  back to the sensor array  10 . The scatterers as imaged in  FIG. 3  are all resolved in range and azimuth by an imaging approach to sensor array data processing.  FIG. 2  illustrates conventional range profile of a single Fraunhofer beam of the field of view of  FIG. 4  produced by prior art technologies. In the prior art, only the range position of scatterers is recovered and no angle information other than the steer angle of the transmitted/received beam is gathered about scatterer position in azimuth or elevation. 
     The field-of-view image may be a volumetric image.  FIG. 5  provides an example field-of-view volumetric image produced by the present invention.  FIG. 5  illustrates the image of a field of view that contains nineteen discrete scatterers, all scatterer positions are resolved in range, azimuth and elevation, as accomplished by an imaging approach to sensor array data processing.  FIG. 5  illustrates a three-dimensional (volumetric) image from the echo of a single pulse with a two-dimensional sensor array.  FIG. 5  illustrates a three dimensional point spread function (PSF) of the imaging device. A point spread function may be descriptive of the quality of the focusing of the imagery formed by the system  1  for a single point scatterer. If the field of view contains multiple scatterers typical of a real environment, the resulting images may be more lifelike. For example,  FIG. 6A  shows a set of scatterers that may result from a line of lamp posts, or fence posts, or other possibilities where a set of disjoint scatterers are configured in a line.  FIG. 6B  shows an example two dimensional field of view image displayed on the image display device  20  of these lamp posts, etc, obtained with a single transmitted pulse. The field of view of  FIGS. 6A-B  has been significantly extended in the cross-range dimension beyond the traditional beamwidth and array size, which are illustrated by the horizontal lines of  FIG. 6A .  FIGS. 7A-B  also show an example image displayed on the image display device  20  based on transmission of a single pulse.  FIG. 7A  shows the refinement of the point spread function that comes from a multiple pulse dwell and movement of the sensor array.  FIG. 7B  shows the further refinement achieved by extending the multiple pulse dwell with additional pulses and with additional sensor movement. 
     Depending on the position of the within-scene reference point of  FIG. 1B , the field of view image may be positioned either near or far from the sensor array  10 , including adjacent to the sensor array  10 . In the context of the present invention, “near” means a field of view that may be within the “near-field” distance range as illustrated in  FIG. 1G ; whereas “far” means a field of view that may be within the “far-field” distance range as illustrated in  FIG. 1G . The boundary between “near-field” and “far-field” in the context of the present invention, as illustrated in  FIG. 1G , is defined as that distance from the sensor array where the beam width of a traditionally formed Fraunhofer plane wave beam is the same size in the cross-range dimension as the cross-range size of the sensor array. 
     Depending on the configuration of the sensor array  10  and processing options of the system  1 , the field-of-view image may be one-dimensional.  FIG. 8  provides an example one-dimensional image of a field of view near the sensor array.  FIG. 9  provides an example one-dimensional image of a field of view relatively far from the sensor array. The field-of-view image may be two-dimensional, such as provided by an image array of pixels.  FIG. 3  provides an example two-dimensional field-of-view image. The field-of-view image may be three-dimensional, such as a voxel based three-dimensional image array.  FIG. 5  provides an example three-dimensional field-of-view image.  FIGS. 3, 5 and 8-9  each contain one or more point scatterers within the field of view. 
     In one embodiment, with reference to  FIG. 10 , the field-of-view image may be associated with a predefined image sample (pixel/voxel) spacing in any dimension. The predefined sample spacing of the field-of-view image in the dimension aligned with the sensor array  10  may be proportional to, including possibly equal to, a predefined spacing between the sensor elements of the sensor array  10 . This means that a physical distance between two adjacent pixels in an image (the associated points in the field of view) is proportional to, including possibly equal to, a physical distance between two sensor elements in the physical environment of the sensor array. For example, the predefined spacing between the sensor elements may be set to one half of the wavelength of a transmitted sinusoidal waveform; and likewise, the predefined distance of the image sample spacing may also be set to one half of the wavelength of this signal. In  FIG. 10 , each black dot in the sensor array  10  may represent a sensor element, and the space between the black dots represent the spacing between the sensor elements. In  FIG. 10 , each black dot on the right side may represent the points of image pixels in the image sample (pixel/voxel) array constructed by the processor  15 . Each pixel may be associated with a location in the physical environment of the field of view. If the image of the field of view is one-dimensional, the black dots represent data sample positions on a line. If the image of the field of view is two-dimensional, then the black dots represent pixel locations in the image and their corresponding locations within the field of view. If the image of the field of view is three-dimensional, then the black dots represent voxel locations in the image and their corresponding locations within the three-dimensional field of view. With continued reference to  FIG. 10 , a total number of pixels that span a cross-range extent of the field of view image may be equal to or be greater than a total number of sensor elements in the sensor array  10 . “Cross-range” may refer to directions orthogonal (e.g., azimuth, elevation) to a line that connects the position of the sensor array  10  and the nominal center position of the field of view. 
     In one embodiment, the sensor array  10  may include a stationary sensor array. Alternatively, the processor  15  may command movement of the sensor array  10  and collect data from echoes of single pulses at each position along a sensor movement path, thereby gathering a multiplicity of echoes from multiple pulses, in order to more quickly (compared to conventional SAR processing methods) improve the cross-range resolution achieved within the field of view image to a value proportional to the cross-range size of the sensor array  10 . The processor  15  may further collect data from a larger number of pulses and a longer sensor movement path, or from a moving field of view (as is done in conventional “inverse SAR” systems), in order to improve the cross-range resolution to a value proportional to the transmitted signal wavelength as illustrated in  FIGS. 6-7 . 
     The system  1  may include the sensor data buffer  40  for receiving sensor element data from the sensor array  10 . Example sensor data buffer  40  contents are illustrated in  FIG. 11A-C , where example sensor array data collected at near-range, medium-range and far-range distances from the sensor array  10  are illustrated. The processor  15  may perform zero padding on the received sensor element data. Example zero-padded sensor data buffer  40  are illustrated in  FIG. 12A-C , where example sensor array data are collected at near-range, medium-range and far-range distance from the sensor array  10  with a partial zero-pad on each side of the sensor array data. The total size of the zero-pad may be equal to the size of the number of samples in the field-of-view image minus the size (number of sensor elements) of the sensor array. If the sensor array size (number of sensor elements) and the field of view image size (number of image samples) are the same, then the zero pad may not be required. The minimum size of the field of view may be set to the size of the sensor array  10 . 
     The processor  15  may perform a temporal discrete Fourier transformation on the sensor data buffer  40  and a spatial discrete Fourier transform on the sensor data buffer  40  to convert zero-padded temporal-spatial data received by the senor array  10  into the frequency-wavenumber domain. The frequency-wavenumber domain are data placed into the sensor wavenumber buffer  43 . Example sensor wavenumber data buffer  43  contents are illustrated in  FIG. 13A-C , where example sensor wavenumber data processed for near-range, medium-range and far-range distances from the sensor array  10  are illustrated. 
     The processor  15  may perform conventional waveform pulse compression, as typically done in radar systems, by multiplication of the sensor wavenumber data buffer  43  data by multiplication with the spectral data of a pulse compression matched filter designed in accordance with the transmitted waveform. The processor  15  may perform pulse compression matched filtering, if required, by multiplication of the matched filter spectrum and the sensor wavenumber buffer data; 
     The processor  15  may determine a spatial reference point for the sensor array  10  and a spatial reference point for the field of view. These spatial reference points identify the locations of the sensor array  10  and the field of view. For example, the processor  15  may execute a reference point determinator  50  and also execute a reference Fresnel field generator  60 . The reference point determinator  50  may determine a spatial reference point that identifies a nominal center point location of the sensor array  10 . The reference point determinator  50 , as executed by the processor  15 , may also determine a spatial reference point that identifies a nominal center point location of the field of view. The spatial reference points of both the field of view and the sensor array  10  may be determined by position determination and motion compensation systems as typically used in airborne or spaceborne synthetic array radar systems. 
     The processor  15  may generate reference Fresnel field sample data that is descriptive of the distance or a space between the spatial reference points of the sensor array  10  and the field of view, and which is also descriptive of the cross-range difference in the size of the sensor array and the field of view as illustrated in  FIG. 14 . The reference Fresnel field generator  60  may determine a reference Fresnel field that has as its origin the spatial position reference point of the sensor array  10  and has as its destination a spatial position reference point of the field of view as shown in  FIG. 14 . The reference Fresnel field as illustrated in  FIGS. 15A-B  may include a spatial isotropic sinusoidal wave field for each monochromatic spectral element of a possibly polychromatic (passband) transmitted waveform.  FIG. 15A  illustrates a monochromatic (corresponding to selection of a continuous wave signal selected for the sensor array transmitted waveform) reference Fresnel field in a two-dimensional format.  FIG. 15B  illustrates a monochromatic (single frequency) reference Fresnel field in a three-dimensional format. As illustrated in  FIG. 14 , the image sample positions within the field of view determine the sample data of the reference Fresnel field. The reference Fresnel field sample data determined along the field of view image sample positions are stored in the reference Fresnel field data buffer  70 . The processor  15  may generate a data buffer containing reference Fresnel field sample data, such as the reference Fresnel field data buffer  70 , with reference signal data sample spacing proportional to, including possibly equal to, the predefined spacing of the sensor elements, and with a total number of data samples in cross-range dimensions identical to a total number of cross-range data samples of the field of view and corresponding pixel counts of the field of view image, as illustrated in  FIG. 16 . Examples of reference Fresnel field sample data stored in the reference Fresnel field data buffer  70  are shown in  FIGS. 17A-C . The reference Fresnel field created by the reference Fresnel field generator  60  may be an expanded (since the field of view image may be larger than the sensor array size), isotropic, harmonic, monochromatic or polychromatic, reference Fresnel wave field that characterizes the electromagnetic or acoustic field that spans the void between the system  1  and the field of view. The extent of the void between the system  1  and the field of view may be determined by the spatial positional reference points of the field of view and the sensor array  10 . 
     The processor  15  may generate one or more disjoint fields of views, each with distinct field-of-view reference points. Accordingly, distinct Fresnel reference signals are generated to place reference data into distinct reference Fresnel field data buffers  70 .  FIG. 18  illustrates an application example of multiple volumetric fields of view defined with respect to one application involving self-driving cars.  FIG. 18  illustrates volumetric imagery built with multiple fields of view boxes  1402 . When the sensor array is electromagnetic and used with a self-driving car as an example, multiple field-of-view images may provide a volumetric imaging capability of the entire surrounding environment of the car. An electromagnetic sensor array may have the advantages of sensing in both day and night operations, and may have advantages of sensing in adverse weather conditions. The adverse weather conditions may include rain, ice, and snow, among other possibilities. 
     The processor  15  may perform a spatial forward discrete Fourier transform  48  on the data produced by the reference Fresnel field generator  60 , stored in the reference Fresnel field data buffer  70 , and store the result in the inverse Huygens-Fresnel transfer data buffer  92 . In one embodiment, a total number of data samples contained in the Huygens-Fresnel inversion data buffer  92  may equal the number of data samples of the reference Fresnel field data buffer  70 . The processor  15  may perform a complex number conjugation of the inverse Huygens-Fresnel transfer data buffer  92 , thereby creating an inverse Huygens-Fresnel transfer function. Example inverse Huygens-Fresnel transfer data buffer  92  contents are illustrated in  FIG. 19A-C , where example inverse Huygens-Fresnel transfer function generation for near-range, medium-range and far-range distances from the sensor array  10  are illustrated. This multidimensional spatial discrete Fourier transform of the reference Fresnel field and complex conjugation performed by processor  15  creates an isotropic Huygens-Fresnel wave field inverter that is operative in the wavenumber domain. Contrary to traditional signal processing technology, the Huygens-Fresnel wave field inversion function based on isotropic wave propagation replaces the Fraunhofer plane wave assumption often used in conventional sensor array beam forming methods. The reference Fresnel field generator  60  implements a spherical (isotropic) wave field model, which removes the plane wave approximation used in traditional signal processing technology. 
     Each element of the sensor wavenumber data buffer  43  may be connected with each corresponding element of the Huygens-Fresnel inversion data buffer  92  to form a plurality of signal paths. With reference to  FIG. 1B , the signal paths are arrows that lead to the multiplication symbols  94 . The processor  15  may multiply sensor wavenumber data buffer  43  contents with inverse Huygens-Fresnel transfer data buffer  92 . Each element of the sensor wavenumber data buffer  43  may multiply with the corresponding element of the Huygens-Fresnel inversion data buffer  92  contents and possibly, with spectral elements of a conventional pulse compression matched filter. Corresponding elements between the sensor wavenumber data buffer  43  and the Huygens-Fresnel inversion data buffer  92  may be parings of wavenumber domain data elements. 
     The system  1  may include the rectilinear spectrum data buffer  80  for receiving the multiplication results. Example rectilinear spectrum data buffer  80  contents are illustrated in  FIG. 20A-C , where example rectilinear spectrum data for near-range, medium-range and far-range distances from the sensor array  10  are illustrated. The processor  15  may convert the rectilinear spectrum data buffer  80  by Stolt formatting with the Stolt format generator  64  to an angular spectrum data buffer  90 . The angular spectrum data buffer  90  are nonuniformly spaced in the wavenumber domain. In one example, the rectilinear spectrum data buffer  80  is one-dimensional, and the angular spectrum data buffer  90  is two-dimensional, as required by conventional Stolt format processing. Example angular spectrum data buffer  90  contents are illustrated in  FIG. 21A-C , where example angular spectrum data for near-range, medium-range and far-range distances from the sensor array  10  are illustrated. 
     The Stolt format generator  64  may also be applied to the angular spectrum data buffer  90  to yield an image spectrum as illustrated in  FIGS. 22A-B . The Stolt format generator  64  resamples elements of the angular spectrum data buffer  90  uniformly to create a Fourier transform invertible spectrum of the field of view image spectrum as illustrated in  FIG. 22C . 
       FIGS. 23A-B  illustrate an example flow diagram performed by the processor  15 . At  102 , the processor  15  may receive echo sensor element data from the sensor array  10 , and a temporal discrete Fourier transform may be performed on the sensor element data to provide a frequency-spatial expression of the received temporal-spatial form of waveform echo data gathered by the sensor array. Example sensor array data in frequency-spatial format are shown in  FIGS. 11A-C . At  103 , the processor  15  determines whether the size of the field of view is larger than a size of the sensor array  10 . At  104   a , the processor  15  may perform zero padding to modify the frequency-spatial sensor element data to a size of the field of view for storage in the sensor data buffer  40 , when the size of the field of view is larger than the size of the sensor array  10 . Example zero-padded sensor array data are shown in  FIGS. 12A-C . If the field of view and the sensor array  10  have the same size, then a zero pad may not be required. At  104   b , the processor stores the sensor element data to the sensor data buffer  40 . At  105 , the processor  15  may perform a spatial discrete Fourier transform of the possibly zero-padded sensor data buffer  40  to produce a sensor wavenumber data buffer  43 . The spatial DFT converts the frequency-spatial expression of the possibly zero-padded sensor array data of the sensor data buffer  40  into frequency-wavenumber domain data of the sensor wavenumber data buffer  43 . Example sensor wavenumber data buffer  43  are shown in  FIGS. 13A-C  for fields of view near-range, midrange and far-range from the sensor array  10 . At  106 , the processor  15  may determine a first reference point location of the sensor array  10  and a second reference point location of the field of view. At  108 , based on the first and second reference point locations of the sensor array  10  and the field of view, also based on a signal waveform transmitted from the sensor array  10 , and based on the size of the field of view, the processor  15  may generate a reference Fresnel field to obtain reference Fresnel field data. At  110 , the processor  15  may perform spatial DFT on the reference Fresnel field data to form forward Huygens-Fresnel transfer data. At  111 , the processor  15  may perform complex number conjugation of the forward Huygens-Fresnel transfer data to form inverse Huygens-Fresnel transfer data for storage in the inverse Huygens-Fresnel transfer data buffer  92 . Example inverse Huygens-Fresnel transfer data are shown in  FIGS. 19A-C  for fields of view near-range, midrange and far-range from the sensor array  10 . At  112 , the processor  15  may multiply data elements of the sensor wavenumber data buffer  43  with corresponding data elements of the inverse Huygens-Fresnel transfer data buffer  92 . At  113 , the processor  15  may multiply each data element of the sensor wavenumber data buffer  43  with a corresponding data element of a filter matched to the signal waveform transmitted from the sensor array  10  for pulse compression if the signal waveform transmitted from the sensor array  10  is a pulse compression waveform. Conventional waveform matched filtering may be performed with multiplication of sensor wavenumber data buffer  43  with corresponding data elements of the spectrum of the matched filter of the signal waveform transmitted by the sensor array  10 . At  114 , the processor  15  may store the multiplied data elements of step  112  into the rectilinear spectrum data buffer  80 . Example rectilinear spectrum data are shown in  FIGS. 20A-C  for fields of view near-range, midrange and far-range from the sensor array  10 . At  116 , the processor may perform Stolt mapping on the rectilinear spectrum data buffer  80  to form a nonuniformly sampled angular spectrum. The nonuniformly sampled angular spectrum data are stored in the angular spectrum data buffer  90 . Example angular spectrum data are shown in  FIGS. 21A-C  for fields of view near-range, midrange and far-range from the sensor array  10 . At step  117 , the processor  16  may uniformly resample the angular spectrum data buffer  90 . At step  118 , the processor may perform spatial inverse DFT on the uniformly resampled angular spectrum data to generate an image such as shown for a single scatterer in  FIGS. 26A-C  for fields of view near-range, midrange and far-range from the sensor array  10 . The image may illustrate contents of the field of view. At step  120 , the processor  15  may format the image for display on the image display device  20 . 
       FIG. 24  illustrates another example flow diagram performed by the processor  15 . At  240 , the processor may determine a spatial reference point for the sensor array  10 . At  242 , the processor may determine a spatial reference point for a field of view to be imaged. At  244 , the processor may generate reference Fresnel field sample data, based on a predefined waveform transmitted from the sensor array  10 , to account for a space between the spatial reference points of the sensor array and the field of view. If the transmitted waveform is a not a monochromatic continuous wave signal, the processor may perform a temporal DFT at  244 . Example polychromatic waveforms that may induce the processor to perform a temporal DFT at  244  may include a single pulse signal at passband. At  246 , the processor may generate a data buffer containing reference Fresnel field sample data. The reference Fresnel field sample data may have reference Fresnel field data sample spacing which is proportional to, including possibly equal to, the predefined spacing of the sensor elements of the sensor array  10 . A total number of Fresnel field data samples of the reference Fresnel field sample data may be identical to a total number of cross-range data samples of a field of view. 
       FIG. 25  illustrates yet another flow diagram of example processes performed by the processor  15 . At  250 , the processor may determine a spatial discrete Fourier transform of reference Fresnel field data to produce forward Huygens-Fresnel transfer data for a forward Huygens-Fresnel transfer buffer. The reference Fresnel field data may have reference Fresnel field data sample spacing which is proportional to, including possibly equal to, the predefined spacing of sensor elements of the sensor array  10 . A total number of Fresnel field data samples of the reference Fresnel field sample data may be identical to a total number of cross-range data samples of a field of view. At  252 , the processor may determine a complex conjugation of the forward Huygens-Fresnel transfer data to produce data for an inverse Huygens-Fresnel transfer buffer. 
     The disclosed technology replaces the multiple pulse beamforming/beamsteering approach used by sensor arrays with a single pulse imaging approach. The disclosed technology provides an imaging alternative to conventional Fraunhofer plane-wave based beamforming. In particular, to overcome the limitations of angle-of-arrival and beamforming/beamsteering based processing of sensor array data as presented in conventional technology, and to provide one-dimensional, two-dimensional or three-dimensional imaging capabilities of the contents of a possibly expanded field of view, the disclosed technology implements the following features. 
     First, the disclosed technology removes the plane wave approximation at the core of legacy sensor array capabilities and replaces the foundational plane wave system formulation with spherical (isotropic) wave field models. 
     Second, the disclosed technology removes any on-array analog combining required for beamforming. For instance, the disclosed technology creates an expanded, isotropic, harmonic, reference, monochromatic or polychromatic, Fresnel wave field that characterizes the electromagnetic or acoustic field that spans the void between the disclosed system and an expanded field of view to be imaged. The disclosed technology creates a wave field inversion operator, which may be referred to as inverse Huygens-Fresnel transfers; these isotropic wave field inverters are created by a multidimensional Fourier transform and complex number conjugation of the reference Fresnel wave field. The disclosed technology performs discrete Fourier transforms to convert temporal-spatial data received by the array into the frequency-wavenumber domain. The disclosed technology inverts the sensed wave field with inverse Huygens-Fresnel transfers with simple multiplications performed in the wavenumber domain; this Fourier transformed data comprise the rectilinear spectrum. The disclosed technology converts via Fourier migration the inverted sensed wave field rectilinear spectrum into angular spectrum descriptive of the spectrum of the contents of the field of view, the resulting Fourier migrated data are nonuniformly spaced. A Stolt formatting operator is used in the Fourier migration that yields the angular spectrum. The disclosed technology resamples the angular spectrum uniformly to create the Fourier transform invertible spectrum of the image spectrum. Inverse Fourier transforms are performed to create a one, two or three-dimensional image of the contents of the sensed field of view. 
       FIG. 27  illustrates realm of failure of prior art in near-field sensor with a linear sensor array.  FIG. 27  illustrates DFT based AoA estimates with incident plane wave and spherical wave fields. The near field scatterer produces a spherical wave field and fails to resolve and provide a usable AoA estimate. By contrast,  FIG. 8  illustrates success of the present technology in creating an AoA estimate of a single scatterer in the near-field of the sensor array. 
       FIG. 8  illustrates success of the disclosed technology to solve failure of prior art of array sensing in near-field.  FIG. 8  illustrates a cross-range image in near field displayed on the image display device  20  according to one aspect of the disclosed technology. 
       FIG. 9  illustrates success of the disclosed technology to solve failure of prior art of array sensing in an expanded field of view in the far-field, where  FIG. 9  shows a cross-range image of the far-field, expanded, field of view according to one aspect of the disclosed technology. In particular, this example illustration demonstrates the value of zero padding sensor array data to the size of a larger, distant, field of view. The number of sensor elements in the sensor array would conventionally only be able to support a cross-range image that spans only a portion of the main lobe of the beam pattern, which corresponds roughly to the main lobe of a conventionally formed Fraunhofer beam. Zero padding allows both main lobe and side lobe characteristics of the distant scatterer to be expressed in the cross-range image point spread function, within an expanded field of view probed with a single transmitted pulse. 
       FIG. 4  illustrates scatterers in field of view (lines  2002  indicate array size, lines  2004  indicate beamwidth at the field of view, lines  2006  indicate processing field of view). 
       FIG. 2  illustrates inability of prior art to provide a range/cross-range image of scattering field and only produce a conventional range profile of a single Fraunhofer plane wave beam. 
     It will thus be seen that the objects set forth above, among those made apparent from the preceding description, are efficiently attained and, because certain changes may be made in carrying out the above method and in the construction(s) set forth without departing from the spirit and scope of the invention, it is intended that all matter contained in the above description and shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense. 
     It is also to be understood that the following claims are intended to cover all of the generic and specific features of the invention herein described and all statements of the scope of the invention which, as a matter of language, might be said to fall there between. 
     While certain implementations of the disclosed technology have been described in connection with what is presently considered to be the most practical and various implementations, it is to be understood that the disclosed technology is not to be limited to the disclosed implementations, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the scope of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation. 
     For example, the disclosed technology may include radar sensor arrays for self-driving cars and radar sensor arrays for surveillance of airborne drone traffic. The disclosed technology may also implement computed imaging for seismic exploration, defense and civilian applications in radar and sonar, and ultrasonic medical imaging devices, among many other possibilities. The disclosed technology may serve multiple purposes, including electromagnetic based communications with utility in multiple-input/multiple-output (MIMO) array processing protocols as part of the Fifth Generation (5G) Long-Term Evolution (LTE) wireless communications and data networks. The disclosed technology may enable MIMO base stations to use sensor array imaging to thereby localize fixed and mobile transmitters such as entities within the Internet-of-Things (TOT) that reside within sensor array fields of view. 
     Certain implementations of the disclosed technology are described above with reference to block and flow diagrams of systems and methods and/or computer program products according to example implementations of the disclosed technology. It will be understood that one or more blocks of the block diagrams and flow diagrams, and combinations of blocks in the block diagrams and flow diagrams, respectively, can be implemented by computer-executable program instructions. Likewise, some blocks of the block diagrams and flow diagrams may not necessarily need to be performed in the order presented, or may not necessarily need to be performed at all, according to some implementations of the disclosed technology. 
     These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means that implement one or more functions specified in the flow diagram block or blocks. 
     Implementations of the disclosed technology may provide for a computer program product, comprising a computer-usable medium having a computer-readable program code or program instructions embodied therein, said computer-readable program code adapted to be executed to implement one or more functions specified in the flow diagram block or blocks. The computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational elements or steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions that execute on the computer or other programmable apparatus provide elements or steps for implementing the functions specified in the flow diagram block or blocks. 
     Accordingly, blocks of the block diagrams and flow diagrams support combinations of means for performing the specified functions, combinations of elements or steps for performing the specified functions and program instruction means for performing the specified functions. It will also be understood that each block of the block diagrams and flow diagrams, and combinations of blocks in the block diagrams and flow diagrams, can be implemented by special-purpose, hardware-based computer systems that perform the specified functions, elements or steps, or combinations of special-purpose hardware and computer instructions. 
     This written description uses examples to disclose certain implementations of the disclosed technology, including the best mode, and also to enable any person skilled in the art to practice certain implementations of the disclosed technology, including making and using any devices or systems and performing any incorporated methods. The patentable scope of certain implementations of the disclosed technology is defined in the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal language of the claims.