2.1.

Function of Transmissive Device for Correcting Asymmetric Aberrations

The device was composed of four laminated LCCs (A0-LCC, A45-LCC, C0-LCC, and C90-LCC) compensating for Astig(0), Astig(45), Coma(0), and Coma(90), respectively. The effective optical diameter of the LCCs was 17.6 mm, which was almost equal to the calculated pupil diameter of the objective lens described later. Each LCC corrected the Zernike aberration of the Zernike coefficient within $\pm 1.96$ and $\pm 0.87$ for wavelengths of 488 nm and 900 to 910 nm, respectively, which were used for the excitations in the observations described later. The segmented transparent electrodes were formed in one of the two glass substrates in A0-LCC to generate the phase distribution required to correct Astig(0) [Figs. 1(a) and 1(b)]. Similarly, the segmented transparent electrodes for correcting Astig(45), Coma(0), and Coma(90) were formed in A45-LCC, C0-LCC, and C90-LCC, respectively [Figs. 1(c)–1(h)]. In each LCC, the segmented electrodes generated a 32-level quantized phase distribution. We applied voltages to the LCCs as required to generate the Astig(0), Astig(45), Coma(0), and Coma(90) components of the Zernike coefficients ($a_{\mathrm{astig}0}$, $a_{\mathrm{astig}45}$, $a_{\mathrm{coma}0}$, and $a_{\mathrm{coma}90}$, respectively) shown in Fig. 1(i), and the phase distribution generated in the four laminated LCCs was measured using a laser interferometer (Zygo PTI 250, Zygo Corporation). When we applied voltage to A0-LCC as required to generate an Astig(0) component of $a_{\mathrm{astig}0}=0.89$, the device showed the phase distribution of Astig(0) [Fig. 1(i)]. When we applied a voltage only to A45-LCC ($a_{\mathrm{astig}45}=0.89$), the phase distribution of the device agreed very well with that of Astig(45). Furthermore, we confirmed that the direction of the astigmatic component was rotated by applying a voltage and changing the ratio between the voltages applied to A0-LCC and A45-LCC. For example, when voltages were applied to A0-LCC and A45-LCC as required to generate a phase distribution with the same-magnitude Zernike coefficients ($a_{\mathrm{astig}0}=a_{\mathrm{astig}45}=0.64$), the device showed the astigmatic component to be in the 22.5-deg direction. Similarly, C0-LCC of $a_{\mathrm{coma}0}=0.89$ and C90-LCC of $a_{\mathrm{coma}90}=0.89$ showed Coma(0) and Coma(90) phase distributions, respectively. When using C0-LCC and C90-LCC ($a_{\mathrm{coma}0}=a_{\mathrm{coma}90}=0.64$), the device showed the coma component to be in the 45-deg direction.

Fig. 1

The function of the transmissive device for correcting asymmetric aberrations. (a), (c), (e), and (g) Phase distributions of Astig(0), Astig(45), Coma(0), and Coma(90), respectively. (b), (d), (f), and (h) Schematics of electrode patterns in A0-LCC, A45-LCC, C0-LCC, and C90-LCC, respectively. (i) Actual phase distributions of the device.

2.2.

Observation Optical System

Observations were conducted using an upright microscope (ECLIPSE FN1, Nikon) equipped with a water-immersion/dipping objective lens (CFI Apo LWD 25XW, NA1.1, Nikon) and a confocal scanner (A1R MP+, Nikon), with excitation wavelengths of 488, 900, and 910 nm. In this study, the confocal pinhole aperture was opened completely. The device, with a thickness of 13 mm, was simply inserted between the objective lens and the microscope revolver [Fig. 2(a)]. The device was controlled by applying a voltage via a drive circuit. Figure 2(b) shows the transmittance of the LCC. For the wavelength range 900 to 910 nm, which was used for excitation in 2P-LSM, the transmittance of the LCC was 97%. For the wavelength range 460 to 600 nm, which was used for the fluorescence measurements and excitation in 1P-LSM, the LCC’s transmittance was 92% to 95%. The transmittance of the device composed of the four LCCs was 88% and 72% to 81% for 900- to 910-nm and 460- to 600-nm light, respectively.

Fig. 2

Experimental setup. (a) Configuration of laser scanning microscope with the liquid-crystal device, and the actual photograph of the device installed between the microscope revolver and the objective lens. (b) Transmittance of the LCC. (c) Schematic of the tilt-sample. The fluorescence beads were placed under the cover slip at tilt angle ${\theta }_t$ in the ${\varphi }_t=0\text{-}\mathrm{deg}$ direction. (d) Schematic of the cyl-sample. The fluorescence beads were placed into the cylindrical glass capillary with the longitudinal direction of ${\varphi }_c=0\mathrm{deg}$.

2.3.

Sample Preparation and Analysis

Fluorescent yellow-green beads with a diameter of $0.2\mu \mathrm{m}$ were mixed into agarose gel with a refractive index of 1.333. The agarose gel containing the fluorescence beads was poured into a glass-bottom dish, attached with a 0.16- to 0.19-mm thick cover slip at the bottom. The glass-bottom dish was placed upside down on a goniometer stage. We thus observed the beads in the gel through the tilting cover slip. The tilt angle ${\theta }_t$ and direction ${\phi }_t$ of the cover slip were defined by those of the goniometer stage [tilt-sample in Fig. 2(c)]. The predominant aberrations while observing this tilt-sample were estimated as the primary coma aberration and a certain astigmatism. Meanwhile, melted agar containing beads was sucked into the cylindrical glass capillary with an outer diameter of 0.1 mm and a glass thickness of 0.01 mm (Mark-tube made of soda lime glass, Hilgenberg GmbH). The capillary was fixed on the bottom of the glass-bottom dish and immersed in water [cyl-sample in Fig. 2(d)]. The predominant aberration in the cyl-sample was estimated to be caused by astigmatism while observing the bead located at the center of the capillary. The fluorescence intensity profiles of the bead image across the intensity center along the $x$-, $y$-, and $z$-axes were fitted with a Breit–Wigner–Fano line shape. The average of the approximate curves for five or more bead images was obtained, and the average peak intensities and the average full width at half maximum values along each axis ($\mathrm{FWHM}x$, $\mathrm{FWHM}y$, and $\mathrm{FWHM}z$) were measured from the average curves.

Thy1-YFP-H mice²² were anesthetized with pentobarbital sodium. They were transcardially perfused with phosphate-buffered saline (PBS) followed by 4% formaldehyde in PBS, and their brains were removed. The fixed whole brain was adhered to the bottom of the glass-bottom dish and immersed in PBS. We observed the cortical layer V neurons under a thick blood vessel at the surface of the cerebral cortex of the left brain. The sloping surface shape of the whole brain was estimated to induce the asymmetric aberration. Furthermore, astigmatism was estimated to be induced, especially under the blood vessel. To estimate the spatial resolution in the sample, we utilized dendritic spines with a size smaller than the spatial resolution. The fluorescence intensity profiles of the dendritic spine image across the intensity center along the $x$-, $y$-, and $z$-axes were fitted with a Breit–Wigner–Fano line shape, and the peak intensities and the FWHM values were measured.

All animal experiments were performed in accordance with the National University Corporation Hokkaido University Regulations on Animal Experimentation and the Guidelines for Proper Conduct of Animal Experiments (Science Council of Japan). The protocol was approved by the Institutional Animal Care and Use Committee of National University Corporation Hokkaido University (Permit Number: 15-0021).

2.4.

Numerical Calculation Using the Object Lens System

The point spread function (PSF) of the 488-nm wavelength $y$-polarized collimated light beam with a top-hat intensity distribution was numerically calculated using the beamlet-based wave propagation algorithm (CODEV, Synopsys, Inc.) under the assumption that light was focused through a continuous phase distribution and a 25x/NA1.1 water-dipping objective lens (JP2011-75982A). In this calculation, the continuous phase distribution was placed in a plane perpendicular to the optical axis, 10 mm away from the front of the objective lens along the $z$-axis (which is where the device was actually placed in the experiment).

3.1.

Numerically Calculated Point Spread Function at 488-nm Wavelength

First, to estimate the correction effect of the device, we numerically calculated the PSF images under a tilted cover slip and in a glass cylinder. The $\mathrm{FWHM}x$, $\mathrm{FWHM}y$, and $\mathrm{FWHM}z$ values of the PSF for the sample without any aberrations were 0.23, 0.28, and $0.79\mu \mathrm{m}$, respectively [Figs. 3(a)–3(b)]. The difference in the FWHM values between the $x$- and $y$-axes was induced by the polarization direction of incident light.

Fig. 3

Numerically calculated PSF images at a wavelength of 488 nm. (a) Lateral and axial images without aberrations. (c) and (d) Lateral and axial images under the cover slip at tilt angle ${\theta }_t=-5\mathrm{deg}$ in the ${\varphi }_t=90\text{-}\mathrm{deg}$ direction (c) before and (d) after correction. (f) and (g) Lateral and axial images in the glass cylinder with longitudinal direction of ${\varphi }_c=0\mathrm{deg}$ (f) before and (g) after correction. Panels (b), (e), and (h) show intensity profiles of the PSF images in (a), (c), (d), (f), and (g), respectively, across the center of the intensity distributions along the $x$-, $y$-, and $z$-axes. The scale bars denote $0.5\mu \mathrm{m}$.

When incident light was focused through a 0.17-mm thick cover slip inclined at ${\theta }_t=-5\mathrm{deg}$ in the ${\varphi }_t=90\text{-}\mathrm{deg}$ direction ($y$-axis), the predominant aberrations were Coma(90) of $a_{\mathrm{coma}90}=1.7$, Astig(0) of $a_{\mathrm{astig}0}=0.25$, and a second coma aberration with a Zernike coefficient of $-0.37$. The peak intensity of the PSF dropped to 13% of the value for the sample without aberrations ($I_{\text{nonaberration}}$). Additionally, the $\mathrm{FWHM}y$ and the $\mathrm{FWHM}z$ values degraded to 0.47 and $2.4\mu \mathrm{m}$, respectively [Figs. 3(c)–3(e)]. After correction with the phase distribution of $a_{\mathrm{coma}90}=-1.7$ and $a_{\mathrm{astig}0}=-0.25$, the $\mathrm{FWHM}y$ and the $\mathrm{FWHM}z$ values improved to 0.31 and $0.88\mu \mathrm{m}$, respectively. The peak intensity was increased to 64% of $I_{\text{nonaberration}}$; i.e., the peak intensity was $4.9\times$ higher than that of the aberrated image. The correction improved the intensity and the FWHM values of the aberrated PSF under the tilted cover slip. However, the PSF was not recovered completely because of the residual second coma aberration.

Next, we numerically calculated the PSF images in a glass cylinder with an outer diameter of 0.1 mm and a glass thickness of 0.01 mm, which longitudinally directed in the ${\varphi }_c=0\text{-}\mathrm{deg}$ direction ($x$-axis). The predominant aberration was Astig(0) of $a_{\mathrm{astig}0}=-0.50$. After correction with a phase distribution of $a_{\mathrm{astig}0}=0.50$, the peak intensity was improved to 93% $I_{\text{nonaberration}}$ from 25% $I_{\text{nonaberration}}$; i.e., the peak intensity was $3.8\times$ higher than that of the aberrated image [Figs. 3(f)–3(h)]. Furthermore, the $\mathrm{FWHM}x$ and the $\mathrm{FWHM}y$ values decreased to $0.23\mu \mathrm{m}$ from $0.37\mu \mathrm{m}$, and to $0.28\mu \mathrm{m}$ from $0.63\mu \mathrm{m}$, respectively. The $\mathrm{FWHM}z$ value decreased to $0.82\mu \mathrm{m}$ from $1.7\mu \mathrm{m}$. The FWHM values of the corrected PSF were nearly equal to those without aberrations, and the peak intensity was recovered almost completely with the correction.

3.2.

Imaging of Beads With Single-Photon Excitation Laser Scanning Microscopy

The correction effect of the device was experimentally evaluated by 1P-LSM illuminated with 488-nm laser light.

First, we observed the tilt-sample, i.e., the fluorescence beads under the tilted cover slip. Under different observation conditions, we observed several beads within a $20\text{-}\mu \mathrm{m}$ cubed volume located at the center of the field of view; the average peak intensity and the average FWHM of those images were obtained. Before correction by the device, the optical system had an inherent coma aberration in the ${\varphi }_t=90\text{-}\mathrm{deg}$ direction ($y$-axis), and, consequently, the highest quality of the bead image was obtained when the cover slip was inclined at ${\theta }_t=3\mathrm{deg}$ in the ${\varphi }_t=90\text{-}\mathrm{deg}$ direction. Therefore, when we say that the cover slip was inclined at ${\theta }_t=-2\mathrm{deg}$ in the direction of ${\varphi }_t=90\mathrm{deg}$ ($y$-axis), then the tilting angle is actually $-5\mathrm{deg}$ relative to ${\theta }_t=3\mathrm{deg}$, at which the highest quality of the bead image was obtained without correction. In the case of a tilt angle of ${\theta }_t=-2\mathrm{deg}$ in the direction of ${\varphi }_t=90\mathrm{deg}$, we first applied a voltage to C90-LCC to correct Coma(90). By varying the voltage applied to C90-LCC repeatedly, we determined the appropriate voltage required to achieve the maximum fluorescence signal. After correction by C90-LCC, the bead image showed an astigmatic point spread function in the 0-deg direction. Therefore, we next applied a voltage to A0-LCC to correct the residual Astig(0). The Zernike coefficients of the phase distributions generated in each LCC, which were required to achieve the maximum fluorescence signal, were $a_{\mathrm{astig}0}=0.56$ and $a_{\mathrm{coma}90}=1.4$ (Table 1). Our device thus improved the spatial resolution and the fluorescence signal in the aberrated bead image by using C90-LCC and A0-LCC [Figs. 4(a)–4(b)]. The $\mathrm{FWHM}y$ value improved to $0.26\mu \mathrm{m}$ from $0.40\mu \mathrm{m}$. Furthermore, the $\mathrm{FWHM}z$ value improved to $1.7\mu \mathrm{m}$ from $2.3\mu \mathrm{m}$, and the fluorescence peak intensity of the corrected image was $1.7\times$ higher than that of the aberrated image [Fig. 4(c)]. Moreover, in the case of a tilt angle of ${\theta }_t=6.5\mathrm{deg}$ and tilt direction of ${\varphi }_t=45\mathrm{deg}$, C0-LCC, C90-LCC, A0-LCC, and A45-LCC corrected both the primary coma and astigmatism in the ${\varphi }_t=45\text{-}\mathrm{deg}$ direction and the system’s inherent aberration. The image quality improved, as shown in Figs. 4(d)–4(f), and the peak intensity was $1.6\times$ higher than that of the aberrated image. Thus, the device improved the spatial resolution and the fluorescence signal, which were degraded by the cover slip with various tilting angles and directions.

Table 1

Zernike coefficients of the phase distributions generated in each LCC during observation of the tilt-sample.

Fig. 4

Images of fluorescence beads in the tilt-sample in 1P-LSM illuminated with 488-nm wavelength laser light. (a) and (b) Lateral and axial images of ${\theta }_t=-2\mathrm{deg}$ and ${\varphi }_t=90\mathrm{deg}$ (a) before and (b) after correction. Panel (c) shows the average intensity profiles and the average curves of seven bead images with ${\theta }_t=-2\mathrm{deg}$ and ${\varphi }_t=90\mathrm{deg}$ across the center of the intensity distributions along the $x$-, $y$-, and $z$-axes. (d) and (e) Lateral and axial images of ${\theta }_t=6.5\mathrm{deg}$ and ${\varphi }_t=45\mathrm{deg}$ (d) before and (e) after correction. Panel (f) shows the average intensity profiles and the average curves of six bead images with ${\theta }_t=6.5\mathrm{deg}$ and ${\varphi }_t=45\mathrm{deg}$ across the center of the intensity distributions along the $x$-, $y$-, and $z$-axes. The scale bars denote $0.5\mu \mathrm{m}$.

Next, the correction for astigmatism was evaluated by observing the cyl-sample, i.e., the fluorescence beads in the cylindrical glass capillary. When the capillary was longitudinally directed in the ${\varphi }_c=0\text{-}\mathrm{deg}$ direction, we first applied a voltage to A0-LCC to correct Astig(0), after which we corrected the system’s inherent Coma(90) by C90-LCC (Table 2). For correcting each aberration, we determined the appropriate voltages required to achieve the maximum fluorescence signal by varying the voltages applied to each LCC. The adjustment of the applied voltages to each LCC was performed in the above-mentioned order by only one round. Thus, Figs. 5(a)–5(b) demonstrate the improvement in the spatial resolution and the fluorescence signal in the corrected image. The device improved the $\mathrm{FWHM}x$ and $\mathrm{FWHM}y$ values to $0.24\mu \mathrm{m}$ from $0.32\mu \mathrm{m}$ and to $0.21\mu \mathrm{m}$ from $0.40\mu \mathrm{m}$, respectively. The $\mathrm{FWHM}z$ value was reduced to $1.3\mu \mathrm{m}$ from $3.3\mu \mathrm{m}$ and the peak intensity was $2.2\times$ higher than that of the aberrated image [Fig. 5(c)]. Furthermore, in the case of the capillary’s longitudinal direction of ${\varphi }_c=67.5\mathrm{deg}$, A0-LCC and A45-LCC corrected the astigmatism in the ${\varphi }_c=67.5\text{-}\mathrm{deg}$ direction, and C90-LCC corrected the system’s inherent Coma(90), as shown in Figs. 5(d)–5(f). For correcting each aberration, we determined the appropriate voltages required to achieve the maximum fluorescence signal by varying the voltages applied to each LCC. The adjustment of the applied voltages to each LCC was performed by only one round. The peak intensity of the corrected images was $3.2\times$ higher than that of the aberrated images. Thus, the device improved the spatial resolution and fluorescence signal, which were degraded in the cylindrical glass capillary in various directions.

Table 2

Zernike coefficients of the phase distributions generated in each LCC during observation of the cyl-sample.

Fig. 5

Images of fluorescence beads in the cyl-sample in 1P-LSM illuminated with 488-nm wavelength laser light. (a) and (b) Lateral and axial images of ${\varphi }_c=0\mathrm{deg}$ (a) before and (b) after correction. Panel (c) shows the average intensity profiles and the average curves of the five bead images with ${\varphi }_c=0\mathrm{deg}$ across the center of the intensity distributions along the $x$-, $y$-, and $z$-axes. (d) and (e) Lateral and axial images of ${\varphi }_c=67.5\mathrm{deg}$ (d) before and (e) after correction. Panel (f) shows the average intensity profiles and the average curves of seven bead images with ${\varphi }_c=67.5\mathrm{deg}$ across the center of the intensity distributions along the $x$-, $y$-, and $z$-axes. The scale bars denote $0.5\mu \mathrm{m}$.

3.3.

Imaging of Beads With Two-Photon Excitation Laser Scanning Microscopy

Before using the device to observe a biospecimen via 2P-LSM, we tested the device in 2P-LSM illuminated by 900-nm wavelength laser light and observed the fluorescence beads to confirm the correction effect of the device.

Figures 6(a)–6(b) show the images of a fluorescence bead under the cover slip at the tilt angle of ${\theta }_t=-2\mathrm{deg}$ in the ${\varphi }_t=90\text{-}\mathrm{deg}$ direction (the tilt-sample). As with the observation in 1P-LSM, C90-LCC and A0-LCC corrected Coma(90) and Astig(0) induced by the tilted cover slip as well as the system’s inherent Coma(90). The Zernike coefficients generated in each LCC were inversely proportional to the laser wavelength: $a_{\mathrm{astig}0}=0.30$ and $a_{\mathrm{coma}90}=0.69$. The $\mathrm{FWHM}y$ and $\mathrm{FWHM}z$ values improved to $0.35\mu \mathrm{m}$ from $0.40\mu \mathrm{m}$ and to $2.1\mu \mathrm{m}$ from $2.4\mu \mathrm{m}$, respectively, and the peak intensity was $1.5\times$ higher than that of the aberrated image [Fig. 6(c)].

Fig. 6

Images of fluorescence beads in 2P-LSM illuminated with 900-nm wavelength laser light. (a) and (b) Lateral and axial images in the tilt-sample with ${\theta }_t=-2\mathrm{deg}$ and ${\varphi }_t=90\mathrm{deg}$ (a) before and (b) after correction. Panel (c) shows the average intensity profiles and the average curves of 10 bead images with ${\theta }_t=-2\mathrm{deg}$ and ${\varphi }_t=90\mathrm{deg}$ across the center of the intensity distributions along the $x$-, $y$-, and $z$-axes. (d) and (e) Lateral and axial images in the cyl-sample of ${\varphi }_c=67.5\mathrm{deg}$ (d) before and (e) after correction. Panel (f) shows the average intensity profiles and the average curves of seven bead images with ${\varphi }_c=67.5\mathrm{deg}$ across the center of the intensity distributions along the $x$-, $y$-, and $z$-axes. The scale bars denote $0.5\mu \mathrm{m}$.

Next, we observed the cyl-sample with the capillary’s longitudinal direction of ${\varphi }_c=67.5\mathrm{deg}$. A0-LCC and A45-LCC corrected the astigmatism in the ${\varphi }_c=67.5\text{-}\mathrm{deg}$ direction and C90-LCC corrected the system’s inherent Coma(90), as shown in Figs. 6(d) and 6(e). The device improved the $\mathrm{FWHM}x$ and $\mathrm{FWHM}y$ values to $0.32\mu \mathrm{m}$ from $0.38\mu \mathrm{m}$ and to $0.32\mu \mathrm{m}$ from $0.45\mu \mathrm{m}$, respectively. The $\mathrm{FWHM}z$ value was reduced to $1.5\mu \mathrm{m}$ from $2.6\mu \mathrm{m}$ and the peak intensity was $3.0\times$ higher than that of the aberrated image [Fig. 6(f)].

In this way, we succeeded in improving the spatial resolution and fluorescence signal as in the 1P-LSM case.

3.4.

Imaging of Biospecimen With Two-Photon Excitation Laser Scanning Microscopy

Finally, we used the device to observe a fixed whole mouse brain using 2P-LSM illuminated by 910-nm wavelength laser light. We observed cortical layer V neurons under a thick blood vessel at the surface of the cerebral cortex of the left brain [Fig. 7(a)]. Figure 7(b) shows the wide-field image of the sample, and the thick blood vessel at the brain surface is indicated in the axial images in Fig. 7(b). Furthermore, we observed the sample within a $20\text{-}\mu \mathrm{m}$ cubed volume located at the center of the field of view at a depth of $150\mu \mathrm{m}$ from the sample surface, i.e., at a depth of $80\mu \mathrm{m}$ from the bottom of the blood vessel [Figs. 7(c)–7(d)]. We first corrected Astig(0) and Astig(45) by A0-LCC and A45-LCC. We determined the appropriate voltage required to achieve the maximum fluorescence signal by varying the voltage applied to A0-LCC, after which we determined the appropriate voltages for A45-LCC. The Zernike coefficients of the phase distributions in each LCC were $a_{\mathrm{astig}0}=0.53$ and $a_{\mathrm{astig}45}=0.87$. The modulations of $a_{\mathrm{astig}45}=0.87$ were maximum phase modulations in A45-LCC. After correcting astigmatisms, C90-LCC of $a_{\mathrm{coma}90}=0.87$ corrected Coma(90), after which C0-LCC of $a_{\mathrm{coma}0}=-0.62$ corrected Coma(0). The modulations of $a_{\mathrm{coma}90}=0.87$ were maximum phase modulations in C90-LCC. The adjustment of the applied voltages to each LCC was performed in the above-mentioned order by only one round. We observed the sample with such a low excitation power that the degradation in the fluorescent intensity induced by photobleaching was $<3\%$. From the images of the dendritic spine, the device clearly improved the image quality [Figs. 7(e) and 7(f)]. After correction with the device, the fluorescence peak intensity of the corrected image was $2.4\times$ higher than that of the aberrated image [Fig. 7(g)]. The device reduced the $\mathrm{FWHM}x$ and the $\mathrm{FWHM}y$ values to $0.55\mu \mathrm{m}$ from $0.71\mu \mathrm{m}$ and to $0.75\mu \mathrm{m}$ from $1.12\mu \mathrm{m}$. Furthermore, the $\mathrm{FWHM}z$ value was reduced to $2.8\mu \mathrm{m}$ from $6.8\mu \mathrm{m}$. This result confirms that the device improves spatial resolution; additionally, the fluorescence signal degraded in the biospecimen, as with the bead sample.

Fig. 7

Images of the fixed whole brain of the thy1-YFP-H mouse in 2P-LSM illuminated with 910-nm wavelength laser light. (a) Schematic of the fixed-whole-mouse-brain sample. (b) Lateral and axial images before corrections in the area indicated by a rectangle in (a). The arrows in the axial images in (b) indicate the blood vessel. Lateral images (c) before and (d) after correction with the device were obtained in the area indicated by a rectangle in (b). Panels (e) and (f) show lateral and axial images (e) before and (f) after corrections in the areas indicated by the rectangles in (c) and (d), respectively. (g) Intensity profiles across the center of the intensity distribution in (e) and (f) along the $x$-, $y$-, and $z$-axes. The scale bars in (b), (c), (d), (e), and (f) denote 100, 5, and $1\mu \mathrm{m}$, respectively.