Autofocus in digital holography with time reversal and depth-dependent sampling.

Accurate object localization is critical for robust autofocus in digital holography (DH). Here, we present a time-reversal (TR) symmetry-enabled autofocus strategy integrated with depth-dependent randomized sparse sampling. Our approach is grounded in the low-rank structure of the TR operator. This inherent property, arising from the dynamical constraints of the wave equation, provides a physical foundation for sparse sampling without compromising subspace separation. By using independent, uniformly distributed test point sets at each axial plane, the method effectively decorrelates sampling-induced clutter and acts as an approximately unbiased Monte Carlo estimator. This analytical, training-free solution preserves the inherent orthogonality of signal and noise subspaces, ensuring high-fidelity localization even at ultra-low sampling rates (e.g., 0.25N). Simulations and experiments demonstrate that the proposed method achieves high-resolution autofocus with significant computational savings, paving the way for real-time dynamic autofocus in diverse sensing environments.