2.2. Phase-Based Methods

Phase-based methods evaluate the axial velocity of flowing particles within a scattering medium, such as blood cells within biological tissues, by utilizing the well-known Doppler effect. This is done by analyzing the phase difference between adjacent A-lines,²⁹ similar to complex signal–based methods. The phase difference between sequential A-lines, Δϕ(z), is linearly related to the flow axial velocity (vaxial) by

where Δt is the time interval between adjacent A-lines and n is the index of refraction of the tissue. Accordingly, a longer Δt is required for detecting slow velocities, which can be challenging for capillary flow detection.

Several variations of phase-based methods for angiography have been reported where the absolute value of the phase difference,³⁰ squared phase difference (i.e., Doppler power),³¹ or the variance of several adjacent A-line phase differences³² are used. The comparison between different methods can be found here.³³ The recent work of You et al.³⁴ showed great promise in quantitative capillary flow detection by using a phase summation method and vessel tracking. Moreover, Doppler optical microangiography (DOMAG)³⁵ has been proposed to improve the performance of phase-based methods. DOMAG utilizes OMAG to separate the static from the dynamic signal, then analyzes the phase difference between adjacent A-scans. In this way, the noise produced by the optical heterogeneous properties of the sample is reduced. Moreover, a variation of DOMAG has recently been introduced³⁶ by selectively skipping A-lines, and therefore the duration of Δt, for analyzing the Doppler signal. This method is simple and straightforward, but important in the investigation of impaired blood flow within microcirculatory tissue beds because it can provide Doppler analyses over a wide velocity range from capillaries to arterioles and venules, providing useful information to aid in the assessment of whether the blood flow within the injured region of interest is compromised or has ceased. Overall, two main factors cause the performance of phase-based methods to deteriorate: (1) the optical heterogeneity of the sample³⁷ and (2) the phase instability caused by the light source or the sample motion artifacts.³⁸