Spatial domain sparse reconstruction algorithm of sheared beam imaging

Sheared beam imaging (SBI) is considered a computational imaging technique that transmits three sheared coherent laser beamlets for illumination, and a sensor array to receive the intensity of the speckle pattern reflected from the target. The SBI can be used to image remote objects through a turbulent medium with no need of any adaptive optics. However, while imaging low-orbit moving targets, the number of detectors of sensor array required by the receiving system of SBI is very large, and the development of sensor array is difficult and costly. In this work, a spatial domain sparse sampling technique is proposed for the SBI system through transmitting five laser beamlets to illuminate the target carrying more of its spectral information, which can reduce the number of detectors of the sensor array. Firstly, the principle of the sparse imaging technique is deduced. Then, a sparse reconstruction algorithm is studied. The phase difference and amplitude information of the target in the echo signal after sparse sampling can be extracted accurately by searching for the accurate positions of the beat frequency components. The wavefront phases can be demodulated by the least-squares method, and wavefront amplitude can be obtained by the algebraic operation of speckle amplitude. The reconstructed wavefront is used to formulate the two-dimension image of the target. Theoretically, without affecting the resolution, the number of detectors of the sensor array can be reduced to half of the traditional three-beam method, which breaks through the limitation that the detector spacing of sensor array is equal to the shear length of beamlet. From the simulation results, when the number of detectors of the sensor array is reduced by 50%, the proposed sparse reconstruction algorithm has almost the same quality as the reconstructed image with the traditional three-beam method.