## 2 BLRFS Principles
### Basic Relationships of the BLRFS Technique  
In the random multiple-scattering media, consideration of interference interactions between partial contributions to a partially coherent light field leads to the following expressions for the normalized second- and third-order statistical moments of spatial fluctuations of the scattered light intensity \(I_{s}\) (for a detailed derivation in these formulas see [29]):  
\[ \begin{split} M_{2}&=\frac{\langle\frac{I_{s}^{2}}{ \langle I_{s}\rangle^{2}}}{\langle I_{s}\rangle^{2}}\approx 1+\int\limits_{0}^{ \infty}\bigl{|}g(\Delta s)\bigr{|}^{2}\rho(\Delta s)d(\Delta s);\\ M_{3}&=\frac{\langle\frac{I_{s}^{2}}{\langle I_{s} \rangle^{3}}}{\langle I_{s}\rangle^{3}}\approx 1+3\int\limits_{0}^{\infty}\bigl{|}g( \Delta s)\bigr{|}^{2}\rho(\Delta s)d(\Delta s)+2\biggl{[}\int\limits_{0}^{ \infty}\bigl{|}g(\Delta s)\bigr{|}\rho(\Delta s)d(\Delta s)\biggr{]}^{2}.\end{split}  \tag{1}\]  
The expressions (1) correspond to the case of stochastic interference of linearly polarized partial contributions; this condition can be achieved by, e.g., applying an additional polarizer in the light-collecting unit. In the case of detection of a non-polarized light, the expressions for the normalized second- and third-order moments are transformed into the following form [29]:  
\[ \begin{split} M_{2}&=\frac{\langle\frac{I_{s}^{2}}{ \langle I_{s}\rangle^{2}}}{\langle I_{s}\rangle^{2}}\approx 1+\frac{1}{2}\int \limits_{0}^{\infty}\bigl{|}g(\Delta s)\bigr{|}^{2}\rho(\Delta s)d(\Delta s); \\ M_{3}&=\frac{\langle\frac{I_{s}^{3}}{\langle I_{s} \rangle^{3}}}{\langle I_{s}\rangle^{3}}\approx 1+3\int\limits_{0}^{\infty} \bigl{|}g(\Delta s)\bigr{|}^{2}\rho(\Delta s)d(\Delta s)+\frac{1}{2}\biggl{[} \int\limits_{0}^{\infty}\bigl{|}g(\Delta s)\bigr{|}\rho(\Delta s)d(\Delta s) \biggr{]}^{2}.\end{split}  \tag{2}\]  
Here \(\bigl{|}g(\Delta s)\bigr{|}\) is a module of the coherence function of the detected spectrally selected light, which is defined in the domain of the path-length differences \(\Delta s\) between interfering partial contributions. The probability density distribution \(\rho(\Delta s)\) of the path-length differences depends on illumination and detection conditions and on the presence or absence of polarization discrimination in the detection channel. Equations (1) and (2) were obtained in terms of the discrete scattering model with the subsequent transition to a continuous path-length distribution \(\rho(s)\) of probe radiation in the medium [29]. This distribution characterizes the ensemble of propagation paths of partial light waves travelling in the medium in case of irradiation by a short light pulse. In turn, the probability density distribution \(\rho(\Delta s)\) of the path-length differences can be obtained from the path-length probability density \(\rho(s)\) using the convolution procedure: \(\rho(\Delta s)=K\!\!\int\limits_{0}^{\infty}\rho(s)\rho(s+\Delta s)ds\) together with the normalization condition \(\int\limits_{0}^{\infty}\rho(\Delta s)d(\Delta s)=1\) (\(K\) is the normalization constant). This follows from the statistical independence of a pair of propagation paths \(s_{i}\), \(s_{j}\) defining a given path-length difference \(\Delta s_{i,j}=s_{i}-s_{j}\). The module of the coherence function \(\bigl{|}g(\Delta s)\bigr{|}\) approaches 1 in the case \(\Delta s<<l_{c}\) and gradually falls to 0 with the increasing path-length difference in the region \(\Delta s>>l_{c}\). Consequently, the values of \(M_{2}\) and \(M_{3}\) are determined by the relationship between the coherence length of the spectrally selected fluorescence radiation \(l_{c}\) and the average path-length difference \(\langle\Delta s\rangle\).