Surface-Encoded Partial Coherence Transformation: Modeling Source Coherence Effects in Wave Optics

TL;DR

This paper introduces a novel mathematical framework for modeling partial coherence in wave optics that explicitly separates surface interactions from propagation effects, improving computational efficiency and understanding of coherence phenomena.

Contribution

The authors develop a surface-encoded transformation approach that models partial coherence effects at surfaces separately from propagation, differing from traditional ensemble averaging methods.

Findings

Framework reduces computational complexity of coherence calculations

Connects the model to the Van Cittert-Zernike theorem

Demonstrates applicability to optical testing and astronomy

Abstract

We present a new mathematical framework for incorporating partial coherence effects into wave optics simulations through a comprehensive surface-to-detector approach. Unlike traditional ensemble averaging methods, our dual-component framework models partial coherence through: (1) a surface-encoded transformation implemented via a linear integral operator with a spatially-dependent kernel that modifies coherence properties at the reflection interface, followed by (2) a propagation component that evolves these coherence properties to the detection plane. This approach differs fundamentally from conventional models by explicitly separating surface interactions from propagation effects, while maintaining a unified mathematical structure. We derive the mathematical foundation based on the coherence function formalism, establish the connection to the Van Cittert-Zernike theorem, and prove the equivalence of our framework to conventional partial coherence theory. The method reduces the dimensional complexity of coherence calculations and offers potential computational advantages, particularly for systems involving multiple surfaces and propagation steps. Applications include optical testing and astronomical instrumentation. We provide rigorous mathematical proofs, demonstrate the convergence properties, and analyze the relative importance of surface and propagation effects across different optical scenarios.