Optical sparse aperture (OSA) imaging system is composed of multiple discrete circular sub-apertures, which attempts to obtain a resolution approximately equivalent to a single filled large aperture system with reduced size, cost, and weight. However, compared with a single aperture system, the performance of these sparse arrays strongly relies on various design parameters, such as the number of sub-apertures, their relative positions, and diameters. Due to the discreteness and sparsity of the sparse aperture array, the pupil function is no longer a connected domain, which further reduces the intermediate frequency modulation transfer function (MTF), thus degrading images. To address this issue and enhance the intermediate frequency MTF while improving the imaging quality, a one-dimensional non-redundant three-aperture structure with a sub-aperture spacing ratio of 1∶2 is selected as a foundational array, and the position of the middle sub-aperture is fixed. Then a novel rotating synthetic aperture structure is designed by rotating the base array several times along the baseline direction at different angles within 360°. Both quantitative and qualitative evaluations of simulation and experimental results demonstrate the effectiveness of the proposed method.

The pupil autocorrelation distribution of one-dimensional multi-aperture arrays is first analyzed. Since the three-aperture structure with a center distance ratio of 1∶2 of two sub-apertures can obtain greater frequency domain coverage with fewer rotation times and a smaller filling factor, this structure is selected as the fundamental array. To create a new synthetic aperture structure, this three-aperture array is rotated by an angle α along the baseline direction around the intermediate sub-aperture. To ensure adherence to the design requirements of the sparse aperture array and prevent overlap between any two sub-apertures in space, various constraint conditions for structural parameters are computed. These constraints encompass parameters such as the center spacings (s₁ and s₂) of the two sub-apertures, the rotation angle α, and the center position coordinates of the rotated sub-apertures. In addition, the pupil function, point spread function (PSF), and MTF of the rotated arrays are derived. The imaging characteristics of the array structure synthesized by a single rotation are simulated. Notably, the MTF frequency domain coverage of the rotating synthetic aperture is not a simple sum of two directions but rather an expansion, and PSF changes from fringe distribution in one direction to speckle and linear distribution in different directions. In order to increase the coverage of the rotating synthetic aperture in the whole frequency domain, rotation is repeated multiple times to synthesize new apertures. Specifically, the rotation within 360° is performed six times per 2π/7, five times per π/3, four times per 2π/5, three times per π/2, and two times per 2π/3, respectively. The obtained arrays are denoted as OR6, OR5, OR4, OR3, and OR2, respectively.

According to the theoretical model, with the increase in the single rotation angle in Fig. 4, the energy of MTF and PSF is mainly concentrated in the central region. The sidelobe energy of MTF is continuous along two directions of the pupil structure and gradually presents a point-like discrete distribution in other directions, covering a wider range of frequency domains. Figure 6 shows the pupil structure, as well as the PSF and MTF distributions of Golay-9 and five rotating synthetic arrays. As the number of rotations decreases, the MTF frequency domain coverage of the rotating synthetic aperture becomes smaller and presents a discrete distribution. The PSF energy of the OR6 array is almost all concentrated in the center, which is close to the PSF distribution of the single aperture. The PSF sidelobe of the OR5 and OR4 arrays is converged toward the center. However, the PSF energy distribution of OR3 and OR2 arrays is more discrete, and the sidelobe energy is continuously enhanced. At the same equivalent diameter, the MTF distribution in the Golay-9 array is relatively uniform, but its intensity is low in the middle and high frequency bands, and the PSF presents a discrete circular spot distribution, which degrades the image. In the f_x direction in Fig. 7, the MTFs of OR5 and OR3 arrays in the frequency range of 0.4-1.0 are close to that of equivalent single aperture and is higher than that of Golay-9 arrays in the whole spatial frequency range. Moreover, the MTF of OR6, OR4, and OR2 arrays in the frequency range of 0.18-0.6 is higher than that of Golay-9. In the f_y direction, the MTFs of four rotating synthetic arrays are greater than that of the Golay-9 array in the frequency range of 0.2-0.6, and the MTF of the OR3 array in the frequency range of 0.15-1.0 is greater than that of the Golay-9 array. At the same equivalent diameter, M_mid-freq, peak signal-to-noise ratio, and structural similarity of rotating synthetic aperture arrays are higher than that of the Golay-9 array.

In this study, the rotating synthetic aperture arrays for improving intermediate frequency MTF and image performance are proposed, which are obtained by rotating a one-dimensional non-redundant three-aperture array several times at different rotation angles within 360°. The MTF of the OR3 array surpasses that of the Golay-9 array across the entire frequency range in both the f_xand f_y directions. However, three evaluation indexes of the five rotating synthetic arrays are higher than those of the Golay-9 array. According to the experimental results, the normalized gray difference values of the sixth group of horizontal and vertical bar pairs of USAF1951 resolution board images of Golay-9, OR4, and OR3 arrays are compared. The maximum difference values of Golay-9, OR3, and OR4 arrays are 0.2728, 0.3548, 0.5851 for horizontal lines, as well as 0.2291, 0.3499, and 0.4647 for vertical lines, respectively. A higher difference implies greater image contrast. Moreover, the MTF estimation of OR3 and OR4 arrays is higher than that of the Golay-9 array, which proves the validity of the proposed array structure design method.