## Materials and Methods
### System Design
#### 2.2.5 Pathlength Multiplexing Element  
An important component to the SAR-OCT system is the pathlength multiplexing element (PME). The PME is a BK7 window, 5 mm thick, with a central clear aperture. The center aperture has a 7 mm diameter. Light in the sample arm of the SAR-OCT system has three potential optical pathlengths: Pathlength 1 is light that travels through the center aperture to and from the retina. Pathlength 2 is light that travels through the PME central aperture once--to or from the retina. Pathlength 3 is light that does not travel through the PME central aperture--to and from the retina. Figure 3 illustrates the three pathlengths. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Measurement Taken after:**} & **Combined 2 nd Order** & **Individual Contribution (s\({}^{2}\))** \\  & **Terms after Element (s\({}^{2}\))** & **Individual Contribution (s\({}^{2}\))** \\ \hline Reflective Collimator & 5.40 \(\times\) 10\({}^{-31}\) & 5.40 \(\times\) 10\({}^{-31}\) \\ Lens 1 & 1.77 \(\times\) 10\({}^{-28}\) & 1.76 \(\times\) 10\({}^{-28}\) \\ Lens 2 & 2.61 \(\times\) 10\({}^{-28}\) & 2.61 \(\times\) 10\({}^{-28}\) \\ Lens 3 & 3.24 \(\times\) 10\({}^{-28}\) & 6.33 \(\times\) 10\({}^{-29}\) \\ Lens 4 & 4.21 \(\times\) 10\({}^{-28}\) & 9.65 \(\times\) 10\({}^{-29}\) \\ Lens 5 & 5.04 \(\times\) 10\({}^{-28}\) & 8.34 \(\times\) 10\({}^{-29}\) \\ Fundus Lens & 5.01 \(\times\) 10\({}^{-28}\) & \(-\)2.87 \(\times\) 10\({}^{-30}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Contribution of each lens (summed and individual) to the dispersion mismatch. Mathematically, the additional pathlengths added for each path through any PME are described generally below:  
Additional pathlength added for Pathlength 1 (\(L_{L}\)) is  
\[L_{L}\ =\ (d+d)-(d+d)\ =\ 0. \tag{3}\]  
Additional pathlength added for Pathlength 2 (\(L_{H2}\)) is  
\[L_{H2}\ =\ (d+n\cdot d)-(d+d)\ =\ d(n-1). \tag{4}\]  
Additional pathlength added for Pathlength 3 (\(L_{H3}\)) is  
\[L_{H3}\ =\ (n\cdot d+n\cdot d)-(d+d)\ =\ 2d(n-1). \tag{5}\]  
In Equations (3)-(5), \(d\) is the physical PME thickness, and \(n\) is refractive index of the glass at the center wavelength of the OCT system. For the 5 mm thick BK7 PME (\(n=1.50\) at 1310 nm), \(L_{L}=0\), \(L_{H2}=2.5\) mm, and \(L_{H3}=5\) mm. Thus, each sub image in the OCT interferogram is separated vertically by 2.5 mm. A more rigorous Fourier optical analysis of the PME operation for imaging was previously published [33]. A Monte Carlo model was developed to determine the effect of PME center aperture size on the intensity of light in each pathlength. Photons were randomly generated within the beam area, and each photon was weighted by its position in the Gaussian beam profile of the OCT source. Then, each photon was assigned a scattering angle off of the sample based on an assigned g-factor (anisotropy) of 0.97, a measured g anisotropy value for the neural retina [34]. The Monte Carlo simulation recorded whether the photon travelled through the PME glass once, twice, or never, and each photon contributed to the intensity of its assigned pathlength (Figure 5). The scattering angle of the photon was also recorded. The results of the Monte Carlo simulation suggested no single PME aperture size exists at which the pathlength intensities are equal. Figure 3: The PME introduces three potential optical pathlengths. Light mapped to Pathlength 1 (P1, blue) travels through the center of the PME to and from the retina. Light mapped to Pathlength 2 (P2, green) travels through the PME central aperture only once—travelling either to or from the retina. Light mapped to Pathlength 3 (P3, red) does not travels through the PME central aperture—both to and from the retina. Permission was granted by the publisher to reprint this figure from [PERSON] et al. with minor modifications [19]. Plotting the angular distribution of backscattered photons for each pathlength revealed that Pathlengths 1 and 2 have greatest angular discrimination (Figure 4).