Transverse motion as a source of noise and reduced correlation of the Doppler phase shift 
in spectral domain OCT

Abstract

Recently, a new phase-resolved Doppler model was presented for spectral domain optical coherence tomography (SD OCT) showing that the linear relation between the axial velocity component of the obliquely moving sample and the phase difference of consecutive A-Scans does not hold true in the presence of a transverse velocity component which is neglected in the widely-used classic Doppler analysis. Besides taking note of the new non-proportional relationship of phase shift and oblique sample motion, it is essential to consider the correlation of the phase shift and its specific characteristic at certain Doppler angles for designing Doppler experiments with SD OCT. A correlation quotient is introduced to quantify the correlation of the backscattering signal in consecutive A-Scans as a function of the oblique sample motion. It was found that at certain velocities and Doppler angles no correlation of the phases of sequential A-Scans exists, even though the signal does not vanish. To indicate how the noise of the Doppler phase shift behaves for oblique movement, the standard deviation is determined as a function of the correlation quotient and the number of complex Doppler data averaged. The detailed theoretical model is validated by using a flow phantom model consisting of a 1% Intralipid flow through a 310 microm capillary. Finally, a short discussion of the presented results and the consequence for performing Doppler experiments is given.

Flow Measurement by Lateral Resonant Doppler Optical Coherence Tomography in the Spectral Domain

“…The bias-free Doppler phase shift ∆ϕ(z) is calculated by the multiplication of the complex Fourier coefficient of one A-scan Γ j+1 (z) and the previous conjugate complex measurement Γ j * (z) [20,22], where the resulting complex data contains the Doppler phase shift ∆ϕ(z) as the argument:…”

“…Since the noise of the Doppler phase shift increases with the amount of transverse displacement in the case of an oblique sample motion [19,20], low signal-to-noise ratio (SNR) [16], and detector dead time [21], the amplitude weighted averaging by Equation (4) is recommended.…”

“…The discrepancy of the relationship of ∆ϕ(z) and v z (z) for any oblique sample motion detected with spectrometer-based OCT systems has been theoretically described in detail in previous studies [19][20][21]. To summarize the general description of the Doppler phase shift ∆ϕ independent of the OCT system parameters, dimensionless coordinates are used as follows:…”

“…This approach uses a moving reference mirror for phase matching the OCT signal by an additional axial reference velocity, to obtain flow-based contrast enhancements of the blood vessels in the OCT images [17,18]. With regard to the nonlinear relationship between the phase shift and axial velocity for an oblique sample movement in SD-OCT [19][20][21], the discrepancy of the assumed linear relation is dramatic in the case of a highly transverse velocity component. Moreover, the measured phase shift always predicts a smaller absolute flow velocity than actually exists.…”

“…Moreover, the measured phase shift always predicts a smaller absolute flow velocity than actually exists. Besides this, the correlation between adjacent A-scans primarily disappears for high transverse velocity components, resulting in a high mean error of the Doppler phase shift [20]. To overcome these limitations for the case of a small Doppler angle between the horizontal direction and the sample velocity, and thereby a highly dominant transverse velocity component, the present approach proposes the matching of the 2D-scanner in the sample arm to the transverse velocity component of the sample motion, comparable to a tracking shot where the camera moves alongside the object to be detected.…”