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

Area of Science:

• Optics and Photonics
• Computational Imaging
• Wave Physics

Background:

• Accurate object localization is crucial for reliable autofocus in digital holography (DH).
• Existing methods may struggle with computational demands or accuracy at low sampling rates.
• Time-reversal (TR) symmetry offers a potential framework for improving DH autofocus.

Purpose of the Study:

• To develop a time-reversal (TR) symmetry-enabled autofocus strategy for digital holography (DH).
• To integrate depth-dependent randomized sparse sampling with TR symmetry for enhanced localization.
• To achieve high-fidelity object localization at ultra-low sampling rates with computational efficiency.

Main Methods:

• Leveraging the low-rank structure of the TR operator, derived from wave equation dynamics.
• Implementing depth-dependent randomized sparse sampling using independent, uniformly distributed test point sets.
• Utilizing Monte Carlo estimation principles to decorrelate sampling-induced clutter.
• Preserving signal and noise subspace orthogonality for high-fidelity localization.

Main Results:

• Demonstrated accurate object localization and robust autofocus in digital holography.
• Achieved high-fidelity localization even at ultra-low sampling rates (down to 0.25N).
• Showcased significant computational savings compared to conventional methods through simulations and experiments.

Conclusions:

• The proposed TR symmetry-enabled sparse sampling method provides an analytical, training-free solution for DH autofocus.
• The approach effectively enhances localization accuracy and computational efficiency.
• This method holds promise for enabling real-time dynamic autofocus in various sensing applications.