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Abstract
Optical coherence tomography (OCT), a promising noninvasive bioimaging technique, has become one of the most successful optical technologies implemented in medicine and clinical practice. Here we report a novel technique of depth-resolved transverse-plane motion tracking with configurable measurement features via optical coherence tomography, termed OCT-MT. Based on OCT circular scanning combined with speckle spatial oversampling, the OCT-MT technique can perform depth-resolved transverse-plane motion tracking. Benefitting from the optical interference and depth-resolved feature, the proposed OCT-MT can reduce the requirements on the input power of the irradiation signal and the surface reflectivity and roughness of the target, when performing motion tracking. Furthermore, OCT-MT can conduct such kind of motion tracking with configurable measurement ranges and resolutions by configuring A-line number per scanning circle, circular scanning radius, and A-line scanning time. The proposed OCT-MT technique may expand the ability of motion tracking for OCT in addition to imaging.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical coherence tomography (OCT) enables high-resolution, noninvasive, tomographic imaging of biological tissues and materials [1,2], having lots of applications, from resolving three-dimensional microstructure to creating projection images of blood vessels. Motion tracking techniques [3] have found widespread applications in many fields, such as the field of imaging correction [4,5], and Each of these motion tracking techniques measures a different physical property and has a resolution and penetration range that prove advantageous for specific applications. In this paper, we briefly discuss depth-resolved transverse-plane motion tracking via OCT in principle. With this technique, it is possible to perform depth-resolved transverse-plane motion tracking with broad-configurable measurement ranges and resolutions, expanding the ability of motion tracking for OCT in addition to imaging.
Conventional motion tracking techniques, such as the techniques based on lasers and microwaves, greatly rely on the irradiation signal’s reflection on the surface of the detected object, which puts requirements on the input power of the irradiation signal and the surface reflectivity and roughness. Recently several velocimetry techniques have also been developed based on OCT, including particle tracking velocimetry [6], tissue Doppler optical coherence elastography (tDOCE) [7], particle streak velocimetry [8], etc. However, those techniques only work well for fluid flows containing motion particles, such as cilia-driven fluid flow and capillaries with motional erythrocytes, and it is difficult for tDOCE to measure transverse-plane motion. Penface [9] method using repeated circular scanning has also been proposed to assess the transverse motion. However, the Penface method has to conduct time-costing repeated circular scanning to obtain a 3D dataset and penface images, which seriously reduces the temporal resolution of motion tracking, and its data processing algorithms are also complex for dealing with 3D datasets. Meanwhile, the Penface method has not demonstrated whether it can perform depth-resolved motion tracking.
Here we proposed a depth-resolved transverse-plane motion tracking technique with configurable measurement features via OCT, termed OCT-MT, based on OCT circular scanning combined with speckle spatial (SS) oversampling. The proposed OCT-MT can perform depth-resolved transverse-plane motion tracking with broad-configurable measurement ranges and resolutions by configuring A-line number, circular scanning radius, and A-line scanning time, which has obvious advantages over that of methods mentioned above. Meanwhile, benefitting from the depth-resolved motion tracking feature and the optical interference, the proposed OCT-MT can better adapt to the input power of the irradiation signal and the surface reflectivity and roughness of the target, than conventional laser methods when performing motion tracking. In the proof-of-concept experiments, we tested the proposed OCT-MT on Scotch tape and demonstrated that the proposed technique, OCT-MT, may extend the ability of motion tracking for OCT in addition to imaging.
2. Methods
2.1 Circular scanning combined with speckle spatial oversampling
Optical coherence tomography based on interferometry techniques inevitably has speckle [10,11], and speckle can also contain information. Speckle can indicate the sample voxel structure and performing spatial-frequency analysis of OCT images containing speckle can indicate the speckle spatial relative frequency of OCT images. In our proposed OCT-MT, we combine OCT circular scanning and speckle spatial oversampling to perform depth-resolved transverse-plane motion tracking. When performing the SS sampling, it can obtain a signal sequence of SS sampling which can be treated as a mathematical series [12] of the speckle patterns contained. By further performing the spatial-frequency analysis of the signal sequence of SS sampling, it can obtain the distribution of speckle spatial relative frequency $f$. Therefore, by performing OCT circular scanning on the moving target which modulates the values of $f$ and leads to different distributions of $f$, the proposed technique ultimately achieves transverse-plane motion tracking, as Fig. 1 shows. More information about f can be found in the following.
Fig. 1. OCT system and circular scanning mode with SS oversampling. (a) OCT system, (b) circular scanning mode with SS oversampling. FC: fiber coupler, PC: polarization controller, GS: galvanometer scanner, L1-L4: lens.
The key part of the proposed technique is the OCT scanning mode used, and here circular scanning combined with the SS oversampling is used, as Fig. 1 shows. OCT circular scanning shows that OCT performs beam scanning along a circular track with an OCT light-beam circular scanning speed of ${v_s}\textrm{ = 2}\pi r/{N_A}{t_e}$, where r is the circular scanning radius of the OCT sample arm light beam, ${t_e}$ is the A-line scanning time used, and ${N_A}$ is the A-line number per circular scanning. Here performing SS oversampling is to make sure that the distance between two adjacent A-line is smaller than the OCT transverse optical resolution to increase the speckle spatial sampling frequency ${f_s}$ of SS sampling and reduce f to avoid the measurement saturation of f.
2.2 Motion-tracking principle
When performing OCT circular scanning on a moving sample with a motion velocity of ${\vec{v}_m}$, the OCT circular scanning beam has a sample-relative motion velocity $\vec{v} = {\vec{v}_S} + {\vec{v}_m}$ that changes at different scanning positions, as Fig. 1(b) shows. The changing $\vec{v}$ further leads to different distances $d({{A_i},{A_{i + 1}}} )$ between the two adjacent A-lines ${A_i}$ and ${A_{i + 1}}$ at different positions in the scanning circle, approximatively given by Eq. (1), where $\theta $ is the angle between the OCT light-beam circular scanning velocity ${\vec{v}_s}$ and the sample transverse motion velocity ${\vec{v}_m}$. When performing OCT circular scanning, we can obtain a signal sequence $\textrm{A} = [{{A_1},{A_2}, \cdot{\cdot} \cdot ,{A_N}} ]$ of SS sampling, which can be defined by the mathematical series [12] of the speckle patterns contained, and the signal sequence $\textrm{A}$ contains different f. Here f means the calculated speckle spatial frequency obtained from performing spatial-frequency analysis on the signal sequence $\textrm{A}$, as the following shows in Fig. 2.
Fig. 2. Main data processing flow to obtain the distribution of the speckle spatial relative frequency $\; f$. To display the results better, shifting zero-frequency component to center of spectrum and colormapping were performed in the following results, such as the obtained results of the spatial-frequency distribution.
Because the speckle is related to the sample structure, the changing distance $d({{A_i},{A_{i + 1}}} )$ indicates that the difference between speckles located at A-line ${A_i}$ and ${A_{i + 1}}$ changes at different circular scanning positions. Therefore, when the bigger difference speckles located at A-line ${A_i}$ and ${A_{i + 1}}$ has, the higher speckle spatial relative frequency f it contains. The changing distance $d({{A_i},{A_{i + 1}}} )$ during the SS sampling indicates that the f contained in the signal sequence $\textrm{A}$ changes during the circular scanning. When performing the spatial-frequency analysis, it can further acquire the distribution of f. Therefore, The above indicates that it can track transverse-plane motion containing the motion speed and direction by measuring the amplitude and distribution of f of the circular scanning, as Eq. (2) shows. Equation (2) indicates how to calculate the difference $\varDelta f$ between the maximum and minimum values ${f_{max}}$ and ${f_{min}}$ of f during the circular scanning, and $\varphi $ is the mapping function between the motion speed ${v_m}$ and $\Delta f$. More details are shown in the following sections. Here ${f_r}$ and $\Delta v$ used below are defined as the motion-tracking measurement resolution of f and speed resolution, respectively.
In more technical detail, the transverse-plane motion velocity ${\vec{v}_m}$ along the X-Y plane. Here $\alpha $ indicates the angle between the X-axis and ${\vec{v}_m}$, and $\beta $ is the angle between the inverse Y-axis and ${\vec{v}_S}$, which can be expressed as $\beta = 2\pi t/{N_A}{t_e}$ at the time t when circular scanning starts at Position D in Fig. 1(b). From Eq. (1), when the sample motion velocity ${\vec{v}_m}$ has the same motion direction as the circular scanning velocity ${\vec{v}_s}$ (A-line ${A_{m1}}$), which means $\theta = {0^o}$, the distance d has its minimum value and the speckle spatial relative frequency f has its minimum value, while when the sample motion velocity ${\vec{v}_m}$ has the inverse motion angle to the circular scanning velocity ${\vec{v}_s}$ (A-line ${A_{m2}}$), which means $\theta = {180^o}$, the distance d has its maximum value and f has its maximum value. Here we set it scanned counterclockwise starting from Point D, then the motion angles of the circular scanning velocity at A-lines ${A_{m1}}$ and ${A_{m2}}$ can be given by Eq. (3), and the angle $\mathrm{\alpha }$ of the sample motion velocity ${\vec{v}_m}$ can be given by Eq. (4). Equation (3) indicates how to calculate the angles ${\beta _1}$ and ${\beta _2}$ of points having the maximum and minimum values ${f_{max}}$ and ${f_{min}}$ of f, and Eq. (4) further indicates how to calculate the motion directions measured after obtaining the angles ${\beta _1}$ and ${\beta _2}$.
2.3 Data processing
Figure 2 shows the main data processing flow of the proposed OCT-MT technique. After performing circular scanning combined with SS oversampling, the backgrounds of the circular scanning images were first removed, then the windowed Fourier transform operation [13] was performed on signal intensities of imaging depth Z(i). After performing windowed Fourier transform and further obtaining the spectrogram using Eq. (5), shifting zero-frequency component to center of the spectrum and color mapping were conducted to obtain the spatial-frequency distribution. Then edge fitting was further performed to obtain the maximum and minimum values ${f_{max}}$ and ${f_{min}}$ of f.
When conducting the spatial-frequency analysis, a Gaussian window was used for the windowed Fourier transform. The width ${S_w}$ and the moving step ${S_m}$ of the Gaussian window were 96 and 10 to balance the spatial and frequency resolutions and the time consuming of the spatial-frequency analysis. To obtain higher precision calculated measurement results when performing the windowed Fourier transform, the proposed can use a larger window width ${S_w}$ and a smaller moving step ${S_m}$.
3. Experiments and results
3.1 Experimental setup
The proposed OCT-MT technique can use any conventional OCT system. Here we built a conventional spectral-domain OCT (SD-OCT) setup as the experimental hardware and its schematic for SD-OCT is shown in Fig. 1(a), with the axial and transverse optical resolutions of ∼2.5 µm and ∼8.5 µm, respectively. In the proof of concept experiments, we demonstrated the transverse-plane motion tracking performance of OCT-MT by imaging Scotch tape as the moving sample. Scotch tape was pasted on a two-dimensional motion stage; the A-line scanning time ${t_e}$ was $25.0\;\mathrm{\mu s},$ and the corresponding system sensitivity was $101\;\textrm{dB}$. In the proof-of-concept experiments, the circular scanning radius r was $1\;\textrm{mm}$, and the A-line number ${N_A}$ used was 4000 per scanning circle. To demonstrate the proposed technique, we performed circular scanning using the above parameters with the sample Scotch Magic tape moving at different speeds in different directions and depths.
3.2 Experimental results
Figure 3(a) shows the OCT circular scanning imaging results of the moving Scotch tape at a speed of 20 mm/s along the X-axis. Figure 3(b) shows the corresponding distribution of f acquired by performing a spatial-frequency analysis using the windowed Fourier transform. Figure 3(c) shows the amplitude distribution of f and its corresponding edge fitting (the red line). As Fig. 3(a) shows, images of some positions appear to be compressed, while images of some positions appear to be stretched, which is caused by the changing f at different scanning positions.
Fig. 3. OCT circular scanning results and corresponding measurement results of the proposed OCT-MT. (a) OCT image having 4000 A-lines using circular scanning, (b) corresponding distribution of f, and (c) the distribution of f and corresponding edge fitting (red line), obtained using the proposed OCT-MT.
Figure 4 shows the quantitative measurement results, and Fig. 4(a) shows the measured motion directions of different motion directions with the same motional speed, and Fig. 4(b) shows the measured differences of f when the sample moves at different speeds along the same motion direction. From Fig. 4, we can see that different motion speeds have correspondingly different difference amplitude intensities of f, and the motion direction can also be measured in the transverse plane. Our proposed technique is based on the mapping between the motion speed ${v_m}$ and differences $\Delta f$ of f, while f is limited by the speckle size which is determined by the OCT setup including 3D point spread function (PSF), so it can be expected that the $\varDelta f$ of f is convergent as the measured motion speed increases. That is why the nonlinearity can be observed in Fig. 4(b).
Fig. 4. Measurement results. (a) Measured motion direction results of different motion directions with the same motional speed, and (b) the difference results $\varDelta f$ of f with different motion speed in the same motion direction. The red points are the measured difference intensities of f, and the blue curve is the fitting curve of the red points using the negative natural exponential function.
Fig. 5. Measurement distribution results of f along with different motion directions at the same motion speed. The directions of the blue arrowhead in the center indicate the corresponding motion direction of the sample in the X-Y transverse plane.
Figure 5 shows the measured distributions of f acquired when the sample moves in different directions at the same speed in the transverse plane. From Fig. 5, we can see that different sample motion directions have different shapes of the f distributions, and when performing motion tracking, the motion directions can be measured using Eq. (4).
Because OCT has depth-resolved capabilities, and the proposed technique uses the windowed Fourier transform of the transverse pixel values of depth Z(i) shown in Fig. 2 and Eq. (5), OCT-MT can achieve a depth-resolved velocity profile. We also performed the proof-of-concept experiments to demonstrate it. We put two tapes close to each other, the upper tape was fixed on the sample arm but in front of the scanning lens using Thorlabs 30 mm cage system model, and the bottom tape was taped on the motion stage. There was ultrasound gel between the two tapes to reduce the surface reflection between them. Then we drove the two-axis motion stage to achieve the upper tape is motionless while the bottom tape was moving at speed of 14 mm/s, and performed circular scanning, as Fig. 6 shows. Here we used the region-averaged motion tracking results in Fig. 6(b) and (c) to reduce the statistical error and improve the measurement accuracy.
Fig. 6. Measurement results of depth-resolved motion tracking. (a) OCT image of the upper and bottom tapes moving with different velocities, (b) and (d) measurement f distribution results of the upper tape without motion, (c) and (e) measurement results of the moving bottom tap.
Figure 6(a) shows the circular scanning results, Fig. 6(b) - (e) show the measurement results. From Fig. 6(a) we can see that the bottom OCT images (corresponding to the bottom moving tape) of some positions appear to be compressed while images of some positions appear to be stretched; there is no such phenomenon happened for the upper OCT images (corresponding to the upper motionless tape). Figure 6(b) and Fig. 6(c) quantitatively show the distribution of f, and Fig. 6(d) and 6(e) further show the measurement results of motions at different depths. Therefore, results in Fig. 6 have proved that the proposed method has the potential to perform depth-resolved transverse-plane motion tracking.
5. Discussion and conclusion
The above proof of concept experimental results have demonstrated that OCT-MT has the potency to perform depth-resolved transverse-plane motion tracking. In our proposed motion tracking method, performing OCT imaging along a scanning circle means conducting the SS sampling on a specific speckle spatial signal defined by the scanning radius. Therefore, when performing SS sampling using the circular scanning as Fig. 1 shows, from the Nyquist-Shannon sampling theorem [14], we can see that the sampling number ${N_A}\; $ and frequency ${f_\textrm{s}}$ affect the motion-tracking measurement resolution and range. In detail, the more sampling number ${N_A}$ per unit length it has, the higher spatial sampling frequency ${f_\textrm{s}}$ it has, as Eq. (6) shows. Here Eq. (6) indicates the numerical expressions of ${f_s}$ and ${f_r}$. Therefore, it has a higher ${f_\textrm{s}}$ when using a larger ${N_A}$. Its corresponding measurement resolution ${f_r}$ of ${f_\textrm{s}}$ will also be more precise when using a larger $\Delta f$, as the following Eq. (6) proves.
Meanwhile, since the SS oversampling signal sequence A is defined by the mathematical series of the speckle patterns contained, so OCT circular scanning radius r and A-line scanning time ${t_e}$ also affect the measurement performance of the proposed method, because r affects the speckle pattern number contained in the SS sampling sequence A and the contained speckle pattern number will further affect the measured f; ${t_e}$ affects the relative velocity $\vec{v}$ of the circular scanning velocity ${\vec{v}_s}$ and the sample motion velocity ${\vec{v}_m}$, which affects the ${f_s}$. Here the measurement resolution of f is the same as the measurement resolution ${f_r}$ mentioned above, and more detailed discussions and experiments results are shown below.
In terms of the measurement range and resolution, the SS sampling number ${N_A}$ and frequency ${f_s}$ affect the motion-tracking measurement resolution and range. As shown in Fig. 1(b), when the sample motion speed ${v_m}$ is equal to the OCT light-beam scanning speed ${v_s}$, the relative speed v will be zero, which means that it's close to sampling at the same position when the relative speed closes to zero. Performing SS sampling at the same position indicates that f is zero. Therefore, the max motion-tracking measurement speed of the proposed method is the OCT light-beam scanning speed. Meanwhile, because the proposed method is based on the difference of f, and different ranges of f are the reflections of different measurement speed ranges, so a smaller measurement motion-tracking speed range with a non-declined sampling number means a more accurate measurement motion-tracking speed resolution.
When performing OCT imaging on a moving sample, the A-line scanning time ${t_e}$ affects OCT light-beam scanning velocity ${\vec{v}_S}$, and further affects the relative velocity $\vec{v}$ of OCT light-beam scanning velocity ${\vec{v}_S}$ and the sample motion velocity ${\vec{v}_m}$. A larger ${t_e}$ will reduce the circular scanning speed ${v_s}$ which further reduces the motion-tracking measurement speed range. A larger ${t_e}$ will lead to a longer motion-track length l because the moving sample will have a longer motion-track length for more moving time. A longer motion-track length l reduces ${f_s}$ when the sample is moving, which indicates a more accurate ${f_r}$, as Eq. (6) shows. A smaller measurement motion-tracking speed range combined with a non-declining sampling number ${N_A}$ indicates a more accurate measurement motion-tracking speed resolution $\Delta v$. Meanwhile, a longer l indicates a higher f in our proposed motion tracking method because of more speckle patterns contained. Figure 7(a) and 7(b) show the measurement distribution results of f when 25 µs and 50 µs A-line scanning time are used, respectively, and the sample is motionless. Figure 7(c) and 7(d) show the measurement distribution results of f when 25 µs and 50 µs A-line scanning time are used, respectively, and the sample is moving.
Fig. 7. Measurement distribution results of f when using different A-line scanning times. (a) and (b) measurement distribution results of f when 25 µs and 50 µs A-line scanning time used, respectively, and the sample is motionless. (c) and (d) measurement distribution results of f when 25 µs and 50 µs A-line scanning time used, respectively, and the sample is moving. Here the axial unit in the figure is the measurement resolution ${f_r} = \frac{{{f_s}}}{{{N_A}}}$.
From Fig. 7(a) and Fig. 7(b), we can see that A-line scanning time ${t_e}$ doesn’t affect the speckle spatial sampling frequency ${f_s}$ and relative frequency f when the imaged sample is not moving. However, when the sampling is moving, a longer motion-track length l results in a higher f in our proposed motion tracking method and a lower ${f_s}$, as Fig. 7(c) and Fig. 7(d) show. Figure 7(c) and Fig. 7(d) also show a larger ${t_e}$ leads to a lager $\Delta f$ indicating a small measurement speed range, and a more accurate ${f_r}$. Therefore, a larger ${t_e}$ will reduce the motion-tracking measurement speed range and ${f_s}$ indicating a precise motion-tracking measurement speed resolution $\varDelta v$.
When the scanning radius r and A-line scanning time ${t_e}$ are fixed, adding the A-line number ${N_A}$ used in a scanning circle will reduce the circular scanning speed ${v_s}$, which indicates a smaller motion-tracking measurement speed range. From the Nyquist-Shannon sampling theorem, we can see that ${f_s}$ will increase because the averaged relative speed $\bar{v}$ will reduce, as Eq. (6) shows. Meanwhile, when increasing the A-line number ${N_A}$, the measurement resolution ${f_r}$ of ${f_s}$ will be more precise because the motion time for the moving sample will increase and the motion-track length l will be larger consequently, which indicates a more precise measurement motion-tracking speed resolution , as Eq. (6) and Eq. (2) shows. Figure 8(a) and 8(b) show the measurement distribution results of f when 4000 and 6000 A-line are used, respectively, and the sample is motionless. Figure 8(c) and 8(d) show the measurement distribution results of f when 4000 and 6000 A-line are used, respectively, and the sample is moving at a fixed motion velocity.
Fig. 8. Measurement distribution results of f when using different A-line numbers per scanning circle. (a) and (b) measurement distribution results of f when 4000 and 6000 A-line used, respectively, and the sample is motionless. (c) and (d) measurement distribution results of f when 4000 and 6000 A-line used, respectively, and the sample is moving. Here the axial unit in the figure is the measurement resolution ${f_r} = {f_s}/{N_A}$.
From Fig. 8(a) and Fig. 8(b), we can see that increasing the A-line number per scanning circle ${N_A}$ enlarges ${f_s}$. From Fig. 8(c) and Fig. 8(d), we can see that increasing the A-line number per scanning circle ${N_A}$ can obtain a more accurate measurement resolution ${f_r}$ of f. Therefore, a smaller measurement motion-track speed range combined an increased sampling number ${N_A}$ indicates a more accurate motion-tracking measurement speed resolution $\varDelta v$, as Eq. (2) also proves. Therefore, a larger A-line number per scanning circle ${N_A}$ will reduce the motion-tracking measurement speed range but enlarges ${f_s}$, it also obtains a more precise motion-tracking measurement speed resolution $\varDelta v$.
When the A-line number per scanning circle ${N_A}$ and A-line scanning time ${t_e}$ are fixed, increasing the scanning radius r will enlarge the motion-track length l, reduce ${f_s}$, and increase speckle pattern number in the corresponding SS sampling signal sequence A, and more speckle patterns in the SS sampling sequence A will further increase f. Meanwhile increasing the scanning radius r will enlarge the scanning speed ${v_s}$, which further enlarges the motion-tracking measurement speed range. A longer motion-track length l indicates a smaller ${f_s}$ and a more accurate resolution ${f_r}$. However, for the measurement motion-tracking speed range becomes larger and the sampling number ${N_A}$ is not added, the measurement motion tracking speed resolution $\Delta v$ will be worse, as Eq. (2) shows. Figure 9(a) and 9(b) show the measurement distribution results of f when 0.5 mm and 1 mm scanning radius are used, respectively, and the sample is motionless. Figure 9(c) and 9(d) show the measurement distribution results of f when 0.5 mm and 1 mm scanning radius, respectively, and the sample is moving.
Fig. 9. Measurement distribution results of f. when using different scanning radius. (a) and (b) measurement distribution results of f when 0.5 mm and 1 mm scanning radius used, respectively, and the sample is motionless. (c) and (d) measurement distribution results of f when 0.5 mm and 1 mm scanning radius, respectively, and the sample is moving. Here the axial unit in the figure is the measurement resolution ${f_r} = {f_s}/{N_A}$.
From Fig. 9(a) and 9(b) and Eq. (6), we can see that increasing the scanning radius r reduces ${f_s}$ but increases f for more speckle patterns are in the SS sampling sequence A. From Fig. 9(c) and 9(d), we can see that increasing the scanning radius r worsens the motion-tracking measurement speed resolution $\varDelta v$. However, a too larger scanning radius will make f larger than the measurement frequency range ${f_s}/2$, which further leads to the measurement saturation and reduces the measurement motion-track speed range. Therefore, a larger scanning radius r will reduce ${f_s}$ but increase the motion-tracking measurement speed range, it obtains a less precise motion-tracking measurement speed resolution $\Delta v$, while a too larger scanning radius r will also lead to the measurement saturation and lower the measurement motion-track speed range.
From the above, we can further see that the proposed OCT-MT technique has configurable measurement ranges and resolutions by configuring the circular scanning radius $\; r$, A-line scanning time ${t_e}$, and A-line number ${N_A}$. Increasing A-line number per scanning circle ${N_A}$ can increase ${f_s}$, which decreases the measurement speed range and direction resolution, and optimizes the measurement speed resolution. Increasing scanning radius r will increase f for more speckle patterns contained in the scanning circle, and enlarges the measurement speed range but worsens a better measurement speed resolution. Increasing ${t_e}$ will increase the measurement speed resolution, but decrease the measurement speed range.
Meanwhile, when using the windowed Fourier transform to obtain the spectrogram and further calculate the motional speed and direction, Eq. (5) shows, it also indicates the calculational motion tracking speed and direction resolutions are affected by the window size and of the windowed Fourier transform. A larger window size gives better speed resolution but poor direction resolution, while a narrower window gives good direction resolution but poor speed resolution, due to the uncertainty properties of the Fourier transform [15]. The balance of measurement resolutions of the calculational motional speed and direction can be further optimized by using the wavelet transform [16] and multiresolution analysis [17]. Different from the Penface method [9] requiring time-costing repeated circular scanning to obtain the 3D dataset, our proposed technique just uses one circular scanning, however, it still has a measurement temporal resolution that can be optimized by using suitable circular scanning parameters. Here we must point out that by now one shortage of this research is that the full mathematical figuration of the proposed is still missing, which will be the key part of our future work.
The proposed technique also has its limitations, nevertheless. Not all imaged structures may show speckle in the OCT images, and the speckle is affected by the sample structures and OCT setup parameters including the numerical aperture of the scanning lens used, therefore our proposed technique may meet some challenges, such as when the speckle size is similar to electronics noise size, which may reduce the stability of the proposed technique. In the proposed technique, it uses the windowed Fourier transform of the transverse pixel values, as Fig. 2 shows, and the axial motion will lead to pixel offset when the axial motion speed is too fast, therefore the axial motion may also affect the performance of the proposed technique, and the pixel offset should be corrected before the windowed Fourier transform. Meanwhile, Defocusing is another factor that may affect the performance of the proposed technique, for defocusing enlarge the speckle size. The work of Hendrik Spahr, et al. [18] has shown some interesting results indicating how defocusing affects motion tracking.
In conclusion, we proposed a new depth-resolved transverse-plane motion tracking technique with configurable measurement features via OCT, termed OCT-MT. The proposed technique can enable depth-resolved motion tracking with configurable measurement ranges and resolutions. Meanwhile, benefitting from the optical interference, the proposed OCT-MT can reduce the requirements on the input power of the irradiation signal and the surface reflectivity and roughness of the target when performing motion tracking, as the tape experiments demonstrated. Such a method may expand the ability of motion tracking for OCT in addition to imaging and would be valuable for various applications, such as eye-tracking and microfluidics rheometry.
Funding
National Natural Science Foundation of China (61905036); China Postdoctoral Science Foundation (2019M663465, 2021T140090); Fundamental Research Funds for the Central Universities (University of Electronic Science and Technology of China) (ZYGX2021J012, ZYGX2021YGCX019).
Acknowledgment
We thank Professer Chao Zhou and all members of Z-lab for their kindly help.
Disclosures
The authors declare no conflicts of interest.
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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