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Abstract
Optical microscopy suffers from multiple scattering (MS), which limits the optical imaging depth into scattering media. We previously demonstrated aberration-diverse optical coherence tomography (AD-OCT) for MS suppression, based on the principle that for datasets acquired with different aberration states of the imaging beam, MS backgrounds become decorrelated while single scattering (SS) signals remain correlated, so that a simple coherent average can be used to enhance the SS signal over the MS background. Here, we propose a space/spatial-frequency domain analysis framework for the investigation of MS in OCT, and apply the framework to compare AD-OCT (using astigmatic beams) to standard Gaussian-beam OCT via experiments in scattering tissue phantoms. Utilizing this framework, we found that increasing the astigmatic magnitude produced a large drop in both MS background and SS signal, but the decay experienced by the MS background was larger than the SS signal. Accounting for the decay in both SS signal and MS background, the overall signal-to-background ratio (SBR) of AD-OCT was similar to the Gaussian control after about 10 coherent averages, when deeper line foci was positioned at the plane-of-interest and the line foci spacing was smaller than or equal to 80 µm. For an even larger line foci spacing of 160 µm, AD-OCT resulted in a lower SBR than the Gaussian-beam control. This work provides an analysis framework to gain deeper levels of understanding and insights for the future study of MS and MS suppression in both the space and spatial-frequency domains.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the life sciences, many studies require deep imaging in scattering biological media. Deeper optical microscopy could usher in a new era for biological research or clinical applications [1–4]. For example, in neuroscience, deep brain imaging in the scattering cortex and white matter is always desired for the study of both functional and clinical questions [5,6]. However, multiple scattering (MS) severely limits the contrast, resolution and penetration depth supported by an imaging system [7]. In many biological tissues, the MS is so high that the desired information carried by single scattering (SS), i.e., the ‘ballistic’ scattering, is buried below the MS contribution. Typically, the penetration depth in biological samples is limited to ∼1–2 mm for a label-free imaging modality such as optical coherence tomography (OCT) [8,9].
Several methods have been proposed to suppress MS, and extend penetration depth of optical microscopy. One class of them is to use longer imaging wavelengths which have a lower scattering coefficient in the turbid tissues [10–12]. Another major class is to shape the incident wavefront via hardware adaptive optics (HAO) to compensate the sample-induced phase distortion [13–15]. Another class of methods utilizes the difference in the properties between MS and SS photons [16–19]. Multiple measurements of the sample are taken such that the SS signal is still correlated while the MS signal gets decorrelated across the different measurements. Based on this principle, our lab has previously proposed aberration-diverse optical coherence tomography (AD-OCT) for MS suppression [19]. Our initial demonstration of AD-OCT introduced astigmatism with different line foci angles into the illumination beam. By correcting the resulting aberrations via computational adaptive optics (CAO) [20], the signal from SS photons remains correlated while the signal from MS photons gets randomized, and therefore coherent averaging preserves SS but suppresses the MS signal magnitude by a factor of $\frac{1}{{\sqrt N }}$, where N is the number of coherent averages.
In our previously published paper, AD-OCT was compared with single-state controls, and demonstrated a ∼10 dB improvement in signal-to-background ratio (SBR) with 12 astigmatic states [19]. However, AD-OCT has never been compared to the traditional Gaussian confocal gating. Here, we propose a space/spatial-frequency domain analysis framework to investigate MS, then, utilize this framework to evaluate the performance of AD-OCT in comparison to standard OCT based on imaging with a Gaussian beam. This adds to previous work that has analyzed the OCT point-spread function (PSF) and modulation transfer function (MTF) in the presence of MS to investigate the effects of MS on the contrast and resolving capability of a beam-scanned OCT system [21].
Through our proposed framework, we quantified the SBR in the space domain, conducted depth-dependent analysis of MS with defocus correction for out-of-focus planes, and investigated the power distribution in the spatial-frequency domain with respect to coherent averages. Previous work utilizing wide-field incoherent microscopy found that MS would exhibit extra frequency contents outside the SS signal bandwidth [22], so it is of interest whether or not MS in OCT shows similar behavior – we investigated this question with our proposed framework in Section 3.1. In Sections 3.2 and 3.3, we explored the effects of coherent average and astigmatic diversity on MS background in the space and spatial-frequency domain, respectively. In Section 3.4, we compared the trends in the space and spatial-frequency domains. In Section 4, we discuss how MS is suppressed by AD-OCT, what the limiting factors are, and possible approaches to address these factors.
2. Methods
2.1 Sample preparation
The sample consisted of a cover glass, scattering layer with optical thickness of 7 scattering mean free paths (MFP), and USAF target (Thorlabs R1DS1P) (Fig. 1(a)). The scattering layer was made with 2.1% w/w 1.5 µm TiO2 beads inside silicone (SMOOTH-ON Dragon Skin 10) according to manufacturer instructions. The estimated refractive index of scattering layer is about 2.1. The scattering MFP was measured from the exponential decay of signal intensity at multiple focal depths inside the scattering layer [23]. Due to the lack of clear confocal signal peak (especially deeper in the scattering layer), we estimated the focus depth by calculating the relative focus depth shift as we scanned the focus in the sample with known refractive index [24].
Fig. 1. Sample preparation and experimental setup. (a) Diagram of sample composition. (b) Sample cross sectional image and the background haze in the USAF target glass. The scale bar represents 10 µm. Gamma correction of 0.7 was applied. (c) Experimental setup of the HAO-OCM system (beam size and path length are not drawn to scale).
2.2 Optical setup for the closed-loop HAO-OCM system
We used a beam-scanning spectral-domain OCM system (Fig. 1(c)) to provide closed-loop HAO with a deformable mirror (DM, Alpao DM97-15) to experimentally introduce astigmatism to the illumination beam. A Shack-Hartmann wavefront sensor (SH-WFS, Imagine Optic HASO4 First) was placed at a conjugate plane to the DM surface to ensure that the DM surface converged to the desired shape. A laser diode at 976 nm (co-propagating with the OCT beam) was used to image the DM surface to the wavefront sensor. The imaging system incorporated a superluminescent diode (SLD) centered at 1310 nm (Thorlabs LS2000B), and the interference signal was collected by a spectrometer (Wasatch Photonics C-00201). The full width of half maximum (FWHM) bandwidth for the systems was about 200 nm. The objective lens (Olympus LCPLN20XIR) in this OCM setup provided a lateral resolution of 2.7 µm FWHM, measured from a resolution phantom (silicone containing 0.5 µm TiO2 beads). The line scan camera exposure time in this study was 95 µs per A-scan, and the A-scan rate was 10 kHz. The sensitivity of the system was about 100 dB.
2.3 Imaging protocol and data processing
During AD-OCT data acquisition, the DM in the sample arm was used to apply astigmatism and rotate the astigmatic line foci angle across acquisitions. For each desired astigmatic state, the shape convergence of the DM was implemented in closed-loop with the Shack-Hartmann wavefront sensor. The spacing of the two line foci in the illumination beam was controlled by the magnitude of astigmatism we applied to the DM. The relationship between line foci spacing and astigmatism magnitude was calibrated in a silicone phantom with TiO2 beads. In this work, we chose foci spacings of 10 µm, 20 µm, 40 µm, 80 µm, and 160 µm. The data was taken in the OCT conjugate configuration where the sample depth axis was anti-parallel to the depth axis of the reconstructed OCT image, to account for the effect of camera roll-off on the OCT images.
For acquiring AD-OCT datasets, besides astigmatism, we also applied defocus to the DM to shift either the deeper or shallower astigmatic line focus to the USAF target plane, which is our plane-of-interest (POI). The relationship between the focus shift and applied defocus magnitude, and the relationship between astigmatic line foci spacing and applied astigmatism magnitude were separately calibrated in a silicone phantom with TiO2 beads. Based on this calibration step, we could determine a relationship between astigmatism and defocus magnitude to ensure that the desired line focus was aligned to the USAF target plane. To validate the calibrated relationship in a scattering phantom, we put the POI at the Gaussian beam focus, applied a certain amount of astigmatism to the DM and then scanned the defocus magnitude centered at the calculated defocus magnitude according to the calibrated relationship with a step value corresponding to a quarter of Rayleigh length, and found that the calibrated defocus magnitude achieved the highest intensity on the POI. Before the data acquisition, we flattened the DM and moved the sample along the beam axis to put the USAF target plane or POI at the Gaussian beam focus by seeking the maximum bar intensity and contrast in both cross-section and en face planes. The sample then remained fixed at this position throughout the rest of the measurements.
For AD-OCT data acquisition, a complete rotation (180°) of astigmatism was equally divided by 50 states. For each state, a coherent temporal average of 3 volumes was utilized to improve the signal-to-noise ratio (SNR). The Gaussian control data was acquired using a flat DM surface. For the entire acquisition, a total of 150 OCM volumes were collected for each AD-OCT line foci spacing and POI position, and for Gaussian control. It took about 11s for the DM to converge to desired aberration profile, and 19s to acquire one OCM volume. The convergence time was primarily determined by the number of iterations in the closed-loop wavefront shaping process. In the reported experiments, we specified the number of iterations to be 30, which takes about 11s. (In the future, the convergence time could be reduced by implementing a convergence criterion based on threshold of wavefront error, e.g. λ/10.) Another possible reason for the long convergence time is that the actuator’s step size in each iteration was limited to a very low value (0.01 V), which may lead to a larger number of iterations. In this study, we prioritized accuracy of the desired wavefront over convergence time.
A flow chart of data processing is presented in Fig. 2. All data processing was performed in MATLAB R2019b, Windows Server 2016 Standard. The raw spectral data were reconstructed following standard algorithms, including background subtraction, spectrum resampling, dispersion correction, inverse Fourier transform, and cover glass registration [25]. It took about 1.2 min to reconstruct an OCM dataset. Chromatic aberration was neglected in the OCT or CAO reconstruction, since Δk is only about 0.1 of kcenter for our spectral signal. We only applied 1D dispersion correction along the k axis in the frequency domain during OCT data reconstruction.
Fig. 3. Space domain analysis of a single standard OCM dataset, (a) en face plane of USAF target, (b) depth-dependent signal. Scale bar represents 10 µm.
Fig. 4. Spatial-frequency domain analysis of a single standard OCM dataset. (a) en face plane of scattering layer at depth 606 µm; (b) Fourier transform of (a); (c) spectral power at depth 17 µm and 606 µm in the scattering layer; (d) normalized spectrum power at depth 606 µm; (e) spectrum average signal power along depth in the sample; (f) normalized spectrum average signal power slightly outside signal bandwidth. The video version of (a-d) for different depths can be found in the Supplement 1 (Visualization 4).
Fig. 5. Coherent averages N = 50 of USAF target plane for (a) Gaussian control, (b) AD-OCT foci spacing = 10 µm, (c) AD-OCT foci spacing = 20 µm, (d) AD-OCT foci spacing = 40 µm, (e) AD-OCT foci spacing = 80 µm, (f) AD-OCT foci spacing = 160 µm. Images are in the same color scale without any gamma correction and scale bar represents 10 µm.
For AD-OCT datasets, computational adaptive optics (CAO) was used to correct aberrations applied by the DM and defocus, to restore the SS signals from various astigmatic states so that their phase can be aligned. CAO-related steps involve wobble correction [19] and aberration compensation [20]. Any slight tilt or misalignment in the system and sample could result in an offset of the experimental pupil from the center of the computational (Fourier space) coordinate system. In that case, the required phase correction in CAO (defined as second-order polynomials for depth-dependent defocus and astigmatism) would lead to a linear-phase ramp in the Fourier domain, and equivalently a transverse shift in the spatial domain. The wobble correction is to ensure the computational pupil aligned with the experimental pupil, by moving the center of the measured spatial frequency signal bandwidth back to the center in the Fourier domain.
Although wobble correction can align the computational pupil with the experimental pupil, there could still be residual transverse shifts in the space domain due to rotation of the DM astigmatic profiles, which could lead to a decay in signal power after coherent averaging. In order to mitigate this problem, we corrected the residual transverse shifts across different states after wobble correction. Similar to the motion correction algorithms implemented in [26], a two-dimensional cross-correlation between the reference plane and en face planes of different aberration states provided the relative shifts of en face planes with respect to the reference plane (Fig. S1 (a-e) and associated text presents detailed analysis of the transverse shift correction). We used the en face plane of the 25th state as the reference plane. The validation of the cross-correlation algorithm is shown in the Supplement 1 (Fig. S1 (g)). From the detected depth-dependent transverse shifts in the resolution phantom, we found that the transverse shifts are relatively constant along depths (Fig. S1(f)). Therefore, we calculated the transverse shifts in the scattering sample at the depth from 0 to 100 µm where the speckles are still stable across aberration states (Fig. S1(d-e)), and took the average of calculated transverse shifts along from this depth range. We used this information to undo any transverse shifts of en face planes across different aberration states by applying the appropriate phase ramp in the Fourier domain. Visualization 3 displays the en face planes before and after residual transverse shift correction across aberration states at four different depths for AD-OCT with 160 µm line foci spacing.
The aberration compensation step was used to correct both the DM-introduced aberration and depth-dependent defocus. In order to determine the proper CAO parameters to correct the aberration introduced by DM, calibration steps were conducted to construct a conversion matrix from applied HAO coefficient to CAO coefficients. Specifically, we applied 33 different aberration profiles ${C_{\textrm{H,Calib}}}$ to a resolution phantom, and detected the corresponding CAO coefficients ${C_{\textrm{C,Calib}}}$ using aberration sensing algorithm. These 33 aberration profiles involve defocus and astigmatism, corresponding to three Zernike polynomial terms, therefore both of the matrix ${C_{\textrm{H,Calib}}}$ and ${C_{\textrm{C,Calib}}}$ are of size 3×33, where 3 corresponds to the number of Zernike polynomial terms and 33 corresponds to the number of aberration profiles for calibration. We set two of the terms to zero, and scanned 11 linearly separated values of the third term, getting 33 aberrations profiles in total. The aberration sensing algorithm searches the space of CAO coefficients to maximize the sum of intensity to the power of two in the resolution phantom. The conversion matrix ${M_{\textrm{H} \to \textrm{C}}}$ was constructed by multiplying the CAO coefficients matrix with the pseudo-inverse of HAO coefficients matrix,
where ${C_{\textrm{H,Calib}}}^{ - 1}$ is the pseudo-inverse of HAO coefficients and is of size 33×3, which results in the size of ${M_{\textrm{H} \to \textrm{C}}}$ to be 3×3. After that, we could get the proper CAO coefficients ${C_\textrm{C}}$ for AD-OCT datasets simply by multiplying the conversion matrix ${M_{\textrm{H} \to \textrm{C}}}$ with the HAO coefficients used during experiments ${C_\textrm{H}}$,In addition to that, we fine-tuned the CAO coefficients at the POI for each dataset by iteratively tuning the three Zernike terms corresponding to defocus and astigmatism, to maximize the intensity on the USAF target bars. The optimization metric for fine-tuning is the sum of intensity to the power of two, and the optimum is usually achieved after 3–4 iterations. Optimized CAO corrections of astigmatism and defocus were applied at all the depths in each volumetric dataset.
2.4 Space-domain analysis
The depth-dependent signal is the OCT (or AD-OCT) signal transversely averaged across en face planes at each depth. SBR, the signal-to-background ratio, is a commonly used metric to access MS. In this paper, the signal is defined as the average power of the bars at the USAF target plane or POI. Background is defined as the reflectance signals that appear in the transparent USAF target glass below the POI [27], specifically the average signal power over the depth range 3-8 coherent lengths (CL) below the bars (Fig. 1(b)). We defined the noise floor as the average signal power between the two surfaces of cover glass, and calculated the background-to-noise ratio (BNR) to quantify how much the background is above the OCT system noise floor. Another possible estimation of noise floor is the average signal power in the “pure silicone” at the same depth range that the MS background is estimated from (Fig. 6). However, in the process to fabricate pure silicone, we may inevitably introduce air bubbles in the pure silicone, which may act as high scattering objects and lead to overestimation of the noise floor. The error bars in Fig. 9(c) represent the standard derivation of SBR, which were calculated by the error propagation formula using the standard deviation of signal and background (Eq. S1).
Fig. 6. Depth-dependent signal power for (a) Gaussian control, (b) AD-OCT foci spacing = 10 µm, (c) AD-OCT foci spacing = 20 µm, (d) AD-OCT foci spacing = 40 µm, (e) AD-OCT foci spacing = 80 µm, (f) AD-OCT foci spacing = 160 µm. Blue, red and orange lines represent 1, 12, 50 coherent averages, respectively. The curves for 1 and 12 coherent averages are plotted with a thicker linewidth to enhance visibility. Purple and green lines represent the noise floor in the pure silicone and air with 50 coherent averages, respectively. The OCM acquisition parameters are exactly the same for the “nothing” (i.e. no sample placed), “pure silicone” and coherent averages. Depth of 0 µm is set to be the interface between cover glass and scattering layer. Positive depth value corresponds to the depth below the interface.
Fig. 7. Signal on the USAF bars at POI, signal on the glass at POI, MS background and noise floor as a function of coherent average numbers for (a) Gaussian control, (b) AD-OCT foci spacing = 10 µm, (c) AD-OCT foci spacing = 20 µm, (d) AD-OCT foci spacing = 40 µm, (e) AD-OCT foci spacing = 80 µm, (f) AD-OCT foci spacing = 160 µm. For AD-OCT, the USAF target plane or POI is positioned at the deeper line focus. Red, magenta, blue, and greens lines corresponds to signal on the UASF bars, signal on the glass, background and noise floor respectively. Dash lines and solid lines represents experimental and theoretical results respectively. The legend is shared across all the figures.
Fig. 8. SBR and BNR as a function of coherent average states for (a) Gaussian control, (b) AD-OCT foci spacing = 10 µm, (c) AD-OCT foci spacing = 20 µm, (d) AD-OCT foci spacing = 40 µm, (e) AD-OCT foci spacing = 80 µm, (f) AD-OCT foci spacing = 160 µm. For AD-OCT, the USAF target plane or POI is positioned at the deeper line focus. Red and blue lines represent SBR and BNR respectively. Dash lines and solid lines represents experimental and theoretical results respectively.
Fig. 9. Summary of SBR for Gaussian control and AD-OCT with different foci spacing. (a) SBR vs. number of coherent average with POI placed at the deeper line focus in AD-OCT. (b) SBR vs. number of coherent average with POI placed at the shallower line focus in AD-OCT. (c) SBR of coherent average of 50 states vs. foci spacing. The error bar represents the standard deviation of SBR. The SBR of Gaussian control is indicated by the green dash line. Error bars represent the standard derivation of SBR, which were calculated by the error propagation formula using the standard deviation of signal and background (see Eq. S1 and associated text for further details).
2.5 Spatial-frequency domain analysis
For spatial-frequency domain analysis, we plotted the spectral power as a function of radial spatial frequency ${k_r}$. The computational frequency coordinate ${k_r}$ was shifted to match the experimental pupil according to the detected Fourier-domain offset in the wobble correction step. The spectral power of MS was obtained from the transverse Fourier transform at the depth 5 CL below POI, and the spectral power of noise floor is obtained from the transverse Fourier transform at one single depth in the middle of cover glass. The spectral average signal power was calculated in the Cartesian coordinate in the Fourier domain with linear scale, and then converted to dB scale.
3. Results
3.1 Analysis of depth-dependent signal for standard OCM
Figure 3 and Fig. 4 presents the analysis of a single standard OCM dataset in the space and spatial-frequency domain, respectively. Figure 3(a) shows the en face plane of USAF target in the space domain, and Fig. 3(b) displays the depth-dependent signal power in the sample. The depth coordinate is referenced to (i.e., 0 µm) the interface of the cover glass and the scattering layer; a positive depth value indicates distance below this interface. The depth ranges for cover glass, scattering layer, USAF target plane (POI) and MS depth range are labeled in Fig. 3(b). According to the definition of space-domain signal, background and noise in Section 2.4, this dataset has a SBR of 18.5 dB and a BNR of 14.4 dB.
The spatial-frequency domain analysis results of standard OCT are presented in Fig. 4. The video version of Fig. 4(a-d), which contains information at different depths, can be found in the Supplement 1 (Visualization 4). In [22], when performing incoherent imaging in a full-field geometry, it was found that MS introduces extra spatial-frequency content outside of the signal bandwidth. In order to investigate this behavior, we plot the spectral power along radial spatial frequency kr at two different depths (17 µm and 606 µm) in the scattering layer in Fig. 4(c), where we expect the level of MS to increase with depth. The signal bandwidth occupies approximately 0–3 rad/µm. Within the signal bandwidth, we observe that deeper depth (606 µm) demonstrates lower spectral power compared to shallower depth (17 µm) because of power loss during optical beam penetration in the scattering sample. To account for this overall power difference at different depths as mentioned above, we plotted the normalized power at depth 606 µm in Fig. 4(d) which is defined as spectrum power at depth 606 µm divided by that at depth 17 µm in the linear scale, and then converted to dB scale. Under the assumption that MS is negligible at the shallow 17 µm depth, this normalized power spectrum represents the relative spectral contribution of MS at depth 606 µm w.r.t. the SS spectrum. We observe that the normalized power within (0–3 rad/ µm) and slightly outside (3–3.4 rad/µm) of the signal bandwidth has less than 2 dB variation, suggesting that MS does not introduce frequency components outside the nominal (single-scattered) OCT signal bandwidth. We chose to define the “outside of signal bandwidth” to be 3–3.4 rad/µm near the boundary where signal meets the noise floor (see Fig. 4(c)). This is because if there are extra spectral components outside the signal bandwidth, it will most likely be detected near the boundary.
To further investigate this conclusion, we also calculated the average signal power of the spectrum in the signal bandwidth (0–3 rad/µm) and slightly outside the signal bandwidth (3–3.4 rad/µm) as labeled in Fig. 4(c, d), and plotted the spectrum average power within these two regions as a function of depth in Fig. 4(e). In addition, we normalized the spectrum power outside the signal bandwidth with the spectrum power inside the signal bandwidth, and plot the normalized power in Fig. 4(f). The normalized power in the scattering layer (depth 0 - 606 µm) remains roughly constant across depth, indicating that MS does not introduce significant spatial-frequency components outside the nominal OCT signal bandwidth. Otherwise, we would expect a more prominent depth-dependent monotonic increase in the normalized spectrum power since MS is expected to increase as a function of depth. Further discussion is provided in Section 4.1.
3.2 Space-domain analysis of AD-OCT and Gaussian control
In this section we compare AD-OCT reconstructions vs. Gaussian beam controls through en face images from the POI (USAF target plane), plots of the average depth-dependent signal, and through quantitative analysis of the SBR. (Visualization 1 and Visualization 2 in the Supplement 1 shows the effect of coherent averaging on the en face planes from multiple depths in the sample. For the case of AD-OCT, speckle patterns from deeper in the sample are more randomized than at shallower depths due to the higher levels of MS at deeper depths.) The en face plane of USAF target after 50 coherent averages are displayed with the same color scale in Fig. 5. The USAF target plane is placed at the deeper line focus of the astigmatic illumination beam in the case of AD-OCT. Gaussian control and AD-OCT with foci spacing equal to 10 µm and 20 µm demonstrate similar image intensity and contrast. However, starting from foci spacing of 40 µm, larger line foci spacing or astigmatism magnitude results in a drop in the overall intensity at the USAF target plane. One reason is that as the line foci spacing of the astigmatic beam is increased, the CAO-reconstructed signal intensity at the POI is reduced relative to the peak signal for a Gaussian beam [28]. This is due to a reduction in the total number of photons collected from the USAF target plane, even in the absence of the scattering layer, and thus CAO cannot fully restore the SS signal relative to the Gaussian beam peak. Another reason is that as the magnitude of astigmatism is increased, the fraction of MS photons in collected signal may increase. The higher fraction of MS photons leads to a loss of image quality [29], but after coherent averaging (which suppresses the MS contribution), the SS signal from the USAF target plane can be revealed more clearly.
Figure 6 presents the depth-dependent signal. The USAF target plane is placed at the deeper line focus of the astigmatic illumination beam in the case of AD-OCT. The OCM acquisition parameters are exactly the same for the “nothing” (i.e., no sample placed), “pure silicone” and coherent averages. For Gaussian control (Fig. 6(a)), the coherent averages of N = 1, 12, and 50 overlap with each other in the MS depth range (3–5 CL below POI), indicating no MS suppression with coherent averages. For AD-OCT, as we increase the foci spacing or astigmatism magnitude, we notice a signal drop in the MS depth range with higher number of coherent averages, where larger line foci spacing leads to larger MS suppression. We also notice signal decay with coherent averages in the scattering layer (depth 0 ∼ 617 µm) for AD-OCT with large line foci spacings (i.e. 80 µm and 160 µm). The signal in the scattering layer contains both MS and SS components, and the proportion of MS components increases with depth. There is a signal decay in the scattering layer because the MS components are suppressed by AD-OCT. The signal decay in the scattering layer increases with depth because the proportion of MS components, which are randomized by AD-OCT, increases with depth.
Figure 7 demonstrates the signal on the bars at POI, signal on the glass at POI, MS background and noise floor as a function of coherent averages N. The USAF target plane or POI is positioned at the deeper line focus in the case of AD-OCT. In this work, the signal for SBR calculation is defined to be the average power on the USAF targets bars at POI. The signal is theoretically expected to be constant for both Gaussian control and AD-OCT, but we observe a decay in the signal for AD-OCT with larger line foci spacings of 40 µm, 80 µm, and 160 µm. A possible explanation is AD-OCT suppression of MS on the USAF target bar, since the backscattered signal on the USAF bars contains both SS and MS components.
In [19], background was defined as the signal on the glass at POI, but in this work, we defined the background to be the backscattered signals that appear inside the transparent USAF target glass below POI. The higher glass signal power and the earlier saturation of glass signal decay relative to the background signal from the MS depth range (see Fig. 7(d-f)) indicate that the reflectance of the glass at POI contains systematic SS components that cannot be suppressed by coherent averaging. Furthermore, in [27], it is demonstrated that one manifestation of MS is background haze originating from the transparent glass below the scattering media. Therefore, in this work, we defined the background to be the average signal power at the depth 3–5 CL below POI.
For Gaussian control, the theoretical value of background is constant due to lack of variability of the MS signal between acquisitions. The experimental Gaussian control background of coherent averages stays constant as expected (Fig. 7(a)). For AD-OCT, the background magnitude is expected to follow a theoretical decay of $1/\sqrt N $ with N coherent averages. However, experimentally, the background decay saturates after a few coherent averages, where the decay persists over a larger number of coherent averages (i.e., larger N) with increasing line foci spacing or aberration magnitude. For foci spacing equal to 10 µm and 20 µm, saturation happens after the first couple of coherent averages (Fig. 7(b, c)), while for foci spacing equal to 160 µm, saturation happens after about 10 coherent averages (Fig. 7. f). We also observe a saturation in the noise floor decay with coherent averaging, and the possible reason for that is discussed in Section 4.5.
To investigate the potential impact of the system noise floor on the suppression of MS (and saturation of the BNR curves), Fig. 8 illustrates SBR and BNR as a function of coherent averages N. For AD-OCT, the USAF target plane or POI is positioned at the deeper line foci. From the plots of BNR, we can more clearly see that larger aberration magnitude leads to smaller improvements in BNR, which corresponds to the background curve shape more closely tracking the shape of the noise floor curve. A constant BNR corresponds to MS suppression provided the noise floor curve continues to drop with number of coherent averages (i.e. before the noise floor curve saturates). However, despite saturation of the noise floor curves, a BNR of >10 dB suggests that saturation of the noise floor is not the main factor leading to saturation of the MS background curves. Further discussion is provided in Section 4.4.
Figure 9 summarizes SBR for Gaussian control and AD-OCT with different line foci spacing in the same plot. Figure 9(a) and (b) corresponds to AD-OCT with POI positioned at the deeper and shallower line focus, respectively. AD-OCT with larger foci spacing generally starts with a lower SBR at N = 1, followed by higher SBR improvement after 50 coherent averages. From Fig. 9(c), after 50 coherent averages, placing the POI at the deeper line focus results in higher SBR than when the shallower line focus is at the POI. The SBR of AD-OCT is close to that of the Gaussian control for line foci spacing smaller than or equal to 80 µm, but degrades with larger line foci spacing. For line foci of 20 µm, 40 µm and 80 µm, the SBR of AD-OCT slightly outperforms that of Gaussian control, but since the improvements are within experimental error, the slightly higher SBR observed for AD-OCT (with deeper line focus at POI) is not statistically significant.
3.3 Spatial-frequency domain analysis of AD-OCT and Gaussian control
In this section we investigate the performance of AD-OCT vs. Gaussian beam controls in the spatial-frequency domain, and compare deep signals where MS is expected to dominate to shallow signals where SS is expected to dominate. In the presence of MS, the spectral energy within the nominal signal bandwidth may be rearranged. For example, the spectral power in the high-frequency part within the nominal bandwidth may increase because the high-frequency region (associated with higher numerical aperture (NA)) corresponds to longer optical travel path in the scattering sample. Given that the spatial-frequency domain connects to angle in the beam, the spatial-frequency domain analysis presented here may provide additional information that is not present in the space domain analysis in Section 3.2.
Figure 10 and 11 demonstrate the spatial-frequency domain analysis of MS background at the depth 5 CL below POI. For the analysis in this section, the USAF target plane or POI is positioned at the deeper line focus in the case of AD-OCT. In Fig. 10, we plot the spectral power of MS with coherent average number N = 1 (red) and 50 (blue), and the spectral power of noise floor with N = 50 (green). For all plots, the 0 dB reference is set to be the flat part of the spectrum in the higher frequency range of Gaussian control with N = 1. Comparing the red and blue lines within the signal bandwidth (0–3 rad/µm) in each plot, we notice that with larger astigmatism magnitude or line foci spacing, the blue line drops further away from the red line, indicating that larger astigmatism magnitude leads to larger spectral power drop with coherent averages in the signal bandwidth.
Fig. 10. Spectral power of MS and noise floor for (a) Gaussian control, (b) AD-OCT foci spacing = 10 µm, (c) AD-OCT foci spacing = 20 µm, (d) AD-OCT foci spacing = 40 µm, (e) AD-OCT foci spacing = 80 µm, (f) AD-OCT foci spacing = 160 µm. Red and blue dots represent the spectrum power of MS with N = 1 and 50 respectively. Green dots represent the spectrum power of noise floor with N = 50. For all the plots, 0 dB reference is set to be the flat part of the spectrum in the higher frequency range of Gaussian control with N = 1. Dash lines are the median trace of their corresponding scatters with the same color. The colored transparent rectangles in (a) indicated the low, medium and high frequency regions within the signal bandwidth for further analysis.
Fig. 11. MS spectrum average power drop within low frequency region (0–1 rad/ µm), medium frequency region (1–2 rad/ µm) and high frequency region (2–3 rad/ µm) for (a) Gaussian control, (b) AD-OCT foci spacing = 10 µm, (c) AD-OCT foci spacing = 20 µm, (d) AD-OCT foci spacing = 40 µm, (e) AD-OCT foci spacing = 80 µm, (f) AD-OCT foci spacing = 160 µm. The black line represents the theoretical line $1/\sqrt N $ in the linear scale.
To further investigate the MS power drop with coherent averages within the signal bandwidth, we divided the signal bandwidth into three frequency regions: low frequency region (0–1 rad/ µm), medium frequency region (1–2 rad/ µm) and high frequency region (2–3 rad/ µm) as indicated in Fig. 10(a), and plot the power drop within these three frequency regions at the MS depth as a function of coherent averages in Fig. 11. Comparing different lines within each plot, we notice that there is more power drop in the higher frequency region. Also, higher foci spacing or astigmatism magnitude is associated with larger power drop, which stands true for all these three regions.
From the results of AD-OCT, we see that the power of the MS signal drops with coherent averages in both space and spatial-frequency domains (Figs. 7 and 11). However, from the space-domain analysis in Fig. 6, we notice that the signal power at the shallow SS depth (1–100 µm in the scattering layer) also drops, but the signal drop in the SS depth is lower than that in the deeper MS depth. In order to investigate this trend in the spatial-frequency domain, we applied the spatial-frequency domain analysis in Figs. 10 and 11, but this time applied this analysis to shallow depth (0.5 scattering MFP below the cover glass, ∼36 µm in the scattering layer) where SS is expected to dominate, and the results are shown in Figs. 12 and 13. We see that, in the spatial-frequency domain, SS spectrum power within the signal bandwidth also experiences decay with coherent averages in the case of AD-OCT. Also, larger line foci spacing leads to larger spectrum power decay. However, compared to Figs. 11 and 13, the spectrum power drop within the signal bandwidth at the SS depth is lower than that at the MS depth, which is a similar trend observed in the space-domain results. In summary, in both space and spatial-frequency domain, AD-OCT results in power decay with coherent averages at both SS and MS signal depths, and a larger line foci spacing or astigmatism magnitude leads to a larger signal power drop. However, the drop is more prominent for MS than SS signal.
Fig. 12. Spectral power of SS and noise floor for (a) Gaussian control, (b) AD-OCT foci spacing = 10 µm, (c) AD-OCT foci spacing = 20 µm, (d) AD-OCT foci spacing = 40 µm, (e) AD-OCT foci spacing = 80 µm, (f) AD-OCT foci spacing = 160 µm. Red and blue dots represent the spectrum power of MS with N = 1 and 50 respectively. Green dots represent the spectrum power of noise floor with N = 50. For all the plots, 0 dB reference is set to be the flat part of the spectrum in the higher frequency range of Gaussian control with N = 1. Dash lines are the median trace of their corresponding scatters with the same color.
Fig. 13. SS spectrum average power drop within low frequency region (0–1 rad/ µm), medium frequency region (1–2 rad/ µm) and high frequency region (2–3 rad/ µm) for (a) Gaussian control, (b) AD-OCT foci spacing = 10 µm, (c) AD-OCT foci spacing = 20 µm, (d) AD-OCT foci spacing = 40 µm, (e) AD-OCT foci spacing = 80 µm, (f) AD-OCT foci spacing = 160 µm. The black line represents $1/\sqrt N $.
3.4 Joint space and spatial-frequency domain analysis
To investigate the depth-dependent response of spectral power with coherent averages for the Gaussian control and AD-OCT cases, we plot the depth-dependent spectral power within three frequency regions in the signal bandwidth: low frequency region (0–1 rad/µm), medium frequency region (1–2 rad/µm) and high frequency region (2–3 rad/µm), as indicated on Fig. 10(a), with coherent averages N = 1 and N = 50 in Fig. 14. The dash and solid lines correspond to N = 1 and N = 50, respectively. The drop of solid lines (N = 50) from dash lines (N = 1) with the same color within each figure corresponds to the amount of MS suppression by 50 coherent averages.
Fig. 14. Depth-dependent spectral power within three frequency regions in the signal bandwidth: low frequency region (0–1 rad/ µm), medium frequency region (1–2 rad/ µm) and high frequency region (2–3 rad/ µm), with coherent averages N = 1 and N = 50 for (a) Gaussian control, (b) AD-OCT foci spacing = 10 µm, (c) AD-OCT foci spacing = 20 µm, (d) AD-OCT foci spacing = 40 µm, (e) AD-OCT foci spacing = 80 µm, (f) AD-OCT foci spacing = 160 µm. The dash and solid lines corresponds to N = 1 and N = 50, respectively. Depth of 0 µm is set to be the interface between cover glass and scattering layer. Positive depth value corresponds to the depth below the interface. The location of three frequency regions is labeled in Fig. 10(a).
Comparing the solid and dashed lines with the same color in each plot, we can see that the drop of solid lines (N = 50) from dash lines (N = 1) increases with line foci spacing or aberration magnitude for all three frequency regions in the case of AD-OCT, but the effect is more prominent in the medium and high frequency region. This is consistent with the space-domain analysis in Fig. 6, but the results here additionally show that the trend of more MS suppression with larger foci spacing occur across the entire spatial frequency bandwidth in AD-OCT. The possible explanations for increasing signal drop under larger line foci spacing are discussed in Section 4.2.
From Fig. 14, comparing the power drop between solid lines (N = 50) and dash lines (N = 1) across different frequency regions in each figure, we see that the high-frequency region is always associated with larger power drop. From the power drop at different depths, we also see that the power drop generally increases with depth, especially in the low-frequency region. This indicates that at larger depth there is higher MS suppression, which is consistent with the fact that a larger depth is generally associated with higher levels of MS in scattering media.
4. Discussion
AD-OCT takes advantage of the difference in correlation characteristics between MS and SS signal under diversified aberration states of the illumination beam. One implementation of AD-OCT introduces astigmatism with different line foci angles to diversify the illumination beams thus achieving a different realization of MS. In this way, MS can be suppressed by simple coherent averaging (Figs. 7–11). Besides MS suppression, we also see signal drop in the SS depth range in both the space and spatial-frequency domain (Figs. 6, 12-14). The signal at the SS depth range would be dominated by SS but likely contains some MS contribution. The MS component gets suppressed by AD-OCT, and this is why there is a drop in the signal at the SS depth range in AD-OCT. This is also consistent with the observation that the level of power drop at the SS depth is lower than that at the MS depth (Figs. 6, 14), since the amount of MS at the SS depth is lower than at the MS depth.
The spatial-frequency domain analysis, which connects to the angle of the beam, provides more insights that cannot be gleaned from the space domain analysis alone. From the spatial-frequency domain analysis, we noticed that the MS background in the higher frequency range is suppressed more than that in the lower frequency range (Figs. 10–14). Across different angles of astigmatism, the line PSF rotates about its center. Although the non-center part of PSF travels through different regions in the scattering media and produces different realizations of MS background, the contribution from the central angles stay relatively stable since they tend to propagate through the same region of the scattering medium. Therefore, the higher frequency range experiences more MS randomization that facilitates more suppression with coherent averages than the lower frequency region. To improve the MS suppression of AD-OCT, we need to further randomize the lower frequency part of MS background, for example by investigating the use of spherical aberration.
In this work, we applied CAO at all the depths, including the cover glass and the USAF glass below POI. As mentioned before, we calculated the noise floor in the cover glass and the MS background in the USAF glass. We investigated the effect of CAO on MS background and noise floor by plotting the noise floor and MS background with and without CAO in Fig. S3. We see that while CAO does not affect the noise floor, it reduces the diversity of MS background. We speculate that aberration correction causes some systematic contributions in the MS background to interfere constructively.
Phase stability is a practical limitation of AD-OCT and other methods requiring coherent averages, especially for in vivo imaging where the sample is susceptible to motions. In such cases, high acquisition speed is desired to maintain the phase stability across different acquisitions. For this purpose, we could reduce the size of the acquired dataset to decrease the time required for a single acquisition. An even better strategy is to use a swept-source FDML laser which can support video-rate volumetric acquisitions [30–32].
4.1 Comparison to prior work on multiple scattering
Previous research has shown that in OCT, one manifestation of MS is a background haze originating within a transparent glass plate below scattering media, and the intensity of the background haze increases with increasing concentration or opaqueness of scattering media [27]. In this work, we also observed similar background haze within the transparent glass below the scattering layer (Fig. 3, Fig. 6). The intensity of the background haze 3–5 CL below the POI ranged between 12–15 dB above the noise floor. The intensity of background haze in dB scale dropped linearly with increasing depth within the glass, similar to Fig. 8 in [27]. In our work, the decay slope of the intensity as a function of depth is about −0.02 dB/µm, compared to −0.04 dB/µm in Fig. 8 of [27] (a scattering cell filled with a 2.5% wt./vol. polystyrene latex with spherical beads 0.48 µm in diameter). The difference in the decay slopes may be caused by differences in the bead size and material in the scattering layer.
Previous work found that MS would exhibit extra frequency contents outside the SS signal bandwidth [22,33]. In [22], the evidence of MS is from the Fourier transform of intensity images of a scattering biological sample taken from an (incoherent) optical diffraction tomography (ODT) system with wide-area illumination, which shows significant spatial-frequency contents outside the signal bandwidth. In [33], from images that were taken from a Linnik interferometer in a full-field OCT configuration, researchers observed decreasing speckle size with increasing level of MS in the space domain, indicating an increase in the effective coherence volume. However, our results (Fig. 4) do not show the same trend. This may be due to the difference between wide-area/full-field imaging geometry implemented in [22,33] and beam-scanning OCT system implemented here. In a wide-area/full-field OCT system without confocal gating, all of the back-scattered photons within the angular acceptance angle in the Fourier domain are collected by the detector without any other filtering. However, in a fiber-based beam-scanned OCT system, the sample arm fiber acts as a confocal pinhole, which not only blocks the MS outside of the collection angle, but also only collects photons that map to the fiber tip. As a result, the spatial frequency bandwidth remains constant with depth, i.e., the potential contribution of out-of-band high frequency content from MS was not significant in our experiments.
In [21], to investigate the effects of MS, researchers measured and analyzed the point-spread function (PSF) in the space domain and modulation transfer function (MTF) in the spatial-frequency domain with an OCT system through scattering layers. In this work, we proposed a space/spatial-frequency domain analysis framework to investigate MS and used this framework to evaluate AD-OCT. Utilizing this framework, we quantified the SBR in the space domain (Figs. 7–9) and studied the response of spectral power with coherent averages in the spatial-frequency domain (Figs. 10–13). With CAO defocus correction for out-of-focus planes, we also conducted depth-dependent joint analysis of MS in both the space and spatial-frequency domains (Figs. 6, 14). Additionally, the optical system NA in this work is significantly higher than [21], and thus our study is more relevant to high-NA OCM. Further work is needed to investigate the performance of AD-OCT at different NAs, both higher and lower than the NA of our current study.
4.2 Signal drop associated with larger line foci spacing
In both space and spatial-frequency, larger line foci spacing is always associated with larger signal drop with coherent averaging (Fig. 6, 14). There are three possible reasons behind this. The first reason is about better MS suppression performance with large aberration. The diversity and randomization of AD-OCT depends on the introduced astigmatism magnitude. Larger aberration leads to larger randomization in the MS, thus MS would be more suppressed with coherent averages.
Another possible reason is that as the line foci spacing of the astigmatic beam is increased, the CAO-reconstructed signal intensity at the POI is reduced relative to the peak signal for a Gaussian beam [28]. As we increase the line foci spacing of an astigmatism beam, the beam intensity at the line foci gets reduced. Therefore, the intensity of collected signal should scale down accordingly. From Fig. 7, the signal intensity decreases with large aberration, but the background intensity does not scale down. This indicates that the percentage of MS in the collected signal increases with line foci spacing (leading to lower SBR), especially in the medium and high-frequency regions in the spatial-frequency domain.
The third reason is related to spatial averaging. As we mentioned before, sight tilt or misalignment in the system and sample could result in an offset of the experimental pupil relative to the center of the computational Fourier-domain coordinates, in which case CAO will lead to a translation in the space domain, and this spatial translation would increase with larger astigmatism in the beam. Although we have conducted wobble correction to align the computational pupil with the experimental pupil and corrected the residual transverse shifts in the space domain, the effect of spatial shifts on the coherent averages is worth investigating. We found that even without residual transverse shift correction, the effect of residual transverse shift is small. Using the cross-correlation algorithm, we detected the transverse shifts across different states for the AD-OCT 160 µm line foci spacing with wobble correction but without residual transverse shift correction. Then, we applied the detected shifts to a single AD-OCT dataset and calculated the depth-dependent power in the spatial-frequency domain (see Fig. S2 (a)). We found that, with transverse shifts, the spectral power decay after 50 coherent averages in the high-frequency region is only about 0.8 dB (Fig. S2 (a)), which is much lower than the power decay we observed in Fig. 14(f). We need to magnify the measured shifts by a factor of 4 to produce a similar level of decay to that observed in Fig. 14(f) (see Fig. S2 (b)). These results indicate that spatial averaging of transversely shifted images is not the dominant reason for the large power drop in AD-OCT with large line foci spacing.
4.3 Improved performance when the deeper line focus is at the POI
From Fig. 9(c), we found that for AD-OCT, placing the POI at the deeper line focus achieves higher SBR compared to placing the POI on the shallower line focus. This is because when placing the POI on the deeper line focus, the other line focus exists above the POI, in which case the beam width above the POI is more compact, and so the beam interacts with a relatively smaller volume in the scattering layer. Therefore, the wavefront of the beam undergoes less disruption by MS in the scattering layer. However, when placing the POI at the shallower line focus (i.e., when the other line foci exists below the POI), in this case the beam width above the POI is greater than the first case, and so travels through a relatively larger area in the scattering layer. As a result, the number of degrees of freedom of the wavefront distortion introduced by the scattering medium is greater, thus making the beam much more susceptible to MS. This suggests that a Bessel beam, which remains relatively compact across depth compared to Gaussian beam, might be less susceptible to wavefront scrambling effects of MS, and so may be an attractive option for deep imaging in optical microscopy [34–36].
4.4 Potential factors contributing to the saturation of SBR curves
We note that the SBR curve in Fig. 8 deviates from the theoretical curve much more than the previously published results in [19]. One possible reason may be due to the resolution of the optical system in [19] (2 µm) being higher than that in this work (2.7 µm). Consequently, the PSF in [19] would be more susceptible to aberration. Due to this increased susceptibility to aberration, a smaller astigmatism magnitude would be enough to fully randomize the MS with the system of [19], whereas the lower-resolution system in our study would require a larger amount of aberration to achieve a similar level of randomization to that obtained in [19]. Therefore, the SBR improvement here deviates more from theory than in [19] due to the trade-off between randomizing the MS and not attenuating the collected SS signal (to achieve sufficient randomization, a large magnitude of astigmatism is needed, which can degrade the SS signal that is collected). This trade-off would also apply under higher resolution, where the collected MS signal is more susceptible to randomization from aberration-diverse illumination, but the PSF is also more vulnerable to MS-induced wavefront distortions. This indicates that system resolution or corresponding NA could have a significant impact on MS suppression with AD-OCT and overall imaging depth, which is supported by a recent theoretical study [37]. Further research is required to study the influence of NA on MS suppression, and to compare experimental findings to theoretical predictions.
Another possible reason for the earlier SBR saturation compared to [19] is that the BNR in [19] is likely lower than the present study, leading to the en face images showing more rapid intensity fluctuations that appear to be smaller than the transverse resolution. This suggests that spatial variations in the noise floor might be responsible for these rapid fluctuations [19]. In this case, the noise floor would play a more significant role in the measured background, and the observed background suppression in [19] could include a large contribution from noise reduction.
Since the background can contain both noise and MS, the saturation in the background drop as a function of number of coherent averages could in principle be related to the saturation in the noise floor (see Fig. 7). To investigate this question, we simulated the noise floor and background with similar characteristics to our experimental noise floor and background and found that the saturation in the noise floor does not lead to the saturation in the background until the BNR is smaller than about 7–8 dB (data not shown). In this work, the BNR is always above 12 dB (Fig. 8), therefore, we concluded that the saturation in the noise floor is not responsible for the saturation in the background or SBR in this paper.
4.5 Impact of the sample on the OCT system noise floor
In Fig. 6, there is an increase in the noise floor in the cover glass of coherent averages and “pure silicone”, compared to the noise floor of “nothing”. The noise floor of “pure silicone” and coherent averages are comparable to each other. This suggests that the increase in the noise floor is not related to the scattering layer, since “pure silicone” does not contain a scattering layer. One possible explanation is that due to the spectral ripple in the SLD light source of our system, the magnitude of spectral fringes is not constant across wavelength. Consequently, any intensity fluctuations of the SLD could lead to incomplete subtraction of the background spectrum during OCT data reconstruction step. The residual fringes, if they contain both slow and rapid fluctuations in the k-domain could lead to a systematic component across all the depths in the reconstructed space-domain OCT data. The problem is made worse in the case of “pure silicone” which contains strong reflections from the coverslip interfaces. That is to say, the residual fringe in the sample arm term and the interference term of the detected OCT signal gets magnified by the strong reflection from the coverslip interfaces of the sample, and therefore increases the systematic component of the noise floor in the space domain. This systematic component may also be the reason why there is saturation in the noise floor decay as a function of coherent averages in Fig. 7.
5. Conclusion
MS is a major bottleneck that limits imaging depth in scattering media. In this paper, we proposed a space/spatial-frequency domain analysis framework for the study of MS, and applied this framework to analyze AD-OCT, a previously published technique for MS suppression. By analyzing a traditional single-shot OCT volume, we found that MS does not introduce extra contents outside the signal bandwidth in the spatial-frequency domain in a fiber-based beam-scanned OCT system. With AD-OCT, both MS background and SS signal experienced a power decay with coherent averages, while the power decay of MS was large than that of SS signal. In the spatial-frequency domain, signals in the higher spatial-frequency range were suppressed more than the signal in the low frequency range. With increasing astigmatism magnitude introduced to the illumination beams (larger line foci spacing) in AD-OCT, we found both MS background and SS signal experienced larger power decay with coherent averages of diversified acquisitions in both the space and spatial-frequency domain. Higher aberration magnitude led to higher levels of randomization or diversity in the MS background, resulting in a larger amount of MS being suppressed with coherent averages. Accounting for the power decay in both the MS background and the SS signal, the overall SBR of AD-OCT slightly outperforms that of Gaussian control when the deeper line foci is positioned at the plane of interest, and line foci spacing was equal to 20 µm, 40 µm and 80 µm, but the improvement is not statistically significant. Future work will investigate other factors (such as NA) influencing MS suppression, and explore methods to introduce more diversity to the lower spatial frequency region of the MS background.
Funding
National Science Foundation (CAREER: CBET-1752405); National Institutes of Health (NIBIB-R21EB022927, NINDS-R01NS120819).
Disclosures
The authors declare that there are no conflicts of interest related to the article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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