2.1.

Mouse Brain Preparation

Mice heterozygous for Cx3Cr1-enhanced green fluorescent protein (GFP) [B6.129P(Cg)-Ptprca Cx3cr1tm1Litt/LittJ]²⁰ and Thy1-yellow fluorescent protein (YFP) [B6.Cg-Tg(Thy1-YFP)HJrs/J],²¹ with fluorescently labeled brain microglia and neurons, respectively, were used for experiments. Mice were intravenously injected with $100\mu \mathrm{l}$ Texas-Red lycopersicon esculentum lectin (Vector Labs TL-1176) 10 min prior to euthanasia to label brain vasculature. Euthanasia was induced by an intraperitoneal injection of pentobarbitol ($150\mu \mathrm{L}$ of $39\mathrm{mg}/\mathrm{mL}$ solution in saline) and then perfused via intracardiac puncture with 30-mL phosphate-buffered saline (PBS) containing $100\mu \mathrm{l}$ Texas-Red lectin at 4°C. The brain was harvested and then stored in PBS at 4°C, sealed in agarose (1%), and imaged within 1 h [Figs. 1(a), 1(b)]. Results from a single brain are reported in this paper, and two additional mice were used for method optimization.

Fig. 1

Sample preparation and data processing. (a) Overview of sample geometry. (b) Photograph of sample. (c) Scheme of focus-scanning and fusion with trapezoidal window. Depth of focus is defined as twice the Rayleigh length of a Gaussian beam. (d) Flowchart of data processing. All the volumes acquired are reconstructed and fused with varying focus spacing. In this study, only defocus was corrected by CAO, and a frequency metric was used to search for optimal CAO coefficients. (e) Illustration of the frequency metric for CAO coefficient search.

2.2.

Optical Coherence Microscopy Imaging Protocol and Image Reconstruction

Imaging was performed on a custom-built spectral-domain (SD)-OCM system, with a central wavelength of 1310 nm, with axial and transverse resolutions of 4.7 and $2.2\mu \mathrm{m}$, respectively. The Rayleigh length of sample arm beam is $9\mu \mathrm{m}$. A-scans were acquired at line rate of 30 kHz, B-scan frame rate of $\sim 25\mathrm{Hz}$, and exposure time of $10\mu \mathrm{s}$. Each acquired volume is composed of $1024\times 512$ A-scans, corresponding to a transverse field of view (FOV) of $960\mu \mathrm{m}\times 480\mu \mathrm{m}$. The power applied to the sample was about 5 mW. The objective lens was LCPLN20XIR (Olympus). For the results presented in this work, 79 volumes were acquired with focus spacing of $10\mu \mathrm{m}$, which is 1.11 Rayleigh lengths of the sample arm beam, by a stepper motor [KST101, Thorlabs, Fig. 1(c)]. For each dataset, subvolumes around the focus were extracted and synthesized²² [by trapezoidal windows, Fig. 1(c)] together to form a new volume, which was upsampled and smoothed with a three-dimensional (3-D) median filter. The dimensions of the resultant volume were $960\mu \mathrm{m}\times 480\mu \mathrm{m}\times 1200\mu \mathrm{m}$. A total of 11 OCM data volumes with focus separation of $80\mu \mathrm{m}$ were fused together to get the CAO-OCM and OCM volumes. Focus spacing of $80\mu \mathrm{m}$ was selected. More information on the factors that determined the selection of $80\mu \mathrm{m}$ can be found in Sec. 4.3.

All data processing was performed in MATLAB R2017a, Windows Server 2016 Standard. The raw spectral data were reconstructed following standard algorithms, including background subtraction, spectrum resampling, dispersion correction, and inverse Fourier transform. CAO-specific steps included focal plane curvature correction,²³ cover glass registration,²⁴ and demodulation.²³

The standard OCM reconstruction (including background subtraction, spectrum resampling, dispersion correction, and inverse Fourier transform) took about 106 s for each data volume. Focal plane curvature calibration only needs to be done once and took about 110 s. Cover glass registration and demodulation took about 20 and 52 s, respectively, for each volume. The fusion of 79 volumes to generate “ground truth” took about 2175 s. The fusion of 11 volumes for OCM and CAO-OCM took about 220 s. The median filtering of ground truth, OCM, and CAO-OCM took about 223 s in total.

For each data volume, we took 90 to 110 planes near the focus to be a subvolume. We only optimized the correction of defocus for the subvolumes (i.e., we did not attempt to correct other optical aberrations). For each subvolume, it took about 150 s to optimize the refocus coefficients and 10 s to apply the correction.

2.3.

Two-Photon Microscopy and Optical Coherence Microscopy Coregistration

A fiduciary mark was made on the cover glass and OCM and two-photon image volumes were acquired at a known distance and direction from the fiduciary. A 2PM was performed on a home-built system equipped with a Ti:sapphire laser (Chameleon Visionjh, Coherent) with the wavelength centered at 880 nm. A galvanometric scanner pair (Cambridge Technology) was used to perform an XY raster scan with the focus at a specified Z position at $\sim 1\text{frame}/\sec$ to generate a $512\text{pixel}\times 512\text{pixel}$ image. Lateral resolution was $0.5\mu \mathrm{m}$ and axial resolution was $3\mu \mathrm{m}$. Emission was separated using a primary dichroic (705 nm); a secondary dichroic (520 nm); two tertiary dichroics (488 and 605 nm); and bandpass filters selective for Texas-Red (641/75), YFP (550/49), and GFP (517/65). Z-stack images were acquired using an Olympus XLPlan N $25\times$ 1.05 NA objective, starting at the brain surface to $500\mu \mathrm{m}$ deep with $1\text{-}\mu \mathrm{m}$ increments using a motorized linear stage DC motor (Newport). Laser scanning, data acquisition, and stage position were controlled by ScanImage software.²⁵

2.4.

Computational Adaptive Optics

In this study, CAO was only used to correct defocus. The computed pupil of OCT system can be modeled as an ideal pupil with an aberration phase factor:

2.5.

Image Quality Metric for Optimization of Computational Adaptive Optics Corrections

The fine-tuning of refocus coefficient $\mathrm{\Delta }z$ were done by exhaustive search (Fig. 2) based on a metric that optimizes spatial frequency content, named as frequency metric. The metric is defined as the ratio of frequency energy within a middle-to-high range [P1 in Fig. 1(e)] of the transverse Fourier transform of the amplitude image to the energy within the middle frequency limit [P2 in Fig. 1(e)].⁶ The frequency metric can be described by the following equation:

Fig. 2

Exhaustive search based on the frequency metric to find the optimal refocus coefficients for a volume with focus at about $124\mu \mathrm{m}$ OPL. (a) Optimal coefficients found by metric versus depth. Red vertical line indicates focus depth. (b)–(d) Frequency metrics versus refocus coefficients that were calculated at each depth (indicated by arrows) and used to identify the optimal value. The corresponding en-face planes (left: OCM, middle: CAO-OCM with optimal coefficients found by metric, right: at-focus ground truth) are also included. Gamma correction was applied to the images with $\gamma =0.7$. Scale bar = $100\mu \mathrm{m}$.

Figure 2 shows how we found the optimal refocus coefficients based on the frequency metric. It demonstrates the exhaustive search of refocus coefficients for a volume with focus at about $124\mu \mathrm{m}$ OPL. Figure 2(a) is the optimal refocus coefficient found by frequency metric at each depth. Figures 2(c) and 2(d) show the frequency metric as a function of refocus coefficient for three planes at 44, 125, and $215\mu \mathrm{m}$ OPL depths, respectively. Video versions of Fig. 2(b)—2(d) can be found in Videos 1–3, respectively. With constant refractive index, the refocus coefficients are expected to be linear with depth. Linear fitting was applied to the optimal refocus coefficients founded by metric. Considering the depth-dependent refractive index in the biological tissue, a tolerance of $18.2\mu \mathrm{m}$ was allowed, compared to the linear fitting. For one plane, if the searched coefficient was within the fitted value of $\pm 18.2\mu \mathrm{m}$, the searched coefficient was used for correction, otherwise the fitted value was used.

2.6.

Normalization and Fusion Procedures

The data volumes are synthesized into a new volume using a trapezoidal window [Fig. 1(c)], following the procedure outlined in the so-called Gabor fusion technique.²² Because of large focus spacing, a larger window is used to fuse CAO-OCM and OCM than at-focus ground truth.

Before fusion, we divided the data volume by the 98th percentile of each plane to normalize the high signal level in the near-focus regions. After fusion, to reduce the banding artifacts along depth caused by low SNR in the out-of-focus regions, we subtracted the synthesized volume by the second percentile of each plane.

2.7.

Signal-to-Background Ratio Estimation

The estimation of signal-to-background ratio (SBR) is based on the assumption that background level is uniformly distributed in the transverse Fourier domain, and there is no signal component but only background in the high frequency range. First, we normalized the transverse frequency range from 0 to 1. Then, we calculated the background energy density in the high frequency range (i.e., 0.95 to 1). By multiplying the background energy density and the spatial domain area of the frequency range we are interested in, we got the background energy level in that frequency range. Therefore, by subtracting the background energy level from the total energy level, we got the signal energy level in that frequency range.

3.1.

Comparison of Optical Coherence Microscopy and Computational Adaptive Optics-Optical Coherence Microscopy with Two-Photon Microscopy

OCM volumes from a region in cortex of the extracted mouse brain, acquired with focus spacing of $10\mu \mathrm{m}$, were fused into a synthetic volume using previously developed methods²² to generate an at-focus ground truth image. To verify the ability of OCM and CAO-OCM with larger focus spacing to resolve small brain structures, 2PM data in the same location were taken immediately after OCT scanning and compared with fused OCM and CAO-OCM (Fig. 3). Because of low backscattering, cell bodies and vessels manifest themselves as dark regions in OCM. Therefore, we utilize minimum intensity projection (MinIP) to highlight those structures in OCM.¹ Similarly, neurites (dendrites and myelinated axons) manifest themselves as bright regions in OCM,¹ so following Srinivasan et al.¹ we utilized a maximum intensity projection (MaxIP) to highlight these structures. MaxIP of 2PM data in the same volume show fluorescently labeled blood vessels, neural dendrites, and microglia. As indicated in Fig. 2, some of the same structures were found in CAO-OCM and 2PM images and included both cell bodies and microvessels.

Fig. 3

Comparison of microstructure observable with fused ground-truth OCM (fusion of datasets taken with $10\text{-}\mu \mathrm{m}$ focus spacing), fused CAO-OCM (fusion of datasets taken with $80\text{-}\mu \mathrm{m}$ focus spacing), and 2PM. Vessels are indicated by arrows and cell bodies are indicated by circles. (a) MinIP of cross-sectional OCM images (MinIP taken over $46\mu \mathrm{m}$ along the slow scan axis of 3-D OCM dataset). (b) MinIP of cross-sectional CAO-OCM images (MinIP taken over $46\mu \mathrm{m}$ along the slow scan axis of 3-D CAO-OCM dataset). (c) MaxIP of 2PM data (over $42\mu \mathrm{m}$), where blue indicates vessel (Texas-Red lectin), green indicates neurons (YFP), and yellow/red indicates microglia (GFP). $\text{Scale bar}=50\mu \mathrm{m}$. Note that the depth range of the cross-sectional OCM and CAOOCM images have been cropped to match the depth range of the 2PM image.

3.2.

Volumetric Computational Adaptive Optics-Optical Coherence Microscopy of Fresh Ex Vivo Mouse Brain

With beam Rayleigh length of $9\mu \mathrm{m}$, focus scanning with step of $80\mu \mathrm{m}$ results in a factor of 4 fewer datasets, compared to focusing scanning with step equal to twice the Rayleigh length. Figures 4 and 5 show planes extracted from volumetric reconstructions of ex vivo mouse brain tissue. Four en-face planes, at optical depths of 83, 556, 914, and $1150\mu \mathrm{m}$ in the tissue (Fig. 4), and one cross section (Fig. 5) are extracted from the volume. Figure 4 displays comparisons of each plane with and without CAO. Fibrous structures can clearly be seen in the upper $\sim 100\mu \mathrm{m}$ [Fig. 4(a)], consistent with the network of myelinated axons and dendrites found in layer 1 of the cortex. Thicker fibers at $\sim 1000\mu \mathrm{m}$ in depth with parallel orientations [Fig. 4(d)] are consistent with myelinated axons found in white matter.^26,27 Fly-through of en-face planes from ground truth, CAO-OCM, and OCM are contained in Video 13.

Fig. 4

Comparison of selected en-face planes from OCM ground truth reconstructed with dense ($10\mu \mathrm{m}$) focus spacing, and CAO-OCM and OCM reconstructed with sparse ($80\mu \mathrm{m}$) focus spacing at optical depths of (a) $83\mu \mathrm{m}$ ($68\mu \mathrm{m}$ to shallower focus, $53\mu \mathrm{m}$ to deeper focus, MaxIP over $8\mu \mathrm{m}$ along depth), (b) $556\mu \mathrm{m}$ ($63\mu \mathrm{m}$ to shallower focus, $58\mu \mathrm{m}$ to deeper focus, MinIP over $8\mu \mathrm{m}$ along depth), (c) $914\mu \mathrm{m}$ ($61\mu \mathrm{m}$ to shallower focus, $60\mu \mathrm{m}$ to deeper focus, MaxIP over $8\mu \mathrm{m}$ along depth), and (d) $1150\mu \mathrm{m}$ ($58\mu \mathrm{m}$ to shallower focus, $20\mu \mathrm{m}$ to deeper focus, MaxIP over $8\mu \mathrm{m}$ along depth). For (a)–(d), the first row shows fused OCM with $10\text{-}\mu \mathrm{m}$ focus spacing (ground truth), the second row shows fused CAO-OCM with $80\text{-}\mu \mathrm{m}$ focus spacing, and the third row shows fused OCM with $80\text{-}\mu \mathrm{m}$ focus spacing; (a)–(d) also contain zoomed-in figures with red or blue margins. (e)–(h) Line plots of magnitude along the green dashed lines in the zoomed images in (a)–(d), respectively. Blue curves are fused OCM with $10\text{-}\mu \mathrm{m}$ focus spacing, red curves are fused CAO-OCM with $80\text{-}\mu \mathrm{m}$ focus spacing, and yellow curves are fused OCM with $80\text{-}\mu \mathrm{m}$ focus spacing. Microstructures can be visualized more clearly in CAO-OCM than OCM [myelinated axons indicated by red and blue arrows in (a), cell body indicated by red arrows in (b), and fibers indicated by blue arrows in (c)]. When approaching (d) $1150\mu \mathrm{m}$ deep, CAO no longer provides any obvious improvement. $\text{Scale bar}=100\mu \mathrm{m}$.

Fig. 5

Cross sections extracted from volumetric reconstructions of mouse brain (MinIP taken over $22\mu \mathrm{m}$ along the slow scan axis of 3-D OCM dataset). (a) Fused OCM with $10\text{-}\mu \mathrm{m}$ focus spacing (ground truth), (b) fused CAO-OCM with $80\text{-}\mu \mathrm{m}$ focus spacing, and (c) fused OCM with $80\text{-}\mu \mathrm{m}$ focus spacing. The bottom two rows show zoomed-in images of the boxes in (a)–(c). Ticks on the vertical axis indicate the relative depths of foci of single OCM volumes that constitute the fused volumes. Microstructures can be visualized more clearly in CAO-OCM than OCM (e.g., the cell body indicated by yellow arrows, microvessels indicated by blue and red arrows, fibers indicated by green arrows in the zoom-in figures). Scale bar = $100\mu \mathrm{m}$.

In the zoomed-in panels in Figs. 4 and 5, microstructures can be visualized more clearly in CAO-OCM than OCM. However, when getting deep in the tissue, the improvement provided by CAO is not as evident as at shallower depths. This is evident from the line plots [Figs. 4(e)–4(g)], where the curves from CAO-OCM have better similarity to the ground truth than OCM without correction by CAO. Furthermore, CAO-OCM makes the cell bodies darker [Figs. 4(e)–4(f)] and the defocused fiber narrower [Fig. 4(g), Video 1]. However, as it gets deeper in the tissue, CAO does not provide much improvement to OCM [Figs. 4(d), 4(h), Video 12]. The limitations of CAO in scattering tissue will be discussed in Sec. 4.

4.1.

Choice of Image Metric for Optimizing Computational Adaptive Optics Corrections

Previous studies have shown the applications of intensity-based metrics for numerical correction of OCT data, i.e., sharpness metric,^28,29 entropy metric,^30,31 and etc. For images with point-like (sharp) features, the intensity-based metrics can easily capture the increasing constructive interference as aberrations are minimized, because the intensity of point-like objects increases with constructive interference. However, in scattering samples without distinct structures, the intensity-based metrics could be disrupted by the ubiquitous speckles. Therefore, we chose a frequency-based metric, which is based on the assumption that middle-to-high frequency components of OCM or CAO-OCM magnitude images increases as the resolution improves (when the aberrations are minimized).⁶

4.2.

Choice of Middle and High Cut-off Values for Frequency Metric

As is mentioned in Sec. 2, we utilized a frequency metric to provide feedback for CAO coefficient search. This is defined as the ratio of frequency energy within a middle–high range [P1 in Fig. 1(e)] of the transverse Fourier transform of the magnitude of each en-face OCM image to the energy within the middle frequency limit [P2 in Fig. 1(e)].⁶ The middle and high cut-off frequencies could affect the performance of this metric. Therefore, the choice of middle and high cut-off frequencies is critical.

To choose these cut-off frequencies, we need to identify the transverse frequency components that are most sensitive to defocus. We randomly chose three at-focus planes at depth of 94, 513, and $932\mu \mathrm{m}$ OPL as reference depths [Fig. 6(a)]. For each reference depth, we found the defocused version from the original focus-scanning dataset acquired with step of $10\mu \mathrm{m}$ [Fig. 6(a)]. Figure 6 demonstrates a defocused version of the reference at $94\mu \mathrm{m}$ OPL depth. The defocused plane is $168\mu \mathrm{m}$ OPL above the focus. Figures 6(b) and 6(c) show the reference and defocused versions, respectively. Figure 6(c) is the difference between spectrum energy of the magnitude of reference and defocused version (in decibel scale), whose total energies are both normalized to 1. To more clearly visualize the spectrum energy difference, we transformed the two-dimensional spectrum energy into a one-dimensional vector along the normalized transverse spatial frequency radius axis $Q_r$ and plotted in Fig. 6(d). From Fig. 6, we found the frequency range where the defocused version generally has lower energy than the reference, and then chose the frequency range limits as the middle and high cut-off frequencies. The cut-off frequencies that we used to calculate the frequency metric are indicated by green dash lines in Fig. 6(d) and green dash circles in Fig. 6(c). Video 4 contains additional information of more defocused versions with respect to reference at $94\mu \mathrm{m}$ OPL depth. The same procedure was also applied to references at 513 and $932\mu \mathrm{m}$ OPL depths. The results can be found in Videos 5 and 6, respectively.

Fig. 6

Variations in transverse spectrum energy distribution of physically defocused images. (a) Scheme to demonstrate how we chose the references and their defocused version. (b) At-focus reference at $94\mu \mathrm{m}$ OPL depth and (b) its defocused version, which is $168\mu \mathrm{m}$ above the focus (positive distance indicates depth above the focus, and negative distance indicates depth below the focus). (d) Difference between spectrum energy of the magnitude of reference and defocused version (in decibel scale). Here $Q_x$ and $Q_y$ are the transverse spatial frequency coordinates. (e) Plot of spectrum energy of magnitude of reference and defocus version, and the difference between them (defocused version minus reference), along normalized frequency radius axis $Q_r$. Green dash lines and green circles in (c) and (d) indicate the cut-off frequencies used for calculating metrics. Gamma correction was applied to the images with $\gamma =0.7$. $\text{Scale bar}=100\mu \mathrm{m}$.

To investigate the sensitivity of the image metric to the choice of cut-off frequencies, we plotted the optimal coefficient found by metrics with different mask sizes in Fig. 7. The values of $f_1$ and $f_2$ correspond to the middle and high cut-off frequencies, respectively. In this paper, we used $f_1=0.04$ and $f_2=0.68$. We found that, for data volume with shallow focus [Fig. 7(a)], CAO is less sensitive to the choice of $f_1$ and $f_2$, whereas for data volume with deeper focus [Fig. 7(c)], CAO is more sensitive to the choice of $f_1$ and $f_2$, particularly when further away from the focus. This is consistent with our discussion about limitations of CAO in Sec. 4.4. For the depth range we used for fusion, the metric is insensitive to the choice of $f_1$ and $f_2$ within variance up to 0.2.

Fig. 7

Plot of the optimal refocus coefficient found by metrics with different cut-off frequencies, for three volumes with focus at (a) 124, (b) 722, and (c) $1085\mu \mathrm{m}$.

4.3.

Determining Appropriate Focus Spacing for Large-Scale Volumetric Computational Adaptive Optics-Optical Coherence Microscopy

In a Gaussian-beam imaging system, signal strength decreases with distance from focus because of confocal gating. The rate of signal decay with distance from focus increases with the numerical aperture of the system, which reduces the depth range over which the signal is above the OCT system noise floor. Therefore, the “usable depth range” of CAO-OCM depends on both the numerical aperture of the confocal gate and the dynamic range of the OCT system.³²

In a highly scattering biological sample, the usable depth range is further reduced by multiple scattering and “cross talk”^33–35 (see Sec. 4.4, for further discussion). Moreover, CAO does not solve the signal loss in the scattering tissue sample. We cannot apply CAO in a single-acquired OCM volume to reconstruct with high resolution and SNR throughout a large depth range. For this reason, focus scanning is required. This leads to a trade-off between resolution and number of required focus-scanned OCT volumes (or the maximum distance between focus positions). The focus spacing is governed by the decay in collected signal with distance from the focus, and the level of scattering of the sample. In this work, we chose $80\mu \mathrm{m}$ as the focus spacing for CAO-OCM, because CAO works reasonably well (visually showed similar tissue microstructure to the ground truth) in this setting but not with focus spacing of $100\mu \mathrm{m}$ or more (see Videos 1–3, for shallow depth in the sample; Videos 7–9, for moderate depth in the sample; and Videos 10–12, for deep in the sample). CAO-OCM with focus separation of $80\mu \mathrm{m}$ provided enabled visualization of tissue microstructures such as dendrites or myelinated axons, cell bodies, and vessels. These microstructures were more clearly visualized than in a CAO-OCM volume fused with $160\text{-}\mu \mathrm{m}$ focus spacing. (The depth-dependent image metric of $160\text{-}\mu \mathrm{m}$ focus spacing also indicated lower image quality—data not shown.) We note that the selection of $80\text{-}\mu \mathrm{m}$ focus spacing was not a result of an optimization process, and so further work is needed to determine the focus separation that minimizes the number of required volumes without compromising CAO-reconstructed image quality too much. Considering the depth-dependent OCT image quality and performance of CAO in any given sample, a nonuniform focus separation may be considered in a future study.

4.4.

Limitations of Computational Imaging in Scattering Tissues

Figure 8 is generated to investigate the limitations of CAO in scattering tissues. Figures 8(a) and 8(b) demonstrate exhaustive search of refocus coefficients for volumes with focus at about 722 and $1082\mu \mathrm{m}$ OPL, respectively. For planes away from the focus, the search of coefficients is less convex than those closer to the focus (Figs. 2, 8(a), and 8(b)]. Furthermore, from the en-face planes in Videos 1–3 and 7–12, CAO cannot provide obvious improvement to planes away from the focus, especially deep in the tissue. This could be due to the reduction of SBR as distance from the focus increases. Figure 8(c) is the plot of SBR versus depth for the volumes in Figs. 8(a) and 8(b). The SBR is higher for planes closer to the focus, and the volume with deeper focal depths has lower SBR.

Fig. 8

Limitations of CAO in the scattering tissue. (a) and (b) Exhaustive search of optimal refocus coefficients for volumes with focus at about 722 and $1082\mu \mathrm{m}$ OPL, respectively. In (a) and (b), the top-left figures are plots of optimal refocus coefficients found maximizing the frequency metric at each depth. Red vertical line indicates focus depth. The boxed figures are examples of frequency metrics versus refocus coefficients that were calculated at each depth (indicated by arrows) and used to identify the optimal value. The corresponding en-face planes (left: OCM, middle: CAO-OCM with optimal coefficients found by metric, right: at-focus ground truth) are also included. The video versions of the boxed figures can be found in Videos 7–12. (c) SBR for the volumes in (a) and (b). Gamma correction was applied to the images with $\gamma =0.7$. $\text{Scale bar}=100\mu \mathrm{m}$.

Figure 9 shows the frequency metric and normalized contrast versus depth in the synthetic volumes. The fluctuation in frequency metric of OCM with $80\text{-}\mu \mathrm{m}$ focus spacing is due to defocus. After CAO correction, the fluctuation still exists but does show some improvement over OCM. The normalized contrast for each depth was calculated from a subvolume (five planes centered about the given depth) by subtracting the 20th percentile of the OCT signal magnitude from the 95th percentile and then dividing by the median signal of the subvolume. The normalized contrast curves show similar fluctuations to frequency metric curves, except the increasing trend deeper in the sample. The increasing contrast for depths in the 800 to $1200\mu \mathrm{m}$ range is likely due to the high-scattering regions of white matter tissue, which contrasts with other relatively low-scattering regions within the transverse FOV (see Video 13).

Fig. 9

Quantitative analysis of depth-dependent image quality for the synthetic volumes of CAO-OCM, OCM, and ground truth. (a) Frequency metric and (b) normalized contrast (see text for definition).

The improvement provided by CAO is less obvious for deeper planes (Fig. 9 and Video 13). The frequency curves show that CAO correction in scattering brain tissue cannot restore all the frequency content obtained with ground-truth focal plane imaging. This suggests that the performance of CAO depends on SBR, which includes the effect of single-to-multiple scattering ratio³⁶ and SNR. An unexpected contribution to the multiple scattering background could arise from the phenomenon of cross talk.^33–35 Although cross talk is traditionally associated with full-field OCT approaches that use spatially coherent illumination, we note that when reconstructing away-from-focus, these depths are illuminated by spatially coherent light over an extended area (governed by the Gaussian beam diameter at that depth). Because of multiple scattering, the usable depth range in mouse brain ($\sim 100\mu \mathrm{m}$) is much shorter than low-scattering cell culture ($\sim 500\mu \mathrm{m}$).³² Low SNR and multiple scattering in deep tissue can limit the ability of CAO to reconstruct accurate, high-resolution sample structure. Fortunately, techniques exist to overcome the limitation caused by multiple scattering, for example, through optical tissue clearing,³⁷ which are applicable to ex-vivo imaging of tissues.

4.5.

Importance of Phase Stability for Computational Adaptive Optics-Optical Coherence Microscopy

Phase-dependent postprocessing techniques, including CAO and interferometric synthetic aperture microscopy, are sensitive to phase stability.³⁸ In previous research, an experiment of localized disturbance on an SD-OCT system demonstrated the depth-dependent phase stability requirements.³⁹ Owing to the expansion of a Gaussian imaging beam with increasing distance from focus, the depths far from the focus experience a longer interrogation time (the dwell time of the Gaussian beam at a given location during XY raster scanning), compared to the depths near the focus. As a result, computational correction of depths far from the focus requires higher phase stability.

In this paper, cover glass phase registration²⁴ was employed to improve the phase stability in the sample. This method of phase registration was sufficient for ex-vivo imaging. However, for in-vivo imaging in mouse brain, further techniques may be required to solve the phase instability issue caused by tissue motion. Several methods have been reported for 3-D motion correction. For in-vivo skin imaging, motion along the optical axis was corrected using phase differences between A-scans, and motion orthogonal to the optical axis was corrected utilizing a speckle-tracking system.⁴⁰ In the retinal CAO imaging, the effect of motion was mitigated through a combination of high-speed acquisition and postacquisition phase correction.⁹