# Can OCT Angiography Be Made a Quantitative Blood Measurement Tool?
## 3 OCTA Signal  
In this section, we provide a unifying framework for the OCT signal to facilitate the discussion of OCTA algorithms in Section 4. Commonly-used symbols or variables and their definitions are summarized in Table 1, while other symbols are defined in the text. All standard OCTA algorithms [41; 42] start from the complex OCT signal. The complex, depth-resolved OCT signal can be expressed as:  
\[S(x,z,t)=|S(x,z,t)|\exp\left\{i\partial(x,z,t)\right\}. \tag{1}\]  
Note that \(S(x,z,t)\) is related to the depth-resolved optical field, integrated over a resolution element (coherence volume). Therefore, the depth-resolved intensity, \(I(x,z,t)\), is equivalent to the magnitude square of the field, i.e., \(I(x,z,t)=|S(x,z,t)|^{2}\). OCTA algorithms may operate on either \(S(x,z,t)\), \(\varnothing(x,z,t)\), or \(I(x,z,t)\) as the \"signal\", and accordingly, can be categorized into complex field-based \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Meaning** \\ \hline S & Complex OCT signal/field \\ \(|S|\) & Amplitude of the OCT signal \\ \(I=|S|^{2}\) & Intensity of the OCT signal \\ \(\varnothing\) & Phase of the OCT signal \\ \(\mathbb{S}_{m}\) & OCT field from one scatterer \\ SV & Speckle variance \\ cmOCT & Correlation mapping OCT signal \\ PV & Phase variance \\ \(\Delta\varnothing\) & Phase difference \\ \(\Delta\)S & Complex field difference \\ CDV & Complex differential variance \\ R & Autocorrelation function \\ P & Power spectral density \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Symbols or variables used and their meaning. techniques, phase-based techniques, and intensity-based techniques. In its simplest form, OCTA employs differences between OCT signals at the same spatial position over a series of time points to highlight scatterer motion. As discussed in Section 2.2, RBCs are the main blood scattering component. Due to the dynamic motion of RBCs, the overall field, phase, and intensity fluctuate. For the field, these variations are determined, in a statistical sense, by the first-order field autocorrelation function, \(r(\tau)\), in which \(r(\tau)\ =\ R(\tau)/R(0)\) and \(R(\tau)\ =\ E[S(x,z,t+\tau)S^{*}(x,z,t)]\), where \(E[\ ]\) represents expectation and \(\tau\) is the time lag. Under some circumstances, all other signal variations, including those of the intensity and phase, derive their statistical properties from the field autocorrelation [43]. OCT complex signal dynamics are illustrated in Figure 3. The complex signal is treated as a complex summation of backscattered fields from individual scatterers within the coherence volume. The coherence volume is defined by the beam waist in the transverse direction and the coherence length in the axial direction. Changes in the fields from individual scatterers over time leads to changes in the total signal over time (Figure 3A,B). In many practical situations, scatterers may be further classified as \"dynamic\" and \"static\" depending on whether they move or not, with both scatterer types contributing to the signal in the same coherence volume (Figure 3C,D). The nature of scatterer dynamics plays a major role in determining the OCT signal changes (Figure 4). Generally, scatterer motion is accompanied by both a Doppler shift and decorrelation [44]. When the scatterer has an axial velocity component, moving towards or away from the incident beam, the complex field rotates, tracing a helix over time (Figure 4A-C). This effect can be described as a linear phase shift over time due to the Doppler effect, or a \"Doppler phase shift\". When the scatterer is undergoing a dynamic conformational change, rotation, or translational motion through the coherence volume, both the OCT signal intensity and phase change randomly (Figure 4D-F). This random change of the complex field is known as decorrelation.