## 2 Phase-Resolved Doppler Model in SD-OCT
### The Impact of Lateral Resonant Scanning on PR-DOCT  
Since the phase-resolved Doppler measurements in SD-OCT are limited for strong transverse components and high sample velocities, the transverse tracking of the obliquely moving sample is proposed in this research and defined as lateral resonant scanning. With this, the impact of the transverse motion component on the Doppler phase shift can be theoretically reduced. For a better comprehension of the subsequent experimental results, a simple geometric model is defined on the basis of Figure 2 for the Doppler measurement in SD-OCT. As shown, a Gaussian sample beam and an oblique sample motion with an arbitrary Doppler angle \(\vartheta\) are assumed. In this case, a group of scattering particles is supposed to be seen at the end of the detection intervals, [\(T_{1}\), \(T_{1}+T_{\rm Int}\)], [\(T_{2}\), \(T_{2}+T_{\rm Int}\)], and [\(T_{3}\), \(T_{3}+T_{\rm Int}\)], of three consecutive A-scans, where the respective position of the particles is shown by three blue distances and labeled with I, II, and III. Three cases of Doppler measurement performance are drawn in Figure 2: (a) with a static sample beam, resulting in a conventional M-scan (time-resolved A-scan); (b) with a laterally moving sample beam in the direction of the sample movement, resulting in a so-called forward lateral scan (FL-scan); and (c) with lateral scanning in the opposite direction, so-called backward lateral scan (BL-scan). Case (a) corresponds to the common phase-resolved Doppler measurement without imaging, where the sample beam of the OCT system is static to guarantee the highest phase correlation between adjacent A-scans. Due to the limited Gaussian sample beam, the group of particles seen in the time interval [\(T_{1}\), \(T_{1}+T_{\rm Int}\)] are only partly detectable in the subsequent time interval [\(T_{2}\), \(T_{2}+T_{\rm Int}\)] (shown by the red dotted lines), for which reason the measured axial displacement \(\Delta z_{d}\) and \(\Delta\varphi\) are reduced, especially for small Doppler angles and large transverse displacements [19; 20; 21]. Case (b) shows the lateral scanning towards the sample movement, where the sample beam in gray represents the position at \(T_{1}+T_{\rm Int}\) and the one drawn in green shows the position at \(T_{2}+T_{\rm Int}\). Since the scanner velocity is matched to the transverse velocity of the moving sample, the group of particles detected at time point \(T_{1}+T_{\rm Int}\) is tracked over the entire A-scan time \(T_{\rm A\mbox{-scan}}\), until \(T_{2}+T_{\rm Int}\). For a temporally invariable sample, the detected movement is purely axial, for which the \(\Delta\varphi\)-\(v_{z}\)-relation will be linear and the absolute sample velocity can be linearly calculated (cp. Equation (2)). For case (c) of the backward scanning, no phase correlation seems to exist, because the scattering particles detected at \(T_{1}+T_{\rm Int}\) within the gray sample beam are not detectable at \(T_{2}+T_{\rm Int}\) within the green one. Due to the continuous movement of the scanner and the gradual movement  
Figure 1: Contour plots of the numerically calculated phase shift \(\Delta\varphi\) between consecutive A-scans as a function of the normalized transverse \(\delta x\) and axial \(\delta z\) displacement of the oblique sample motion [20; 21] for detector dead times \(\Delta T/T_{\rm A\mbox{-scan}}\) of (**a**) 0.0 and (**b**) 0.05. The central dashed line with \(\vartheta^{\prime}\) of 29\({}^{\circ}\) corresponds to the expected phase shift of the 1% Intralipid flow experiment presented in Section 4. Additional shifted dashed lines with \(\vartheta^{\prime}\) of 29\({}^{\circ}\) are given for the LR-scanning explained in Section 2.2.  
of the scattering particles out of the scanning sample beam within \(T_{\text{A-scan}}\), a strongly reduced phase correlation exists, leading to a strongly reduced \(\Delta z\) and a significantly decreased \(\Delta\varphi\).