Sampling of Time- and Frequency-domain Signals in Monte Carlo Simulations of Photon Migration

We compare two fundamentally different ways to evaluate the time dependence in Monte Carlo simulations of photon migration: estimating the pulse response in time versus evaluating the transfer function at discrete points in the frequency domain. We show that these two methods differ in accuracy owing to quantization and sampling errors, whereas the statistical error is essentially the same for both methods. From our analysis we also derive alternative methods to sample the time-domain pulse response with reduced quantization and sampling error. Simulation results are included to illustrate our theoretical analysis.