2.2. Signal Calculation by iMC

An in-house developed individual photon tracking MC (iMC) code was employed to calculate signals as Rdc,Tdc and Tfc from given P for a phantom of the same shape as the sample inside a spacer between two glass slides by tracking N₀ photons, which imports the parameters of sample size and detection configuration as input data.^16,19,20 The code injects each of the N₀ photons incident on the sample assembly and then tracks the photon once it transports inside a glass slide or sample until it is either absorbed inside the sample or escapes into air. The exit location and propagation direction of an escaping photon on a glass slide surface are used to determine if it hits a detector for detection. A counter associated with each detector records the number of detected photons as NRd,NTd, and NTf by the detector D2,D3, and D4, respectively. The above process repeats until the total number of injected photons reaches N0 and the calculated signals are given by Rdc=NRd/N0, Tdc=NRd/N0 and Tfc=NTf/N0. Because of independence in trajectory among the N0 photons, the numbers of detected photons follow Poisson distributions.²¹ To estimate the variance in these photon numbers, one can draw a random number q of Poisson distribution with f(q,qm) as probability mass function and qm as the mean. In the case of NRd calculated by an iMC simulation, qm equals to N0Rdc∞ if distribution of NRd follows f(NRd,qm) and Rdc∞ yields the variance-free value of Rdc by tracking “infinite” number of photons. One thus can use f(q,qm) to quantify the effect of variance on calculated signals and optimize the objective function for variance reduction.