# Can OCT Angiography Be Made a Quantitative Blood Measurement Tool?
## 4 OCTA Algorithms
### Classification of Present OCTA Algorithms  
Historically, all of the OCTA algorithms described above were novel at the time they were introduced. However, with the benefit of hindsight, we propose basic categories to classify OCTA algorithms in Table 2.  
The primary distinction between algorithms, discussed in Section 4.1, Section 4.2, Section 4.3, is the OCT signal(s) employed. The second distinction, which is emphasized in the literature, is between variance/difference-based methods and correlation-based methods. However, here we argue \begin{table}
\begin{tabular}{c c} \hline \hline
**Category** & **Classification** \\ \hline OCT signal & Field vs. Intensity/Amplitude vs. Phase \\ Calculation & Variance/Difference vs. Correlation \\ Averaging method & Temporal vs. Spatial vs. Spectral \\ Normalization & Normalized vs. Non-normalized \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Classification of OCTA algorithms. Figure 9: OCTA of the skin on a pig ear. OCT cross-sectional intensity image (**A**) and angiogram (**B**) determined by complex subtraction. (**C**) Overlay of superficial vessels in the epidermis (red) with deeper vasculature in the dermis (green). (**D–I**) Maximum intensity projections centered at different axial (z) positions relative to the surface. that in some cases, this distinction is meaningless. Difference-based methods are actually estimating the following:  
\[\mathrm{D}(\mathrm{T})=\mathrm{E}[|\mathrm{X}_{\mathrm{t+T}}-\mathrm{X}_{ \mathrm{t}}|^{2}], \tag{13}\]  
where \(\mathrm{D}(\mathrm{T})\) denotes the difference at a time lag of \(\mathrm{T}\) and \(\mathrm{X}_{\mathrm{t}}\) can be the OCT field, intensity, or amplitude at time \(\mathrm{t}\). Variance-based methods are estimating the following:  
\[\mathrm{V}=\mathrm{E}[|\mathrm{X}_{\mathrm{t}}-\mathrm{E}(\mathrm{X}_{ \mathrm{t}})|^{2}]. \tag{14}\]  
On the other hand, the un-normalized autocorrelation is defined as:  
\[\mathrm{R}(\mathrm{T})=\mathrm{E}[\mathrm{X}_{\mathrm{t}}{}^{*}\mathrm{X}_{ \mathrm{t+T}}]. \tag{15}\]  
Further expanding Equation (13), the difference can be written in terms of the autocorrelation:  
\[\mathrm{D}(\mathrm{T})=\mathrm{E}[|\mathrm{X}_{\mathrm{t+T}}|^{2}]+\mathrm{E} [|\mathrm{X}_{\mathrm{t}}|^{2}]-2\mathrm{Re}[\mathrm{E}[\mathrm{X}_{\mathrm{t }}{}^{*}\mathrm{X}_{\mathrm{t+T}}]]=2\mathrm{R}(0)-2\mathrm{Re}[\mathrm{R}( \mathrm{T})]. \tag{16}\]  
Therefore, difference and correlation methods are very closely connected if \(\mathrm{R}(\mathrm{T})\) is real. If \(\mathrm{R}(\mathrm{T})\) is complex, as would be the case if \(\mathrm{X}_{\mathrm{t}}\) represented the field and Doppler shifting were present, the difference \(\mathrm{D}(\mathrm{T})\) depends only on the real part of \(\mathrm{R}(\mathrm{T})\). From Equations (14) and (15), it can be readily shown that \(\mathrm{R}(0)=\mathrm{V}\) if \(\mathrm{E}[\mathrm{X}_{\mathrm{t}}]=0\). Thus, every difference method corresponds to an equivalent correlation method via Equation (16). The third distinction between algorithms is the way that the expectation, \(\mathrm{E}[\;]\), is realized in practice. One method of realizing the expectation is by averaging over time. Another way is by averaging over space, at different tissue locations. Yet another way is spectral or optical wavelength averaging, employed in split-spectrum methods [51]. Under the assumption of ergodicity [64], all averaging methods are asymptotically equivalent, and in practice, all can be used to some degree. However, note that averaging over one dimension will automatically degrade the resolution in that dimension. Fourth, OCTA methods can be distinguished by the use of normalization. The normalized correlation is divided by the signal power, \(\mathrm{R}(0)\):  
\[\mathrm{r}(\mathrm{T})=\mathrm{R}(\mathrm{T})/\mathrm{E}[|\mathrm{X}_{\mathrm{ t}}|^{2}]=\mathrm{R}(\mathrm{T})/\mathrm{R}(0) \tag{17}\]  
For the complex signal, the power \(\mathrm{R}(0)\) is related to the total scattering within a coherence volume.