Non-iterative aberration correction of a multiple transmitter system

Abstract

Multi-transmitter aperture synthesis provides aperture gain and improves effective aperture fill factor by shifting the received speckle field through the use of multiple transmitter locations. It is proposed that by utilizing methods based on shearing interferometry some low-order aberrations, such as defocus, can be found directly rather than through iterative algorithms. The current work describes the theory behind multi-transmitter aberration correction and describes experiments used to validate this method. Experimental results are shown which demonstrate the ability of such a sensor to solve directly for defocus and toric curvature in the captured field values.

Deep-turbulence wavefront sensing using digital-holographic detection in the off-axis image plane recording geometry

“…In practice, digitalholographic detection allows for the estimation of the complex field in the presence of an extended noncooperative object via speckle averaging and image sharpening algorithms or the angular diversity created by using multiple transmitters and receivers. [7][8][9][10][11][12][13][14][15][16][17][18] This versatility allows for long-range imaging, 19 three-dimensional imaging, 20 laser radar, 21 and synthetic-aperture imaging. 22 In general, the applications are abundant.…”

Multi-transmitter aperture synthesis with Zernike based aberration correction

“…As illustrated in Fig.1 and described in [4,10], the modeled multi-transmitter system illuminates a scene with one transmitter at a time and independently captures the backscattered fields in the pupil plane. Because of the shift in the transmitter locations, the backscattered target field U b (x, y) is shifted by the same amount (in the reverse direction).…”

“…Instead of forming a set of sparsely distributed apertures, the transmitter locations can be placed close enough so that the pupil field captured by the shifted apertures overlap [10]. Overlapped aperture data is used to estimate the aberrations common to all of the aperture realizations based on techniques similar to lateral shearing interferometry.…”

“…The technique is based on the assumption that the static and atmospheric aberrations present in the aperture aside from piston are constant across the measurements; this requires that all measurements are recorded within the atmospheric coherence time in order to reconstruct the dynamic atmospheric aberrations. In [10], the idea is demonstrated with low-order aberrations by modeling the aberrations with bivariate polynomials. Instead of bivariate polynomials, Zernike polynomials could be used to model optical aberrations.…”

“…In this paper, we present a method to estimate aberrations for multi-transmitter aperture synthesis. The aberrations are modeled with Zernike polynomials and the difference front is directly used without any polynomial fitting unlike the method in [10]. We segment the difference front into sub-regions; each sub-region has an unknown phase offset, which is added to the set of linear equations to be solved.…”