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

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 2nΔs/c, where Δs 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 ejkδn, where e is Euler's number, j is the square root of minus 1, k is a wave number defined by 2π divided by frequency, and δn 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.

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 ejkδn, where e is Euler's number, j is the square root of minus 1, k is a wave number defined by 2π divided by frequency, and δn 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.