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The photoacoustic effect relies on optical transmission, which causes thermal expansion and generates acoustic signals. Coherence-based photoacoustic signal processing is often preferred over more traditional signal processing methods due to improved signal-to-noise ratios, imaging depth, and resolution in applications such as cell tracking, blood flow estimation, and imaging. However, these applications lack a theoretical spatial coherence model to support their implementation. In this article, the photoacoustic spatial coherence theory is derived to generate theoretical spatial coherence functions. These theoretical spatial coherence functions are compared with k-Wave simulated data and experimental data from point and circular targets (0.1-12 mm in diameter) with generally good agreement, particularly in the shorter spatial lag region. The derived theory was used to hypothesize and test previously unexplored principles for optimizing photoacoustic short-lag spatial coherence (SLSC) images, including the influence of the incident light profile on photoacoustic spatial coherence functions and associated SLSC image contrast and resolution. Results also confirm previous trends from experimental observations, including changes in SLSC image resolution and contrast as a function of the first M lags summed to create SLSC images. For example, small targets (e.g., <; 1-4 mm in diameter) can be imaged with larger M values to boost target contrast and resolution, and contrast can be further improved by reducing the illuminating beam to a size that is smaller than the target size. Overall, the presented theory provides a promising foundation to support a variety of coherence-based photoacoustic signal processing methods, and the associated theory-based simulation methods are more straightforward than the existing k-Wave simulation methods for SLSC images.

Photoacoustic Spatial Coherence Theory and Applications to Coherence-Based Image Contrast and Resolution