1. Introduction

Optical clearing methods involve matching the refractive index (RI) of the sample by removing or replacing the scattering structures such as lipid, to significantly extend the optical imaging penetration depth [1–4]. Combining the optical clearing methods with two-photon microscopy (TPM), researchers can observe neurons in a transparent brain (treated by optical clearing agents) up to a depth of 4 mm [5]. However, optical clearing agents generally have a different RI with respect to the immersion media of standard objective lenses (air = 1, water = 1.33, and oil = 1.51) [4]. Focusing through RI mismatch materials causes spherical aberration (SA), leading to a substantial degradation of fluorescence signal intensity and image resolution [6].

Several approaches have been proposed to alleviate the adverse effect of SA caused by RI mismatch. An easy approach is to adjust the correction collar equipped in a high-level objective. It corrects SA by adjusting both the collar position and the axial focal position manually to maximize the fluorescence intensity at a target depth. Consequently, this approach requires repeated adjustments to reduce the depth-induced SA. Moreover, not all objectives have a correction collar. Some microscope vendors provide objective lenses that are designed for particular optical clearing agents; however, these objectives are limited to several special agents and cannot be extended to others. A few years ago, Matsumoto et al. proposed another method to correct the SA. It calculates the distorted wavefront using a mathematical model and compensates the aberration using a spatial light modulator (SLM) [7]. This method is efficient and automatic for SA correction; however, the restricted issue is how to accurately obtain some important parameters for SA calculation, such as the RI of samples.

Adaptive optics (AO) is a powerful technique for correcting the optical aberration (including the SA) introduced by the optical systems and the samples [8–10]. Among all AO methods, the modal-based AO and the pupil segmentation AO are two facilitated approaches for SA correction. The modal-based AO aims at maximizing the fluorescence intensity or the image quality by systematically testing a group of basis functions that are orthogonal on the pupil plane [11–13]. In the modal-based AO, the SA can be expressed in terms of rotationally symmetrical polynomials and thereby can be corrected efficiently [14]. However, this approach is derived from the assumption of small aberration. It is not suitable for the correction of large SAs, which usually emerge in optically cleared samples [13]. For example, the peak-to-valley (PV) value of SA could be 18 μm when using a dry objective lens to image a phantom sample mimicking optically-cleared-tissue (RI = 1.55) [7]. Some pupil segmentation AO methods were presented to compensate the large aberration [15–17]. It restores the distorted focus by dividing the pupil plane into subregions so that the beamlets in each subregion could be modulated and corrected separately [15,17]. Nevertheless, these methods indiscriminately compensate the high-order aberrations that vary dramatically in space, making the wavefront correction pattern only valid for a small volume [15]. Further, the pupil segmentation is inefficient for SA correction compared to the modal-based AO, as it does not utilize the symmetrical characteristic of the SA. Consequently, the increment of iteration rounds and the elongation of exposure time for SA correction of the pupil segmentation will increase the photo-bleaching and photo-toxicity on samples, which is critical for biological studies.

In this study, we propose a new AO method based on pupil ring segmentation to improve the accuracy and efficiency of SA correction. This method takes advantage of the symmetry of SA from the modal-based and the phase correction principle from the pupil segmentation. Moreover, it can calculate a whole SA correction map over the imaging volume only using three measurements at different depths for optical clearing samples. From the images of a bead phantom sample, we found that our pupil ring segmentation method can improve the fluorescence intensity 5-6 fold and recovered the axial and lateral resolution to the near-diffraction-limited at 900 μm depth below the sample surface. We also applied our pupil ring segmentation method to image brain tissues, which were treated with different types of optical clearing agents such as the CUBIC and SeeDB. The results show that the synaptic structures of neurons can be clearly distinguished in the deep region owing to the accurate SA correction.

2. Materials and methods

2.1 Two-photon fluorescence microscope with pupil ring segmentation

For SA correction, we incorporated a SLM into the TPM system to modulate the wavefront of the excitation light using the pupil ring segmentation method. The schematic of the system is given in Fig. 1(a). In brief, the excitation light (920 nm, 80 MHz repeat rate) from a Ti: Sapphire laser (Chameleon Ultra, Coherent) was expanded to a 1/e² diameter of 12 mm for overfilling the panel of SLM (HSP1920-600-1300-HSP8, Meadowlark Optics). A half-wave plate was placed before the SLM to orientate the polarization of the laser to match the SLM. Because the zeroth order light of SLM would contain the specular light, we loaded a blazed grating pattern on the SLM as a background pattern to separate the modulated light and the specular light [17]. A field stop placed at the image plane of the SLM was used to block the specular light. After the field stop, the excitation beam was raster scanned by a pair of galvanometer mirrors (5-mm aperture; TS8203, Sunny Technology) to create a two-dimensional image. An objective (CF175 25x Water, NA 1.1, Nikon) focused the scanning beam onto the samples and collected the epi-fluorescence signal from the samples. In the detection path, the emission fluorescence signal was reflected by a long-pass dichroic mirror (T715LP, Chroma) for being separated from the excitation light and conducted by a pair of singlet lens (LA1145-A, LA1805-A, Thorlabs) into a photomultiplier tube (PMT, H7422P-40, Hamamatsu). A bandpass filter (ET520/40 nm, Chroma) was placed before the PMT to purify the fluorescence signal. To ensure that the phase pattern from the SLM is projected onto the objective rear pupil plane accurately during the beam scanning, the SLM, the paired galvanometers, and the objective rear pupil plane were made mutually conjugated by three pairs of relay lens (from the SLM to the objective: AC254-200-B, AC254-100-B; AC508-080-B, AC508-080-B; LSM54-1050, AC508-200-B, Thorlabs). We used a custom MATLAB code and ScanImage program to control the EOM, the SLM, the scanning mirrors, and the z-axis actuator (KMTS25E, Thorlabs), as well as capture the images.

 

Fig. 1. Principles of pupil ring segmentation. (a) Schematic of the system setup. EOM, electro-optical modulator; λ/2, 1/2 λ wave plate; SLM, spatial light modulator; FS, field stop; SL, scan lens; DCM, Dichroic Mirror; Obj, objective lens; F, filter; PMT, photomultiplier tube. (b) Stratified structures under the objective cause spherical aberration. Paraxial (brown lines) and peripheral rays (red lines) are focused at different depths of the sample, leading to an elongated focus with lower peak intensity. (c) Phase modulation in pupil plane. The pupil plane was divided into 20 rings. The phase of each ring was modulated to produce interference intensity variation near the focus. (d) The relationship between the phase and fluorescence intensity was fitted by a sine function to find an optimal phase offset (red squares).

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2.2 Pupil ring segmentation-based SA correction

The principle and the schematic of pupil ring segmentation method are shown in Fig. 1(b)-(d). The RI mismatch between the immersion media of the objective (n₁) and the sample itself (n₂) introduces the SA. Consequently, the excitation rays with different convergence angles are focused into different depths of the sample (Fig. 1(b)). The intuition of our pupil ring segmentation method for SA correction is to manipulate the ray of different converged angles to focalize them at the same depth. Basically, we virtually divide the circular pupil into concentric rings, where each is considered as a subregion with the same cone angle, and modulate the phase of each ring to maximize the image intensity. The details of the method are described by the following steps:

In step (1), the width of each ring is chosen based on the following criteria. The first is to ensure each subregion with equivalent excitation energy by considering the non-uniform intensity distribution of the Gaussian beam. The second is to ensure a nearly uniform phase variation rate along the rings from center to edge. For the SA, the phase sharply varies along the radius in the area of large numerical aperture, and the width of the ring close to the pupil edge are designed to be narrower than that close to the pupil center. It should be noted that increasing the number of rings can improve the accuracy of SA correction; however, it will prolong the correction time and reduce the constructive interference intensity of each subregion. In the experiment, we found that 20 rings are sufficient to correct the SA and to restore the degraded resolution if the NA is lower than 1.1, the imaging depth is less than 1 mm and the RI mismatch is less than 0.2.

In step (2), we loaded the phase patterns and acquired the corresponding images at a frame rate of 60 Hz. Consequently, the exposure time of the whole measurement (six phase offsets for each ring and three iterations) was around 6 s, which is acceptable for tissue imaging. To obtain high-contrast feedback images that provide stable intensity feedbacks, we generally chose the fluorescent beads of beads samples and the somas of neurons of brain slices as the guide stars.

To create a smooth surface that resembles the SA distribution, the phases of rings versus the radius were fitted with a polynomial function. In addition, we added a defocus factor into the fitted curve to obtain an SA correction curve with a small PV value. The small-PV curve is favorable in the system using SLM as a phase modulator, because SLM compensates aberration with amplitude larger than one wavelength through phase wrapping, which causes diffraction effects.

2.3 Deriving an SA map for different depths

Previous studies have demonstrated that the SA in an RI homogenous sample varies linearly with the increase of imaging depth [18]. Therefore, we could calculate an SA correction map over the imaging volume from measurements at a few representative depths. More specifically, we first adopted the pupil ring segmentation method to measure the SA correction curves at two or more representative depths, where a bright guide star located. Then we used these measured curves and the linear relationship to predict the SA correction curves at arbitrary depth of the RI-homogenous samples.

The SA in the sample consists of two parts: (i) an initial SA that is caused by the mismatch between the correction collar of the objective and the cover glasses; (ii) a depth-induced SA that is introduced by the RI mismatch between the immersion media and the sample, and depends on the imaging depth. Therefore, we could evaluate the SA correction curve at an arbitrary depth as follows:

The SA correction map is derived before image acquisition and the whole procedure (three measurements) costs around three minutes, including localization of guide stars, measurements of SA correction curves at each depth, and the map derivation. The correction map allows us to correct the SA during image acquisition, avoiding repetitive real-time measurements at every depth. Besides, it could provide an SA correction map in the region, where the fluorescent substances are not bright or stable enough as the guide stars.

2.4 Zernike modal-based AO

As a comparison, we used a Zernike modal-based AO method for SA correction [13]. Essentially, we adjusted the coefficient of each Zernike mode and observed the variation of corresponding image metrics. To exert the full capacity of the modal-based AO, we used 15 measuring points equally spaced from –3 to 3 for each Zernike mode. Then, we recorded the fluorescence intensity at each point, applied Gaussian fitting to the fluorescence intensity versus the coefficients of Zernike mode, and find the Zernike mode’s best coefficient that maximizes the peak intensity of the focal spot. We employed five rotationally symmetrical modes of the Zernike polynomials for SA correction without considering azimuthal dimension, since higher rotationally symmetrical modes contribute little to the SA correction in this case [14]. Besides, we iterated the correction procedures three times to guarantee the convergence of this method [13].

2.5 Evaluation of the theoretic SA correction curve in bead samples

As a comparison, we also calculated a theoretic SA correction curve in the polyacrylamide gel sample. We first measured the RI of sample using an Abbe refractometer and then calculated the depth-induced SA using the following formula [7]:

2.6 Evaluation of lateral and axial resolution

To quantify the spatial resolution at different depths for with and without SA correction, we observed 0.2-μm-diameter fluorescent beads embedded in the polyacrylamide gel and acquired their 3D images for point spread functions (PSF) evaluation. For lateral PSF evaluation, we calculated the full width at half maximum (FWHM) of the beads by fitting their lateral intensity profile with a standard Gaussian function. For axial PSF evaluation, we first used a 1-pixel 3D Gaussian filter (0.13×0.13×1 μm) to counteract the artifacts caused by the vibration of beads. Then, to accurately evaluate the FWHM of an asymmetrical PSF caused by SA [6], we fitted the axial intensity profiles of beads using the following equation,

2.7 Preparation of fluorescent beads embedded in polyacrylamide gel

To simulate the SA caused by the RI mismatch between the biological sample and the immersion medium, we immobilized 0.2-μm (F8811, ThermoFisher) or 1-μm (F8823, ThermoFisher) fluorescent beads in polyacrylamide gel. A detailed protocol for the polyacrylamide gel preparation was described in Ref. [19]. Briefly, the solution contains a mixture of 1000 μL de-ionized water, 1000 μL 30% acrylamide, 100 μL 10% aqueous ammonium persulfate (APS), and 5 μL of 0.2-μm beads solution or 15 μL of 1-μm beads solution. The total solution is mixed with 10 μL catalyst tetramethylethylenediamine (TEMED) and deposited into a glass-bottomed dish (D35-10-1.5-N, Cellvis) immediately. After standing for approximately two hours, the solution polymerized completely into a gel. The RI of this gel is measured as 1.355 using an Abbe refractometer and is close to that of the mouse brain cortex [20].

2.8 Preparation of optically cleared mouse brain slices

To prepare the brain slices, three Thy1-GFP-M (Stock number 007788, The Jackson Laboratory) mice (∼ six weeks old) were first deeply anesthetized with a mixture of 2% α-chloralose and 10% urethane (8 mL/kg) by intraperitoneal injection. Then, transcranial perfusion with PBS and 4% (wt/vol) paraformaldehyde (PFA) was performed. After the perfusion, the mice were sacrificed. Next, the brains were excised and fixed with 4% PFA at 4 °C overnight. Finally, 2-mm-thick coronal slices were freehand sectioned using a brain matrix.

To prepare the optically cleared tissues, the brain slices were treated with CUBIC [1] or SeeDB [3]. For CUBIC treatment, the fixed brain slices were cleared with reagent 1 (25 wt% urea, 25 wt% N,N,N’,N'-tetrakis(2-hydroxypropyl) ethylenediamine, and 15 wt% Triton X-100, RI = 1.38) for about three hours with gentle shaking at 25 °C to completely remove lipid components of the brain slices. After treatment with reagent 1, the brain slices were washed with PBS several times at room temperature while gently shaking, and immersed to reagent 2 (50 wt% sucrose, 25 wt% urea, 10 wt% 2,2’,2''-nitrilotriethanol, and 0.1% (v/v) Triton X-100, RI = 1.48) for about eight hours. Particularly, treating with reagent 2 is an optional procedure for clearing brain slices [1]. We used it in one of our experiments to increase the RI of the brain slices. For SeeDB treatment, the fixed brain slices were serially incubated in 20%, 40% and 60% (wt/vol) fructose, each for four hours, with gentle shaking at 25 °C. Samples were then incubated in 80% (wt/vol) fructose for 12 h, 100% (wt/vol) fructose for 12 h and finally in SeeDB37 (86.7% wt/wt fructose, RI = 1.48) for 24 h with gentle shaking at 37 °C.

Once the optical clearing process was finished, the slices were placed into a custom-built container, which allows the cleared slices immersed in their optical clearing agents during imaging. Then we covered the container with a glass slip to ensure a flat surface of the sample and sealed it with nail polish meticulously to avoid air bubbles.

All the experiments were performed in compliance with protocols approved by the Guangdong Provincial Animal Care and Use Committee and following the guidelines of the Animal Experimentation Ethics Committee of Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences.

3. Results and discussion

3.1 Pupil ring segmentation provides superior performance for SA correction

To test the SA correction performance of our pupil ring segmentation-based AO, we compared it with the Zernike modal-based AO based on 1-μm fluorescent beads embedded in polyacrylamide gel (Fig. 2). The results show that both the Zernike modal-based AO and the pupil ring segmentation AO can correct the SA effectively and thereby improve the fluorescence intensity at each depth. Comparing the AO correction at different depth indicates that the pupil ring segmentation method provides superior correction for large SA in the deep sample. For example, at the shallow depth (20 μm below the surface), where the PV value of SA is small than 0.5 wavelength, both methods present a similar SA correction curve and intensity improvement (Fig. 2(a)-(c)). However, at the depth of 400 μm where the PV value of SA is larger than two wavelengths, the pupil ring segmentation yields a 5-fold intensity improvement, which is larger than the 2.5-fold improvement caused by the Zernike modal-based AO (Fig. 2(d) and (e)).

 

Fig. 2. Comparison of SA correction between the pupil ring segmentation method and the Zernike modal-based method. (a) x-y projected images at a depth of 20 μm obtained without SA correction, with the ring segmentation AO and with the Zernike modal-based AO, respectively. (b) Intensity profiles of the same bead indicated by the corresponding colored lines in (a). (c) SA correction curves measured by the pupil ring segmentation (red) and the Zernike modal-based (yellow). (d-f) Corresponding figures of (a-c) at the depth of 400 μm. Scale bar = 5 μm.

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To assess the accuracy of SA correction curves of two methods, we calculated the theoretical curve at the depth of 400 μm with the parameters: λ = 0.92 μm, d = 400 μm, α = 0.0256, n₁= 1.33, n₂ = 1.355, and NA = 1.089. The three curves were shown in Fig. 2(f). Comparing with the theoretic curve, the curve of the modal-based AO was found to bend abnormally outside the NA of 0.88. It is probably due to the presence of crosstalk between the modes and multiple local optimal solutions when the SA is larger than two wavelengths [13]. Comparing the theoretical curve with that of the pupil ring segmentation method, we find two curves are nearly identical, indicating that our pupil ring segmentation can provide accurate SA correction. This result lays a foundation for predicting the SA of optically cleared samples in the following studies.

3.2 Pupil ring segmentation could derive an SA map for all the observing depths

Given the accurate SA correction curves provided by pupil ring segmentation and the linear relationship between the SA and the imaging depth, we can derive an SA correction map over the imaging volume based only on three measurements at representative depths. To test the feasibility of this method, we assessed the performance of SA correction within 1 mm depth in a RI-mismatched sample using a derived SA correction map. To quantify the resolution improvement after SA correction, we used a phantom sample of 0.2-μm-diameter fluorescent beads embedded in the polyacrylamide gel. We first measured the SA at the depth of 0, 200, and 400 μm, and then derived an SA correction map over all the imaging volume, within the depth of 1 mm. This map allowed us to correct the SA every 100-μm depth during the imaging acquisition. To facilitate the analysis of intensity improvement versus imaging depth, the excitation power under the objective was fixed at 12 mW for with and without SA correction at all the observed depths.

The comparisons between the images with or without SA correction, using the pupil ring segmentation method, are presented in Fig. 3. Figure 3(a) and (b) show the x-y and x-z maximum intensity projected (MIP) images before and after the SA correction. Beyond the depth of 400 μm, 0.2-μm beads are hardly resolved without SA correction, whereas they can be clearly observed after the SA correction. The intensity profiles of beads (Fig. 3(c)) demonstrated that the fluorescence intensity with SA correction is approximately six times higher than that without SA correction at 800 μm depth. Figure 3(e) shows that the decline of fluorescence intensity caused by depth-induced SA was completely compensated by our SA correction method.

 

Fig. 3. Pupil ring segmentation could derive an SA correction map for different depths. (a) x-z projected image from the depth of 0 μm to 900 μm without (left) and with (right) SA correction using the correction map. (b) Higher magnification views of the x-y and x-z plane images at different depths. (c) Lateral and axial intensity profile of 0.2-μm beads at 800 μm depth. (d) Measured and predicted SA correction curves. The measured curves (dashed blue lines) are from depths of 0 to 800 μm with an interval of 200 μm. We predicted the SA correction curves of 600 and 800 μm depth using the curves measured at 0, 200, 400 μm. (e) Fluorescence intensity as a function of the imaging depth. (f, g) The box plots of lateral and axial resolution as a function of the imaging depth, respectively. Scale bar = 5 μm.

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We also analyzed the lateral and axial PSFs by plotting and fitting the intensity profile of 10 beads every 200 μm in the depth. The results in Fig. 3(f) and (g) show that the lateral and axial resolution degraded from 0.45 to 0.55 μm and from 3.5 to 5 μm, respectively, as the depth increased from 0 to 800 μm due to the RI mismatch. After the SA correction, both the lateral and axial resolution at the depth of 800 μm were restored to the near-diffraction-limited performance. Moreover, we compared the SA correction curves predicted by our method and that measured directly at the depth of 600 and 800 μm (Fig. 3(d)). The similarity between them proves the feasibility of the derived SA correction map in RI-homogenous samples. Noted that, compared with other AO methods, our methods could provide SA corrections at arbitrary depths, even the region where the SA cannot be directly measured due to the weak fluorescence.

It should be mentioned that the PV value of SA measured at the depth of 400 μm in Fig. 3(d) is smaller than that in Fig. 2(f). It arises from the fact that a smaller effective NA of 0.9079 was used for imaging of 0.2-μm beads samples. We chose this effective NA, because we found this NA is sufficient for imaging a synaptic feature while blocking the beamlets of the large convergence (outside the effective NA) that contribute little to the focus formation in the deeper region. The beamlets of the large convergence are susceptible to the reflection at the RI-mismatched interfaces, and they have longer traveling distance in samples in comparison to the paraxial beamlets. Therefore, they may suffer more energy loss due to scattering and absorptions. This effective NA is also adopted in the following TPM imaging of optically cleared brain tissues.

3.3 Pupil ring segmentation improves TPM imaging of optically cleared samples

Imaging the neurons with synaptic resolution greatly aids study of the neuron networks in the mammalian brain. To maintain the synaptic resolution in deep regions of the brain, a variety of optical clear methods have been developed. However, the RI mismatch introduced by these optical clear agents will cause SA, which degrades the TPM imaging of the small features in neurons. To test if our pupil ring segmentation method could correct the SA and provide a synaptic resolution in deep region of optically cleared samples as well as its compatibility with various optical clear agents, we observed brain slices that were treated by three types of optical clear agents with different RIs and applied SA correction maps to compensate their SAs for all the imaging depths.

We first observed a brain slice cleared by the CUBIC reagent 1 [1]. We measured the SA correction curves at 0, 200, and 400 μm depth below the tissue surface using our pupil ring segmentation method and derived an SA correction map from the depth of 0 to 900 μm (Fig. 4(e)). To offset the effects of scattering and absorption, excitation powers ranged from 20 mW in surface to 30 mW at 900 μm depth, for with and without SA correction. Moreover, we adjusted the correction collar of the objective to the maximum before the measurements, to introduce a negative SA at the surface of the sample, and to obtain an SA with small PV value in the deep region.

 

Fig. 4. TPM imaging of Thy1-GFP-M brain tissue treated with CUBIC reagent 1 using an SA correction map. (a) 3D volume rendering of neurons network with SA correction. (b,c) x-y and x-z projected images at 0, 400, and 800 μm depth without and with SA correction. (d,f) x-y and x-z spatial frequency representation at 800 μm depth, showing that the pupil ring segmentation method restores the spatial resolution to the near-diffraction-limited resolution after SA correction. (e) SA correction map of the imaging volume. The blue curves were derived from the measured curves (red). (g) Intensity plots corresponding to the same area indicated by the lines in (c), showing that the fluorescence intensity is significantly improved. Scale bar = 20 μm.

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The TPM images of the optically cleared brain slice with and without SA correction are shown in Fig. 4. Figure 4(b) and (c) show x-y and x-z MIP images from 0 to 800 μm depths, respectively. The fluorescence intensity slightly raised with SA correction at the surface of the sample. Below the depth of 400 μm, the individual neuronal dendrite becomes unresolved without AO, whereas they are still distinguishable after the SA correction. To investigate the resolution improvement, we compared the Fourier transformation of the x-y (Fig. 4(d)) and x-z (Fig. 4(f)) images at 800 μm depth. Both the lateral and axial resolution was restored to the near-diffraction-limited, and thereby the dendritic structures can be clearly identified.

We also measured an optically cleared mouse brain slice treated by SeeDB [3], and the results were shown in Fig. 5(a)-(d). To offset the fluorescence signal degradation with depth, the powers ranged from 25 to 80 mW. We measured the SA correction curves at 0, 150, and 200 μm depth below the surface and calculated an SA correction map within the depth of 600 μm (Fig. 5(d)). The x-y projected images beyond 400 depth were shown in Fig. 5(b). As observed, after SA correction, the contrast of images is obviously enhanced, and the dendritic structures could thereby be observed clearly. We also analyzed the SA correction curves’ variation as the function of imaging depth in this cleared brain slice. Since the major component of such aberration is the 1st SA of Zernike polynomials, we denote the amount of measured SA with the coefficient of its 1st SA component. The plot of the SA components of the measured curves versus imaging depths (Fig. 5(c)) indicated that the SA remains increasing linearly in optically cleared biological samples with complicated fine structures, and thereby the SA correction map could efficiently restore the degraded intensity and resolution at deeper region of the optically cleared samples.

 

Fig. 5. TPM imaging of Thy1-GFP-M brain tissue treated with different optical clearing methods using SA correction maps. (a,e) 3D volume rendering of neurons network treated with SeeDB. (a) and CUBIC reagent 1 and reagent 2 (e). (b,f) x-y projected images without and with SA correction. (c) Measured SAs increase linearly with depth in the optically cleared sample. (d,h) SA correction map over the imaging volume. The blue curves were derived from the ring segmentation measured curves (red). (g) Spatial frequency representation in arbitrary units (a.u.) at 800 μm depth. Scale bar = 20 μm.

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Compared with the CUBIC treated sample, we found the SA correction performance for the SeeDB treated sample is slightly inferior. The reasons are not fully understood; however, they are believed to be in part due to the increase of the background signals caused by the SeeDB process. Our procedures of SeeDB included a longer incubation period in the fructose solution at 37 °C, which will cause the autofluorescence accumulation due to the Maillard reaction [3]. As a result, their images contain more background signals than the slices treated with CUBIC. Besides, more power was demanded when imaging deep into the SeeDB treated samples.

Finally, we observed a brain slice treated by CUBIC reagent 1 and reagent 2 [1], and the results are shown in Fig. 5(e)-(h). CUBIC reagent 2 has a RI of 1.48, and was used here to match the tissue RI and increase the transparency of slices. We measured the SA correction curves at 0, 200, and 400 μm depth, and derived an SA correction map within the depth of 1 mm (Fig. 5(h)). The powers ranged from 20 to 60 mW. In this sample, we observed a volume with densely distributed fluorescence (Fig. 5(e) and (f)). From the x-y projected images, we found that the lateral resolution at 800 μm depth is notably improved after SA correction (Fig. 5(f) and (g)) owing to the enhancement of signal to noise ratio and the restored PSF that reduced overlaps of structures axially.

For the derivation of SA correction maps, we used the linear relationship between the SA and the imaging depth along the optical axis. In the lateral plane, the SA remains nearly stationary as long as refraction interfaces are perpendicular to the optical axis. In contrast, the high-order aberration, that was introduced by small scattering structures, such as microvascular, varies significantly in space, leading to the correction performance is only valid in a small volume. Therefore, our method that specifically targets SA compensation has a remarkably larger effective area than high-order aberration correction methods that indiscriminately compensate various aberrations. Moreover, it is worth noting that for most AO it is a time-consuming process for measuring the distorted wavefront over a large volume. However, we can synchronously correct the SA and observe synaptic structures in the optically cleared brain slices, because we evaluated an SA correction map before image acquisition and implemented the high-speed SLM with a frame update time of 3 ms, which is negligible relative to the image acquisition time. Additionally, we will combine our ring segmentation method with parallel measurement [15] to further improve the SA correction speed in future.

4. Conclusion

In summary, we proposed an SA correction method that segments the pupil into concentric rings for respective phase correction. This method compensates large SA more accurately than the Zernike modal-based AO. To enhance the efficiency of SA correction in optically cleared samples, we utilized the linear relationship between the SA and the imaging depth to evaluate an SA correction map over the whole imaging volume based on only three measurements. We applied this method into transparent samples, including the beads samples and the optically cleared brain slices. The results show that the lateral and axial resolution at 900 μm depth were restored to the near-diffraction-limited, which enables differentiation between the synaptic structures in the deep region. Further, the observation of brain slices treated by different optical clearing methods indicated that our methods are suitable for SA correction of different optical clearing methods. In future studies, we hope our pupil ring segmentation method could be extended into a broad range of applications, such as neuronal activities and larval development in fruit flies, zebrafishes, and mice.