## 3 Material and Methods
### Bi-Directional Lateral Scanning Protocol and Image Correction for Doppler Analysis  
The two galvanometer scanners integrated in the scanning unit are controlled by custom developed software based on LabVIEW(r) (National Instruments, Inc., Austin, TX, USA), with which arbitrary 2D-scanning patterns along the sample surface are realizable. Conventionally, the orthogonally driven \(X\)- and \(Y\)-galvanometer scanners are controlled for 2D-beam deflection, to allow 3D-imaging. The corresponding scanning protocol can be found in Figure 4a, where B-scans consisting of an arbitrary number of A-scans are detected by the lateral fast scanning \(Y\)-scanner and are spatially separated by the \(X\)-scanner. The resulting orthogonally running cross section and longitudinal section of the exemplary glass capillary with flowing 1% Intralipid are presented in Figure 4b. The modified scan protocol for LR-DOCT is shown in Figure 4d. The first of the three B-scans with the stationary \(Y\)-scanner is an M-scan, and within the second B-scan, the \(X\)-scanner is driven along the moving direction of the sample (forward lateral scan, FL-scan). The third B-scan implies the reversely driven \(X\)-scanner (backward lateral scan, BL-scan). The resulting M- and lateral resonant B-mode images, each consisting of 512 A-scans, detected close to the capillary center with \(f_{A\text{-scan}}\) = 12 kHz and a detector dead time \(\Delta T/T_{A\text{-scan}}\) of 0.05, are presented in Figure 4e. For the FL-scan, the \(X\)-scanner was lateral resonantly driven to the flowing oil particles of the 1% Intralipid emulsion at the capillary center  
Figure 3: Dualband SD-OCT system, where the long wavelength band centered at 1250 nm with a full spectral width of 200 nm is used with a fiber-coupled customized scanning unit. Abbreviations: SMF: single mode fiber, C: collimator, BS: beam splitter, DC: dichroic mirror, \(\vartheta\): Doppler angle. The flow phantom consists of a 312 μm glass capillary connected to an infusion pump by a tubing system and filled with 1% Intralipid and diluted fresh human blood, respectively. The result of the Doppler analysis by Equation (3) is presented in Figure 5a for the FL-scan of the glass capillary with flowing 1% Intralipid. The calculated Doppler phase shifts are overlaid to the structural information. As the obliquely running direction of the sample hampers the averaging of phase shifts in \(x\)-direction, consecutive A-scans are shifted in the \(z\)-direction by introducing a k-dependent phase shift. This correction is demonstrated in Figure 5b, using the example of the FL-scan. In analogy to the first shift theorem of the Fourier transform, an additional phase \(\varphi_{\text{shifted}}(k,j)\) is inserted into the real-valued interferometric signal I\({}_{j}\)(\(k,z\)), as shown in Equation (7). According to Equation (8), the fractional shift of each interference spectrum of the lateral resonant scan corresponds to the tangent of the Doppler angle \(\vartheta\), where \(N\) is the number of points of the Fourier transformation (FT). With this, the originally obliquely running direction of the capillary, and consequently, the Doppler phase shift due to the fast laterally moving \(X\)-scanner across the oblique surface of the glass capillary, are eliminated. \[\text{I}_{\text{shifted},j}(k,z)=\text{I}_{j}(k,z)e^{i\varphi_{\text{shifted} }(k,j)} \tag{7}\]  
\[\varphi_{\text{shifted}}(k,j)=\frac{2 nkj}{N}\tan\vartheta \tag{8}\]  
Further processing is identical to the conventional OCT and Doppler OCT processing: a Fourier transform is applied to I\({}_{\text{shifted},j}\)(\(k,z\)) in accordance with Equation (1) and the Doppler phase shift \(\Delta\varphi\) is calculated by multiplying a complex A-scan with the conjugate complex one (cp. Equation (3)). Figure 4: Conventional (**a**) and bi-directional lateral (**d**) scanning protocol of the \(X\)- and \(Y\)-galvanometer scanners. (**b**) Cross section and longitudinal section of the Intralipid-filled glass capillary generated from the detected 3D-scan.