Multi-aperture imaging with Fermat spiral sub-aperture arrangement

Abstract

Multi-aperture optical telescopes have been extensively studied owing to their high resolution, low cost, and light weight. The next generation of optical telescopes is predicted to be equipped with dozens or even hundreds of segmented lenses; therefore, it is necessary to optimize the arrangement of the lens array. This paper proposes a new structure called the Fermat spiral array (FSA) to replace the conventional hexagonal or ring array for the sub-aperture arrangement of a multi-aperture imaging system. The point spread function (PSF) and modulation transfer function (MTF) of the imaging system are compared in detail at single and multiple incident wavelengths. The FSA can effectively weaken the sidelobe intensity of the PSF, which is 12.8 dB lower on average than conventional ones with a single incident wavelength in the simulation and 4.45 dB lower in the experiment. A new MTF evaluation function is proposed to describe the mean level of MTF at mid-frequencies. The FSA can improve the MTF of the imaging system and weaken the ringing effect in the images. The imaging simulation indicates that FSA has superior imaging quality compared to conventional arrays, with a higher peak signal-to-noise ratio (PSNR) and structural similarity (SSIM). The imaging experiments also achieve a higher SSIM with the FSA, which agrees well with the simulation results. The proposed FSA multi-aperture will help improve the imaging performance of next-generation optical telescopes.