Sensorless adaptive optics based on focal-plane second-moment matrix sensing

Sensorless adaptive optics (SAO) commonly relies on scalar focal-plane metrics, requiring many probe measurements for high-degree-of-freedom correction. We propose second-moment matrix sensorless adaptive optics (SMM-SAO), which uses the full focal-plane second-moment matrix (SMM) as a vector-valued sensing metric. By retaining directional spot-width and cross-correlation information from each probe image, SMM-SAO provides complementary observation channels under reduced probing. A Grassmann-manifold optimization is used to select probe subspaces that preserve modal observability. Experiments show that SMM-SAO outperforms scalar-metric SAO with the same number of probes. For tested Zernike aberrations, SMM-SAO approaches conventional N-probe scalar performance with N/3 probes and gives a slight overall improvement with N/2 probes. Time-varying turbulence correction further demonstrates improved focal-spot quality, highlighting the potential of SMM sensing for faster, measurement-efficient wavefront-sensorless aberration correction.