Analysis of the redundancy of Fourier telescopy transmitter array and its redundancy-strehl ratio-target texture distribution characteristic
Authors: Zhang Yu  , Luo Xiu-Juan  , Cao Bei  , Chen Ming-Lai  , Liu Hui  , Xia Ai-Li  , Lan Fu-Yang  ,   Xi'an Institute of Optics and Precision Mechanics of CAS, Xi'an 710119, China
Published: December 2020

The Fourier telescopy is a kind of active illumination imaging with high resolution by using multi-interfering fringes generated by the multi-beams from the large transmitter arrays. According to the imaging principle, the beams from one laser source are split and each beam is applied with a different tiny frequency shift so that the interfering fringes may moving across the target. The configuration of the beams changes so that they would generate fringes in different spatial frequencies and different directions. Recently, most of researches focused on the factors such as the baseline scale and data sampling efficiency that may affect the imaging quality. However, there are other two factors, i.e., the configuration of the transmitter and its redundancy, which need studying. In Fourier telescopy, if the direction and spatial frequency of the fringe patterns that are generated by the change of different baseline configurations match each other, the target surface information would be a crucial factor that affects the image quality.In the first part of this article, the practicability of zero redundancy of baseline is analyzed. The results show that the baseline cannot have zero redundancy due to the iteration algorithm. Then the minimum redundancy is analyzed and the minimum redundancy line is proposed. By using the Strehl ratio as the merit of the imaging quality, the concept of redundancy-strehl ratio-target texture distribution (RST) and calculation method are proposed. This method integrates the transmitter redundancy, target detail information and image quality together. The distribution of RST value on the frequency plane is compared with the minimum redundancy line. If the RST point is located on the horizontal side compared with the line, the target detail information on this baseline is mainly in the horizontal direction. On the other hand, if the RST point is located on the longitude side, the target information is mainly in the longitude direction. Therefore this new proposed method reveals the relationship between target spatial information and the baseline configuration. In this article T-shaped transmitter array is adopted, and the Fourier components are mainly distributed on the rectangle plane. According to this relationship and calculated RST value, the working transmitter may continuously rectify its scale and shifting patterns so that the spatial frequencies and directions of fringes may match the target Fourier components in time. In this article, three simulated images and two real images are tested by the proposed method, and the results show that the RST values and the distributions well reveale the relationship between the detailed information and the baseline configurations.Now the Fourier telescopy follows the procedure from laboratory setup to the real system research. Considering the convenience and cost of project realization, this method is helpful for analyzing the real system of the transmitter configuration and enhancing working efficiency.