Study on the mathematical relationship existing between single-photon laser-Doppler flowmetry and diffuse correlation spectroscopy with static background

In the present contribution, the theoretical relationship existing between the blood flow index measured by diffuse correlation spectroscopy and single-photon laser-Doppler flowmetry (SP-LDF) is investigated. A specific mathematical description that accounts for the properties of single-photon detectors for SP-LDP was developed. Static background has also been considered and, to the best of our knowledge, this has never been included before in SP-LDF analytical theories. The comparisons were realized for two SP-LDF implementations: for “classical” and “fast” algorithms. “Classical” SP-LDF is not sensitive to small changes on the number of detected speckles and coherence length of the laser, usually described by a unique parameter “beta.” This is a strong point when assessing blood flow index, e.g., in humans, where “beta” is particularly difficult to be determined in real time. The proposed theory may be utilized, e.g., to investigate other SP-LDF setups and optical/physiological parameter ranges or, generally, to optimize real SP-LDF instrumentation.