Model of dynamic speckle evolution for evaluating laser speckle contrast measurements of tissue dynamics

We introduce a dynamic speckle model (DSM) to simulate the temporal evolution of fully developed speckle patterns arising from the interference of scattered light reemitted from dynamic tissue. Using this numerical tool, the performance of laser speckle contrast imaging (LSCI) or speckle contrast optical spectroscopy (SCOS) systems which quantify tissue dynamics using the spatial contrast of the speckle patterns with a certain camera exposure time is evaluated. We have investigated noise sources arising from the fundamental speckle statistics due to the finite sampling of the speckle patterns as well as those induced by experimental measurement conditions including shot noise, camera dark and read noise, and calibrated the parameters of an analytical noise model initially developed in the fundamental or shot noise regime that quantifies the performance of SCOS systems using the number of independent observables (NIO). Our analysis is particularly focused on the low photon flux regime relevant for human brain measurements, where the impact of shot noise and camera read noise can become significant. Our numerical model is also validated experimentally using a novel fiber based SCOS (fb-SCOS) system for a dynamic sample. We have found that the signal-to-noise ratio (SNR) of fb-SCOS measurements plateaus at a camera exposure time, which marks the regime where shot and fundamental noise dominates over camera read noise. For a fixed total measurement time, there exists an optimized camera exposure time if temporal averaging is utilized to improve SNR. For a certain camera exposure time, photon flux value, and camera noise properties, there exists an optimized speckle-to-pixel size ratio (s/p) at which SNR is maximized. Our work provides the design principles for any LSCI or SCOS systems given the detected photon flux and properties of the instruments, which will guide the experimental development of a high-quality, low-cost fb-SCOS system that monitors human brain blood flow and functions.