Additive noise models for photoacoustic spatial coherence theory

Directly displaying the spatial coherence of photoacoustic signals (i.e., coherence-based photoacoustic imaging) remarkably improves image contrast, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and imaging depth when compared to conventional amplitude-based reconstruction techniques (e.g., backprojection, delay-and-sum beamforming, and Fourier-based reconstruction). We recently developed photoacoustic-specific theory to describe the spatial coherence process as a function of the element spacing on a receive acoustic aperture to enable photoacoustic image optimization without requiring experiments. However, this theory lacked noise models, which contributed to significant departures in coherence measurements when compared to experimental data, particularly at higher values of element separation. In this paper, we develop and implement two models based on experimental observations of noise in photoacoustic spatial coherence measurements to improve our existing spatial coherence theory. These models were derived to describe the effects of incident fluence variations, low-energy light sources (e.g., pulsed laser diodes and light-emitting diodes), averaging multiple signals from low-energy light sources, and imaging with light sources that are > 5mm from photoacoustic targets. Results qualitatively match experimental coherence functions and provide similar contrast, SNR, and CNR to experimental SLSC images. In particular, the added noise affects image quality metrics by introducing large variations in target contrast and significantly reducing target CNR and SNR when compared to minimal-noise cases. These results provide insight into additional requirements for optimization of coherence-based photoacoustic image quality.