Transmissive liquid-crystal device for correcting primary coma aberration and astigmatism in biospecimen in two-photon excitation laser scanning microscopy

Abstract. All aberrations produced inside a biospecimen can degrade the quality of a three-dimensional image in two-photon excitation laser scanning microscopy. Previously, we developed a transmissive liquid-crystal device to correct spherical aberrations that improved the image quality of a fixed-mouse-brain slice treated with an optical clearing reagent. In this study, we developed a transmissive device that corrects primary coma aberration and astigmatism. The motivation for this study is that asymmetric aberration can be induced by the shape of a biospecimen and/or by a complicated refractive-index distribution in a sample; this can considerably degrade optical performance even near the sample surface. The device’s performance was evaluated by observing fluorescence beads. The device was inserted between the objective lens and microscope revolver and succeeded in improving the spatial resolution and fluorescence signal of a bead image that was originally degraded by asymmetric aberration. Finally, we implemented the device for observing a fixed whole mouse brain with a sloping surface shape and complicated internal refractive-index distribution. The correction with the device improved the spatial resolution and increased the fluorescence signal by ∼2.4×. The device can provide a simple approach to acquiring higher-quality images of biospecimens.

Transmissive liquid-crystal device for correcting primary coma aberration and astigmatism in biospecimen in two-photon excitation laser scanning microscopy Ayano Tanabe, a,b,c Terumasa Hibi, b Sari Ipponjima, a,b Kenji Matsumoto, c Masafumi Yokoyama, c Makoto Kurihara, c Nobuyuki Hashimoto, c and Tomomi Nemoto a,b, *

Introduction
Confocal laser scanning microscopy (LSM) has enabled impressive three-dimensional fluorescence imaging. Furthermore, in the case of two-photon excitation LSM (2P-LSM), fluorescent molecules are excited within a very small focal volume. 1,2 This high degree of localization in the 2P method enables cross-sectional fluorescence imaging in the absence of a confocal aperture. In addition, near-infrared laser light used for 2P processes is barely absorbed by or scattered in a biospecimen. 2P-LSM can three-dimensionally visualize deep regions within a biospecimen because of these advantages. However, a mismatch of refractive indices in an optical path can induce wavefront aberrations, which degrades the spatial resolution and fluorescence signal of an image. 3,4 Spatial light modulators have been shown to correct these aberrations and improve the image quality of biospecimens. 5,6 However, these reflective spatial light modulators require the user to change the basic design of an optical path in a conventional microscope.
Transmissive liquid-crystal devices have been used in various applications, e.g., radially polarized beam generators, holographic microscopes, stimulated emission depletion microscopes, and optical pickups, to modulate light waves. [7][8][9][10][11] These liquid-crystal devices consist of liquid-crystal cells (LCCs), wherein a layer of liquid-crystal molecules is sandwiched between a pair of glass substrates equipped with transparent electrodes. 12 These liquidcrystal molecules exhibit directional refractive-index anisotropy that is electrically controllable; therefore, a segmented pattern of a transparent electrode generates a phase distribution that corresponds to the segmented pattern in the wavefront of penetrating light. Phase modulation is controlled by changing the applied voltage.
We previously reported a transmissive liquid-crystal device that can compensate for spherical aberrations. 13,14 Spherical aberrations are predominant aberrations produced during observations of deep regions in samples and are usually caused by refractive-index differences between a sample and immersion medium. 15 This device, which is inserted between the objective lens and revolver of a microscope for correcting spherical aberrations, improved the quality of fluorescence images of deep regions in a fixed-mouse-brain slice treated by an optical clearing reagent in 2P-LSM.
However, asymmetric aberrations can also be induced by the shape of a biospecimen and/or a complicated refractive-index distribution in the sample; they can degrade optical performance considerably, even near the sample surface. 16 Aberrations in biospecimens and their effects have been experimentally investigated by several authors. [17][18][19] Further, wavefront aberrations can be described using Zernike polynomials. 20 Low-order Zernike aberrations, such as primary coma aberration and astigmatism, increase wavefront variance, degrading the Strehl ratio of an optical system considerably. Furthermore, specimeninduced aberrations tend to be dominated by these low-order Zernike aberrations.
In the current study, we developed a transmissive liquid-crystal device that can compensate for four low-order asymmetric aberrations: astigmatism in the 0-deg and 45-deg directions, and primary coma aberration in the 0-deg and 90-deg directions [Astig(0), Astig(45), Coma(0), and Coma(90), respectively]. 21 The device experimentally succeeded in improving the spatial resolution and fluorescence signal (which was originally degraded by asymmetric aberrations) of a bead image under a tilted cover slip and in a cylindrical glass capillary using single-photon excitation LSM (1P-LSM). In this study, we compared this experimental result in 1P-LSM with the numerically calculated results. Furthermore, in preparation for using the device to observe a biospecimen, we observed the bead samples and confirmed the correction effect of the device in 2P-LSM. Finally, we used the device to observe a biospecimen using 2P-LSM. In conclusion, we experimentally demonstrated that the device enhanced the image quality of the biospecimen with a sloping surface shape and a complicated internal refractive-index distribution. 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 astig0 , a astig45 , a coma0 , and a coma90 , 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 astig0 ¼ 0.89, the device showed the phase distribution of Astig(0) [ Fig. 1(i)]. When we applied a voltage only to A45-LCC (a astig45 ¼ 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 astig0 ¼ a astig45 ¼ 0.64), the device showed the astigmatic component to be in the 22.5-deg direction. Similarly, C0-LCC of a coma0 ¼ 0.89 and C90-LCC of a coma90 ¼ 0.89 showed Coma (0) and Coma(90) phase distributions, respectively. When using C0-LCC and C90-LCC (a coma0 ¼ a coma90 ¼ 0.64), the device showed the coma component to be in the 45-deg direction.

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. . 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 (FWHMx, FWHMy, and FWHMz) were measured from the average curves. Thy1-YFP-H mice 22 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).

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).

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  The peak intensity was increased to 64% of I nonaberration ; i.e., the peak intensity was 4.9× 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 φ c ¼ 0-deg direction (x-axis). The predominant aberration was Astig(0) of a astig0 ¼ −0.50. After correction with a phase distribution of a astig0 ¼ 0.50, the peak intensity was improved to 93% I nonaberration from 25% I nonaberration ; i.e., the peak intensity was 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.

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-μm 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 φ t ¼ 90-deg direction (y-axis), and, consequently, the highest quality of the bead image was obtained when the cover slip was inclined at θ t ¼ 3 deg in the φ t ¼ 90-deg direction. Therefore, when we say that the cover slip was inclined at θ t ¼ −2 deg in the direction of φ t ¼ 90 deg (y-axis), then the tilting angle is actually −5 deg relative to θ t ¼ 3 deg, at which the highest quality of the bead image was obtained without correction. In the case of a tilt angle of θ t ¼ −2 deg in the direction of φ t ¼ 90 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 astig0 ¼ 0.56 and a coma90 ¼ 1.4 (Table 1) The FWHMy value improved to 0.26 μm from 0.40 μm. Furthermore, the FWHMz value improved to 1.7 μm from 2.3 μm, and the fluorescence peak intensity of the corrected image was 1.7× higher than that of the aberrated image [ Fig. 4(c)]. Moreover, in the case of a tilt angle of θ t ¼ 6.5 deg and tilt direction of φ t ¼ 45 deg, C0-LCC, C90-LCC, A0-LCC, and A45-LCC corrected both the primary coma and astigmatism in the φ t ¼ 45-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× 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. 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 φ c ¼ 0-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  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× 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.

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.   Next, we observed the cyl-sample with the capillary's longitudinal direction of φ c ¼ 67.5 deg. A0-LCC and A45-LCC corrected the astigmatism in the φ c ¼ 67.5-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 FWHMx and FWHMy values to 0.32 μm from 0.38 μm and to 0.32 μm from 0.45 μm, respectively. The FWHMz value was reduced to 1.5 μm from 2.6 μm and the peak intensity was 3.0× 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.

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-μm cubed volume located at the center of the field of view at a depth of 150 μm from the sample surface, i.e., at a depth of 80 μm 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 astig0 ¼ 0.53 and a astig45 ¼ 0.87. The modulations of a astig45 ¼ 0.87 were maximum phase modulations in A45-LCC. After correcting astigmatisms, C90-LCC of a coma90 ¼ 0.87 corrected Coma(90), after which C0-LCC of a coma0 ¼ −0.62 corrected Coma(0). The modulations of a coma90 ¼ 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× higher than that of the aberrated image [ Fig. 7(g)]. The device reduced the FWHMx and the FWHMy values to 0.55 μm from 0.71 μm and to 0.75 μm from 1.12 μm. Furthermore, the FWHMz value was reduced to 2.8 μm from 6.8 μm. This result confirms that the device improves spatial resolution; additionally, the fluorescence signal degraded in the biospecimen, as with the bead sample.

Discussion
Previously, our transmissive device for correcting spherical aberrations, which was inserted between the objective lens and the microscope revolver, improved the image quality by eliminating spherical aberrations. However, asymmetric aberrations, induced by the shape of a sample and/or a complicated refractive-index distribution in the sample, were not corrected by our previous device. In this study, we developed a transmissive device that can correct astigmatism and primary coma aberrations. The device succeeded in improving the spatial resolution and the fluorescence signal originally degraded by asymmetric aberrations in bead samples as well as in a biospecimen. LCC with the matrix electrodes can correct various aberrations as well as astigmatisms and primary coma aberrations with only one LCC, 23 increasing the transmittance of the device. However, the unsmooth phase distribution generated by the small number or low fill factor of matrix electrodes might degrade the aberration correction effect. Furthermore, optical performance can be degraded by the diffraction light induced by the gap between matrix electrodes. Conversely, our device can achieve a smooth continuous phase distribution with the small number of electrodes, while the shape of a phase distribution is fixed by the segmented electrode pattern. Furthermore, the aperiodic pattern in the small number of electrodes might reduce the diffraction light.
In the case of asymmetric aberrations, the reduction of the Strehl ratio induced by the Zernike aberration of the order n þ 1 is decreased to n þ 1∕n þ 2 of that induced by the Zernike aberration of the order n with the same-magnitude Zernike coefficient. 24 Furthermore, specimen-induced aberrations tend to be dominated by low-order Zernike aberrations. [17][18][19] The aberrated image, thus, was improved considerably by correcting only astigmatism of the second order and primary coma aberration of the third order. Meanwhile, the results of our study suggest that the device can also correct residual higher-order Zernike aberrations by laminating LCCs for correcting these higherorder Zernike aberrations. However, in fact, the many laminated LCCs degrade the transmittance of the device considerably. In the future, improvements of the device's transmittance will be accomplished and the device will be able to correct more types of aberrations. If the two kinds of electrode patterns for correcting different Zernike aberration functions are, respectively, formed on opposite sides of a glass substrate, independent compensations for these two kinds of the Zernike aberration functions can be achieved with only one LCC. 11 The experimental result in the bead samples qualitatively agreed with the numerically calculated result . The slight differences between the numerical and experimental results, such as the peak intensity values and the magnitude of each Zernike coefficient required for the correction, might be induced by several unpredictable differences in presuppositions for the calculation, including the glass thickness in the bead samples, the system's inherent aberration, and the intensity distribution of incident light.
The correction effect of the device was also experimentally confirmed with 2P-LSM. The device showed similar improvements of the fluorescence signal in the bead image to that in 1P-LSM [Figs. 4(c), 5(f), 6(c), and 6(f)]. An adequate result was not obtained in the numerical calculation because the optical performance of the objective lens system used in the calculation was too poor for near-infrared wavelengths. 14 However, the similar correction effect in 1P-and 2P-LSM can be explained as follows. The increases in the fluorescence signal are in proportion to the square of the excitation light intensity in the 2P process. Conversely, the Zernike coefficient of the wavefront aberration is inversely proportional to the wavelength and the degradation of the excitation light intensity induced by the wavefront aberration decreases; the increase in the excitation light intensity by the correction in 2P-LSM is lower compared to that in 1P-LSM. These properties suggest that the device can show similar improvements of the fluorescence signals for both 1P-and 2P-LSM.
Several aberrations that occurred in the bead samples were estimated using numerical calculations and fluorescence bead images. Indeed, the predicted predominant aberration, i.e., primary coma aberration in the tilt-sample and astigmatism in the cyl-sample, was first corrected in the bead samples. However, such an estimate of the predominant aberration cannot be performed accurately, especially in a biospecimen. We suggest that correction of astigmatism should be performed first and the primary coma aberration should be corrected next, as shown in the observation of the fixed whole brain (see Sec. 3.4), because correction of astigmatism is more effective than that of the primary coma aberration for the improvement of image quality. 24 In the observation of the fixed whole mouse brain, the device showed sufficient improvement both in the spatial resolution and in the fluorescence signal, which were estimated using the results in the bead samples. However, the device required the maximum phase modulation of Astig(45) and Coma(90) for correction of the biospecimen. The increase in the phase modulation of the device possibly achieves a greater improvement of the image quality in the fixed whole mouse brain.
Our device can provide a simple approach to acquiring highquality images in a biospecimen with a complicated surface shape and/or distribution of the internal refractive index. This approach does not require biologists to either slice a biospecimen or uniformize a refractive-index distribution in the sample. Furthermore, the device can be applied to a conventional laser scanning microscope without changing the fundamental optical system. Therefore, adaptive optics techniques using our device will be helpful for such fields as clinical research and pathology where prompt preparation and observation are needed. Of course, further improvements of the image quality during the observation of a biospecimen may be achieved by combining our adaptive optics technique and optical clearing reagents to increase the transparency of a sample and to even out the refractive-index distribution in the sample. 25,26 In the future, we hope our transmissive device will be able to improve more types of Zernike aberrations and achieve the dynamic correction of various aberrations, including asymmetric and spherical aberrations.

Conclusion
Our transmissive device for correcting primary coma and astigmatism showed improvements of the spatial resolution and fluorescence signal in bead samples, which was in agreement with the numerical calculation. Furthermore, the device succeeded in improving the image quality of a fixed whole mouse brain in 2P-LSM. The device can provide a simple approach for acquiring higher-quality images in a biospecimen with a complicated surface shape and/or a complicated internal refractive-index distribution.