Diffuse correlation spectroscopy (DCS) is an optical technique that non-invasively quantifies an index of blood flow (BFi) by measuring the temporal autocorrelation function of the intensity fluctuations of light diffusely remitted from the tissue. Traditional DCS measurements use continuous wave (CW) lasers with coherence lengths longer than the photon path lengths in the sample to ensure that the diffusely remitted light is coherent and generates a speckle pattern. Recently, we proposed time domain DCS (TD-DCS) to allow measurements of the speckle fluctuations for specific path lengths of light through the tissue, which has the distinct advantage of permitting an analysis of selected long path lengths of light to improve the depth sensitivity of the measurement. However, compared to CW-DCS, factors including the instrument response function (IRF), the detection gate width, and the finite coherence length need to be considered in the model analysis of the experimental data. Here we present a TD-DCS model describing how the intensity autocorrelation functions measured for different path lengths of light depend on the coherence length, pulse width of the laser, detection gate width, IRF, BFis and optical properties of the scattering sample. Predictions of the model are compared with experimental results using a homogeneous liquid phantom sample that mimics human tissue optical properties. The BFis obtained from the TDDCS model for different path lengths of light agree with the BFi obtained from CW-DCS measurements, while the standard simplified model underestimates the BFi by a factor of ~2. This Letter establishes the theoretical foundation of the TD-DCS technique and provides guidance for future BFi measurements in tissue.
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