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 |

## 1.## IntroductionThe basic science applications of optical coherence tomography (OCT) and optical coherence microscopy (OCM, the high-lateral-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 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. 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., ## 2.## Method## 2.1.## Mouse Brain PreparationMice heterozygous for Cx3Cr1-enhanced green fluorescent protein (GFP) [B6.129P(Cg)-Ptprca Cx3cr1tm1Litt/LittJ] ## 2.2.## Optical Coherence Microscopy Imaging Protocol and Image ReconstructionImaging 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 $2.2\text{\hspace{0.17em}\hspace{0.17em}}\mu \mathrm{m}$, respectively. The Rayleigh length of sample arm beam is $9\text{\hspace{0.17em}\hspace{0.17em}}\mu \mathrm{m}$. A-scans were acquired at line rate of 30 kHz, B-scan frame rate of $\sim 25\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{Hz}$, and exposure time of $10\text{\hspace{0.17em}\hspace{0.17em}}\mu \mathrm{s}$. Each acquired volume is composed of $1024\times 512$ A-scans, corresponding to a transverse field of view (FOV) of $960\text{\hspace{0.17em}\hspace{0.17em}}\mu \mathrm{m}\times 480\text{\hspace{0.17em}\hspace{0.17em}}\mu \mathrm{m}$. 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 $10\text{\hspace{0.17em}\hspace{0.17em}}\mu \mathrm{m}$, 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 synthesized 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, 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 CoregistrationA 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 $\sim 1\text{\hspace{0.17em}\hspace{0.17em}}\text{frame}/\mathrm{sec}$ to generate a $512\text{\hspace{0.17em}\hspace{0.17em}}\text{pixel}\times 512\text{\hspace{0.17em}\hspace{0.17em}}\text{pixel}$ image. Lateral resolution was $0.5\text{\hspace{0.17em}\hspace{0.17em}}\mu \mathrm{m}$ and axial resolution was $3\text{\hspace{0.17em}\hspace{0.17em}}\mu \mathrm{m}$. 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 $500\text{\hspace{0.17em}\hspace{0.17em}}\mu \mathrm{m}$ 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. ## 2.4.## Computational Adaptive OpticsIn 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: where, ${Q}_{x}$ and ${Q}_{y}$ are the transverse angular spatial frequency coordinates, $|H({Q}_{x},{Q}_{y})|$ is the ideal pupil, and ${e}^{i{\phi}_{\text{aberration}}}$ is the aberration phase factor. CAO compensates the aberrated pupil via a phase filter: where ${H}_{\mathrm{AC}}({Q}_{x},{Q}_{y})$ is the corrected pupil and ${e}^{i{\phi}_{AC}}={e}^{-i{\phi}_{\text{aberration}}}$ is the phase filter. Since CAO was only used to correct defocus in this work, the phase filter is given as## Eq. (3)$${\phi}_{\mathrm{AC}}=\sqrt{{(2{k}_{c})}^{2}-{Q}_{x}^{2}-{Q}_{y}^{2}}\text{\hspace{0.17em}}\mathrm{\Delta}z,$$## 2.5.## Image Quality Metric for Optimization of Computational Adaptive Optics CorrectionsThe 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)]. ## Eq. (4)$$\frac{\sum {\{|{\mathrm{FT}}_{x,y}[|S(x,y,z)|]|*\text{mask}1\}}^{2}}{\sum {\{|{\mathrm{FT}}_{x,y}[|S(x,y,z)|]|*\text{mask}2\}}^{2}},$$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 $124\text{\hspace{0.17em}\hspace{0.17em}}\mu \mathrm{m}$ 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 $215\text{\hspace{0.17em}\hspace{0.17em}}\mu \mathrm{m}$ 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 $18.2\text{\hspace{0.17em}\hspace{0.17em}}\mu \mathrm{m}$ was allowed, compared to the linear fitting. For one plane, if the searched coefficient was within the fitted value of $\pm 18.2\text{\hspace{0.17em}\hspace{0.17em}}\mu \mathrm{m}$, the searched coefficient was used for correction, otherwise the fitted value was used. ## 2.6.## Normalization and Fusion ProceduresThe 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. 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 EstimationThe 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.## Results## 3.1.## Comparison of Optical Coherence Microscopy and Computational Adaptive Optics-Optical Coherence Microscopy with Two-Photon MicroscopyOCM volumes from a region in cortex of the extracted mouse brain, acquired with focus spacing of $10\text{\hspace{0.17em}\hspace{0.17em}}\mu \mathrm{m}$, were fused into a synthetic volume using previously developed methods ## 3.2.## Volumetric Computational Adaptive Optics-Optical Coherence Microscopy of Fresh |

*ex vivo*," Journal of Biomedical Optics 24(11), 116002 (26 November 2019). https://doi.org/10.1117/1.JBO.24.11.116002