Sheared-beam imaging of object with depth information

Abstract

Sheared-beam imaging technique is a non-conventional imaging method which can be used to image remote objects through atmospheric turbulence without needing any adaptive optics. In this imaging technique, the target is coherently illuminated by three laser beams which are laterally sheared at the transmitter plane and arranged into an L shape. In addition, each beam is modulated by a slight frequency shift. The speckle intensity signals scattered from the target are received by a detector array, and then the image of target can be reconstructed by computer algorithm. By far, most of studies in this field have focused on two-dimensional imaging. In real conditions, however, the surface of targets we are concerned about reveals that different depths introduce various phase delays in the scattering signal from target. This delay causes the phase-shift errors to appear between the ideal target Fourier spectrum and the Fourier spectrum received by detector array. Finally, this would result in poor image quality and low resolution. In this study, a three-dimensional target imaging model is established based on the two-dimensional target imaging model. The influence of modulated beat frequency between sheared beam and reference beam is studied on the objects with depth information, and the result shows that large beat frequency may have an adverse effect on reconstructed images. The simulation we have developed for this three-dimensional imaging model uses three targets with different shapes. Each target is divided into several sub-blocks, and we set different depth values (within 10 m) for these blocks. Then beat frequencies are increased from 5 Hz to about 1 MHz, respectively. At each pair of frequencies, the reconstructed image is recorded. Srehl ratio is used as the measure of the imaging quality. Computer simulation results show that the Srehl ratio of reconstructed images descends with the increase of beat frequency, which is fully consistent with the theory of three-dimensional target imaging proposed before. Meanwhile, we find that the depth distribution of target also has an effect on imaging quality. As for actual space targets, the maximum depth is usually not more than 10 m. Compared with the influence caused by beat frequencies, the effect produced by depth distribution is negligible. Therefore when a space target is imaged, beat frequencies play the major role in reconstructing high-quality image. The results presented in this paper indicate that in order to achieve better imaging quality in the practical application, it is necessary to select the smallest beat frequency according to the detector performance and keep the candidate frequencies away from the low-frequency noise of the detector.