chapter 9, Reference Monte Carlo Results

Excerpt

9.1 Introduction

Almost all the analytical solutions reported in Chapters 4–7 and the related software described in Chapter 8 are approximate solutions of the RTE. Before using them, it is useful to know the level of their accuracy in order to establish their applicability in different fields of interest. For this purpose, the enclosed CD-ROM reports examples of solutions of the RTE obtained with MC simulations. With MC simulations, the RTE can be solved without the need of simplifying assumptions and with an accuracy only limited by the statistical fluctuations related to the stochastic nature of the method. The MC results can therefore be used as a standard reference for comparison. This chapter is mainly devoted to describe the MC results reported in the CD-ROM (Sec. 9.6). The MC results have been obtained using several different MC programs. For a better understanding and a proper use of the MC results, a description of the MC programs we used is reported in Secs. 9.2–9.5. Examples of comparisons will be shown in Chapter 10.

9.2 Rules to Simulate the Trajectories and General Remarks

The MC method provides a physical simulation of light propagation. For each launched energy packet (photon packet or simply photon for brevity), the trajectory is numerically generated using the probability functions that govern propagation through the turbid medium. A photon is received if the simulated trajectory enters the receiver within the acceptance angle. With conventional MC simulations, the impulse response or temporal point spread function (TPSF), i.e., the probability (per unit time and per unit area of the receiver) of receiving emitted photons, is reconstructed by classifying the received photons in a histogram on the basis of their time of flight. The temporal resolution is only limited by the length of the intervals chosen for the temporal histogram and has a feature similar to the one obtained with a time-resolved experimental setup in which photons are detected using the time-correlated single-photon counting (TCSPC) technique. As for the experiment, the simulated response is noisy: Owing to the central limit theorem, the standard error decreases proportionally to the inverse of the square root of the number of received photons.