2.1.1.

Comparison of images

When making comparisons among images, a slight focal shift ($\sim 0$ to $3\mu \mathrm{m}$) occurs due to spherical aberration.¹ This is depth dependent. When removing spherical aberration during imaging this focal shift is removed causing the focus to be shifted to a slightly different plane. Consequently, when comparing the slices from stacks at the same ($x$ and $y$) location, but differing in the amount of refractive aberrations removed, they are matched by features rather than measured depth or slice number. Depths shown are the nominal focal position as measured by the stage movement rather than the actual depth which takes into account the focal shift. For the images in this paper, the difference between corrected and uncorrected images was always less than 1%.

2.1.2.

Reporting Zernike aberration values

There are several different single-index methods for reporting Zernike aberrations (modes). We report them in Noll form as shown in Table 1.²² Only the first 22 Zernike modes are reported in our calculations, since those of higher order do not contribute to a significant amount of RMS wavefront error. Zernike modes 1 to 4 (piston, tip, tilt, and focus) are ignored; piston being the absolute distance from the object, and tip, tilt, and focus being simply movements of the focal point in $X,Y$, and $Z$. Zernike modes are normalized so that a value of 1.0 for any mode corresponds to 1.0 wave of RMS error for that mode.

Table 1

First 11 Zernike aberrations in Noll single-index order.

2.6.1.

Reference wavefront measurements

Images from the Shack–Hartmann (SHWF) sensor were used to determine an unaberrated reference wavefront. The reference images were taken from a 100-nm fluorescent bead on a slide under a #1.5 ($170\text{-}\mu \mathrm{m}$) coverslip mounted with Vectashield (Vector Laboratories). This became the reference wavefront representing an unaberrated wavefront. The bead slide was then replaced with the sample slide for imaging and wavefront measurements were made at various depths.

2.6.2.

Aberration measurements

The first 22 Zernike aberrations were measured, and the RMS wavefront error and Strehl ratio were determined. The excitation wavelength was centered at 900 nm. The emission wavelength was centered at 515 nm. Wavefronts were measured with descanned light at the emission wavelength. The correction during imaging was applied to the 900-nm excitation after compensating for dispersion by manual optimization. Dispersion compensation was done in two ways. The first was to compensate for the dispersion of the optical system and attain the minimum pulse width of the laser. This was done using grating pairs in the actual laser system. The second was to compensate for the combined dispersion of the optical system and the tissue to compensate for the fact that the wave front measurement was made at the emission wavelength and the compensation was applied at the excitation wave length.

3.1.1.

Comparing aberrations from 0 to 1500  μm

We examined a whole CLARITY treated mouse brain immunostained for the astrocytic marker (GFAP). At $1500\text{-}\mu \mathrm{m}$ depth, we measured the wavefront and calculated RMS wavefront error and the Strehl ratio (Fig. 4). As expected, we found a decreased Strehl ratio and increased RMS wavefront error values as the depth of the measurements increased.

Imaging with AO wavefront correction resulted in an increase of the signal-to-noise ratio in the background corrected measurements from 43% to 253% (Fig. 2). AO correction revealed fine details of small astrocytic processes. Astrocytes are involved in regulating neural signaling and tissue homeostasis and are important signal mediators between the brain and the vasculature. Most of these processes are performed through contact with astrocytic end feet, a process that could be studied in greater detail with the help of AO.

Fig. 2

$12\text{-}\mu \mathrm{m}$ thick, two-photon image stack ($Z$ step size $0.8\mu \mathrm{m}$) of astrocytes at $1500\text{-}\mu \mathrm{m}$ depth in a CLARITY mouse brain. (a) Uncorrected maximal projection, (b) AO-corrected maximal projection, (c) line profile plot of the magenta lines in (a) and (b) with peaks highlighted as areas 1 to 6, (d) data analysis of the line profile plot and areas 1 to 6. Max peak values were obtained by dividing the peak value for each numbered area by the background, 3800. The background was an average of all values in the plot. The integrated area was obtained by adding all samples in the numbered area after subtracting the background. Total integrated area is the sum of all samples in the plot minus the background.

Figure 3 shows the increasing contribution of the major nonspherical aberrations compared to the spherical aberration. Figure 4 shows the reduction in the Strehl ratio compared to the total RMS wavefront error as the depth increased. At a depth of $1500\mu \mathrm{m}$, the RMS wavefront error contributed by the spherical aberration was approximately equal to that of the nonspherical aberrations, as shown in Fig. 5. See Sec. 2.5 for an analysis of the fluctuations of the aberrations with depth. In Fig. 3 it is important to note that horizontal coma was not decreasing as depth increased, it was increasing in a negative direction and thus adding RMS wavefront error to the total RMS of the wavefront. In Fig. 4, the RMS error at 0 depth is at the surface of the brain, but is imaged through a small amount of residual index matching fluid. The tilt of the organ relative to the objective and the irregularity of the surface add a slight amount of aberration over the field.

Fig. 3

Major Zernike aberrations and their trend lines. Aberrations increase as depth increases. NB: horizontal coma does not decrease with depth; it is increasing in a negative direction and adding RMS error to the wavefront. For clarity, only the largest magnitude aberrations are shown.

Fig. 4

Decreasing Strehl ratio and increasing RMS wavefront error versus depth in the optically cleared mouse brain indicated the diminished wavefront quality as focal depth increased. The RMS error at 0 depth is at the surface of the brain but imaged through a small amount of residual index matching fluid. The tilt of the organ relative to the objective and the irregularity of the surface add a slight amount of aberration.

Fig. 5

Comparison of spherical versus other aberrations versus depth. See Sec. 2.5 for a discussion of the causes of variations of spherical aberrations with depth.

Figure 5 shows that the nonspherical aberrations were significant, increasing, and dominated until a depth of almost $1500\mu \mathrm{m}$. Spherical aberration is stronger than the nonspherical and increases faster with depth. However, all aberrations do increase with depth and all contribute to a reduction in imaging quality. Only an AO system can effectively reduce these aberrations. At larger depths, spherical aberrations would dominate. However, the amount of nonspherical aberrations at these depths would degrade imaging even if all spherical aberrations were removed.

3.1.2.

Analysis of aberrations in CLARITY mouse brains sections at 500-μm depth

The relationships among the different aberrating components were determined by analyzing images and corresponding wavefront measurements under three conditions: (1) without AO, (2) with only spherical aberration compensated by AO, and (3) with all aberrations corrected with AO.

Stacks were collected at a depth of $\sim 500\mu \mathrm{m}$ below the coverslip, where features were readily observable without AO but were obviously improved with the appropriate AO correction. Figure 6 is a representative images showing the improved resolution upon correction for spherical aberration and the even greater correction achieved when all Zernike modes were considered for the wavefront correction. Comparing Figs. 6(d) and 6(f), it shows that the signal-to-noise ratio and the resolution in (f) are visibly greater than (d). This can be seen as illustrated by the arrows. Figure 7 clearly shows that the amount of cumulative RMS wavefront error generated by nonspherical aberrations was significant (spherical aberration is index 11 and has a value approximately of 0.1). The large value of index 8 (horizontal coma at $\sim 0.22$) was due to the combination of the angle of the coverslip and the upper surface of the tissue relative to the objective lens and could only be effectively removed with an AO system. The relative tilt of various tissue layers with differing bulk RI with respect to each other, the cover slip, or objective will have the same effect and cannot be corrected by aligning to a particular layer since they are not colinear.²⁸

Fig. 6

Brain slice, neurite bundle at a depth of $500\mu \mathrm{m}$. (a)–(c) Field of view is $85\mu \mathrm{m}\times 85\mu \mathrm{m}$ and is a maximal $Z$ projection of 19 sections spaced at $1.0\text{-}\mu \mathrm{m}$ intervals. (a) No aberration correction. (b) Only spherical aberration corrected. (c) First 22 Zernike aberrations corrected. The insets are shown in (d)–(e). (e) Removing spherical aberration only increased resolution somewhat. (f) Removing the first 22 Zernike aberrations showed a significant improvement.

Fig. 7

Brain slice at $500\mu \mathrm{m}$. Zernike modes (waves RMS) (in Noll order) of the neurite bundle wavefront prior to AO correction (piston, tip/tilt, focus removed) (spherical aberration is index 11, at $\sim 0.1$). The large value of index 8 (horizontal coma at $\sim 0.22$) was due to the combination of the angle of the coverslip and tissue upper surface relative to the objective lens.

Figure 8 shows a CLARITY brain slice where contrast was significantly improved over correction for spherical aberration only. With full AO correction, the PSF had a smaller axial profile as well as a smaller lateral profile. This reduced axial profile reduced imaging of structures that are above or below the level of the current slice. Removing spherical aberration only increased the $S/N$ 29%. Removing all of the first 22 Zernike aberrations increased the $S/N$ a total of 50%. Photobleaching from multiple scans decreased the overall intensity in the full AO image since it was taken last.

Fig. 8

Images of a CLARITY brain slice neurite bundle at a depth of $500\mu \mathrm{m}$. (a) No AO correction: $S/N=1.7$. (b) Correction for spherical aberration only showed an $S/N=2.1$ an increase of 29%. (c) First 22 Zernike aberrations corrected showed an $S/N=2.6$ an increase of 19% over correcting for spherical aberration only and a total increase of 50%. The reduction in intensity in (c) is because it was measured last and some photobleaching had occurred. Scale bar is $20\mu \mathrm{m}$. The horizontal bars indicate the noise floor used in calculations of the $S/N$.

Figures 9 and 10 show images and wavefront measurements across additional samples. Figure 9 shows images at a depth of $500\mu \mathrm{m}$, both with and without AO compensation. It can be seen in Fig. 10 that even with AO compensation there were still significant residual aberrations. These prevented the images with AO correction from achieving maximum enhancement. This shortcoming in our compensation was due to a combination of the size of the aberrations compared to the capabilities of the DM and a limitation in our open-loop control system where we cannot sense or compensate adequately in the presence of large aberrations. We are addressing this by optimizing our open-loop algorithm to correctly sense a larger range of aberrations, incorporating an optional closed-loop mode, which has proven capable of reducing residual errors to a minimum, and measuring and compensating for the effects of dispersion. All of the residual Zernike values were below 0.1, most were below 0.05. and RMS wavefront error was reduced by a factor of 3 (from 0.32 to 0.11). Additionally, we were able to significantly increase the Strehl ratio from 0.02 (poorly corrected) to 0.63.

Fig. 9

Brain slice at a depth of $500\mu \mathrm{m}$. A dendritic segment with dendritic spines is centered in the field of view. The fine structures were more readily resolved after AO correction. Field of view is $55\mu \mathrm{m}\times 55\mu \mathrm{m}$, maximal $Z$-projection of 20 sections at 500-nm intervals.

Fig. 10

Zernike modes of the wavefront aberrations for the images in Fig. 9 illustrating the improved quality of the wavefront after AO correction. Shown before and after AO compensation. (Spherical aberration is index 11, at approximately $-0.23$.) The large value of index 8 (horizontal coma at $\sim 0.19$) was due to the combination of the angle of the coverslip and tissue upper surface relative to the objective lens.