Computed optical coherence microscopy of mouse brain ex vivo

Abstract. The compromise between lateral resolution and usable imaging depth range is a bottleneck for optical coherence tomography (OCT). Existing solutions for optical coherence microscopy (OCM) suffer from either large data size and long acquisition time or a nonideal point spread function. We present volumetric OCM of mouse brain ex vivo with a large depth coverage by leveraging computational adaptive optics (CAO) to significantly reduce the number of OCM volumes that need to be acquired with a Gaussian beam focused at different depths. We demonstrate volumetric reconstruction of ex-vivo mouse brain with lateral resolution of 2.2  μm, axial resolution of 4.7  μm, and depth range of ∼1.2  mm optical path length, using only 11 OCT data volumes acquired on a spectral-domain OCM system. Compared to focus scanning with step size equal to the Rayleigh length of the beam, this is a factor of 4 fewer datasets required for volumetric imaging. Coregistered two-photon microscopy confirmed that CAO-OCM reconstructions can visualize various tissue microstructures in the brain. Our results also highlight the limitations of CAO in highly scattering media, particularly when attempting to reconstruct far from the focal plane or when imaging deep within the sample.


Introduction
The basic science applications of optical coherence tomography (OCT) and optical coherence microscopy (OCM, the highlateral-resolution version of OCT) are expanding, especially in the field of experimental neuroscience. Studies have revealed that OCM has the capability to visualize brain architecture and neural activity of rodents in vivo. [1][2][3] For example, optical coherence tractography using intrinsic scattering contrast can provide imaging and quantitative analysis of fibrous structures in the brain. 4 OCT has also been utilized to measure the refractive index of rat somatosensory cortex in vivo. 5 As an interferometric imaging modality, OCT is sensitive to the complex optical field, containing both amplitude and phase (wavefront) information, which makes it well suited for computational postprocessing methods to restore the resolution in out-of-focus regions. Computational adaptive optics (CAO) can compensate for aberrations and defocus via a filtering operation in the transverse Fourier domain of the OCT data. 6,7 Moreover, it can also correct high-order aberrations without complex hardware adaptive optics. [8][9][10][11] The compromise between lateral resolution and depth coverage represents a significant challenge for OCM to achieve large-volume imaging with cellular resolution. For example, in Srinivasan et al., 1 a Gaussian beam focus was scanned in depth with a step of 5 μm, and only a small portion of OCM volumes acquired at each focus depth was extracted and synthesized into a composite volume combining high transverse resolution and signal-to-noise ratio (SNR), which results in large data size and long acquisition time. A number of methods have been demonstrated to alleviate this trade-off, including illumination with a nondiffracting Bessel beam 12,13 and numerical methods to compensate defocus. 6,8,[14][15][16][17] However, these solutions either have nonideal side lobes in their point spread function or low SNR at out-of-focus depths. A combination of numerical methods and focus scanning has been proposed to generate volumetric reconstructions to combine high SNR and focal-plane transverse resolution and was demonstrated in a resolution phantom. 14 Here, we combine focus scanning 1,18,19 and CAO for high-resolution volumetric imaging deep in the scattering mouse brain. Using this method, only 11 OCT volumes acquired with focus planes 80 μm apart were required for imaging up to 1.2 mm optical path length (OPL) deep in the mouse brain with high spatial resolution. Two-photon microscopy (2PM) data was also taken to compare with OCM and CAO-OCM reconstructions.

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  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.

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 ∼1 frame∕ sec to generate a 512 pixel × 512 pixel image. Lateral resolution was 0.5 μm and axial resolution was 3 μm. Emission was separated using a primary dichroic (705 nm); a secondary dichroic (520 nm); two tertiary dichroics (488 and 605 nm); and bandpass filters   (11) selective for Texas-Red (641/75), YFP (550/49), and GFP (517/ 65). Z-stack images were acquired using an Olympus XLPlan N 25× 1.05 NA objective, starting at the brain surface to 500 μm deep with 1-μm increments using a motorized linear stage DC motor (Newport). Laser scanning, data acquisition, and stage position were controlled by ScanImage software. 25

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: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 6 3 ; 6 2 3 HðQ x ; Q y Þ ¼ jHðQ x ; Q y Þje iφ aberration ; where, Q x and Q y are the transverse angular spatial frequency coordinates, jHðQ x ; Q y Þj is the ideal pupil, and e iφ aberration is the aberration phase factor. CAO compensates the aberrated pupil via a phase filter: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 6 3 ; 5 4 7 H AC ðQ x ; Q y Þ ¼ HðQ x ; Q y Þe iφ AC ; where H AC ðQ x ; Q y Þ is the corrected pupil and e iφ AC ¼ e −iφ aberration is the phase filter. Since CAO was only used to correct defocus in this work, the phase filter is given as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 6 3 ; where k c is the central wavenumber (refractive index n × free-space wavenumber k 0 ) and Δz is the refocus coefficient (equal to −1 × displacement from focus). We first applied the estimated refocus coefficient and then fine-tuned it using an image metric as feedback.

Image Quality Metric for Optimization of Computational Adaptive Optics Corrections
The fine-tuning of refocus coefficient Δz 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-tohigh 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: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 4 ; 3 2 6 ; 5 9 0 P fjFT x;y ½jSðx; y; zÞjj Ã mask1g 2 P fjFT x;y ½jSðx; y; zÞjj Ã mask2g 2 ; where FT x;y is the Fourier transform in the transverse dimension and Sðx; y; zÞ is the corrected complex image. The choice of middle and high cut-off frequency, i.e., the boundaries of mask1 and mask2 in Fig. 1(e), will be discussed in Sec. 4. 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 μm 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 μm OPL depths, Fig. 2 Exhaustive search based on the frequency metric to find the optimal refocus coefficients for a volume with focus at about 124 μm 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 γ ¼ 0.7. Scale bar = 100 μm.
Journal of Biomedical Optics 116002-3 November 2019 • Vol. 24 (11) 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 μm was allowed, compared to the linear fitting. For one plane, if the searched coefficient was within the fitted value of AE18.2 μm, the searched coefficient was used for correction, otherwise the fitted value was used.

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.

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.

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 μm, were fused into a synthetic volume using previously developed methods 22 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.

Volumetric Computational Adaptive Optics-Optical Coherence Microscopy of Fresh Ex Vivo Mouse Brain
With beam Rayleigh length of 9 μm, focus scanning with step of 80 μm results in a factor of 4 fewer datasets, compared to focusing scanning with step equal to twice the Rayleigh length.

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 Journal of Biomedical Optics 116002-6 November 2019 • Vol. 24 (11) 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 μm 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 μm [ Fig. 6(a)]. Figure 6 demonstrates a defocused version of the reference at 94 μm OPL depth. The defocused plane is 168 μm 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 μm OPL depth. The same procedure was also applied to references at 513 and 932 μm OPL depths. The results can be found in Videos 5 and 6, respectively.
To investigate the sensitivity of the image metric to the choice of cut-off frequencies, we plotted the optimal coefficient 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 γ ¼ 0.7. Scale bar ¼ 100 μm.
Journal of Biomedical Optics 116002-7 November 2019 • Vol. 24 (11) 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 ¼ 0.04 and f 2 ¼ 0.68. We found that, for data volume with shallow focus

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][34][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 μm 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 μm 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 μm 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-μm focus spacing. (The depth-dependent image metric of 160-μm focus spacing also indicated lower image quality-data not shown.) We note that the selection of 80-μm 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 CAOreconstructed image quality too much. Considering the depthdependent OCT image quality and performance of CAO in any given sample, a nonuniform focus separation may be considered in a future study. The SBR is higher for planes closer to the focus, and the volume with deeper focal depths has lower SBR. Figure 9 shows the frequency metric and normalized contrast versus depth in the synthetic volumes. The fluctuation in frequency metric of OCM with 80-μm 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 μm 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).

Limitations of Computational Imaging in Scattering Tissues
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  Journal of Biomedical Optics 116002-9 November 2019 • Vol. 24 (11) scattering ratio 36 and SNR. An unexpected contribution to the multiple scattering background could arise from the phenomenon of cross talk. [33][34][35] Although cross talk is traditionally associated with full-field OCT approaches that use spatially coherent illumination, we note that when reconstructing away-fromfocus, 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 (∼100 μm) is much shorter than low-scattering cell culture (∼500 μm). 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.

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 depthdependent 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 registration 24 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

Conclusion
We have demonstrated that CAO can improve the resolution at planes distant from the focus in fresh ex-vivo mouse brain. In this work, a volumetric image of mouse brain with cellular resolution and depth range of 1.2 mm OPL was reconstructed. Various structures can be visualized by CAO-OCM reconstructions, including branching microstructure associated with neural networks in layer 1 of the cortex, myelinated axons in white matter, cell bodies, and blood vessels. Although CAO works well in shallow regions of scattering mouse brain tissue, its performance degrades with distance from focus and overall imaging depth. Furthermore, unlike hardware wavefront shaping, which results in increased photon collection at the time of data acquisition, CAO cannot solve the fundamental problem of away-from-focus signal loss caused by confocal gating. The performance of CAO is also degraded by additional corruption from multiple scattering and cross talk. Further study is needed to investigate the factors limiting the performance of computational methods in scattering tissue, and potential approaches to mitigate these factors. Future work will also attempt to address motion artifacts, in order to achieve the phase stability required for in-vivo volumetric CAO-OCM in the scattering mouse brain.  [16][17][18][19][20][21] in this appendix are representative of videos that provide visualization of the CAO optimization process at selected depths below the surface of mouse brain. Figures 13-15 are representative of videos showing the sensitivity of the frequency metric to physical shifts of the optical focus. Figure 22 is representative of a video that provides a visualization of at-focus "ground truth" OCM, CAO-OCM, and OCM across all depths.

Disclosures
The authors have no relevant financial interests in the article and no other potential conflicts of interest to disclose.