Spectrally Extended Line Field Optical Coherence Tomography Angiography

Optical coherence tomography angiography (OCTA) has been established as a powerful tool for investigating vascular diseases and is expected to become a standard of care technology. However, its widespread clinical usage is hindered by technical gaps such as limited field of view (FOV), lack of quantitative flow information, and suboptimal motion correction. Here we report a new imaging platform, termed spectrally extended line field (SELF) OCTA that provides advanced solutions to the above-mentioned challenges. SELF-OCTA breaks the speed limitations and achieves two-fold gain in FOV without sacrificing signal strength through parallel image acquisition. Towards quantitative angiography, the 'frequency flow' imaging mechanism overcomes the imaging speed bottleneck by obviating the requirement for superfluous B-scans. In addition, the 'frequency flow' imaging mechanism facilitates OCTA-data based motion tracking with overlap between adjacent line fields. Since it can be implemented in any existing OCT device without significant hardware modification or affecting existing functions, we expect that SELF-OCTA will make non-invasive, wide field, quantitative, and low-cost angiographic imaging available to larger patient populations.

OCTA relies on moving red blood cells to contrast microvasculature against static tissue. This contrast signal induced by blood flow is extracted by detecting variations of OCT signals between consecutive scans taken at the same location within a Y-scan cycle. A typical OCT device adopts the pointscanning mechanism, in which the beam scanners steer the beam so that the light spot dwells at one lateral position at a time. Because of the sequential nature of this mechanism, achievable lateral FOV is solely dependent on A-line rate. This dependency is especially acute in OCTA, since 2-5 repeated B-scans are required for motion contrast. As a result, FOV of most ophthalmic OCTA systems is much smaller than the standard-of-care technologies [1,2], even though capillary fine details are always sacrificed due to under-sampling [1,7]. Swept-source technologies are promising in achieving ultrawide field OCTA with dramatically improved A-line rate, whereas, increases in imaging speed decrease the OCT signal and speed is ultimately limited by the signal to noise requirements given the constraint of allowable light exposure [2]. Therefore, the trade-off between FOV and signal quality is inherent with current OCTA, as long as both are solely dependent on the A-line rate.
Wide-field OCTA is not possible without effective tracking and correction of motion artifacts. For ophthalmic applications, eye tracking relies on additional imaging hardware such as infrared fundus camera or scanning laser ophthalmoscopy [8][9][10], which can extend the available imaging time beyond the few seconds when patients can fixate without saccades or blinking [2]. However, fundus images are not adequately sensitive to small motions due to their relatively low resolution. Since there is always a latency, there are errors that are not correctable by hardware-based eye tracking [2]. In addition, the increased system complexity and cost are also practical concerns. Self-navigated motion correction method represents a new trend to tackle these issues, which suppresses eye motion and blinking artifacts on wide-field OCTA without requiring any hardware modification [11]. However, none of the existing software-based techniques is able to track lateral motion, leaving significant artifacts uncorrected. Improvement in motion artifact management requires a new technology that is capable of tracking motion with high precision and minimal latency, and ideally without additional hardware.
Quantification of flow velocity is of great interest with regards to disease diagnosis and management [1,2,[12][13][14][15]. It has been well understood that OCTA flow signal is primarily affected by inter-scan time, which is the time interval between repeated B-scans at the same position. If the inter-scan time is long, the OCTA signal saturates easily for higher range of velocities, so that relation between flow speed and signal is nonlinear and complicated [14,[16][17][18]. In contrast, a short inter-scan time can better distinguish higher range of velocities; however, sensitivity to slow flow is reduced, as the red blood cells do not have sufficient time to move far enough to produce a detectable signal variance [2]. Choi [12] and Wei [19] have managed to extend the dynamic range of detectable flow velocity by generating OCTA signals of multiple inter-scan time. However, these point-scanning based approaches requires more B-scan repeats than the standard OCTA, further limiting the FOV. A new technique capable of acquiring OCTA signals of multiple inter-scan time independent of the number of B-scan repeats is needed to have this important metric in routine applications.
The core of OCTA techniques is algorithms that computes OCT signal variations, which include, but not limited to, optical microangiography [20], speckle variance [21], phase variance [22], splitspectrum amplitude-decorrelation angiography (SSADA) [22] and correlation mapping [23]. Interestingly, split-spectrum and subsequent frequency compounding increase the image quality for the algorithms most commonly implemented for ophthalmic applications [24,25]. The reason is that because speckle pattern is wavelength dependent, by splitting the full OCT spectrum into a number of narrower bands, frequency compounding reduces spectral-dependent speckle noise in flowgenerated speckle signals [26]. The representative technique, SSADA, has been extensively validated in clinical settings [12,14,15,27]. Splitting spectrum creates a new dimension for parallel image acquisition. Spectrally encoded OCT have been proposed to achieve parallel structural image acquisition [28]. However, towards high-quality blood flow imaging, how different frequency components can be compounded at the same image position is not known.
We report a novel imaging platform, termed spectrally extended line field OCTA (SELF-OCTA), which achieves frequency-temporal compounding through a 'frequency flow' imaging mechanism. SELF-OCTA provides advanced solutions to the above-mentioned challenges towards significantly improved clinical utility of OCTA.

Method
We have developed a spectral-domain OCT (SD-OCT) device working at the center wavelength of ~1310 nm, which allows convenient switching between the SELF scheme and the standard pointscanning scheme (Fig. 1A). The construction of the imaging system is mostly the same as a typical OCT device except a set of prisms in the sample arm. Detailed information on system construction is provided in Supplementary Information. With a collimating lens of 10 mm focal length and objective lens of 50 mm focal length, the theoretical lateral spot size at 1310 nm is ~27 µm (full-width at half maximum, FWHM). SELF-OCTA achieves 2D (depth and slow axis) priority scan by spectrally extending the polychromatic beam to a line field along Y-axis in the focal plane of the objective lens (Fig. 1B). In this study, we imaged skin vasculatures at the palm side of the proximal interphalangeal (PIP) joint of the middle finger with healthy human subjects. This study was approved by the Institutional Review Board (IRB) of Nanyang Technological University (IRB-2016-10-015 and IRB-2019-05-050). For the experiments conducted with the point-scanning scheme and total image acquisition time of 4.096 s ( Fig. 3 and Supplementary Fig. 7), the optical power incident on the sample was 4.74 mW. For the experiments conducted with the point-scanning scheme and total image acquisition time of 3.26 s, the optical power incident on the sample was 9.1 mW (Fig. 4). We used ~9.10 mW for all the experiments with the SELF scheme. The optical power incident on the skin is below American National Standards Institute (ANSI) exposure limit for skin safety.
Since the thermal damage threshold of an extended source is higher than the corresponding point source [29][30][31], higher maximum permissible exposure (MPE) is allowed in favour of signal strength [32]. The optical power limit in the SELF scheme, is calculated using the correction factor for exposure limit of extended sources for ocular safety [32,33]. By applying the 'Most Restrictive Ratio' method [34,35], the angular subtense in Y-axis generated by the prisms is ~3.176 mrad and the normalized partial power within the angular subtense is 0.799 (Supplementary Fig. 1). The corrected optical power incident on the skin in the SELF scheme is 9.25 mW. Detailed method to determine the corrected sample power is provided in Supplementary Information.
The X-axis scanning protocol is identical between both schemes: the scanning step size Δx is set to be 12.8 µm to satisfy the Nyquist sampling requirement, and the number of repeated B-scans at the same location N equals to 2. The Y-axis scanning protocol, however, may be different. For the ease of comparison, we define Y-scan positions as Y positions illuminated by the first spectral band during each Y-scan cycle (Figs. 1C&D). In the point-scanning scheme, the inter-scan distance, which is the distance between two adjacent Y-scan positions, is equal to the X-axis scanning step size Δx, that is, Y image positions are the same as Y-scan positions (Fig. 1C). We followed SSADA algorithm for processing data acquired from the point-scanning system [22], in which we split the source spectrum into M = 16 equally spaced bands in wavenumber domain using Hamming filters (Supplementary Fig. 2A and Supplementary Information), and all M partial-spectrum decorrelation frames are averaged to obtain the OCTA signal at one Y image position. In SELF-OCTA, we also split the source spectrum into M = 16 equally spaced bands using the same Hamming filters. The spacing between adjacent bands is Δy = Δx, so that each spectral band samples a distinct Y image position ( Fig. 1D and Fig. 2A). The positioning error caused by the nonlinear frequency-space relation is negligible (Supplementary Fig. 3). By setting the inter-scan distance to be L·Δx (L = 2, 4, 8, or 16), achievable FOV is multiplied by a factor of L. In general, M spectral bands acquired at j-th Y-scan position illuminate M consecutive Y image positions: (j -1)·L+1, (j -1)·L+2, …(j -1)·L+M, respectively. In other words, M/L light beams of distinct spectral bands dwell at the same lateral image position sequentially in time during Y-axis scan. This is analogous to the flow production process, where a number of Y image positions are addressed in parallel, and frequency components at each image position is 'assembled' during a number of consecutive Y-scan cycles. We term this slow axis imaging mechanism 'frequency flow'.
The split-spectrum data is processed to generate M partial-spectrum decorrelation frames through Discrete Fourier transform (DFT) and amplitude decorrelation, which is similar to SSADA [22]   The Hamming window length is ~39 nm (Supplementary Figs. 2A), so that the axial resolution is measured to be 28.5 µm in tissue with refractive index of tissue of 1.38 (Fig. 2C). We model the multiplication between interferometric spectral data and a Hamming filter as a convolution in Y-axis, that is, the polychromatic lateral point-spread function along Y-axis is the convolution between the monochromatic point-spread function (PSF) and the Hamming window (Supplementary Figs. 2B&C). The lateral resolution is characterized by use of the 10-90% width of an edge scan profile as well as imaging a resolution chart (Figs. 2D&E). The lateral PSF in Y-axis is broadened to 1.51 times of the monochromatic PSF due to the convolution in Y-axis, which agrees well with the model (Supplementary Fig. 2C). We use a one-dimensional deconvolution algorithm to restore the lateral resolution along Y-axis in the en face projections (Fig. 2B). The 10-90% edge width restored by deconvolution is comparable to that of monochromatic light (Fig. 2D), so that isotropic spatial resolution is achieved in SELF-OCTA, which are also corroborated by the en face images of resolution chart (Fig. 2E). After deconvolution (lower panel, Fig. 2E), group 4 element 5 with line width of 19.69 µm can be unequivocally resolved in both X and Y directions, and Y-axis resolution is comparable to that of X-axis, which is the point-scanning direction. Details of Hamming filters, deconvolution, and OCT structural image processing are provided in Supplementary Information.
Images were acquired at an A-line rate of 50,000 Hz and 512 A-lines per B-frame for both schemes unless otherwise specified. For side-by-side comparison, we imaged the same skin region by careful alignment using cross-sectional OCT previews, except for Supplementary Fig. 7. We used homemade vertical and horizontal hand rests to minimize motion. We manually segmented the crosssectional angiograms into three layers according to image depth with respect to the top of capillary loops (Figs. 3A-D): the first layer is ~180 µm thick in tissue, which includes most of capillary loops; the second layer is also ~180 µm thick in tissue, which mainly depicts subpapillary plexus; the third layer is ~360 µm thick in tissue, which corresponds to the skin layer with deep vascular plexus. Detailed information on image acquisition and image format are provided in Supplementary Information.
In addition, to demonstrate motion tracking and correction, we acquired OCTA images while deliberately moving hands along the lateral directions (Fig. 6). Before image acquisition, we immobilized a short segment of piano wire (F1-8265, Fiber Instrument Sales, Inc.) to the skin surface with the refractive index matching gel. The wire was aligned along Y-axis or oblique with respect to Y-axis so that it served as the reference for lateral motion (Fig. 6A). As mentioned above, a 3D OCTA dataset is acquired during each Y-scan cycle with the SELF-OCTA scheme, which allows us to track lateral motion using en face projects of these 3D angiograms. Since each en face projection is 512 × 16 pixels (X × Y) in size, with L = 2 there is an overlap of 14 pixels along Y-axis between projects of adjacent Y-scan cycles (Fig. 6B). We measured lateral displacement between the overlap portions by 2D cross-correlation [36]. Note that we excluded the piano wire image from the input of the motion tracking. Details of motion tracking and correction algorithms are provided in Supplementary Information.

Results
We compared FOV between two schemes under the same conditions: 512 A-lines per B-frame, 400 Y-scan positions, and a total acquisition time of 4.096 s (Fig. 3). The FOV scanned with the pointscanning scheme is 6.55 mm x 5.12 mm (Figs. 3E1-4). SELF-OCTA provides twice as large FOV when we doubles the inter-scan distance as illustrated in Fig. 1D (Figs. 3F1-4&G1-4). With the same display contrast, the image quality of SELF-OCTA is comparable to that of the point-scanning scheme. First, through one-to-one comparison the vascular microstructures are almost identical between the point-scanning and SELF-OCTA images, including the capillary loops (Figs. E2, F2&G2). The SELF-OCTA en face images are slightly less crispy before deconvolution because of the convolution effect mentioned above (Figs. 3F1-4). Nevertheless, this insignificant issue is corrected after deconvolution (Figs. 3G1-4). Secondly, the penetration depth is also comparable as can be seen in the en face images of deep vascular plexus (Figs. E4, F4&G4), and cross-sectional angiograms (Figs. 3B-D and Supplementary Fig. 4). Thirdly, the mean decorrelation, measured from one-to-one matched vascular areas (Supplementary Fig. 5), are also comparable between the point-scanning OCTA (0.206 ± 0.006) and SELF-OCTA (0.204 ± 0.004) (Fig. 3H) (student's t-test, p = 0.23). The speckle contrast of en face SELF-OCTA images (0.439 ± 0.059) is close to that of the point scanning scheme (0.353 ± 0.036), although the number of partial-spectrum decorrelation frames to be averaged at each Y image position is half of that of the point-scanning scheme. We attribute this relatively low speckle contrast to the fact that the partial-spectrum decorrelation frames at a Y image position are acquired at different time.  Fig. 4B1-3). This artifact damping mechanism is analogous to a selective low-pass filter along Y direction, which does not affect the signal. In a separate experiment, we deliberately generated motion artifacts by removing the vertical hand rest before image acquisition. Corresponding motion artifacts in SELF-OCTA en face images appear as low-intensity variations in the background (Supplementary Fig. 6, Fig. 7B&C and Supplementary Movie 1).
SELF-OCTA allows tailoring exposure time and inter-scan time without affecting FOV or total acquisition time. To validate this, we firstly acquired a 3D dataset with the point-scanning scheme with a nominal FOV of 6.55 mm x 6.55 mm and a total acquisition time of 3.28 s. The inter-scan time was 6.4 ms with an A-line rate of 80,384 Hz and 512 A-line per B-frame (Figs. 4A1-4). In the SELF scheme, we set the inter-scan distance to be 4Δx and the A-line rate to be 22,000 Hz, so that we were able to achieve 3.65 times longer inter-scan time and the same nominal FOV within 2.98 s (Figs. 4B1-3). Obviously, the advantage of longer inter-scan time is the significantly increased sensitivity to flow in small vessels and capillaries, which are largely invisible in the point-scanning OCTA images due to relatively shorter inter-scan time (Figs. 4A1-3, 4B1-3, 4D&4E). Notably, a practical advantage of longer integration time is ~10% larger X-scan duty cycle (Figs. 4A3&B3).
In addition, most SD-OCT devices are relative intensity noise (RIN) and electrical noise limited at working A-line rate. In the current device, total SNR is measured to be 9.94 dB lower at 80,384 Hz than that at 22,000 Hz A-line rate (Fig. 4C), which can be approximately broken down to 5.84-dB drop in signal due to reduced exposure time and 4.1-dB drop in signal to RIN ratio (SNRRIN). This SNRRIN drop significantly elevates the noise background and overwhelms weak vessel signals from small vessels (Fig. 4A1-3&4D) compared with SELF-OCTA images (Fig. 4B1-3&4E). Towards flow velocity quantification with high dynamic range, we have developed a partial B-frame scanning protocol that realizes multiple inter-scan time without increasing the number of B-scan repeats based on the SELF-OCTA platform. We split each B-scan of 384 A-lines into a half B-scan of 192 odd points (odd scan) and a half B-scan of 192 even points (even scan), so that there are 4 half-B-scans in a Y-scan cycle when N = 2 (Fig. 5A). OCTA images with inter-scan time of ΔT = 7.68 ms and ΔT/2 = 3.84 ms respectively can be achieved by re-arranging the order of half B-scans (Fig. 5A). Owing to the 'frequency flow' imaging mechanism, this protocol does not introduce any artifact since at each Y imaging position there are equal number of partial-spectrum decorrelation frames with interscan time of ΔT and ΔT/2. It is worth mentioning that this partial B-frame scanning protocol is not supported by the point-scanning platform since the inter-scan time, and consequently OCTA signal at odd and even pixels will be different. For demonstration purpose, we introduce a simplified model to reconstruct angiograms with high dynamic range (Fig. 5B). Briefly, we assume that, over the decorrelation signal range of [σ, Dmax-σ], flow velocities and decorrelation signals are linearly related, where Dmax is the mean saturation decorrelation and σ is the standard deviation of the saturation decorrelation. Based on this assumption, the ratio between decorrelation signals acquired with ΔT (DΔT) and ΔT/2 (DΔT/2) is a constant, α. If we multiply decorrelation profile of ΔT/2 with α, the new decorrelation profile, α*DΔT/2, has a higher saturation limit (Fig. 5B). The high dynamic range en face angiogram is reconstructed using both the angiogram acquired with ΔT and the angiogram corresponding to α*DΔT/2. Detailed process to generate the high dynamic range angiogram is provided in the Supplementary Information. Since this simplified model is based on a number of assumptions and approximations, readers are referred to previous phantom studies for an accurate model [16][17][18]. Nevertheless, this high dynamic range angiogram combines the merits of both inter-scan time (Figs. 5C-E): signals from small vessels with slow flow speed are retained which are otherwise invisible or silent in angiograms acquired with ΔT/2 (orange dash-line boxes, Fig. 5 C&E); signals from vessels with high flow velocities that are saturated in angiogram acquired with ΔT become approximately linearly related with the corresponding flow velocities (blue solid-line boxes, Fig. 5 D&E). The high dynamic range is also evident in the corresponding histograms (Fig. 5F).
To demonstrate motion tracking and correction, the subject deliberately moved the hand in the lateral directions during image acquisition. Since the piano wire attached with the skin blocks the light (Fig.  6A), in the en face angiograms the shadow appears bright due to high decorrelation of background noise (Figs. 6B, 6F&6G). There is a 14-pixel overlap in Y-axis between en face projections of 3D angiograms acquired in each two adjacent Y-scan cycles, as can be appreciated with the images of an air bubble in the refractive index matching gel (arrow, Fig. 6B). In a representative experiment, 2D lateral motions can be measured at the subpixel level throughout the whole FOV (Figs. 6C&D). The range of detected motion velocity was from 0-2.2 µm/ms (Fig. 6E). The performance of motion correction can be evaluated by comparing en face angiograms before (Fig. 6F) and after motion correction (Fig. 6G). The distorted piano wire image is largely corrected, which validates motion tracking and correction in the X direction. With an oblique direction of the piano wire with respect to Y-axis, the performance in both directions is demonstrated in Supplementary figs. 8&9.

Discussions
Unlike OCT structural imaging where cross-sectional viewing is preferred, OCTA is inherently three dimensional and typically displayed with en face projections. Therefore, 2D and 3D priority scanning mechanisms are superior to the conventional depth priority scanning mechanism in terms of imaging speed [28,[37][38][39]. As a 2D priority scanning platform, SELF-OCTA enables simultaneous signal acquisition from parallel lateral locations. This parallelization makes volumetric signal acquisition faster compared with the point-scanning scheme running with the same A-line rate. In achieving larger FOV, an important feature of SELF-OCTA lies in that it has more sensitivity budget than the pointscanning scheme as higher MPE is allowed. In this study, we show a two-fold gain in FOV with no penalty in signal compared with the point-scanning scheme. Larger FOV can be readily achieved by increasing inter-scan distance independent of specifications of light source or signal detection hardware. Currently, ultrafast OCT systems are not clinically available, at least not to large patient populations. SELF-OCTA makes it possible for clinical OCTA devices to break their speed limit and achieve more than two times wider FOV by simply adding one optical element in the sample arm. Future translation of SELF-OCTA to ophthalmic imaging will fill the gap between OCTA and the standard-of-care tools in FOV, providing invaluable information about vascular changes that involve peripheral retinal regions.
Lack of flow velocity information in the current clinical systems is also associated with the imaging speed limitation as revealed by previous phantom studies [16][17][18][19]. Because of the above-mentioned trade-off between flow-signal linearity and sensitivity to slow flow, a wide range of inter-scan time from tens of microseconds to a few milliseconds are needed in order to cover the full range of retinal capillary flow from 0.4-3.0 mm/s [16,19]. Current ultrahigh speed research prototypes provide an inter-scan time range of 1.5-4.5 ms, which are only applicable to flow velocity of <0.6 mm/s [16,19]. Even this modest dynamic range requires at least three B-scan repeats [19]. Eventually, more B-scan repeats will be needed to extend the range to the higher flow speed, which will be at substantial cost of imaging speed, and consequently FOV. The 'frequency flow' mechanism offered by the SELF-OCTA realizes multiple inter-scan time independent of B-scan repeats. This unique capability overcomes the imaging speed bottleneck for velocimetry over large FOV. More importantly, since the inter-scan time of each partial-spectrum decorrelation frames can be adjusted independently over a wide range through the partial B-frame approach, the optimal trade-off between dynamic range and sensitivity of flow detection can be achieved. Therefore, SELF-OCTA will potentially overcome a wide variety of challenges where differentiation of flow velocity and degrees of flow impairment is of great clinically significance, for example, lack of flow velocity in flow index of large vessels for assessing optic disc perfusion [14] and difficulties in quantifying slow flow in microaneurysms [40].
The total spectral bandwidth determines the angular subtense, which further determines the MPE and the length of line field. The most restrictive scenario for SELF-OCTA will be posterior segment imaging centred at 1060 nm, where the maximum usable bandwidth is no more than 100 nm due to water absorption. The performance of SELF-OCTA will not be significantly affected by this limitation. For example, one can set the angular subtense to be 6 mrad, so that the corresponding length of line field at retina is 6 mrad x 17 mm = 102 µm. Setting the spacing between adjacent spectral band to be 7.7 µm and Hamming window length to be 40 µm (~40 nm), the spectrum can be split into 12 bands. Under these conditions, the axial resolution is estimated to be 16.5 um in tissue (refractive index = 1.38), and the lateral spot size in Y-axis is estimated to be 1.36 times larger than that of the monochromatic beam.
Deconvolution works well in restoring lateral resolution in Y-axis. Because deconvolution is an intensity-based model, there have been concerns when phase information is involved in the 3D coherent image formation [41]. Other concerns of using deconvolution in imaging scattering tissues are that the optical transfer function may not be accurate and that it is sensitive to speckle and noise [41]. In SELF-OCTA, artifacts associated with deconvolution are unnoticeable due to the following facts. First, the convolution involves phase information only in the depth dimension. Second, the speckle contrast is substantially reduced by frequency-temporal compounding as speckles of partialspectrum decorrelation frames are fully uncorrelated (Supplementary Fig. 10). Thirdly, the optical transfer function is accurate since convolution is done digitally.
In the 'frequency flow' imaging mechanism, line-fields of adjacent Y-scan positions are overlapped in Y-axis, which for the first time makes it possible to track lateral motion with OCTA data. Current selfnavigation motion correction method can only provide an indicator that motion occurred, and lack of quantitative lateral motion trajectory information results in artifacts such as vessel interruptions and low sensitivity of ocular drift [11]. SELF-OCTA may complement the self-navigation method. The typical angular velocity of ocular drift during fixation is 1°/s, which corresponds to a translational retinal motion of 0.17 µm/ms if the radius of retina is 10 mm. Such slow motions should be readily detected with SELF-OCTA as shown in Fig. 6. The overlap between scanned areas of adjacent Y-scan cycles may be used to correct vessel interruptions. Combination of SELF-OCTA and self-navigation motion correction method will potentially obviate the problems with hardware-based tracking systems.
Currently, SD-OCT is the most widely used system, mainly due to the matured technology, excellent phase stability for functional imaging, and lower cost. In SD-OCT, RIN is inversely proportional to exposure time, prohibiting this well-established technology from high-speed applications, particular when compared with SS-OCT where RIN is largely suppressed by dual-balanced detection [6]. As a result, the speed of SD-OCT clinical devices is limited to 70k Hz in contrast to 100-200 kHz of SS-OCTA [2]. SELF-OCTA disassociates imaging speed with exposure time, which overcomes this standing problem and will make SD-OCTA viable for high-speed OCTA applications.
In conclusion, SELF-OCTA platform facilitates multiple important technological advancements towards wide field, quantitative, and low-cost angiographic imaging. SELF-OCTA breaks the speed limitation without sacrificing sensitivity, so that wide field imaging will be realistic in devices with speed limitation, in particular, SD-OCT. SELF-OCT also overcomes the speed bottleneck of quantitative flow velocity imaging, making this important function available with little cost. Last but not the least, OCTAdata based motion tracking capability may potentially simplify the complexity and reduce the cost of OCTA devices. In principle, by simple modifications in the sample arm, all the existing clinical devices, regardless of type and A-line rate, should acquire these advanced imaging capabilities without affecting existing functions. We expect that SELF-OCTA will make wide field, quantitative OCTA an inexpensive technology, therefore, widely available to larger patient populations.

Imaging system construction and characterization
We combine two superluminescent diode modules (IPSDS1313 and IPSDS1201C, Inphenix, CA, USA) with a 50:50 fibre coupler (TW1300R5A2, Thorlabs Inc, USA) (Fig. 1). The combined light source provides a radiation from 1230 nm to 1360 nm (-6 dB). The outputs of the fibre coupler are connected to two optical circulators (PIBCIR-1214-12-L-10-FA, FOPTO, Shenzhen, China), which guide the light beams to the sample arm and reference arm, respectively. The light back reflected from the reference arm and back-scattered from the sample arm are combined using a 95:5 fibre coupler (WP3105202A120511, AC Photonics, CA, USA). In the sample arm of the point scanning scheme, the sample beam is firstly collimated by an achromatic lens L1 (AC050-010-C, Thorlabs Inc., USA) before reflected by a mirror (RM) and a pair of galvanometer scanners and focused by an objective lens L2 (AC254-050-C, Thorlabs Inc, USA).
In the SELF-OCTA scheme, the mirror (RM) is replaced by a set of three identical prisms (N-SF11, PS872-C, Thorlabs Inc.) with apex angle of 30° and angular spacing of ~56.9°. Switching between the point scanning scheme and SELF-OCTA scheme is realized with a manual translation stage (Fig.  1A). The prism is with anti-reflection coating so that one-way transmission efficiency of three prisms was measured to be 94%. The polychromatic sample beam is dispersed by the prisms into a line along the slow (Y) axis in the focal plane of the objective lens L2 (Fig. 1B). The spectrometer is comprised of a collimating lens L5 (AC254-035-C, Thorlabs Inc., USA), a transmission grating (PINGsample-106, Ibsen Photonics, Denmark), a home-made multi-element camera lens and a line scan camera (LDH2, Sensors Unlimited, USA). The camera pixel size is 25 µm by 500 µm (width by height) and we used all 1024 pixels. The total spectrometer efficiency was measured to be 0.61, including the quantum efficiency of the camera. The spectral resolution is 0.148 nm, resulting in a total ranging depth of 2.89 mm in air. The axial resolution was measured to be 9.82 µm in air. The 6-dB ranging depth was measured to be 1.6 mm in air and the sensitivity roll-off over depth is ~3.75 dB/mm. With the optical power incident on the sample being 4.74 mW, the sensitivity measured at ~150 µm from DC is 108.52 dB, 102.56 dB, and 98.58 dB at the A-line rate of 22k Hz, 50k Hz, and 80k Hz, respectively, which agree with the theoretical predictions (Fig. 4C).
We used 16 Hamming windows with size of 263 pixels and spacing of 52 pixels to generate 16 spectral bands (Supplementary Fig. 2A), respectively. The axial resolution (FWHM) of each band was measured to be ~28.5 µm in tissue (refractive index = 1.38) (Fig. 2C). The transverse resolution (FWHM) of each band was measured to be 39.6 µm (10-90% width of an edge scan) because of the convolution between the Hamming window and monochromatic point-spread function (PSF) (Supplementary Fig. 2B), which is 1.51 times larger than the monochromatic transverse resolution and agree well with theoretical prediction (Supplementary Fig. 2C). The trade-off between axial and transverse resolution along Y-axis is characterized in Supplementary Fig. 2D.
The theoretical transverse spot size at 1310 nm is ~27 µm (full-width at half maximum, FWHM) since the nominal mode field diameter of SMF-28e fibre is 9.2 µm at 1310 nm. The monochromatic transverse resolution at 1310 nm was approximated to be 26.2 µm by measuring 10-90% width of an edge scan using the part of signal at the centre of the spectrum with a narrow line width (~1.5 nm FWHM) (Fig. 2D). For a Gaussian spot, the lateral resolution, defined at its e -2 radius, can be shown to be 0.78 times the 10-90% edge width [42], so that the monochromatic spot size (FWHM) is estimated to be 24.1 µm.
For deconvolution along Y direction, we used Lucy-Richardson method (deconvlucy in MATLAB®). We used the Hamming window mentioned above as the point-spread function (PSF in deconvlucy) and damping threshold of 2.

Maximum permissible exposure of line field
Following the literature [35], the relevant 'most restrictive' evaluation angular subtense is the one with the maximum ratio of partial power/ evaluation angular subtense. The partial power is the total optical power contained in the evaluation angular subtense. The intensity profile of the line field was measured by scanning a fiber tip (SMF-28e) along Y-axis in the focal plane of the objective lens and record the optical power coupled into the fiber (Supplementary fig. 1A). Since it is a line illumination, the angular subtense along X-axis takes 1.5 mrad [34]. Therefore, the ratio of partial power/ evaluation angular subtense According to the equation (1), the angular subtense in Y-axis (ߙ ) obtained using 'Most restrictive ratio' analysis is 3.176 mrad (Supplementary fig. 1B). The extended source correction factor CE is (3.176 +1.5 mrad) /2/1.5 mrad = 1.5587. Note that power limit calculated using CE applies only to the partial power within the angular subtense δ, instead of the total power. There are 20.11% of total power that is outside the angular subtense δ. For the experiments conducted with the point-scanning scheme and total image acquisition time of 4.096 s ( Fig. 3 and Supplementary Fig. 8

Image acquisition
The sample beam focused by the objective lens L2 propagates along the horizontal direction to the sample (Fig. 1B). We used a compact lab jack (L200, Thorlabs Inc.) as the vertical hand rest and a cage plate (CP33T/M, Thorlabs Inc.) as the horizontal hand rest to minimize motion. We applied ultrasound transmission gel (Aqua Sonic 100) to the skin area to be imaged to avoid high reflection signal from the skin surface.
Most of the images are acquired at 50k Hz A-line rate, except for Fig. 4 in which 22k Hz and 80 k Hz are used. There are 512 A-lines per B-scan, except for Fig. 5 where 384 A-lines per B-scan is used. For images generated with the point-scanning scheme, there are 400 cross-sectional angiograms so that the field of view (FOV) is 6.55 mm by 5.12 mm (width by height). For images generated with SELF-OCTA and L = 2, there are 800 cross-sectional angiograms so that the FOV is 6.55 mm by 10.24 mm (width by height). For all the OCTA images in this study, the number of repeated B-scans N is 2.

OCT structural image processing
Owning to the 'frequency flow' scanning mechanism, there are M/L partial-spectrum decorrelation frames at each Y image position, acquired during M/L consecutive Y-scan cycles. Note that N = 2 repeated B-scans at a Y-scan position are considered as one complete Y-scan cycle. We corrected bulk motion among all the partial-spectrum interference data before coherently added them into a spectrum interference data with the full spectral bandwidth. The phase differences between B-scans of consecutive Y-scan positions are calculated following the method described by An et al [20]. The axial resolution of SELF-OCT cross-sectional images are comparable to that of the point-scanning OCT ( Supplementary Fig. 4). However, due to residual bulk motion and local tissue motion such as blood flow, SELF-OCT cross-sectional images are not as crispy as that of the point-scanning OCT.

Speckle contrast analysis
The speckle contrast is calculated using the following equation introduced in a literature [39]. We additionally analyzed speckle contrast of en face SELF-OCTA images with 1, 2, 4, and 8 partialspectrum decorrelation frames at each Y image position, which corresponds to the cases of L = 16, 8, 4 and 2, respectively.
Where ‫ܫ‬ ௌ ഥ is the averaged intensity over the area of signal, and ߪ ௌ is the standard deviation of signal intensity. We selected 24 regions of interest (ROIs) in a blood vessel with most of the pixels saturated (maximum decorrelation) as shown in Supplementary Figs. 10A-D.

Multiple inter-scan time and high dynamic range
The model of dynamic range extension is based on the autocorrelation equation of the laser speckle signal [19,43] ‫ܦ‬ Where ‫ܦ‬ ഥ is the amplitude decorrelation, τ is the exposure time, which can be correlated to inter-scan time ΔT in OCTA. ‫ݒ‬ ௪ is the velocity of the blood flow, ‫ݒ‬ ௪ and ‫ݒ‬ ௨ are velocity related with Brownian and bulk motion of the tissue. k is a constant.