Adaptive local-minimum escape strategies for SPGD-based space telescope alignment

Abstract

Stochastic Parallel Gradient Descent (SPGD) is widely used for model-free optical alignment because it produces an implicit descent signal when no explicit gradient is available. We use SPGD in the third of four sequential stages (blind-scan, model-based fit, SPGD, focus-diverse phase retrieval) of the commissioning pipeline developed by Blomquist et al. for a three-mirror anastigmat (TMA) space telescope, and this work is a direct continuation of that effort. The SPGD stage must drive the five actuated degrees of freedom of the M2 hexapod from a model-based residual of ∼ 0.3–1.0 mm average focal-plane RMS spot size down to the focus-diverse phase retrieval (FDPR) entry threshold of 2λ peak-to-valley wavefront error, which corresponds to a convergence limit of 0.03 mm RMS spot size at the 650 nm design wavelength. Prior implementations of this stage stagnated above the 2λ threshold for many Monte Carlo misalignment configurations, and the published handoff target was therefore relaxed to 4–5λ to help alleviate that issue at the cost of an enlarged downstream phase-retrieval capture range. The variant deployed in this pipeline is a one-sided accept/reject SPGD whose accepted steps form a biased implicit descent signal rather than an unbiased gradient estimate, a property that constrains which acceleration mechanisms can work. This paper contributes four adaptive local-minimum escape strategies for the SPGD stage (Merit-Adaptive, Wide-Search, Ensemble-Restart, and Basin-Escape SPGD). Each targets a distinct failure mode of the deployed baseline, and all are evaluated on a fixed 12-case Monte Carlo benchmark with three trials per method and a 10 000-iteration budget. Basin-Escape SPGD, which couples a stagnation-triggered multi-DOF escape with a near-convergence gradient-probing phase, achieves the highest success rate on this benchmark: it reaches the original 2λ target in 75% of trials (27/36) versus 44% (16/36) for the baseline, with a 35% reduction in median iterations to convergence among successful trials. The three intermediate strategies provide controlled comparisons (Merit-Adaptive 58%, Wide-Search and Ensemble-Restart 67%), indicating how much of the improvement comes from progress-aware step sizing, wider upstream search, and restart variance reduction. We also analyze why classical momentum, AdaGrad-style methods, and direct physics-aware couplings fail to improve on the baseline: they treat the biased, noisy accepted-step signal as if it were a gradient.