Complex amplitude correlations of dynamic laser speckle in complex ABCD optical systems

Area of Science:

• Optical physics and engineering
• Wave propagation and coherence theory

Background:

• Understanding the statistical properties of optical fields is crucial for various applications.
• Complex optical systems with apertures and surface roughness introduce challenges in field analysis.
• Existing models often simplify speckle phenomena, limiting applicability to diverse surface structures.

Purpose of the Study:

• To derive exact theoretical expressions for space-time-lagged cross-covariance functions.
• To analyze these functions within the framework of complex ABCD-matrix theory for arbitrary optical systems.
• To investigate the impact of Gaussian apertures and partially developed speckle on field correlations.

Main Methods:

• Application of complex ABCD-matrix theory to derive field cross-covariance functions.
• Development and application of two surface models for varying RMS surface heights, alongside the standard model for fully developed speckle.
• Analysis of three generic optical configurations: free-space propagation, Fourier transform, and imaging systems.

Main Results:

• Exact theoretical expressions for space-time-lagged cross-covariance functions are obtained for complex ABCD optical systems.
• The study presents and discusses results for free-space propagation, Fourier transform, and imaging configurations.
• Theoretical predictions for free-space propagation are validated through interferometric measurements.

Conclusions:

• The derived theoretical framework accurately describes field correlations in complex optical systems with apertures and partial speckle.
• The models effectively handle various surface roughness conditions, enhancing the applicability of optical field analysis.
• Experimental validation confirms the accuracy of the theoretical results for free-space propagation scenarios.