Stabilizing the phase of swept-source optical coherence tomography by a wrapped Gaussian mixture model

Shuwen Wei; Jin U. Kang

doi:10.1364/OL.420898

Optics Letters
Vol. 46,
Issue 12,
pp. 2932-2935
(2021)
•https://doi.org/10.1364/OL.420898

Stabilizing the phase of swept-source optical coherence tomography by a wrapped Gaussian mixture model

Shuwen Wei and Jin U. Kang

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Shuwen Wei and Jin U. Kang, "Stabilizing the phase of swept-source optical coherence tomography by a wrapped Gaussian mixture model," Opt. Lett. 46, 2932-2935 (2021)

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Table of Contents Category
- Fourier Optics, Image and Signal Processing
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: January 27, 2021
- Revised Manuscript: May 3, 2021
- Manuscript Accepted: May 20, 2021
- Published: June 14, 2021

Abstract

The phase of an optical coherence tomography (OCT) signal carries critical information about particle micro-displacements. However, swept-source OCT (SSOCT) suffers from phase instability problems due to trigger jitters from the swept source. In this Letter, a wrapped Gaussian mixture model (WGMM) is proposed to stabilize the phase of SSOCT systems. A closed-form iteration solution of the WGMM is derived using the expectation–maximization algorithm. Necessary approximations are made for real-time graphic processing unit implementation. The performance of the proposed method is demonstrated through ex vivo, in vivo, and flow phantom experiments. The results show the robustness of the method in different application scenarios.

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Supplementary Material (4)

Name	Description
Supplement 1	Supplemental document.
Visualization 1	The video is recorded in real-time during the in-vivo mice eye imaging. The first window shows the OCT structural image of the in-vivo mice eye cornea, lens, retina, and surrounding tissues. The second window shows the original phase difference which is corrupted due to the trigger jitter from the swept source. The third window shows the reconstructed Doppler phase by using our proposed algorithm. Yellow and red colors indicate a velocity from bottom to top, while aqua and blue colors indicate a velocity from top to bottom. During the recording, the anesthetized mice moves involuntarily.
Visualization 2	The video is recorded in real-time during the in-vivo mice eye imaging. The first window shows the OCT structural image of the in-vivo mice eye cornea, lens, retina, and surrounding tissues. The second window shows the original phase difference, which is corrupted due to the trigger jitter from the swept source. The third window shows the reconstructed Doppler phase by using our proposed algorithm. Yellow and red colors indicate a velocity from bottom to top, while aqua and blue colors indicate a velocity from top to bottom. During the recording, we manually induce axial bulk motions using an axial translation stage.
Visualization 3	The video is recorded in real-time during the flow phantom experiments. The first window shows the OCT structural image of the microtube containing diluted milk powder solution. The second window shows the original phase difference, which is corrupted due to the trigger jitter from the swept source. The third window shows the reconstructed Doppler phase by using our proposed algorithm. Yellow and red colors indicate a velocity from bottom to top, while aqua and blue colors indicate a velocity from top to bottom. During the recording, the syringe pump first injects fluids and then withdraws fluids.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Equations (10)

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Variables	Descriptions
$N$	length of an A-scan without the c.c. term
$M$	number of A-scans within a group
$2 L + 1$	number of all possible $z$
$i$	integer index from 0 to $N - 1$
$j$	integer index from 0 to $M - 1$
$k$	integer index from $- L$ to $L$
$φ_{j, i}$	OCT phase difference at $i$ th depth in $j$ th A-scan
$I_{j, i}$	OCT signal intensity at $i$ th depth in $j$ th A-scan
$z_{j}$	difference of interferogram shift in $j$ th A-scan
$[2 L + 1]$	vector of size $2 L + 1$
$τ$	prior distribution of $z$
$γ_{k}$	slope of the linear phase component
$μ$	bulk motion
$σ$	noise level

1:	initialize $τ^{(0)}, μ^{(0)}, σ^{(0)}$
2:	for $t = 0 : max_i t e r a t i o n - 1$
3:	obtain $T_{j, k}^{(t)}$ for all $j$ and $k$ by Eq. (5)
4:	update $τ_{k}^{(t + 1)}$ for all $k$ by Eq. (6)
5:	if $τ^{(t + 1)}$ is not symmetric
6:	circularly shift both $τ_{k}^{(t + 1)}$ and $T_{j, k}^{(t)}$ along $k$
7:	update $μ^{(t + 1)}$ by Eq. (7)
8:	update $σ^{(t + 1)}$ by Eq. (8)
9:	obtain $z_{j}^{(t)}$ for all $j$ by Eq. (9)
10:	if $t ⩾ 1$ and $z_{j}^{(t)}$ is the same as $z_{j}^{(t - 1)}$ for all $j$
11:	end iteration
12:	obtain $ψ_{j, i}$ for all $i$ and $j$ by Eq. (10)

Variables	Descriptions
$N$	length of an A-scan without the c.c. term
$M$	number of A-scans within a group
$2 L + 1$	number of all possible $z$
$i$	integer index from 0 to $N - 1$
$j$	integer index from 0 to $M - 1$
$k$	integer index from $- L$ to $L$
$φ_{j, i}$	OCT phase difference at $i$ th depth in $j$ th A-scan
$I_{j, i}$	OCT signal intensity at $i$ th depth in $j$ th A-scan
$z_{j}$	difference of interferogram shift in $j$ th A-scan
$[2 L + 1]$	vector of size $2 L + 1$
$τ$	prior distribution of $z$
$γ_{k}$	slope of the linear phase component
$μ$	bulk motion
$σ$	noise level

1:	initialize $τ^{(0)}, μ^{(0)}, σ^{(0)}$
2:	for $t = 0 : max_i t e r a t i o n - 1$
3:	obtain $T_{j, k}^{(t)}$ for all $j$ and $k$ by Eq. (5)
4:	update $τ_{k}^{(t + 1)}$ for all $k$ by Eq. (6)
5:	if $τ^{(t + 1)}$ is not symmetric
6:	circularly shift both $τ_{k}^{(t + 1)}$ and $T_{j, k}^{(t)}$ along $k$
7:	update $μ^{(t + 1)}$ by Eq. (7)
8:	update $σ^{(t + 1)}$ by Eq. (8)
9:	obtain $z_{j}^{(t)}$ for all $j$ by Eq. (9)
10:	if $t ⩾ 1$ and $z_{j}^{(t)}$ is the same as $z_{j}^{(t - 1)}$ for all $j$
11:	end iteration
12:	obtain $ψ_{j, i}$ for all $i$ and $j$ by Eq. (10)

Abstract

Supplementary Material (4)

Data Availability

Cited By

Figures (3)

Tables (2)

Equations (10)

Optics Letters