On generalized photocurrent spectral moments and the recovery of speed distribution in laser Doppler flowmetry

Laser Doppler flowmetry (LDF) is a noninvasive method to assess tissue blood flow. By calculating the first moment of the Doppler signal power spectral density, a real-time output is generated that scales linearly with the perfusion flux defined as the product of average speed and concentration of moving blood cells (MBCs) if multiple scattering is negligible. However, this first spectral moment alone is apparently unable to provide further information about the MBCs under study. Without assuming any specific MBC speed or scattering vector distribution, a generalized formula for photocurrent spectral moments is derived in the case of low and moderate MBC concentration. Using the formula, the speed distribution of MBCs is obtained by means of the Henyey-Greenstein phase function and a Fourier inversion. The implications and applications of this formulation for extracting more MBC information are discussed together with some other related issues.