Optimized Hydrophone Array Empowering Deep Learning–Based Phase Error Correction in Synthetic Aperture Sonar

This study addresses motion robust synthetic aperture sonar by coupling deep learning-based phase error estimation with hydrophone array optimization under 6 degrees of freedom. The objective is to deliver low sidelobe and high-fidelity imagery when surge, sway, heave, roll, pitch, and yaw inject residual phase errors that conventional autofocus and inertial aiding do not fully remove. The method is physics informed and trains an optimized array to predict residual phase from profile stacks and small image patches using a composite loss that blends image consistency, smooth proxies for peak and integrated sidelobe ratios, and phase smoothness. Array geometry is expressed in closed form and is co tuned in the loop with the corrector so that motion sensitivity is reduced before phase correction. Four hydrophone arrays are examined, namely a planar dual spiral, two helices on a cylinder, a hemispherical Fibonacci layout, and an optimized oblate hemisphere with equatorial densification and a mild tilt. Evaluation spans 24 scenarios across 6 motion axes over a 16 targets grid with PSLR, ISLR, PSNR, and RMSE as metrics. Three dimensional and nearly isotropic layouts consistently outperform planar and cylindrical baselines after correction. The optimized array ranks first overall, typically reaching side-lobe floors near −26 to −27 dB with PSNR near 49 to 50 dB and RMSE near 0.0033 and shows aggregated gains over the planar baseline of about −8 dB in sidelobe metrics and about +12 dB in PSNR, while retaining smaller but measurable advantages over the hemi-spherical Fibonacci design. The contribution unifies physics informed deep correction with interpretable array design that advances motion robust SAS image quality and offers actionable guidance for future hydrophone arrays.