Computationally effective 2D and 3D fast phase unwrapping algorithms and their applications to Doppler optical coherence tomography

Abstract

We propose a simplification for a robust and easy to implement fast phase unwrapping (FPU) algorithm that is used to solve the phase wrapping problem encountered in various fields of optical imaging and metrology. We show that the number of necessary computations using the algorithm can be reduced compared to its original version. FPU can be easily extended from two to three spatial dimensions. We demonstrate the applicability of the two-and three-dimensional FPU algorithm for Doppler optical coherence tomography (DOCT) in numerical simulations, and in the imaging of a flow phantom and blood flow in the human retina in vivo. We introduce an FPU applicability plot for use as a guide in the selection of the most suitable version of the algorithm depending on the phase noise in the acquired data. This plot uses the circular standard deviation of the wrapped phase distribution as a measure of noise and relates it to the root-mean-square error of the recovered, unwrapped phase.

Blood flow rate estimation in optic disc capillaries and vessels using Doppler optical coherence tomography with 3D fast phase unwrapping

“…3D 4FT FPU in combination with STdOCT rendered Doppler OCT images with visibly smaller noise as compared to other combinations and not affected by phase unwrapping artefacts. This observation is in agreement with our previous studies, where we showed that STdOCT offers higher SNR than PR-Doppler OCT [13,44] and, in another study, that 3D 4FT FPU is less likely to generate artifacts than 2D 4FT FPU [29]. It is interesting to relate these observations to the total computation times of the implemented algorithms presented in Table 2.…”

“…Measurement of velocities exceeding the v z max value requires implementation of numerical phase unwrapping methods. We used our recently developed [29] three-dimensional (3D) fast phase unwrapping (FPU) calculated using four complex Fourier transformations (4FT) (i.e. 3D 4FT FPU).…”

“…We have implemented a processing pipeline consisting of the transformation of OCT spectra into complex A-scans [42,43] followed by one of the two Doppler OCT methods (PR-Doppler OCT [22] or STdOCT [13]), with one of the two versions of the 4FT FPU algorithms [29]. We used the STdOCT method with a window of four A-scans and 128-point Fourier transforms.…”

“…Many phase unwrapping methods have been introduced to Doppler OCT [23][24][25][26][27][28]. Recently, we developed a robust and computationally efficient phase unwrapping method, namely four Fourier transform fast phase-unwrapping (4FT FPU) [29], and showed that it is specifically suited for multidimensional Doppler OCT data. Similar method was also presented for 2-dimensional data acquired using stroboscopic interferometry [30].…”

“…The focus of our previous article was on the development of algorithms suitable for Fourierdomain OCT imaging [29]. Capability to unwrap the phase was tested in numerical simulation of flow and in a flow phantom for 2-dimensional and 3-dimensional data sets was presented.…”