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Megahertz multi-parametric ophthalmic OCT system for whole eye imaging

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Abstract

An ultrahigh-speed, wide-field OCT system for the imaging of anterior, posterior, and ocular biometers is crucial for obtaining comprehensive ocular parameters and quantifying ocular pathology size. Here, we demonstrate a multi-parametric ophthalmic OCT system with a speed of up to 1 MHz for wide-field imaging of the retina and 50 kHz for anterior chamber and ocular biometric measurement. A spectrum correction algorithm is proposed to ensure the accurate pairing of adjacent A-lines and elevate the A-scan speed from 500 kHz to 1 MHz for retinal imaging. A registration method employing position feedback signals was introduced, reducing pixel offsets between forward and reverse galvanometer scanning by 2.3 times. Experimental validation on glass sheets and the human eye confirms feasibility and efficacy. Meanwhile, we propose a revised formula to determine the “true” fundus size using all-axial length parameters from different fields of view. The efficient algorithms and compact design enhance system compatibility with clinical requirements, showing promise for widespread commercialization.

© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

It is well known that the eye is an intricate optical system [1], and obtaining whole eye parameters is one of the most important determinant of person to assess disease progression and treatment plans in ophthalmology [2]. Yet, existing imaging techniques, like ultrasound and magnetic resonance imaging, are often involve physical contact, costly, or lack the spatial resolution for detailed retinal visualization. Optical coherence tomography (OCT) [3] is non-contact, noninvasive, high-resolution tomographic imaging modality with high signal-to-noise ratio (SNR). With the advance to OCT technology, micrometer resolution with centimeter depth of field can be provided. But, individual variations in optical aberrations limit the quantitative analysis of the retina size, preventing retinal dimensions measured by OCT from being the same as of anatomical morphometry [4]. The information on eye axial length (AL) contributes to the quantification of retinal dimensions, it is limited to the central field of view (FOV) [5]. As a result, the development of a whole eye OCT with AL and even peripheral AL parameters becomes imperative in clinical applications.

Achieving whole eye OCT faces many challenges [6,7]. The first challenge arises from the eye's intrinsic refractive ability, which hinders simultaneous focusing on both the cornea and retina. This necessitates the use of specialized devices such as biometers, corneal topography maps, and anterior and retinal imaging systems to identify distinct clinical features. In early studies, a dual-wavelength SD-OCT for simultaneous imaging of the whole eye segments from cornea to the retina was proposed [8], yet the strong sensitivity attenuation problem limited its image quality and imaging depth. Another method to achieve simultaneous whole eye imaging is by utilizing polarization multiplexing technology to separate P-polarized and S- polarized for imaging the anterior and posterior segments [9,10], respectively. Multiple polarizing beam splitters in the sample arm reduce light collection efficiency, resulting in lower image quality. It will also be challenging to maintain stable laser power in retinal path. To improve the SNR and fit the actual needs, some research has utilized tunable lens [11] or switchable optical paths [12,13] to achieve the anterior and posterior segments imaging. However, the retinal FOV of these systems is typically limited, generally less than 30°. This limitation arises from their A-scan speed (≤ 100 kHz) and optical design that does not facilitate wide-field imaging. Moreover, all of the mentioned whole eye OCT systems lack the ability to image OCTA and measure peripheral AL, which is desired by doctors.

The second challenge is that the normal person cannot maintain annotation for a long time, otherwise subjects will blink. To achieve image acquisition within the blink of an eye, it is necessary to increase the scanning speed to MHz levels. Many efforts have been reported to improve the A-scan rate of SD-OCT to MHz [14,15], yet optimal choice is the swept source OCT (SS-OCT). Most swept lasers are based on mechanical scanning for wavelength sweeping and when the speed is in the MHz range, sinusoidal or quasi-sinusoidal scanning pattern are used. However, due to the amplifier properties as well as mechanical response of the laser, such as the micro-electro-mechanical systems vertical-cavity surface-emitting (MEMS-VCSEL) sources [16,17], the up forward and down backward sweeping spectra will exhibit different wavelength versus time behavior, which poses a challenge for image reconstruction. Hence, the swept source primarily utilizes the forward scanning spectrum, with the A-scan speed limited to a few hundred kHz. Fourier domain mode-locked lasers can achieve multi-MHz by buffering technique, which splits, delays, and recombines the sweeping spectra and achieve a nearly 100% duty cycle [18,19]. However, this is not ideal since the delayed spectra will experience extra dispersion and attenuation due to the longer fiber used. Beyond that, other methods with non-mechanical scanning have been investigated research. One of the methods is integrated semiconductor opto-electronic design [20] of Insight Photonic Solutions, Inc., USA, but the A-scan speed is only a few hundred kHz. Another type of inertia-free is time-stretched method [21], in which, a broadband ultra-short pulse is stretched or spectrally dispersed in the time domain. The swept laser based on time stretched method provides an effective A-scan rate equal to the repetition rate of the laser, which are in the range of tens of MHz. However, the current research mainly focuses on the 1310 nm or 1550 nm band, and the system sensitivity is low, which is not suitable for retinal OCT [22].

Finally, the MHz whole eye OCT system requires a high-speed and stable scanning system. For wide-field imaging, the B-scan speed will exceed 500 Hz, the galvanometer will no longer have optimal performance. A raster scanning pattern with 30% or more flyback portion in a B-scan is typically used. The flyback portion in the B-scan is not used for imaging and this will eventually reduce the effective imaging speed even reduce the imaging FOV of the system. Expanding the imaging area to the peripheral retina is a prerequisite for diagnosing retinal detachments, peripheral retinal degenerations [23], and choroidal pathologies [24]. To address this, bidirectional scans [25], spiral scans [26], and ammonite scanning [27] have been proposed, but these methods require complex reconstruction algorithms, which may fail during the situation where microsaccades or eye blinks happen for in vivo application. Moreover, these methods cannot resolve the problem of deteriorated repeatability in the galvanometer due to high-speed scanning.

In this paper, we present an ultrafast multiparametric ophthalmic SS-OCT system with a bidirectional scanning MEMS-VCSEL swept laser. The system is able to imaging the anterior eye, posterior eye as well as measure ocular biometry without switching lens manually. The optical system is designed to achieve the diffraction limit for both the anterior chamber (14 mm x 14 mm) and retina (60°). Taking advantage of bi-directional scanning MEMS-VCSEL, our system improves the duty cycle and effectively doubles A-line speed while keeping the same sweeping rate. With two fiber Bragg gratings (FBGs) in the system, we propose new method to correct spectrum difference during the forward and backward laser sweeping period. We adopt a quasi-sinusoidal galvo scanning pattern to improve effective A-line usage and implement a novel way for registration B-scan images based on position feedback signals. The registration method reduces pixel offsets between the forward and backward galvos scanning by 2.3 times in 500 Hz B-scan frequencies. Feasibility and efficacy of our algorithms was demonstrated through non-biological and as well as in vivo human studies. In addition, with the knowledge of the ocular biometry parameters, we were able to determine the “true” fundus dimension with a modified calculation formula.

2. Methods

2.1 Experimental setup

The megahertz multiparametric whole eye OCT imaging system is shown in Fig. 1(a). The system source, a MEMS-VCSEL laser (custom-made, Thorlabs Inc, USA), operates at a center wavelength of 1060 nm and features two modes for high axial resolution and deep imaging range. In Mode 1, the laser exhibits a sweep bandwidth of 101 nm, an output power of 50 mW, and a bidirectional repetition frequency of 500 kHz. In Mode 2, the laser presents a sweep bandwidth of 50 nm, an output power of 30 mW, and a repetition frequency of 50 kHz, characterized by a 50% duty cycle. The laser beam travels through an optical fiber splitter, which divides into 1% entering the Mach–Zehnder interferometer (MZI) module and 99% proceeding into the OCT imaging path. The MZI module consists of two 50/50 optical fiber couplers, a photodetector, two FBGs, and a polarization controller, which provides frequency-adjustable clock signals for later image reconstruction. The polarization controller is used to adjust the shape of the interference envelope, preventing local weakness. The customized FBGs, with central reflection peaks at 1010 nm (reflectivity $> $ 90%, bandwidth: 0.1 nm) and 1090 nm (reflectivity $> $ 90%, bandwidth: 0.1 nm), are utilized to mark characteristic wavelengths for aligning the forward sweeping and backward sweeping spectra of the laser. The OCT imaging path is divided into a reference arm path and a sample arm path via a 10:90 fiber-optic coupler. A schematic is illustrated in Fig. 1(b), where the pink beam represents the retinal pathway, and the purple beam represents the anterior pathway. A varifocal lens (EL-10-30-C-NIR-LD-MV, Optotune, USA) is employed to change the beam divergence angle, focusing the beam on the location of interest. A flip mirror is used to switch between posterior and anterior optical pathways with a response time of 0.5 s. A set of XY galvanometric mirrors (6210, Cambridge Technology, USA) was used for beam scanning to achieve B-scan scanning at different speeds. To address the issue of poor repeatability in B-scan of ≥ 500 Hz, we propose a correction algorithm. The core of this algorithm involves utilizing the position feedback signal obtained from the galvanometer driver to register the B-scan images. A dielectric mirror is used to separate the NIR OCT light and visitable light for fixation target. Lens2 and the objective lens form a 4F system, with the fixation target screen positioned at the focal plane of Lens2, enabling the subject to achieve clear visibility by adjusting the position of Lens2. Two cameras are used for pupil imaging and ensuring the subject is at the working distance. Due to the different optical paths between the anterior imaging and posterior imaging section of the sample arm, two MEMS optical switches and two optical delay lines are employed to adjust the path lengths of the reference arm. Interference occurs at the 50/50 optical fiber coupler where the backscattered sample light interferes with the reference light. The OCT signal is detected by a balanced photodetector with a bandwidth of 2.5 GHz (PDB482C-AC, Thorlabs Inc., USA). The detector signal is then passed through a 10 MHz high-pass filter and 1200 MHz low-pass filter. Finally, OCT signals and MZI signals are captured in parallel by a dual-channel digitizer (ADQ32, Teledyne SP Devices, Sweden). The 10 MHz high-pass filter is attenuate the low frequency and DC part of OCT signals, while the 1200 MHz low-pass filter is applied to attenuate high-frequency OCT signals beyond the Nyquist limit. A 12 dB attenuator is employed to attenuate the signal to match the input voltage range for the digitizer.

 figure: Fig. 1.

Fig. 1. Schematic diagram of the experimental setup and timing diagram. (a) System schematic diagram. SS Laser, swept source laser; FOC, fiber optic coupler; OS, optical switch; ODL, optical delay line; BPD, balanced photodetector; FBG, fiber Bragg grating; PD, photodetector; PC, polarization controller. (b) The 3D modeling diagram illustrates the sample arm optical path, with purple indicating the anterior segment pathway and pink indicating the retinal pathway. FC, fiber collimator; VL, varifocal lens; GS, galvanometer scanners; FM, flip mirror; SL, scan lens; DM, dichroic mirror; CM, camera; DS, display screen; OB, objective lens; L1-L2, lens; M1-M3, mirror; MZI: Mach–Zehnder interferometer. (c) Sequential logic diagram of the System. T1, output spectral signals of the swept source Laser; T2, output trigger signals of the swept source Laser; T3, clock signals of galvanometer scanners. Tx, driving signals of X-Galvanometer. Ty, driving signals of Y-Galvanometer. Up and down refer to the output spectra of the laser during the forward and backward sweeping. ${\lambda _1}$ and ${\lambda _2}$ refer to the starting and ending wavelengths of the output spectra.

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As shown in Fig. 1(c), the laser generates a single trigger signal T2 for the forward and backward sweeping with a speed of ∼500 kHz. Upon each triggering event of T2, the digitizer captures signals for both the forward and backward sweeping regions. Meanwhile, ${\lambda _1}$ and ${\lambda _2}$ refer to the starting and ending wavelengths of the output spectra. Paired A-lines signals can be separated based on the characteristic peaks of the FBG. A multifunctional control card (PCIe 6353, National Instruments, USA), is used to double the frequency of T2 (500 kHz) to T3 (1 MHz), which serves as the clock signal for driving the galvanometer scanners. The same control card is used to output analogy signals, ${T_x}$ and ${T_y}$, that driver the galvo scanner. In addition, one analog input port of the multifunctional card is utilized to capture the position feedback signal from the X-Galvanometer.

2.2 Optical design

Retinal OCT imaging pathways typically constitute a reduced 4F system. A larger ratio permits a proportional reduction in the galvanometer scanning angles, thereby easing the scanning pressure. While some studies have achieved wide-angle 4F systems using multiple plano-convex lenses, achromatic lenses [28], or commercially available binocular indirect ophthalmoscopy lenses [29], anterior segment OCT imaging were not demonstrated in those studies. In retinal OCT, the imaging FOV is primarily determined by the numerical aperture of the objective lens. To achieve a wide FOV, researchers often face a choice: they can opt for small-diameter lenses, which are susceptible to contamination from eyelashes, or they can choose large-diameter lenses, which come with the challenges of increased processing complexity and potential nasal collisions. In order to prioritize the comfort of the subjects, we set specific constraints for the application scenario, requiring a working distance of over 20 mm and an objective lens diameter less than 45 mm. To manage the considerable manufacturing expenses, we made extensive use of readily available optical components from the market while designing the optical system. Additionally, when designing the optical path for anterior segment imaging, it is essential to ensure a FOV greater than 13 mm to provide information on the angle of the anterior chamber.

Considering the trade-off between depth-of-field and lateral resolution, a proper parameter was obtained using Zemax software. The 4F system we designed has a magnification of 3.33x and consists of a telecentric scanning lens (LSM05-FBB, Thorlabs Inc., USA) and a double-sided aspherical lens (customized, D = 44 mm, f = 30 mm). The telecentric scanning lens can eliminate distortions and other aberrations caused by the galvanometer scanning, resulting in a flat image plane. Figure 2(a) shows the layout diagram of retinal imaging, where different colors represent different FOV. In order to enhance the fiber coupling efficiency of the sample return light, an achromatic lens (AC064-015-C, Thorlabs Inc., USA) is utilized as a collimator instead of a conventional spherical lens, yielding an output beam diameter of 4.2 mm. The beam is reflected by an automated flip mirror (MFF102/M, Thorlabs Inc., USA) after galvanometer scanning and directed to the scanning lens, subsequently passing through a reflecting mirror and a dichroic mirror (64472, Edmund, USA), and finally entering the eye through the objective lens. By employing the 4F system, the scanning angle at the pupil is enlarged from the original ±9° to ±30°, providing a retinal imaging field of ±8 mm. Through simulated spot diagrams at the main wavelengths of 1.0 µm, 1.06 µm, and 1.10 µm, the optical system for retinal imaging demonstrates diffraction-limited performance at four representative normalized fields of 0, 0.5, 0.707, and 1.0, as shown in Fig. 2(b). Besides, the retinal system has a working distance of 21.69 mm and the Airy disk radius is 18 µm. Furthermore, we incorporated three gold-plated mirrors (customized, reflectivity > 99%) and a set of lens assembly to establish the anterior optical path, in conjunction with the 4F system of the retinal segment, as illustrated in Fig. 2(c). The lens assembly comprises a biconvex lens with a 110 mm focal length and a planoconcave lens with a -90 mm focal length. By calculating spot diagrams at the primary wavelengths of 1.0 µm, 1.06 µm, and 1.10 µm, we determined that the anterior optical system consistently achieves diffraction-limited performance across four representative fields: 0.00 mm, 3.50 mm, 4.95 mm, and 7.00 mm, with an Airy radius of 20 µm, as illustrated in Fig. 2(d).

 figure: Fig. 2.

Fig. 2. Optical design of the sample arm. (a-b) Retinal imaging modality with optical ray trace, showing optical spot diagram for three wavelengths across a ± 8 mm scan, revealing diffraction-limited performance. The Airy radius is 18 µm. (c-d) Anterior imaging modality with optical ray trace, showing optical spot diagram for the three design wavelengths over a ± 7 mm scan, indicating diffraction-limited performance. The Airy radius is 20 µm. GS-X, X-galvanometer scanners; GS-Y, Y-galvanometer scanners; FM, flip mirror; SL, scan lens; DM, dichroic mirror; L1, lens; M1-M3, mirror; OB, objective lens.

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2.3 Bidirectional sweeping MEMS-VCSEL laser

In order to improve imaging speed, we have adopted a bidirectional swept source of MEMS-VCSEL. This configuration offers a ∼100% sweeping duty cycle, thereby increasing the A-line rate from 500 kHz to 1 MHz. However, a drawback of this setup is that the spectral profiles during forward and backward scanning phases are different. In addition, the laser only provides a single trigger for the round-trip scanning and the digitizer acquire the round-trip signal in a sweep with the trigger. It will be challenging to separate the signals acquired during the forward sweeping an those acquired during the backward sweeping. Specifically, during up scanning, MEMS is primarily propelled by electrostatic force, while during down scanning, spring force predominates [17]. The resultant asymmetry in wavelength scanning engenders variable time durations for adjacent A-lines to traverse the same wavelength range.

To solve these issues, we introduced a spectral correction method, which relies on the reflection wavelength of two FBGs. By employing this method, we can identify characteristic wavelengths of 1010 nm and 1090 nm from FBGs reflection, enabling the differentiation of the signals from the forward and backward sweeping regions and resolving this issue. The main steps of the spectral correction algorithm are as follows:

  • a) Calculate the phase of the pair of A-line output spectra in MZI signals and unwrap it;
  • b) Derive the unwrapped phase;
  • c) Apply filtering to identify characteristic wavelengths, denoted as ${\lambda _1}$, ${\lambda _2}$, $\lambda _1^{\prime}$ and $\lambda _2^{\prime}$;
  • d) Based on the positions of ${\lambda _1}$, ${\lambda _2}$, $\lambda _1^{\prime}$ and $\lambda _2^{\prime}$, reconstruct these two A-lines;
  • e) Scale these two A-lines to equalize their lengths;
  • f) Align the corresponding OCT signals for this A-line pair.

Due to the composition of OCT signals by different frequencies, it is difficult to extract the characteristic wavelength in the OCT imaging path. We placed two FBGs with different characteristic wavelength reflection peaks in the MZI module, and through the processing of the MZI signal, the characteristic wavelength peaks can be extracted. As illustrated in Fig. 3(a), the period of the swept source is 2 µs, resulting in two output spectra within a single period by the blue curve, one in the forward direction and the other in the backward direction. Phase calculating and unwrapping were applied to these spectra, yielding the results shown in Fig. 3(a) with the red curve. Subsequent differentiation, as shown in Fig. 3(b), revealed the presence of the characteristic wavelength. After additional filtering, clean characteristic wavelength peaks of ${\lambda _1}$, ${\lambda _2}$, $\lambda _1^{\prime}$ and $\lambda _2^{\prime}$ were obtained, as demonstrated in Fig. 3(c).

 figure: Fig. 3.

Fig. 3. The principles and results of the proposed spectral correction algorithm. (a) Spectrogram and unwrapped phase image of one cycle of the bidirectional MEMS-VCSEL. (b) The results after phase differentiation. (c) Phase results after filtering. (d)-(g) B-scans of a 1mm glass slide after correction. δ=0 signifies that the actual calibration coefficient is the same as the optimal calibration coefficient. δL = 20, δL = 50 and δL = 100 respectively denote the outcomes when the actual correction coefficient deviates from the optimal correction coefficient by 20, 50, and 100 sampling points in spectral length.

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To validate the feasibility of this method, we initially employed a 1mm glass slide with clear boundary features for OCT imaging. When calibrating the forward and backward spectra, the distinction between employing and not employing this algorithm is primarily evident in two aspects: the starting point and the spectral length. An identical starting point implies ${\mathrm{\lambda }_1} = \mathrm{\lambda }_1^\mathrm{^{\prime}}$, and an identical spectral length implies $\Delta t = \Delta t^{\prime}$. By processing the experimental data in Fig. 3(c), it was observed that $\Delta t \ne \Delta t^{\prime}$, and the difference in spectral length between them is 20 sampling points. During image reconstruction, the optimal calibration coefficient for aligning the forward and backward spectrum were determined by extracting the starting point and length from the spectrum in Fig. 3(a). $\delta L$ and $\delta S$ refer to the number of sampling points by which the actual calibration value deviates from the optimal calibration value in terms of the spectral length and the starting point, respectively. The image reconstructed using the optimal calibration values, denoted as $\delta = 0$ and illustrated in Fig. 3(d), demonstrates a precise alignment of both the upper and lower surfaces of the glass slide. To further investigate the impact of varying point disparities along the spectral length on image reconstruction results, we set $\delta L$ to be 20, 50, and 100, as illustrated in Fig. 3(e)–3(g). The results indicate that as the point disparities increase, the misalignment phenomenon between adjacent A-scan images becomes more pronounced.

In order to further verify the performance of the correction method in highly scattering biological tissues, a high-definition image was acquired with a 16 mm wide FOV and an average of 30 times. As shown in Fig. 4(a), the corrected image is well aligned at different depths and different A-line positions. The macular region was selected as the region of interest, delineated by a red rectangular box, and the corresponding images were then magnified. To explore the influencing factors of the algorithm, we selected calibration parameters of $\delta = 0,\delta L = 50$ and $\delta S = 50$ for image reconstruction. The results are presented in Fig. 4(b)–4(d). In comparison to the results corresponding to $\delta = 0$, both $\delta L = 50$ and $\delta S = 50$ exhibit poorer image quality. Boundary features such as the internal limiting membrane (ILM), external limiting membrane (ELM), ellipsoid zone (EZ), interdigitation zone (IZ), and retinal pigment epithelium (RPE), labeled with yellow arrows, appear more blurred. Therefore, precise alignment of the spectral length and the starting point of the bidirectional laser is crucial for obtaining clear OCT images.

 figure: Fig. 4.

Fig. 4. Retinal OCT imaging results using the spectral correction algorithm. (a) High-resolution B-scan image of retinal OCT after correction (averaged 30 times). (b) $\delta = 0$ denotes that the actual calibration coefficient is identical to the optimal calibration coefficient. (c) $\delta L = 50$ represent the outcomes when the actual correction coefficient deviates from the optimal correction coefficient by 50 sampling points in terms of the spectral length. (d) $\delta S = 50$ represent the outcomes when the actual correction coefficient deviates from the optimal correction coefficient by 50 sampling points in terms of the starting point. ILM, internal limiting membrane; ELM, external limiting membrane; EZ, ellipsoid zone; IZ, interdigitation zone; RPE: retinal pigment epithelium.

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2.4 Registration for the galvanometric scanner position

For 3D imaging, OCT systems typically adopt raster scanning method, which has a typical 10-30% of the scanning time for flying back portion. For high-speed scanning, a resonant scanner shall be used and the resonant scanner will require a sinusoidal driving waveform. With the sinusoidal driving waveform, the galvo mirror will response differently during the forward and backward scanning stage even though the same voltage applied. This will introduce a shift in the scanning location between the forward and backward scanning. A few ways have been introduced to realign the B-scan images for 3D OCT, such as intensity difference, cross-correlation, and design-detection-deformation strategy [30,31], yet the process of registering two-dimensional images is time-consuming. Here, to address this issue, we propose a new 1D registration method which based on hardware feedback of the galvo mirror position.

Firstly, while acquiring OCT volume signals, the position feedback signal (PFB) from the galvanometric driver card was simultaneously detected through the ADC port of the multifunction control card at a speed of 50 kS/s. As shown in Fig. 5(a), the blue curve represents input control signals, and red curve represents PFB signals, which exhibits a response delay of 130 µs relative to the input signal. Subsequently, the acquired PFB signal underwent filtering to eliminate noise, ensuring monotonicity within a B-scan. Finally, offset correction is applied to the original en face image using the processed PFB signal. To accurately determine the number of pixels offset between galvanometric forward and backward scans, three fixed positions in each B-scan are selected as the basis for calculation the average offset value. After calibrating the entire image using pixel offsets, an interpolation step is performed between adjacent B-scans, further facilitating image registration.

 figure: Fig. 5.

Fig. 5. Results of the registration method applied to galvanometric scanners. (a) The blue and red curves depict the input control signal and the PFB signal, respectively. (b)-(c) Original results and processed results with the PFB signal for a USAF 1951 resolution target (10 line-pairs per millimeter). (d) Boxplot of the statistical distribution of pixel offsets between the positive and negative scans of the galvanometer. (e)-(f) Original results and processed results with the PFB signal for en face images of the retinal OCT. (g)-(l) Magnified images of the region of interest selected by the red rectangles in (e)-(f).

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The feasibility of our registration method was demonstrated by imaging a USAF 1951 resolution target (10 line-pairs per millimeter). Due to the impact of scan angles and scan speeds on galvanometric performance, experiments were conducted with the imaging parameters set to the maximum FOV corresponding to a mechanical scan angle of ±4.5° and a B-scan speed of 500 Hz. The maximum intensity projection en face image of the target was obtained, as shown in Fig. 5(b). Figure 5(c) represents the results after applying the proposed registration method. More uniform edges could be seen from Fig. 5(c). For quantitative assessment of pixel offsets between galvanometric forward and backward scans, statistical analysis was performed on the data within the region highlighted by the green rectangle in Fig. 5(b)–5(c), resulting in the boxplot shown in Fig. 5(d). The results indicated that the offset in the original data was concentrated within ±2 pixels, while the offset in the processed data was concentrated within ±0.6 pixels, reducing the offset pixels by a factor of 2.3. Finally, the experiment on human retinal tissue further confirmed the advantages of the scanner's registration method in dealing with complex absorption and scattering structures. As the offset pixels between galvanometric forward and backward scans varied between different B-scans, aligning the middle position B-scan was adopted as the standard to obtain the original image results, as shown in Fig. 5(e). Figure 5(f) displays the results using the registration. Three regions of interest were zoomed in and compared, labeled as I, II, and III. As depicted in Fig. 5(g)–5(l), the comparative results demonstrate that the proposed registration method effectively eliminates offset errors between galvanometric forward and backward scans throughout the entire image.

3. Imaging results

3.1 Measurement of system performance

Before proceeding with eye imaging, it is imperative to validate the stability of the bidirectional sweeping MEMS-VCSEL laser. Interference signals exhibit a high sensitivity to the stability of the swept spectrum, in contrast to non-interfering signals. Adjusting the optical path difference of the MZI enabled the output of a clock signal with a maximum frequency of approximately 600 MHz. Subsequently, this signal was captured continuously 5000 times at a sampling rate of 2.5 GS/s, with each set of signals containing 4864 sampling points. Figure 6(a) demonstrates the consistency in signal intensity across 5000 repetitions of both forward and backward spectra in the interference signals. Each clock signal set, comprising a pair of A-lines, is represented using different colors. Figure 6(b) represents the magnified view of the region selected by the blue rectangle in Fig. 6(a), depicting clock signals of the forward spectrum. Similarly, Fig. 6(c) shows the magnified view of the region selected by the red rectangle in Fig. 6(a), illustrating clock signals of the backward spectrum. The results indicate that the interference signals from the forward and backward spectra exhibit a sampling error of ±1 pixel across 5000 repetitions, indicating excellent stability. Therefore, the swept-source in bidirectional spectrum output mode can be utilized for OCT and OCTA imaging.

 figure: Fig. 6.

Fig. 6. The stability analysis of interference signals based on the bidirectional MEMS-VCSEL laser. (a) A set of clock signals obtained based on the bidirectional spectra, repeated 5000 times. (b) An enlarged view of the selected area in the forward spectra marked by a blue rectangle. (c) An enlarged view of the selected area in the backward spectra marked by a red rectangle.

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In order to achieve whole eye OCT imaging, it is necessary to optimize the trade-off between A-line speed, spectral bandwidth, and imaging depth within the limitations of acquisition bandwidth. Benefit from the MEMS-VCSEL laser with adjustable parameters, our system has two scanning mode. Mode 1 can achieve high axial resolution for retina imaging at 1MHz speed and Mode 2 enables deeper depth eye length imaging at 50 kHz. The axial resolution of the OCT is directly proportional to the spectral bandwidth and inversely proportional to the central wavelength. The swept laser output spectrum in Mode 1 has a swept bandwidth of 101 nm. The axial resolution in air was determined by measuring the full width at half maximum (FWHM) of the reflectance point spread function (PSF) through a glass plate. The measured axial resolution was 9 µm in air. In Mode 2, the laser output spectrum has a swept bandwidth of 50 nm. The measured axial resolution in this mode is 15 µm in air. The OCT system's imaging range is quantified by measuring the point spread function at various delays between the reference arm and the sample arm. As illustrated in Fig. 7(a), with a sampling rate of 2.5 GHz, the imaging range in Mode 1 is approximately 3.75 mm in air. The sensitivity decreased by 3 dB, mainly due to the limited 1 GHz bandwidth of the acquisition card. In Fig. 7(b), when employing a 625 MHz sampling rate, the imaging range for Mode 2 is approximately 40 mm in air with virtually no sensitivity loss. To determine the SNR in various modes, a reflective mirror was used as the sample and a neutral density attenuator were introduced into the sample arm to prevent interference signal saturation. The results indicated an SNR of 94 dB at 1 MHz and 102 dB at 50 kHz. The difference in SNR mainly stems from two factors: as the A-line speed increases, the number of photons collected by the photodetector from the sample decreases, and the substantial increase in analog bandwidth introduces more electronic noise.

 figure: Fig. 7.

Fig. 7. Quantifying the performance of the OCT System. (a)-(b) Sensitivity roll-off curves of the OCT system in both Mode 1 and Mode 2.

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3.2 Anterior segment OCT and retinal OCTA

Before conducting in vivo experiments, laser safety was firstly assessed. The sample arm power is limited to 1.8 mW on the cornea in both imaging modalities, which is lower than the safe exposure limit defined by ANSI (ANSI Z80.36-2016). Our imaging setup was mounted on a slit lamp stand, stabilizing the head of a healthy volunteer with a chin rest. Initially, the laser operated in Mode 2, with the flip mirror moved out of the optical path for anterior segment OCT imaging. The repetition count for this high-definition B-scan was 50, with each B-scan comprising 1000 A-lines. As illustrated in Fig. 8(a), the multilayered structure of the lens was fully displayed. The iris and fundus areas, indicated by yellow arrows, showed no artifacts, and exhibited excellent resolution. Furthermore, by observing the enlarged view of the region outlined by the yellow rectangle in Fig. 8(a), the layered structure of the corneal surfaces could be clearly identified (Fig. 8(b)). Subsequently, the flip mirror was moved into the optical path, and the laser operated in Mode 1 for posterior segment OCTA imaging. The imaging FOV was 60°, equivalent to 16 mm × 16 mm, with 2000 A-lines acquired for each B-scan at a scanner frequency of 500 Hz and the acquisition time is 4 s. The split-spectrum phase-gradient angiography algorithm [32] was employed for OCTA reconstruction of the B-scans repeated four times. To optimize the OCTA signal, the full spectrum was divided into eight narrower bands. Due to the suboptimal stability of the galvanometric scanner in this mode, we utilized the registration method of the galvanometric scanner, resulting in the final image results shown in Fig. 8(c). The results indicate that blood vessels throughout the entire FOV exhibit good contrast and smooth boundaries. Therefore, our proposed system is deemed feasible for application in the human eye.

 figure: Fig. 8.

Fig. 8. OCT and OCTA imaging of the whole eye. (a) The high-definition B-scan of anterior segment OCT in Mode 2. The average repetition is 30 times. (b) The enlarged view of the region outlined by the yellow rectangle in (a). (c) Retinal ${60^\circ }$ OCTA imaging on Mode 1, 2000 A-lines ${\times} $500 B-scans ${\times} $4 times.

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The microsaccades of the eye, particularly in the anterior segment, has a more pronounced impact on OCT imaging compared to the posterior segment. This necessitates a shorter acquisition time for effective imaging. In Fig. 9(a)–9(c), we demonstrate 3D images of the anterior segment, constructed from 1000 A-lines and 100 B-scans, with an imaging time of 2 seconds. Furthermore, the 3D images of the anterior segment provide comprehensive corneal information. Future work includes measuring the curvature at various points on the cornea after refractive index correction, enabling the generation of detailed corneal topography maps. An interesting feature observed in the 3D images of the anterior segment is a prominent ‘bright line’ that traverses the entire eye. This line is typically interpreted as the line from the apex of the cornea to the fovea of the macula, known as the AL. Utilizing the spatial positioning of AL, we have successfully aligned and merged the 3D images of the anterior and posterior segments, as showcased in Fig. 9(c). Figure 9(a)-(c) also displays cross-sectional views of the 3D images from different perspectives. The imaging FOV for the anterior segment is 14 mm, while it is 16 mm for the posterior segment. The comprehensive 3D imaging of the whole eye holds significant promise for enhancing disease diagnosis, offering clinicians cross-sectional views from any angle, and enriching the dimensions of diagnosis.

 figure: Fig. 9.

Fig. 9. The 3D imaging results of whole eye OCT. Cross-sectional views of the 3D images from different perspectives are shown in panels (a)-(c). The yellow arrows indicate the position of the AL.

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3.3 Accurate measurement of fundus size

Due to the angular nature of the FOV in fundus OCT imaging, as opposed to linear distance, accurate measurement of retinal dimensions requires the acquisition of axial parameters, particularly the axial length under different scanning angles. Axial length, generally defined as the distance from the corneal vertex to the macular fovea, serves as the primary evaluation indicator for refractive errors. To distinguish it from the commonly recognized “axial length (AL)”, in the subsequent discussions, we will use “ all-axial length (AAL)” to represent the distance from the corneal apex to the upper surface of the retina under any FOV. As depicted in Fig. 10(a), the divergence of the incident beam in the fundus renders OCT in the anterior segment incapable of discerning the macular region. Consequently, using anterior segment OCT to measure axial length parameters is inaccurate. In this study, we propose employing the fundus OCT optical path to measure the all-axial length of the eye under different FOV. Utilizing the whole eye OCT system, featuring a 40 mm imaging depth in air at Mode 1, enables comprehensive depth imaging of the entire eye. As illustrated in Fig. 10(a) and 10(b), Retinal OCT images of myopic eyes with refractive errors of -1D and -5D present complete information of the posterior segment and corneal vertex. In the optical path of the fundus OCT, the corneal position is a collimated beam with a diameter of approximately 1 mm. As a result, the OCT signal from the corneal vertex is approximated as a straight line in the image. The yellow arrows indicate the structural features of the eye, including the macular area, optic disc, and the posterior and anterior surfaces at the apex of the cornea. The axial lengths of eyes with refractive errors of -1D and -5D are 24.8 mm and 25.9 mm, respectively, as indicated by the white arrows in the Fig. 10(a) and 10(b).

 figure: Fig. 10.

Fig. 10. The precise measurement of retinal size. (a) - (b) Retinal OCT images of myopic eyes with -1D and -5D, obtained using the Mode 2 that has an ultralong imaging depth. Structural features of the eyes, denoted by yellow arrows, encompass the macular area, optic disc, and the posterior and anterior surfaces of the cornea. (c) and (d) The relationship between the axial length and the FOV for two myopic eyes. (e)-(f) The enlarged views of the white rectangular region in (a) and (b). The red curve delineating the boundary of the retina.

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In order to measure the all-axial lengths across the entire ±24° FOV, we initiated retinal segmentation to identify the upper surface of the retina as a reference. Subsequently, we calculated the geometric distance from the corneal apex to this reference surface for each A-line individually. The relationship between all-axial length and FOV was established, as depicted in Fig. 10(c) and 10(d). The blue circle represents the raw data, and the red curve represents the fitted results. In particular, we introduce the concept of peak-to-valley of all-axial length, $P{V_{AAL}}$ which represents the maximum difference in all-axial length between the corneal apex to the fovea and the corneal apex to the peripheral retina. Based on the experimental results, it can be concluded that myopic eyes with a refractive error of -1D exhibit a smaller peak-to-valley of all-axial length, measuring only 0.33 mm. In contrast, for -5D myopic eyes, the peak-to-valley of all-axial length is enlarged by a factor of 2.9 compared to the -1D value. This coefficient directly reflects the degree of ocular deformation. Furthermore, by integrating the all-axial length and scanning angle of the eye across various FOV we can accurately determine the true fundus size, ${L_{true}}$.

$${L_{\textrm{true}}} = \mathop \sum \limits_{i = 1}^{n - 1} \frac{1}{2}({AA{L_{i + 1}} + AA{L_i}} )\Delta \theta$$

As expressed in Eq. (1), where i = 1, 2, $\cdots $, n denotes the ith A-line, $AA{L_i}$ represents the all-axial length of the ith A-line, and $\mathrm{\Delta }\theta $ signifies the incident angle between adjacent A-lines. Figure 10(e) and 10(f) is the enlarged views of the white rectangular region in Fig. 10(a) and 10(b). Utilizing the approach outlined in Eq. (1), eyes with different refractive errors, when scanned at the same ±24° FOV, yield actual retinal sizes of 20.71 mm and 21.47 mm, respectively. Taking into consideration that the shape of the optic disc in B-scans can impact the actual length of the red curve, we also separately evaluated the region without the optic disc, as depicted by the white arrows in Fig. 10(e) and 10(f). The results indicate that, within the scanning range of -24° to 0°, the true fundus sizes are 10.35 mm and 10.8 mm for -5D and -1D eyes, respectively. In conclusion, our proposed method allows for accurate determination of the actual retinal sizes in eyes with different refractive errors.

4. Discussion

This manuscript introduces a 1 MHz-speed whole eye OCT imaging technique. In contrast to relying solely on a data acquisition card with a K-clock, the adoption of a standard dual-channel acquisition card not only amplifies imaging depth but also bestows a heightened level of flexibility upon the entire system. What makes this flexibility particularly noteworthy is the revelation that the data acquisition card need not be exclusively sourced from AlazarTech company. The freedom to choose from various suppliers enhances the adaptability of the technology to different settings and budgets, making it a more accessible and versatile solution for researchers, practitioners, and businesses alike. There were several directions to optimize our OCT performance.

We designed an objective lens with a 44 mm aperture, ensuring a large numerical aperture while maintaining a working distance of no less than 20 mm to ensure the comfort of the subjects. Employing materials with a high refractive index can enhance the numerical aperture of the objective lens, thereby expanding the FOV. On the other hand, a 60° FOV implies an optical path difference of 2-5 mm in the focal plane for highly myopic individuals. Due to the divergence characteristics of Gaussian beams, there is a trade-off between focal size and focal depth length. Therefore, if combined with non-diffracting beam [33] or Fourier-spectrum optics [34], a modified system would be designed to achieve an extended depth of field and isotropic lateral resolution across all FOV.

Due to inherent characteristics of OCT signals, there is a trade-off between imaging depth, A-scan speed, interference signal frequency, and SNR. Benefiting from the advantage of the MEMS-VCSEL, the proposed system is the ability to switch operating modes and generate adjustable sweep rates and adjustable spectral bandwidth. The custom laser operates in Mode 1 with a 1 MHz scan speed and 101 nm scan bandwidth, enabling high-resolution wide-field retinal OCT/OCTA. In Mode 2, the laser ensures a minimum 40 mm imaging depth, ensuring feasibility for anterior segment and axial length imaging. The current configuration parameters allow scanning of a 60° OCT (2000 × 500) in just 1 s, and OCTA (2000 × 500 × 4) in only 4 s. When acquiring 3D anterior segment images (1000 × 200), it takes 4 s, and there is slight jitter between images. It may be considered to increase the Mede2 scanning speed from 50 kHz to 200 kHz. Following the principle of a fourfold increase in speed and signal frequency, the current acquisition card with a 2.5G sampling rate is just sufficient. Combining deep learning to optimize OCT images has become a hot topic in recent years [35,36]. A recent study compared four typical network structures [37], including single-path models, U-shaped models, models based on generative adversarial networks, and multi-path models. It was found that U-shaped models and multi-path models achieve better OCTA reconstruction results. Therefore, studying network models suitable for wide-field OCT and OCTA imaging in MHz systems can reduce the number of repeated acquisitions and achieve 60° OCTA imaging within 1-2 s, which holds significant clinical value.

For data with A-line size 2000 × 500 × 1, it takes 100 s to reconstruct an OCT image using Matlab software. For data with A-line 2000 × 500 × 4, it takes 260 s to reconstruct an OCTA image using Matlab software, with an additional 130 s needed for retinal layering. The CPU model used in our system is Intel Core i7-12700K, and the GPU model is NVIDIA GeForce RTX 3070. In addition to optimizing algorithms, another approach to improve computation speed is to directly perform OCT data reconstruction on the acquisition card using a field-programmable gate array (FPGA). However, this requires disclosing the algorithm process to the manufacturer before customizing the FPGA, which poses an issue of expensive costs.

Many swept lasers typically utilize either forward or backward sweeping spectra and block or neglect the spectra in another sweeping direction. This will lead to a usable sweeping duty cycle of about 50% and A-scan speeds of only a few hundred kHz. Therefore, utilizing bidirectional scanning spectra for OCT imaging is the most direct approach to doubling the imaging speed. For the spectral correction algorithm, adding the number of FBGs theoretically contributes to better aligning the bidirectional spectrum. However, an excessive number of FBGs will impact the phase continuity of MZI signals, leading to interpolation errors. In the OCT image reconstruction process, our proposed spectral correction algorithm does not significantly extend the computation time, as the most time-consuming step is the NUDFT [38]. Due to the requirement for switching laser swept speeds, fixed-frequency resonant mirrors are not suitable for this system. To address the issue of poor repeatability in 500 Hz B-scans, we tested various galvanometer scanning, including Saturn5 (ScannerMAX), 6210, and 6215 (Cambridge Technology). The 6210 model exhibited the best performance. Aligning each B-scan using position feedback signals reduces requirements on the scanner itself, allowing for a broader range of suppliers and lowering costs. Additionally, optimizing the scanner's response to specific waveforms for faster B-scan scanning will be achieved by adjusting the proportional-integral-derivative controller on the driver board [39].

Myopia is a widespread refractive error issue globally, sparking increased interest in understanding the link between peripheral eye length, retinal contour, and myopia. However, methods centered around TD-OCT require rotating the subject's eyes or head to measure peripheral eye length, leading to inevitable motion errors. Our approach directly extracts AAL parameters from B-scan images, offering a rapid, motion-error-free solution with a broad FOV. Utilizing dual-axis simultaneous scanning [40] and under-sampling [41] to extend OCT imaging depth will be crucial for obtaining AAL parameters of the entire fundus. This information holds great value for designing functional lenses and evaluating therapeutic effects, particularly for multifocal center distance soft lenses and orthokeratology lenses.

Retinal pathologies can potentially lead to irreversible vision impairment, such as macular ischemia observed in conditions like diabetic retinopathy and other retinal vascular diseases. Quantitative assessment of superficial retinal vessel density and foveal avascular zone area serves as a promising biomarker for various retinal conditions. While previous studies [42,43] indicated that using only axial length for correcting ocular magnification errors is accurate, they are only suitable for measuring the central FOV. With our whole eye OCT system and Eq. (1), accurate measurements of the true fundus size across all FOV can be obtained, representing a significant advancement. When measuring AAL for all fields, the current challenge lies in adjusting the slit lamp's position. This can be addressed by incorporating a scanning laser ophthalmology module, making imaging at any position on the fundus more accessible.

5. Conclusion

We have developed a 1 MHz SS-OCT imaging system for comprehensive in vivo whole eye imaging. The spectral correction algorithm significantly improves the precise alignment of adjacent A-lines, enhancing the image quality of ocular structures and revealing the microstructure of various retinal layers. We recording unprecedented (to our knowledge) high-quality en face OCT/OCTA images with a 500 Hz B-scan rate using the registration method of galvanometric scanning. Whole eye imaging, achieved by switching of the optical path between the anterior segment and the retina, can provide a more comprehensive set of ocular parameters. The AAL parameter, we proposed, enables precise measurement of retinal dimensions. The MHz whole eye OCT imaging system proposed in the report can be regarded as a versatile in vivo ophthalmic imaging platform with the capability for quantitative size measurements.

Funding

National Natural Science Foundation of China (62394310, 62394311, 82371112); Beijing Municipal Natural Science Foundation (Z210008); Shenzhen Science and Technology Program (KQTD20180412181221912).

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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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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Figures (10)

Fig. 1.
Fig. 1. Schematic diagram of the experimental setup and timing diagram. (a) System schematic diagram. SS Laser, swept source laser; FOC, fiber optic coupler; OS, optical switch; ODL, optical delay line; BPD, balanced photodetector; FBG, fiber Bragg grating; PD, photodetector; PC, polarization controller. (b) The 3D modeling diagram illustrates the sample arm optical path, with purple indicating the anterior segment pathway and pink indicating the retinal pathway. FC, fiber collimator; VL, varifocal lens; GS, galvanometer scanners; FM, flip mirror; SL, scan lens; DM, dichroic mirror; CM, camera; DS, display screen; OB, objective lens; L1-L2, lens; M1-M3, mirror; MZI: Mach–Zehnder interferometer. (c) Sequential logic diagram of the System. T1, output spectral signals of the swept source Laser; T2, output trigger signals of the swept source Laser; T3, clock signals of galvanometer scanners. Tx, driving signals of X-Galvanometer. Ty, driving signals of Y-Galvanometer. Up and down refer to the output spectra of the laser during the forward and backward sweeping. ${\lambda _1}$ and ${\lambda _2}$ refer to the starting and ending wavelengths of the output spectra.
Fig. 2.
Fig. 2. Optical design of the sample arm. (a-b) Retinal imaging modality with optical ray trace, showing optical spot diagram for three wavelengths across a ± 8 mm scan, revealing diffraction-limited performance. The Airy radius is 18 µm. (c-d) Anterior imaging modality with optical ray trace, showing optical spot diagram for the three design wavelengths over a ± 7 mm scan, indicating diffraction-limited performance. The Airy radius is 20 µm. GS-X, X-galvanometer scanners; GS-Y, Y-galvanometer scanners; FM, flip mirror; SL, scan lens; DM, dichroic mirror; L1, lens; M1-M3, mirror; OB, objective lens.
Fig. 3.
Fig. 3. The principles and results of the proposed spectral correction algorithm. (a) Spectrogram and unwrapped phase image of one cycle of the bidirectional MEMS-VCSEL. (b) The results after phase differentiation. (c) Phase results after filtering. (d)-(g) B-scans of a 1mm glass slide after correction. δ=0 signifies that the actual calibration coefficient is the same as the optimal calibration coefficient. δL = 20, δL = 50 and δL = 100 respectively denote the outcomes when the actual correction coefficient deviates from the optimal correction coefficient by 20, 50, and 100 sampling points in spectral length.
Fig. 4.
Fig. 4. Retinal OCT imaging results using the spectral correction algorithm. (a) High-resolution B-scan image of retinal OCT after correction (averaged 30 times). (b) $\delta = 0$ denotes that the actual calibration coefficient is identical to the optimal calibration coefficient. (c) $\delta L = 50$ represent the outcomes when the actual correction coefficient deviates from the optimal correction coefficient by 50 sampling points in terms of the spectral length. (d) $\delta S = 50$ represent the outcomes when the actual correction coefficient deviates from the optimal correction coefficient by 50 sampling points in terms of the starting point. ILM, internal limiting membrane; ELM, external limiting membrane; EZ, ellipsoid zone; IZ, interdigitation zone; RPE: retinal pigment epithelium.
Fig. 5.
Fig. 5. Results of the registration method applied to galvanometric scanners. (a) The blue and red curves depict the input control signal and the PFB signal, respectively. (b)-(c) Original results and processed results with the PFB signal for a USAF 1951 resolution target (10 line-pairs per millimeter). (d) Boxplot of the statistical distribution of pixel offsets between the positive and negative scans of the galvanometer. (e)-(f) Original results and processed results with the PFB signal for en face images of the retinal OCT. (g)-(l) Magnified images of the region of interest selected by the red rectangles in (e)-(f).
Fig. 6.
Fig. 6. The stability analysis of interference signals based on the bidirectional MEMS-VCSEL laser. (a) A set of clock signals obtained based on the bidirectional spectra, repeated 5000 times. (b) An enlarged view of the selected area in the forward spectra marked by a blue rectangle. (c) An enlarged view of the selected area in the backward spectra marked by a red rectangle.
Fig. 7.
Fig. 7. Quantifying the performance of the OCT System. (a)-(b) Sensitivity roll-off curves of the OCT system in both Mode 1 and Mode 2.
Fig. 8.
Fig. 8. OCT and OCTA imaging of the whole eye. (a) The high-definition B-scan of anterior segment OCT in Mode 2. The average repetition is 30 times. (b) The enlarged view of the region outlined by the yellow rectangle in (a). (c) Retinal ${60^\circ }$ OCTA imaging on Mode 1, 2000 A-lines ${\times} $500 B-scans ${\times} $4 times.
Fig. 9.
Fig. 9. The 3D imaging results of whole eye OCT. Cross-sectional views of the 3D images from different perspectives are shown in panels (a)-(c). The yellow arrows indicate the position of the AL.
Fig. 10.
Fig. 10. The precise measurement of retinal size. (a) - (b) Retinal OCT images of myopic eyes with -1D and -5D, obtained using the Mode 2 that has an ultralong imaging depth. Structural features of the eyes, denoted by yellow arrows, encompass the macular area, optic disc, and the posterior and anterior surfaces of the cornea. (c) and (d) The relationship between the axial length and the FOV for two myopic eyes. (e)-(f) The enlarged views of the white rectangular region in (a) and (b). The red curve delineating the boundary of the retina.

Equations (1)

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L true = i = 1 n 1 1 2 ( A A L i + 1 + A A L i ) Δ θ
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