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Abstract
Optical coherence tomography (OCT) is a high-speed non-invasive cross-sectional imaging technique. Although its imaging speed is high, three-dimensional high-spatial-sampling-density imaging of in vivo tissues with a wide field-of-view (FOV) is challenging. We employed convolved Lissajous and slow circular scanning patterns to extend the FOV of retinal OCT imaging with a 1-µm, 100-kHz-sweep-rate swept-source OCT prototype system. Displacements of sampling points due to eye movements are corrected by post-processing based on a Lissajous scan. Wide FOV three-dimensional retinal imaging with high sampling density and motion correction is achieved. Three-dimensional structures obtained using repeated imaging sessions of a healthy volunteer and two patients showed good agreement. The demonstrated technique will extend the FOV of simple point-scanning OCT, such as commercial ophthalmic OCT devices, without sacrificing sampling density.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical coherence tomography (OCT) is a high-resolution, three-dimensional (3D) visualization modality of biological tissues [1,2]. It is widely used in clinical ophthalmology for diagnosing and monitoring retinal diseases [3,4]. Although high-spatial-resolution tomographic imaging is useful, the conventional OCT field-of-view (FOV) is narrower than that of other modalities. Extending the FOV by simply reducing the spatial sampling density, however, reduces the benefits of the high spatial resolution; high-density spatial sampling is required to resolve fine structures [5,6]. The extension of the OCT imaging FOV with high-density spatial sampling enables the 3D investigation of microstructures and microvasculatures over a wide range.
However, it is difficult to achieve wide FOV and high spatial resolution OCT in in vivo human eye imaging. The acquisition of 3D volumetric OCT takes a long time, that is, several seconds using commercial OCT devices (typically ~100,000 A-lines/s). Three-dimensional volumetric and en face imaging obtained using Fourier-domain OCT suffer from the effects of eye movements and require motion correction [7–9]. Using an ultrahigh-speed OCT system, wide FOV imaging with a short acquisition time is possible [10–13]. However, this imaging requires expensive devices, such as ultrahigh-speed wavelength-swept lasers or high-speed cameras. In addition, the reduced exposure time decreases the sensitivity of the system. High-dense spatial sampling with a wide FOV requires a longer acquisition time. When performing 3D volumetric imaging with high-density spatial sampling in a short acquisition time, the FOV is limited.
One approach to extending the FOV is to stitch together multiple images that have been shifted. Several OCT stitching have been demonstrated [14–17] in en face 2D space. Stitching of multiple volumetric images even with coarse sampling densities requires a sophisticated algorithm to connect structures smoothly [18]. Stitching dense-sampled volumes smoothly would be challenging because more volume is required and finer structures are visualized.
We have developed Lissajous OCT [19,20], which enables motion-free 3D volumetric imaging. Because temporally short segments multiply overlap in space, registering them results in high consistency in fine structures. In this scanning mode, a wider FOV is covered by continuously and slowly shifting the scanning location.
In this paper, we demonstrate an extended FOV of retinal OCT imaging with high-density spatial sampling. A method that combines a Lissajous scan pattern and a slow shift, called convolutional Lissajous scanning, is employed. First, we discuss a feasible convolutional Lissajous scan pattern design and analyze its performance. Then, in vivo imaging of a healthy volunteer and patients was performed using a convolutional Lissajous scan. The evaluation of the correction was performed by comparison with fundus photography and of repeated scans. Three-dimensional volumetric imaging of the eyes of several patients is demonstrated.
2. Methods
The concept of the convolutional Lissajous scan OCT method is shown in a schematic diagram Fig. 1. The probe beam is scanned with a Lissajous trajectory, and they are slowly shifted during a long acquisition time. The sampling location of the Lissajous scan is shifted during the slow shift, and sampling density and imaging FOV are increased. Even with eye movements, short segments of time are considered rigid. The coverage areas of the segments overlap and have shifted slightly over time. Retinal motion is estimated by registering short segment data with each other. Due to the long acquisition time, the eyes blink and cause saccades several times during that time. Acquired data will be blank and corrupted during blinks and saccades, respectively. Because multiple segments at different timing overlap, other segments fill corresponding locations. The following subsections describe the design of the scanning pattern (Section 2.1), system setup and signal processing (Section 2.2 and 2.3), and motion estimation and correction (Section 2.4).
Fig. 1. Convolutional Lissajous scanning pattern in 3D spatio-temporal space and en face OCT images of short segments at several time points.
2.1 Convolutional Lissajous scanning pattern
A convolutional Lissajous scan is achieved by driving the beam scanner with a combination of the basic Lissajous scan pattern $(x_b, y_b)$, which rapidly oscillates, and a slow shifting pattern $(x_s, y_s)$, as follows:
The basic Lissajous scanning pattern consists of sinusoidal functions with slightly different frequencies in orthogonal directions: where $(A_x, A_y)$ and $(f_x, f_y)$ are the scanning amplitudes and frequencies of the basic Lissajous trajectory along the horizontal and vertical directions, respectively. Here, $f_x$ and $f_y$ satisfy the relationship where $N (\in \mathbb {N}^{*})$ is a positive integer. The existence of $N$ means that there is a fundamental period $T = (f_x - f_y)^{-1}$ of the basic Lissajous scanning pattern [21].In this manuscript, we apply the following circular pattern as a slow shift:
Fig. 2. Lissajous scanning pattern with slow circular shift. blue curve: convolutional Lissajous trajectory, black curve: slow shift trajectory, black dots: starting points, and red crosses: end points.
The radius of the circular shift $R_{\mathrm {s}}$ should be carefully selected. A large radius extends the FOV more; however, it increases the risk of gaps at the center of the FOV. Moreover, $R_{\mathrm {s}}$ should be smaller than $(A_x^{2} + A_y^{2})^{\frac {1}{2}}$, otherwise there is a gap at the center. Although the radius is smaller than this limit, there is a risk of gaps due to the motion of the object. There should be a safe margin to avoid a gap at the center; $R_{\mathrm {s}} = r (A_x^{2} + A_y^{2})^{\frac {1}{2}}$, where $r < 1$ is the safe margin factor. In this study, we choose $r = 0.9$. Then, the FOV is $2 (A + R_{\mathrm {s}}) = 2 A (1 + \sqrt {2}r)$, when $A = A_x = A_y$. This extends the imaging FOV by $1 + \sqrt {2}r$ times.
An example of the scanning trajectory ($N$ = 15) of the convolution of Lissajous and circular slow shift scans ($r$ = 0.9) is shown in Fig. 3(a). The phase of the slow circular shift is $\phi _{\mathrm {s}} = \pi /4$, which sets the starting point of the scanning at the bottom-right corner [red dot in Fig. 3(a)]. The scanning trajectory is continuously moving and extends the imaging FOV. Note that the vertical position $y$ increases from top to bottom in Fig. 3. This is to match the orientation of the en face images that appear in the following figures, which correspond to the anatomical positional relationships. The designed scanning position values are input as control voltages for the galvanometer scanning mirrors, but the sign correspondence varies depending on the configuration of the device and the way the coordinate axes are taken. In the configuration of the device used in this study, increasing the vertical control voltage results in scanning from the superior to the inferior retina.
Fig. 3. Simulation of a convolutional Lissajous scanning pattern. (a) Trajectory of a convolutional Lissajous scan pattern ($N$ = 15), which is the continuously shifted basic Lissajous scan trajectory, covers a wider imaging field. (b) Sampling density of the designed convolutional Lissajous scan ($N$ = 181, $A$ = 1.5 mm, $f_{\mathrm {s}} = 1/8T$, $r$ = 0.9, and $\phi _{\mathrm {s}} = \pi /4$).
The scanning pattern is then modified to repeat each fast horizontal cycle to enable OCT angiography. See the detais in Section S1.
2.1.1 Sampling density with the basic Lissajous scan
The sampled data is going to be assigned to a Cartesian grid to reconstruct images. The minimum grid size required to fill all grids with sampling points is a suitable metric for the sampling density. In the case of the basic Lissajous scan with $\Delta L$ = 2, this can be approximated by the square with its edge length as the maximum distance of successive sampling points $\Delta l_{\max }$ (Fig. S1) as follows:
where $\Delta l_{\max }$ is the maximum distance between successive A-lines. It is approximately the product of the maximum scanning velocity and sampling interval $1/f_A$. The maximum scanning speed can be approximated as $\sqrt {A_x^{2} (2 \pi f_x)^{2} + A_y^{2} (2 \pi f_y)^{2}}$ [21]. The maximum distance between successive A-lines can be expressed using Eqs. (S16) and (3) as2.1.2 Designed scanning pattern and numerical simulation
The scanning speed of the slow circular shift $V_s = \sqrt {\dot {s}_x^{2} + \dot {s}_y^{2}}$ described in Eq. (4) is
It should not be too fast to avoid gaps. Previous Lissajous scan OCT studies [19,20,22] suggest that a Lissajous scan can image the target area without significant gaps caused by eye drift. In this study, we define the scanning pattern as $N$ = 181, $A_x = A_y = A$ = 1.5 mm, $M$ = 2, $f_{\mathrm {s}} = 1/8T$, $r$ = 0.9, and $\phi _{\mathrm {s}} = \pi /4$ by considering a sampling rate of 100,000 A-lines/s and a simulation of spatial sampling density. Here, $f_{\mathrm {s}} = 1/8T$ means that during one period of the slow circular shift, the basic Lissajous scan pattern is iterated eight times. From Eq. (S6), $T$ = 261,364/$f_A$ and $f_s$ = 0.0478 Hz ($f_A$ = 100 kHz). The scanning frequencies of the basic Lissajous pattern are $f_x$ = 138.50 Hz and $f_y$ = 138.12 Hz [Eq. (S5)]. The slow circular speed $V_s$ is around 574 $\mathrm {\mu }\textrm {m}$/s, which is on the same order as the speed of eye drift (see Section 4.1). Note that the total scanning time for one period of the convolutional Lissajous scan is longer than $1/f_s = 8T$ because of the repetition of fast cycles for OCTA and a margin between repeated cycles $\Delta T$. The scanning time of one period of the designed scan pattern is $8 \times {} T' \simeq {}$ 42 s. The 2D histogram of the simulated sampling points obtained using these designed parameters [Fig. 3(b)] exhibits at least one sample within the scanning region with a bin size (13 $\times {}$ 13 $\mathrm {\mu }\textrm {m} ^{2}$). The designed pattern results in the minimum grid size required to achieve a 100% grid fill rate for the basic Lissajous scan sampling α100% = $18^{2}$ $\mathrm {\mu }\textrm {m}^{2}$. The selected bin size results in a fill rate of approximately 50% at the center of the basic Lissajous scan sampling. The simulation of the convolutional Lissajous scan shows that almost all grids are filled by the sampling points in the scanning area.2.2 OCT setup and OCT signal reconstruction
A 1-$\mathrm {\mu }\textrm {m}$ swept-source OCT system with polarization-diversity detection [23] was used for the experiment. This system has a scan rate of 100,000 A-lines per second and 6.2-$\mathrm {\mu }\textrm {m}$ axial resolution. The signal was recorded using a $k$-clock and wavelength trigger generated by a fiber-Bragg grating. The OCT signal was reconstructed by Fourier transform, numerical dispersion compensation, and fixed-pattern-noise removal.
2.3 OCT intensity and OCT angiography signal generation
Using the repeated scanning cycle, OCT intensity and OCT angiography signals were generated by using repeated cycles. The OCT intensity signal $I$ was calculated by summing the squared amplitude of the two polarization channels over the repeated cycles.
The OCTA signal was reconstructed by calculating temporal complex correlation coefficient, $r_s(x'_{i, n}, y'_{i, n}, z)$[24,25]. The window size is 5 pixels along the axial direction (~21.6 $\mathrm {\mu }\textrm {m}$). False high-flow signals in the low-signal regions due to noise were suppressed by the noise-immune correlation calculation [25].
2.4 Eye-motion corrected imaging
Three-dimensional motion estimation and correction were applied. First, the lateral motion was estimated with en face projection images. Then, the 3D OCT intensity volume and estimated lateral motion were used for axial motion estimation and correction.
2.4.1 Lateral motion estimation
In the lateral motion estimation step, multiple en face projection images, i.e., the OCTA of the entire depth, mean projection of the OCT amplitude, and mean and maximum projections of the log-scaled OCT intensity, were used [22]. Each projection was split into strips $\mathbf {S}_{m, k}(x'_{i, n}, y'_{i, n})$, which denotes $m$-th strip of $k$-th projection type. The rapid eye movements were detected by line artifacts because of the high de-correlation in the OCTA projection, and eye blinks were identified by blanks in the OCT projection [20]. The data affected by the rapid eye movements and eye blinks were discarded and split into different strips at these time points. According to the scanning position [Eq. (S13)], each strip was remapped into Cartesian coordinates $(x, y) = (p \delta x, q \delta y)$, $\mathbf {S'}_{m, k, p, q}$. The strips were registered with each other using normalized cross-correlation with multi-image types [22]. The lateral displacements among the strips were first estimated roughly, and then estimated precisely using sub-strips, which are a division of the strips (see Section S5).
2.4.2 Axial motion estimation
The axial motion estimation involves OCT intensity volume and the results of the above lateral motion estimation [19]. The overlap region between a strip and a reference is selected, and OCT intensity data of the region is extracted. Then, the 1D cross-correlation is calculated to estimate the axial displacement among the strip and the reference. The reference is updated by merging data of the registered strip. For details, please see Section S5.
2.4.3 Reconstruction and image formation
To reconstruct 3D volumetric data, each A-line is first shifted according to the axial displacement estimation described in Section 2.4.2. Then, they are transformed into the Cartesian coordinates of the object by taking into account the lateral displacement estimation described in Section 2.4.1.
En face images are generated by first projecting them in the axial direction and then transforming them into the Cartesian coordinates. Each en face slab image is provided by employing the retinal layer segmentation results using the Iowa Reference Algorithms (Retinal Image Analysis Lab, Iowa Institute for Biomedical Imaging, Iowa City, IA, USA) [26–28].
In the lateral remapping into the Cartesian coordinate for both volume and en face data, each data is assigned to a point in the 820 $\times {}$ 820 grid. The data assigned to the same grid point are then averaged.
The retinal blood vessels are surrounded by the tissues of the transparent sensory retina and hence exhibit higher scattering. This can cause the retinal vessels to be contrasted in both OCT intensity and angiography (flow) [29]. To employ both scattering and flow properties, the retinal capillary images were obtained using the maximum intensity projection (MIP) of the product of OCT intensity and complex de-correlation. The en face OCTA projection images of the retinal slabs were calculated by the maximum intensity projection of the product of the complex de-correlation and the log-scaled intensity, as follows:
2.5 Subjects
In vivo human eyes were scanned using the proposed convolutional Lissajous scan pattern. The study was approved by the Institutional Review Boards of Tokyo Medical University and adhered to the tenets of the Declaration of Helsinki. The nature of the present study and the implications of participating in this research project were explained to all study participants, and written informed consent was obtained from each participant before any study procedures or examinations were performed.
2.6 Computational cost
The motion estimations were processed using Python 3.8 (NumPy and CuPy with CUDA 11.2 packages). The personal computer with a central processing unit (CPU: Core i9–7900X, Intel Corporation), 128 GB RAM, and a graphical processing unit (GPU: GeForce GTX 1080 Ti, Nvidia Corporation) has been used. The processing times of the lateral motion estimation and axial motion estimation per volume were around 530 seconds and 150 seconds.
3. Results
3.1 Qualitative evaluation
The right eye of a healthy volunteer (41 years old, male) was scanned with the convolutional Lissajous scan. The macular region OCT intensity and OCTA volumes are shown in Fig. 4. The reconstructed motion-free 3D OCT and OCTA volumes are able to show the arbitrary cross-section of the posterior pole over an area 6.8 mm in diameter [Figs. 4(C), and 4(D)]. Visualization 1 shows virtual radial scanning cross-sections. The reconstructed en face OCTA images are shown in Fig. 5. The superficial retinal OCTA [Fig. 5(A)] visualizes the retinal capillaries. The slab en face OCTA images of the deep capillary plexus [Fig. 5(B)] visualize the capillary. The full-thickness retinal OCTA image was registered with a fundus photograph with rigid transformation, and the vasculatures in both images are in good agreement [Fig. 5(E)]. Retinal capillaries along the nerve fiber are well visualized at the bottom right and top right corners of the superficial retinal OCTA [Fig. 5(A)][16]. The superficial retinal OCTA of a commercial device (DRI-OCT, Topcon) was obtained with a 6 $\times {}$ 6 mm$^{2}$ scanning area and 320 $\times {}$ 320 points [Fig. 5(F)]. In addition, a coarse Lissajous pattern was also used [Fig. 5(G)], which is the same as the basic Lissajous scanning pattern of the convolutional Lissajous scan, except for the scanning range and total acquisition time. This is the same as the scanning pattern of a previous work [22] with larger FOV. The parameters for different scanning patterns are summarized in Table 1. A high-spatial sampling density of the convolutional Lissajous scan visualizes the retinal capillaries more clearly than the coarse raster scan of the commercial device and the coarse Lissajous scan, as also shown in Fig. 5(H). The realized sampling density distributions on the tissue coordinates of the convolution Lissajous scan [Fig. S3A] and the coarse Lissajous scan [Fig. S3B] show that the sampling density of the convolutional Lissajous scan is higher (approximately $\geqq {}$ 5 samples/15$^{2}$ $\mathrm {\mu }\textrm {m}^{2}$) than the coarse Lissajous at the center of the scanning range (≧ 0 samples/152 µm)2. Note that the corresponding sampling density of the raster scan of the commercial device is approximately 0.64/152 $\mathrm {\mu }\textrm {m}^{2}$.
Fig. 4. The en face and arbitrary cross-sectional images of a healthy volunteer eye at the macular region obtained by the convolutional Lissajous scan. (a, b) En face-slice and (c, d) radial-slice images of (a, c) OCT and (b, d) OCTA reconstructed volumes (see Visualization 1). Scale bars are 1 mm.
Fig. 5. The en face projection images of a healthy volunteer eye with the convolutional Lissajous scan (a-d), the fundus photograph with overlapped OCTA (e), OCTA of a commercial OCT device (f), and coarse Lissajous scan (g). The OCTA of the superficial retinal layer (a) vasculature is more apparent than the commercial OCTA (f) and coarse Lissajous scan (g), as also shown in enlarged images at the fovea (h). The OCTA manually registered to the fundus photograph with rigid translation shows that the retinal vessels are in good agreement. Deep capillary plexus and blood flow signal of choriocapillaris are shown in the OCTAs of the deep retinal layer (b) and beneath the RPE (c). The OCT intensity projection of the superficial retinal layer (d) displays the nerve fiber bundles at the temporal side. Scale bars are 1 mm.
Table 1. Parameters for different scanning patterns.
The optic nerve head (ONH) of the subject was also scanned. The virtual cross-sections can be obtained from the reconstructed motion-free OCT and OCTA volumes [Fig. 6]. Visualization 2 shows the arbitrary radial scans. En face slab OCTA images at the ONH are shown in Fig. 7. The superficial retinal OCTA [Fig. 7(A)] clearly visualize the radial peripapillary capillary (RPC). The whole projection OCTA image [7C] visualizes retinal and choroidal vasculature. The superficial retinal OCTA with the coarse Lissajous scan [Fig. 7(D)] exhibits blood flow signals of the RPC. The vasculature is ambiguous at the optic disk. This is because the segmentation algorithm in Lissajous coordinates did not work well due to the different appearance of the optic disc in cross-sectional images [Fig. S5]. The realized sampling densities of the convolutional and coarse Lissajous scans [Fig. S3C and S3D] show that a high sampling density is achieved even in the peripheral region with the convolutional Lissajous scan.
Fig. 6. Cross-sectional images of a healthy volunteer eye with the convolutional Lissajous scan at the ONH. (a, b) En face-slice and (c, d) radial-slice images of (a, c) OCT and (b, d) OCTA reconstructed volumes (see Visualization 2). Scale bars are 1 mm.
Fig. 7. The en face OCTA projection images of a healthy volunteer eye with the convolutional Lissajous scan at the ONH: (a) superficial retinal layer, (b) intermediate capillary plexus, and (c) whole depth; and the coarse Lissajous scan (d). The radial peripapillary capillary is well visualized in the case of convolutional Lissajous scan, as also shown in (e) and (f). Scale bars are 1 mm.
Representative images of pathologic eyes scanned by the designed convolutional Lissajous scan are presented. The first case is the right eye of an age-related macular degeneration (AMD) patient (64 years old, male). Convolutional Lissajous scan images, a color fundus photograph, and a commercial OCTA image are shown in Fig. 8. The realized sampling density distribution on the tissue coordinates of the convolution Lissajous scan is shown in S4A. Owing to high-dense spatial sampling, retinal capillaries are visualized more clearly [Fig. 8(D)] than in the results of a commercial device [Fig. 8(B)], which covers the 6-mm FOV by reducing the spatial sampling density (320 $\times {}$ 320 points). The deep retinal layer OCTA [Fig. 8(E)] visualizes the deep capillary plexus. The slab en face OCTA under the retinal pigment epithelium (RPE) [Fig. 8(F), enlarged in Fig. 8(H)] visualizes the abnormal vasculature well. The orthogonal view [Fig. 8(C)] visualizes abnormal vessels in exudation (green circle) and the elevation of the RPE (light blue arrows). The vasculature of abnormal vessels in exudation is visualized in sub-RPE OCTA [Fig. 8(F), enlaged in Fig. 8(H)]. In Visualization 3, the vitreous cortex, hyper-scattering spots on the retinal surface, and abnormal blood flows that appear under the undulated RPE region are well visualized.
Fig. 8. Right eye with age-related macular degeneration (64 years old, male). (a) Fundus photograph, (b) commercial OCTA at the superficial retinal layer (DRI-OCT, Topcon), (c) orthogonal view of the OCT and OCTA with the convolutional Lissajous scan (see Visualization 3), and en face slab OCTA images of (d) the superficial retinal layer, (e) intermediate slab, and (f) sub-RPE. Convolutional Lissajous scan OCTA image (d) visualizes more retinal capillaries than that of a commercial device (b), as also shown in enlarged images (g). The sub-RPE OCTA (f) shows abnormal vasculature [enlarged in (h)]. Scale bars are 1 mm.
The second example is the left eye of a branch retinal vein occlusion (BRVO) patient (76 years old, male) [Fig. 9]. The realized sampling density distribution on the tissue coordinates of the convolution Lissajous scan is shown in S4B. En face OCTA projection images clearly show the drop in blood flow signals of retinal capillaries and abnormal vasculature [green circles in Figs. 9(B) and Fig. 9(D)]. The superficial retinal OCTA obtained using the proposed method [Fig. 9(D)] also shows more dense retinal capillaries than the results of the commercial device [Fig. 9(B)]. Furthermore, parts of some vessels are only visualized in the case of the convolutional scan [cyan arrows in Figs. 9(E) and Fig. 9(F)]. The blurriness of some blood vessels [red circles in Figs. 9(E) and Fig. 9(F)] may be due to residual registration errors. In the orthogonal view [Fig. 9(C)], complicated abnormal vasculature around the avascular zone and several cysts are observed. In Visualization 4, the complex structure of abnormal vasculature, the fine 3D structure of cysts in the retina, and small deposits in the retina are well visualized.
Fig. 9. Left eye with branch retinal vein occlusion (76 years old, male). (a) Fundus photograph, (b) commercial OCTA at superficial retinal layer (DRI-OCT, Topcon), (c) orthogonal view of the OCT and OCTA with the convolutional Lissajous scan (see Visualization 4), (d) en face superficial retinal OCTA image. Some vessels are visualized in the case of convolutional Lissajous scan but not clearly visualized with the commercial device [cyan arrows in (e) and (f)]. Some vessels are blurred maybe due to residual registration errors [red circles in (e) and (f)]. Scale bars are 1 mm.
The last case is the right eye of the second AMD subject (69 years old, male) [Fig. 10]. The 3D volumetric OCT visualizes the morphology of the disease in wide FOV. The realized sampling density distribution on the tissue coordinates of the convolution Lissajous scan is shown in S4C. In the orthogonal view [Fig. 10(C)], complicated deformed retinal structure and abnormal vasculature (green rectangles) are observed, as also shown in enlarged images [Fig. 10(F)]. In Visualization 5, abnormal vasculature around the avascular zones, several cysts, and the complex structure and vasculature of exudation of the retina are observed. RPE elevations associated with abnormal blood flow signals are shown. The estimated lateral motion of this eye in the motion correction step is shown in Fig. S6B. This eye exhibits huge eye drift during the scan, however, the motion correction and image reconstruction have been performed well. The OCT projection shows good morphology and agrees well with the scanning light ophthalmoscope image [Fig. S6A]. The superficial retinal OCTA [Fig. 10(D)] shows clear retinal capillaries, however, there is an artifact at the fovea [red arrow in Figs. 10(D). As shown in Visualization 5, there is thinning of the retina at this location. Hence, this artifact might be caused by a segmentation error [red circle and arrow in Fig. 10(C)]. The sub-RPE OCTA [Fig. 10(E)] and its magnified images [Fig. 10(G)] shows the wide distribution of abnormal vasculature. The commercial OCTA image [Fig. 10(B)] exhibits several artifacts, and retinal capillaries are lost at the left bottom region. They may also be due to segmentation errors.
Fig. 10. Right eye with age-related macular degeneration (69 years old, male). (a) Fundus photograph, (b) commercial OCTA at the superficial retinal layer (DRI-OCT, Topcon), (c) orthogonal view of the OCT and OCTA with the convolutional Lissajous scan (see Visualization 5), (d, e) en face slab OCTA images. (d) En face slab OCTA of the superficial retinal layer. (e) Sub-RPE OCTA shows abnormal vasculature. Enlarged cross sections (f) and sub-RPE OCTA (g) show the detils of the abnormal vasculature. Scale bars are 1 mm.
3.2 Repeatability
To assess the performance of the motion correction, the same eyes were scanned twice, and the 3D volumes were compared. The 3D OCT intensity volumes were reconstructed independently. They were registered using a rigid transformation, i.e., only translation and rotation, without deformation [Elastix [30]]. A healthy volunteer eye at the macular and the ONH were scanned and the registered volume of the first and second imaging sessions are shown in Figs. 11(a–c) and 11(e–g), respectively (see Visualization 6 and Visualization 7). If two volumes overlap, the region appears monochrome. Cross-sectional images show good agreement between the two sessions. The registered OCTA images [Figs. 11(d) and 11(h)] also show good agreement. The estimated motions in the motion correction step [Figs. 11(i–l)] show different eye motions in the two sessions. The mean-squared error (MSE) and Pearson’s product-moment correlation coefficient between the OCT intensity of the two sessions were calculated. Regions exhibiting a signal-to-noise ratio (SNR) of over 2.94 dB in both imaging sessions data were included in the evaluation to avoid the effect of random overlap of noise. In the case of the macular, the MSE is 3.23 dB$^{2}$ and the correlation coefficient is 0.93. In the case of the ONH, the MSE is 4.08 dB$^{2}$ and the correlation coefficient is 0.93. Three-dimensional OCTA volumes of the two imaging sessions were also compared. OCTA signals (complex de-correlation [0, 1]) at the same region exhibiting significant SNR (> 2.94 dB) were binarized with a threshold level of 0.18. The Dice coefficients were calculated with the binarized OCTA signals and are 0.87 for the macular data and 0.88 for the ONH data.
Fig. 11. Comparison between two successive sessions in (a-c, e-g) 3D OCT volumes (see Visualization 6, Visualization 7) and (d, h) en face OCTA projection images of a healthy volunteer eye at the macular (a-d) and ONH (e-h). The estimated motions for each data are plotted in (i-l). Scale bars are 1 mm.
The same procedure was applied to diseased eye cases. The registered OCT volumes and en face OCTA images of two patient cases are shown in Fig. 12. The estimated motions in the motion correction step [Figs. 12(g–j)] show different estimated eye motions in the two sessions (see Visualization 8 and Visualization 9). In both cases (a 76-year-old male BRVO patient [Figs. 12(a–c)] and a 70-year-old male drusenoid pigment epithelium detachment (PED) [Figs. 12(d–f)]), the registered images show good agreement between the registered motion-corrected images of two sessions. The agreement is good in the appearance of abnormalities, for example, the structures of cysts in the BRVO case [Figs. 12(a, c)] and boundaries of non-perfusion regions in en face OCTA [Fig. 12(b)]. The elevated RPE structure is matched [Figs. 12(d, f)]. Even small hyper-scattering spots agree well [Fig. 12(f)]. Note that the motion-corrected volumetric data enable us to extract a cross-sectional image along an arbitrary path [Figs. 12(c, f)]. The MSE and correlation coefficient between the OCT intensity of both sessions were 4.48 dB$^{2}$ and 0.93 in the case of the BRVO, and 5.94 dB$^{2}$ and 0.92 in the case of the drusenoid PED, respectively. The Dice coefficients of the binarized OCTA were 0.89 in the case of the BRVO, and 0.81 in the case of the drusenoid PED, respectively. The agreement metrics of these are in the same order as they would be for the healthy volunteer’s eye.
Fig. 12. Comparison of two successive sessions in (a, c, d, f) 3D OCT volume (see Visualization 8, Visualization 9) and (b, e) en face OCTA projection images of two diseased eyes of a 76-year-old male BRVO patient (a-c) and a 70-year-old male drusenoid PED patient (d-f). The estimated motions for each data are plotted in (g-j). Scale bars are 1 mm.
4. Discussion
4.1 Sampling density with slow shift
In the case of the Lissajous scan, the exact location is sampled several times if the object is static, and the distance between the successive sampling points is large. Hence, the spatial sampling density will be low when compared with that of a raster scan taken at the same imaging time, scanning area, and sampling rate. However, this problem is mitigated by a slow shift. When there is a slow shift or sample motion, the sampling locations at different time points are slightly shifted. In other words, the sampling density problem is mitigated by increasing the number of sampling points and scanning time [23]. The image will hence be reconstructed using several images with different sampling lattices. This is similar to super-resolution reconstruction [31]. The sampling density of the Lissajous scan will be significantly improved when slow sample motion exists.
The sampling density of the Lissajous scan with and without slow shift was numerically simulated [Fig. S7]. The simulated velocity of the slow motion is 150 $\mathrm {\mu }\textrm {m}$/s, which is close to the mean eye drift speed (~100 $\mathrm {\mu }\textrm {m}$/s in a retinal image, which is approximately 82% [32] of ~120 $\mathrm {\mu }\textrm {m}$/s in eyeball rotation obtained by ~50 arcmin/s mean drift speed [33] and an ~8-mm distance from the center of rotation of the eye to the retina [34]) and is on the same order as the slow circular shift speed applied in the convolutional Lissajous scan (574 $\mathrm {\mu }\textrm {m}$/s). The simulation shows that the slow shift during the Lissajous scan significantly improves the sampling density. The convolutional Lissajous scan not only extends the FOV but also mitigates this drawback in the sampling density of a Lissajous scan. Hence, a slight slow shift during the Lissajous scan is preferable even in conventional FOV imaging with stable eyes.
4.2 Degradation of resolutions and signal power due to transversal scanning
The wide FOV imaging with coarse spatial sampling density increases the speed of acquisition. In addition to the coarser sampling density, the potential disadvantages of longer scanning distances between consecutive sampling points may include reduced SNR and resolution [35]. The less degradation of resolutions and the signal power is an advantage of the convolution between a narrow FOV scanning pattern with a slow shift.
The beam scanning speed with Lissajous scan patterns is not static and the maximum velocity occurs near the center of the basic Lissajous scan area. The maximum distance between successive sampling points is 18 $\mathrm {\mu }\textrm {m}$ in the proposed scanning pattern. However, the sampling duration for a single wavelength sweep is approximately 50% of the period of the sweep. In addition, a window function is multiplied with the acquired spectra before the Fourier transformation from $k$-domain to the depth. The effective displacement of the beam during the acquisition is smaller than the sampling distance by these factors. The maximum elongation of the transversal resolution along the scanning direction and the axial resolution is calculated as around 1.3 from Eq. (25) in Ref. [35] if we assume the effective integration factor $\sigma$ = 0.4. The maximum degradation of the SNR when the sample is random tissues might be around -2 dB from Eq. (26) in Ref. [35].
In the case of the coarse Lissajous scan, the maximum distance is around 36.8 $\mathrm {\mu }\textrm {m}$. The maximum elongation of the transversal resolution along the scanning direction and the axial resolution is calculated as around 2.0, and the maximum degradation of the SNR when the sample is random tissues might be around -6 dB. The distance for the raster scan used in this study is around 19 $\mathrm {\mu }\textrm {m}$ and is constant for linear sweeps. Since the specifications of the OCT setups are almost the same, the maximum degradation in the case of convolutional Lissajous scans always occurs in the case of raster scans.
4.3 Advantages over stitching
A simple straightforward method of extending the FOV is to stitch multiple images [15–18]. In the case of stitching, multiple data at different locations should be successfully scanned. One advantage of the proposed method is that the motion correction and extending imaging FOV are performed simultaneously based on temporally short segments. When these segments are sufficiently short compared to eye movements, they can be considered spatially rigid. Sophisticated image registration with deformation may not be required.
A comparison with simple volumetric stitching was performed. Eight small Lissajous scans with an area of 3 $\times {}$ 3 mm$^{2}$ were obtained to cover almost the same FOV of the convolutional Lissajous scan at the ONH. Thus, the total number of A-lines and acquisition time are the same as for the convolutional Lissajous scan. For volume stitching, translation correction and linear blending were applied. This is because the convolutional Lissajous scan method corrects only the translation of strips. A comparison with simple stitching is shown in S8. The stitched volume exhibits several discontinuities. By contrast, when the convolutional Lissajous scan method is used, smooth and continuous three-dimensional morphology of the ONH is observed. In the convolutional Lissajous scan method, data are split into small strips and registered with each other. It might be crucial to connect images from different locations and extend the FOV smoothly.
5. Conclusion
In this study, we demonstrated an extension of the OCT retinal imaging FOV with a high spatial-sampling density using a convolutional Lissajous scan. In vivo 3D human retinal imaging was achieved with an imaging FOV of about 6.8 mm diameter and a spatial sampling density of about a sample per 13$^{2}$ $\mathrm {\mu }\textrm {m}$$^{2}$. The volumetric OCT and OCTA data of repeated scans show good repeatability in the imaging. The approach presented in this study may be suitable for assessing changes in microscopic abnormalities over a wide FOV.
Funding
Core Research for Evolutional Science and Technology (JPMJCR2105); Japan Society for the Promotion of Science (18H01893, 18K09460, 21H01836, 21K09684, 22K04962); JST-Mirai Program (JPMJMI18G8).
Disclosures
SM: Topcon (F), Tomey (P), Yokogawa Electric (F), Nikon (F), Sky Technology (F), Kao (F). MM: Santen (F). SA: Topcon (E). TM: Topcon (E). TY: Topcon (E). YY: Topcon (F), Tomey (P), Yokogawa Electric (F), Nikon (F), Sky Technology (F), Kao (F).
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.
Supplemental document
See Supplement 1 for supporting content.
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