Bi-static and mono-static synthetic aperture radar (SAR) imaging using a short-pulse laser

Abstract

SAR imaging may be performed using a short-pulse laser to generate range-resolved reflection data. A short-pulse laser may be advantageous over other techniques to acquire the range-resolved data, especially in cases with very distant targets or other cases with low signal-to-noise ratio information, because a short-pulse laser can determine the range to individual reflectors with a single photon return and is more adaptable to a photon-starved inversion algorithm. This technique can be used with both mono-static and bi-static SAR configurations.

Claims

1. A method, comprising: periodically transmitting short-pulse laser bursts for a predetermined period of time over an interrogation path, by a transmitter; receiving individual photons reflected from a target during each short pulse laser burst, by a receiver; and building up, by a computing system, a Fourier image from range information generated over the interrogation path by integrating one photon at a time without using a heterodyne receiver, wherein each photon providing range information on reflections from the target, the range information being derived from a time lapse, the time lapse being a duration between a time the photon is transmitted to the target as part of a short laser pulse to a time the photon is received after reflecting back from the target; and incrementally contributing, using the range information, to the Fourier image an amount equal to an amplitude of a return signal divided by range distance squared, multiplied by e.sup.jk.sup.n, where e is Euler's number, j is the square root of minus 1, k is a wave number defined by 2 divided by frequency, and .sub.n is the difference in traversed distance between reflected photon n and a photon that reflects from the center of the target, and a Fourier inversion back to a reflection image includes frequency integration from a minimum frequency of zero to a maximum frequency equal to 1 over a timing resolution of each short pulse.

2. The method of claim 1, wherein the receiver is a mono-static receiver at a same location as the transmitter.

3. The method of claim 2, wherein the building up of the image comprises: identifying range-resolved reflection data along each angular view of a plurality of angular views using the received individual photons, by the computing system; separating the range-resolved reflection data into n bins, by the computing system, wherein a return from bin n is separated in time from a return at a center of a target patch at (x,y)=(0,0) and is given by 2ns/c, where s is a width of each bin, and bin number n=0 includes reflections from the target center; approximating a reflection function from reflection data at each of a plurality of angular views, by the computing system; and reconstructing the approximate reflection function using inversion, by the computing system.

4. The method of claim 3, wherein the approximating of the reflection function from reflection data at each angular view Bis given by: $G_{\mathrm{approx}}\left(k,\right)=\underset{n}{.Math.}\frac{A_n}{R_n^2}{e}^{jk{}_n}$ where A.sub.n is an amplitude returned for range bin n, R.sub.n is a distance to range bin n, and .sub.n=R.sub.nR.sub.0, where R.sub.0 is defined as a distance to a center of a patch; and the inverting of the approximate reflection function is performed using: $f\left(x,y\right)=\frac{1}{2}{}_{/2-{}_0}^{\frac{}{2}}G\left(k,\right)e^{-jk{}_{xy}}k\mathrm{dk}d$ where .sub.xy=R.sub.xyR.sub.0 and R.sub.xy is a distance from the transmitter and the mono-static receiver to a point (x,y).

5. The method of claim 1, wherein the receiver is a bi-static receiver at a different location than the transmitter.

6. The method of claim 5, wherein the bi-static receiver is stationary.

7. The method of claim 5, wherein the building up of the image comprises: identifying range contours corresponding to positions with equivalent range for range-resolved scattering amplitudes, by the computing system; separating range-resolved data into n bins, by the computing system; approximating a target function and a reflection function, by the computing system; and reconstructing the reflection function via inversion, by the computing system.

8. The method of claim 5, wherein the periodically transmitting of the short-pulse laser bursts over the interrogation path occurs from a fixed transmitter location as the receiver moves along an interrogation path.

9. The method of claim 5, wherein the transmitter is located on a first aircraft and the bi-static receiver is located on a second aircraft.

10. The method of claim 1, wherein a pulse length and a bandwidth of the short pulse laser bursts are 100 picoseconds and 10 GHz, respectively.

11. The method of claim 1, wherein intervals between the short pulse laser bursts are sufficiently long such that photons received from different bursts do not overlap in time.

12. The method of claim 1, wherein a number of individual photons N.sub.pixel that are received per pixel to build up the image is between 100 and 125.

13. The method of claim 1, wherein a number of individual photons N.sub.pixel that are received per pixel to build up the image is greater than number of solar photons N.sub.solar that are received per pixel.

14. A method, comprising: periodically transmitting short-pulse laser bursts for a predetermined period of time over an interrogation path, by a transmitter; receiving individual photons reflected from a target during each short pulse laser burst, by a mono-static receiver at a same location as the transmitter; identifying range-resolved reflection data along each angular view of a plurality of angular views using the received individual photons, by the computing system; separating the range-resolved reflection data into n bins, by the computing system, wherein a return from bin n is separated in time from a return at a center of a target patch at (x,y)=(0,0) and is given by 2ns/c, where s is a width of each bin, and bin number n=0 includes reflections from the target center; approximating a reflection function from reflection data at each of a plurality of angular views, by the computing system; and reconstructing the approximate reflection function using inversion, by the computing system, wherein the reconstructing of the reflection function comprises building up an image from range information generated over the interrogation path by integrating one photon at a time without using a heterodyne receiver, each photon providing range information on reflections from the target, the range information being derived from a time lapse, the time lapse being a duration between a time the photon is transmitted to the target as part of a short laser pulse to a time the photon is received after reflecting back from the target, and incrementally contributing, using the range information, to the Fourier image an amount equal to an amplitude of a return signal divided by range distance squared, multiplied by e.sup.jk.sup.n, where e is Euler's number, j is the square root of minus 1, k is a wave number defined by 2 divided by frequency, and .sub.n is the difference in traversed distance between reflected photon n and a photon that reflects from the center of the target, and a Fourier inversion back to a reflection image includes frequency integration from a minimum frequency of zero to a maximum frequency equal to 1 over a timing resolution of each short pulse.

15. The method of claim 14, wherein the approximating of the reflection function from reflection data at each angular view Bis given by: $G_{\mathrm{approx}}\left(k,\right)=\underset{n}{.Math.}\frac{A_n}{R_n^2}{e}^{jk{}_n}$ where A.sub.n is an amplitude returned for range bin n, R.sub.n is a distance to range bin n, and =R.sub.nR.sub.0, where R.sub.0 is defined as a distance to a center of a patch; and the inverting of the approximate reflection function is performed using: $f\left(x,y\right)=\frac{1}{2}{}_{/2-{}_0}^{\frac{}{2}}G\left(k,\right)e^{-jk{}_{xy}}k\mathrm{dk}d$ where .sub.xy=R.sub.xyR.sub.0 and R.sub.xy is a distance from the transmitter and the mono-static receiver to a point (x,y).

16. The method of claim 14, wherein a pulse length and a bandwidth of the short pulse laser bursts are 100 picoseconds and 10 GHz, respectively.

17. The method of claim 14, wherein intervals between the short pulse laser bursts are sufficiently long such that photons received from different bursts do not overlap in time.

18. A method, comprising: periodically transmitting short-pulse laser bursts for a predetermined period of time over an interrogation path, by a transmitter; receiving individual photons reflected from a target during each short pulse laser burst, by a bi-static receiver at a different location than the transmitter; identifying range contours corresponding to positions with equivalent range for range-resolved scattering amplitudes, by the computing system; separating range-resolved data into n bins, by the computing system; approximating a target function and a reflection function, by the computing system; and reconstructing the reflection function via inversion, by the computing system, wherein the reconstructing of the reflection function comprises building up a Fourier image from range information generated over the interrogation path by integrating one photon at a time without using a heterodyne receiver, each photon providing range information on reflections from the target, the range information being derived from a time lapse, the time lapse being a duration between a time the photon is transmitted to the target as part of a laser pulse to a time the photon is received after reflecting back from the target, and incrementally contributing, using the range information, to the Fourier image an amount equal to an amplitude of a return signal divided by range distance squared, multiplied by e.sup.jk.sup.n, where e is Euler's number, j is the square root of minus 1, k is a wave number defined by 2 divided by frequency, and .sub.n is the difference in traversed distance between reflected photon n and a photon that reflects from the center of the target, and a Fourier inversion back to a reflection image includes frequency integration from a minimum frequency of zero to a maximum frequency equal to 1 over a timing resolution of each short pulse.

19. The method of claim 18, wherein the periodically transmitting of the short-pulse laser bursts over the interrogation path occurs from a fixed transmitter location as the receiver moves along an interrogation path.

20. The method of claim 18, wherein intervals between short pulse laser bursts are sufficiently long such that photons from different bursts do not overlap.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) In order that the advantages of certain embodiments of the invention will be readily understood, a more particular description of the invention briefly described above will be rendered by reference to specific embodiments that are illustrated in the appended drawings. While it should be understood that these drawings depict only typical embodiments of the invention and are not therefore to be considered to be limiting of its scope, the invention will be described and explained with additional specificity and detail through the use of the accompanying drawings, in which:

(2) FIG. 1 is a schematic diagram illustrating spotlight-mode SAR parameters and definitions.

(3) FIG. 2 is a graph illustrating Fourier domain locations for received information for a case with nine angular views and ten transmitted frequencies.

(4) FIG. 3 is a graph illustrating notional reflectors in a target with reflection coefficient R.

(5) FIG. 4 is a graph illustrating range-resolved data corresponding to reflectors A, B, C, and D for a specific view angle .

(6) FIG. 5 is an architectural view illustrating a hybrid SAR system, according to an embodiment of the present invention.

(7) FIG. 6 is a flowchart illustrating a process for performing mono-static SAR, according to an embodiment of the present invention.

(8) FIG. 7 is a flowchart illustrating a process for performing bi-static SAR, according to an embodiment of the present invention.

(9) FIG. 8 is a block diagram illustrating a computing system configured to perform mono-static and/or bi-static SAR imaging using a short-pulse laser, according to an embodiment of the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(10) Some embodiments of the present invention pertain to bi-static and mono-static SAR imaging using a short-pulse laser. At each angular look of the target, range-resolved reflections may be obtained from scatterers within the target. The range-resolved reflections may be generated, for example, by using the short-pulse laser.

(11) Consider an example implementation, including a transmitter laser in motion on an aircraft 510, a stationary distant target 520, and a receiver on another aircraft 530 along an interrogation path, as shown in hybrid SAR system 500 of FIG. 5. While the receiver is shown as part of an aircraft 530 in this embodiment, in other embodiments, the receiver may or may not be stationary (e.g., a ground receiver, a hovering helicopter, etc.). Alternatively, the transmitter laser may be stationary and the receiver may be in motion. Any combination of stationary/moving transmitters and receivers may be employed without deviating from the scope of the invention, so long as at least one of the transmitter, receiver, or target is in motion relative to the others.

(12) In addition to a laser, transmitter aircraft 510 includes a transmitter telescope and adaptive optics. Receiver aircraft 530 includes a receiver telescope and a photodetector.

(13) The transmitter laser of transmitter aircraft 510 emits short pulses of pulse length r separated by intervals. Knowing the position of the transmitter and the receiver and the timing of the emitted laser pulse gives the range distance of a reflector in the target to an accuracy of c/2 by observing the time that a reflected photon is received at the detector. Transmitter aircraft 510 and receiver aircraft 530 would share position information that is determined by respective global positioning systems (GPSs), and/or receive this information from satellites, ground stations, and/or any other suitable positioning technology without deviating from the scope of the invention. The intervals between pulses should to be long enough so photons from different pulses cannot be received at the same time. In other words, the received photons from different pulses, or bursts, do not overlap in time, where from time t.sub.0 to t.sub.1, photons from a first pulse would be received, from t.sub.1 to t.sub.2, photons from a second pulse would be received, etc.

(14) A minimum number of photons received per pixel (N.sub.pixel) of approximately 100 is needed for a fair image in some embodiments. For a 100100 pixel image, approximately 10.sup.6 total received photons may be needed in some embodiments. At this level, receiver dark counts are negligible.

(15) Solar photons reflecting off target 520 may be the leading cause of noise, requiring N.sub.pixel>N.sub.solar, where N.sub.solar is the number of solar photons received per pixel. Low laser repetition rates, while maintaining the average laser power, can make the effect from solar photons negligible by allowing the receiver to be time gated.

(16) Mono-Static SAR Scheme

(17) In the SAR scheme of some embodiments, unlike the receiver of aircraft 530 of FIG. 5, location of the receiver is at the same location as the transmitter. In other words, for aircraft-based implementations, both the transmitter and receiver would be on that aircraft. In this case, the Fourier transform of the reflection function G is approximated from the reflection data at each angular view by

(18) $\begin{array}{cc}{G}_{\mathrm{approx}}\left(k,\right)=\underset{n}{.Math.}\frac{A_n}{R_n^2}{e}^{jk{}_n}& \left(9\right)\end{array}$

(19) where A.sub.n is the amplitude returned for range bin n, R.sub.n is the distance to range bin n, and .sub.n=R.sub.nR.sub.0, where R.sub.0 is defined as the distance to the center of the patch. This approximate reflection function is then inverted by using

(20) $\begin{array}{cc}f\left(x,y\right)=\frac{1}{2}{}_{/2-{}_0}^{\frac{}{2}}G\left(k,\right)e^{-jk{}_{xy}}k\mathrm{dk}d& \left(10\right)\end{array}$

(21) where .sub.xy=R.sub.xyR.sub.0 and R.sub.xy is the distance from the transmitter/receiver to the point (x,y).

(22) While Fourier inversion is used in this example, it should be noted that other inversion techniques may be used. For instance, the Maximum Entropy Method may be used to perform image reconstruction. This is a deconvolution algorithm that functions by minimizing a smoothness function (i.e, entropy) in an image. However, any suitable inversion technique may be used without deviating from the scope of the invention.

(23) Bi-Static Sar Scheme

(24) The mono-static SAR scheme is modified for a bi-static geometry (where the receiver is at a different position than the transmitter, as shown in FIG. 5) by changing .sub.n to be the total distance from the transmitter to reflector and then to the receiver, R.sub.0 as the total distance from the transmitter to the center of the target and then to the receiver, and .sub.xy as the total distance from the transmitter to the point (x,y) and then to the receiver.

(25) For a photon-starved system, the image can be generated incrementally as each photon is detected by the receiver. Alternatively, received photons can be accumulated over some time interval and the function G.sub.approx(k,) can be created from a summation from different photons over that time interval. However, as with mono-static SAR schemes, it should also be noted that any suitable inversion technique may be used without deviating from the scope of the invention.

(26) FIG. 6 is a flowchart 600 illustrating a process for performing mono-static SAR, according to an embodiment of the present invention. The process begins with identifying range-resolved reflection data along each angular view at 610. Range-resolved data is separated into n bins at 620. The return from bin n is separated in time from the return at the center of the target patch at (x,y)=(0,0) and is given by 2ns/c, where s is the width of each bin, and bin number n=0 includes reflections from the target center. The target function and reflection function are approximated at 630. The reflection function is then reconstructed, by Fourier inversion, at 640.

(27) FIG. 7 is a flowchart 700 illustrating a process for performing bi-static SAR, according to an embodiment of the present invention. The process begins with identifying range contours corresponding to positions with equivalent range for the range-resolved scattering amplitudes at 710. Range-resolved data is separated into n bins at 720. The target function and reflection function are approximated at 730. The reflection function is then reconstructed, by Fourier inversion, at 740.

(28) FIG. 8 is a block diagram illustrating a computing system 800 configured to perform mono-static and/or bi-static SAR imaging using a short-pulse laser, according to an embodiment of the present invention. Computing system 800 includes a bus 805 or other communication mechanism for communicating information, and processor(s) 810 coupled to bus 805 for processing information. Processor(s) 810 may be any type of general or specific purpose processor, including a central processing unit (CPU) or application specific integrated circuit (ASIC). Processor(s) 810 may also have multiple processing cores, and at least some of the cores may be configured to perform specific functions. Multi-parallel processing may be used in some embodiments. Computing system 800 further includes a memory 815 for storing information and instructions to be executed by processor(s) 810. Memory 815 can be comprised of any combination of random access memory (RAM), read only memory (ROM), flash memory, cache, static storage such as a magnetic or optical disk, or any other types of non-transitory computer-readable media or combinations thereof. Additionally, computing system 800 includes a communication device 820, such as a transceiver and antenna, to wirelessly provide access to a communications network.

(29) Non-transitory computer-readable media may be any available media that can be accessed by processor(s) 810 and may include both volatile and non-volatile media, removable and non-removable media, and communication media. Communication media may include computer-readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media.

(30) Processor(s) 810 are further coupled via bus 805 to a display 825, such as a Liquid Crystal Display (LCD), for displaying information to a user. A keyboard 830 and a cursor control device 835, such as a computer mouse, are further coupled to bus 805 to enable a user to interface with computing system. However, in certain embodiments such as those for mobile computing implementations, a physical keyboard and mouse may not be present, and the user may interact with the device solely through display 825 and/or a touchpad (not shown). Any type and combination of input devices may be used as a matter of design choice.

(31) Memory 815 stores software modules that provide functionality when executed by processor(s) 810. The modules include an operating system 840 for computing system 800. The modules further include a SAR imaging module 845 that is configured to perform SAR perform mono-static and/or bi-static SAR imaging using a short-pulse laser via any of the approaches discussed herein or derivatives thereof. Computing system 800 may include one or more additional functional modules 850 that include additional functionality.

(32) One skilled in the art will appreciate that a system could be embodied as an embedded computing system, a personal computer, a server, a console, a personal digital assistant (PDA), a cell phone, a tablet computing device, or any other suitable computing device, or combination of devices. Presenting the above-described functions as being performed by a system is not intended to limit the scope of the present invention in any way, but is intended to provide one example of many embodiments of the present invention. Indeed, methods, systems and apparatuses disclosed herein may be implemented in localized and distributed forms consistent with computing technology, including cloud computing systems.

(33) It should be noted that some of the system features described in this specification have been presented as modules, in order to more particularly emphasize their implementation independence. For example, a module may be implemented as a hardware circuit comprising custom very large scale integration (VLSI) circuits or gate arrays, off-the-shelf semiconductors such as logic chips, transistors, or other discrete components. A module may also be implemented in programmable hardware devices such as field programmable gate arrays, programmable array logic, programmable logic devices, graphics processing units, or the like.

(34) A module may also be at least partially implemented in software for execution by various types of processors. An identified unit of executable code may, for instance, comprise one or more physical or logical blocks of computer instructions that may, for instance, be organized as an object, procedure, or function. Nevertheless, the executables of an identified module need not be physically located together, but may comprise disparate instructions stored in different locations which, when joined logically together, comprise the module and achieve the stated purpose for the module. Further, modules may be stored on a computer-readable medium, which may be, for instance, a hard disk drive, flash device, RAM, tape, or any other such medium used to store data.

(35) Indeed, a module of executable code could be a single instruction, or many instructions, and may even be distributed over several different code segments, among different programs, and across several memory devices. Similarly, operational data may be identified and illustrated herein within modules, and may be embodied in any suitable form and organized within any suitable type of data structure. The operational data may be collected as a single data set, or may be distributed over different locations including over different storage devices, and may exist, at least partially, merely as electronic signals on a system or network.

(36) The process steps performed in FIGS. 6 and 7 may be performed by a computer program, encoding instructions for the nonlinear adaptive processor to perform at least the processes described in FIGS. 6 and 7, in accordance with embodiments of the present invention. The computer program may be embodied on a non-transitory computer-readable medium. The computer-readable medium may be, but is not limited to, a hard disk drive, a flash device, a random access memory, a tape, or any other such medium used to store data. The computer program may include encoded instructions for controlling the nonlinear adaptive processor to implement the processes described in FIGS. 6 and 7, which may also be stored on the computer-readable medium.

(37) The computer program can be implemented in hardware, software, or a hybrid implementation. The computer program can be composed of modules that are in operative communication with one another, and which are designed to pass information or instructions to display. The computer program can be configured to operate on a general purpose computer, or an ASIC.

(38) It will be readily understood that the components of various embodiments of the present invention, as generally described and illustrated in the figures herein, may be arranged and designed in a wide variety of different configurations. Thus, the detailed description of the embodiments of the present invention, as represented in the attached figures, is not intended to limit the scope of the invention as claimed, but is merely representative of selected embodiments of the invention.

(39) The features, structures, or characteristics of the invention described throughout this specification may be combined in any suitable manner in one or more embodiments. For example, reference throughout this specification to certain embodiments, some embodiments, or similar language means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases in certain embodiments, in some embodiment, in other embodiments, or similar language throughout this specification do not necessarily all refer to the same group of embodiments and the described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

(40) It should be noted that reference throughout this specification to features, advantages, or similar language does not imply that all of the features and advantages that may be realized with the present invention should be or are in any single embodiment of the invention. Rather, language referring to the features and advantages is understood to mean that a specific feature, advantage, or characteristic described in connection with an embodiment is included in at least one embodiment of the present invention. Thus, discussion of the features and advantages, and similar language, throughout this specification may, but do not necessarily, refer to the same embodiment.

(41) Furthermore, the described features, advantages, and characteristics of the invention may be combined in any suitable manner in one or more embodiments. One skilled in the relevant art will recognize that the invention can be practiced without one or more of the specific features or advantages of a particular embodiment. In other instances, additional features and advantages may be recognized in certain embodiments that may not be present in all embodiments of the invention.

(42) One having ordinary skill in the art will readily understand that the invention as discussed above may be practiced with steps in a different order, and/or with hardware elements in configurations which are different than those which are disclosed. Therefore, although the invention has been described based upon these preferred embodiments, it would be apparent to those of skill in the art that certain modifications, variations, and alternative constructions would be apparent, while remaining within the spirit and scope of the invention. In order to determine the metes and bounds of the invention, therefore, reference should be made to the appended claims.