Sub-Rayleigh characterization of a binary source by spatially demultiplexed coherent detection

Area of Science:

• Quantum optics
• Optical imaging
• Statistical physics

Background:

• Characterizing composite thermal sources is challenging, especially below the classical diffraction limit (Rayleigh limit).
• Coherent detection offers potential for enhanced measurement precision in optical systems.

Purpose of the Study:

• To theoretically investigate coherent detection for characterizing thermal sources below the Rayleigh limit.
• To develop a super-resolution algorithm for estimating parameters of two-dimensional symmetric binary sources.

Main Methods:

• Theoretical derivation of the relationship between source intensity distribution and field amplitude covariance matrix.
• Development and Monte Carlo simulation-based verification of a parameter estimation algorithm.
• Implementation of simultaneous coherent detection on orthogonal spatial modes.

Main Results:

• A general relation connecting source properties to image-plane measurements was derived.
• The devised algorithm achieves super-resolution, determining source separation down to SNR^-1/2.
• The algorithm demonstrates near-optimal data utilization in the sub-Rayleigh regime.

Conclusions:

• Coherent detection is a viable method for sub-Rayleigh characterization of composite thermal sources.
• The developed algorithm provides significant super-resolving capability, especially at high signal-to-noise ratios (SNR).
• This approach offers a powerful tool for high-precision optical measurements beyond classical limits.