Step-by-step detection of co-phase errors for Golay6 optical sparse aperture via deep learning

The co-phase errors (piston and tip-tilt errors) in optical sparse aperture (OSA) imaging systems severely degrade the imaging quality. We propose a step-by-step co-phase errors detection method based on deep learning and the Point Spread Function (PSF). Taking the Golay6 OSA system as an example, the feasibility of the proposed method is discussed when the system contains both piston and tip-tilt errors within the range of [-1,1]λ. First, the relationship between PSF and piston/tip-tilt errors is derived, demonstrating that tip-tilt errors detection is unaffected by piston errors, whereas piston error is challenging to detect directly due to its coupling with tip-tilt errors. Subsequently, a dual-model detection network is designed: the T-model detects tip-tilt errors using the original PSF as input, followed by the P-model detecting piston error using the PSF corrected for tip-tilt errors as input. Simulation results show that our method can achieve high-precision step-by-step detection of co-phase errors using only a single network and PSFs. Meanwhile, our method exhibits robustness against other system wavefront aberrations and noise.