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Abstract
A smaller point spread function (PSF) is desirable for high-resolution image acquisition. In two-photon excitation microscopy, the focus size of the excitation light is directly related to the two-photon fluorescence PSF. To achieve a small PSF, we designed amplitude-modulation-type multi-ring pupil masks using two design methods. When the intensity distribution of the excitation light has a top-hat form, the volume of the PSF obtained with the first designed multi-ring mask is 1.46 times smaller than that obtained without the mask. Furthermore, the second multi-ring mask is less influenced by spherical aberration occurring during observation inside the sample. Our method, which is robust against spherical aberration, reduces the size of the PSF in the observation of fluorescent beads and biological samples.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Scanning two-photon excitation microscopy can provide three-dimensional images of biological samples with cellular-level resolution. Combining this observational ability with appropriate probes enables a better understanding of physiological and pathological cellular morphology changes [1]. In addition, observations of finer sub-cellular structures, such as organelles and cytoskeletons, can lead to a deeper understanding of cellular changes. Thus, a microscopy technique with higher resolution is required; optimization of the point spread function (PSF) of the imaging system is important for increasing the resolution of the microscope [2]. In two-photon excitation fluorescence microscopy, the PSF depends on the following factors: the focus shape of the excitation light determined by the numerical aperture (NA) of the objective lens; the wavelength of the excitation light; and the spatial distribution of the amplitude, phase, and polarization of the light in the pupil plane of the optical system. Although an objective lens with a high NA is often employed to reduce the PSF size, the PSF of two-photon excitation fluorescence microscopy with a high NA and a long-working-distance objective lens is slightly larger than the size of sub-cellular structures. Therefore, stimulated-emission depletion (STED) [3,4] and PSF engineering [5–8] have been developed as super-resolution imaging techniques that optically improve the PSF.
PSF engineering improves the PSF by controlling the complex amplitude distribution of the excitation light in the pupil plane of the optical system. The most convenient method for improving the PSF is to physically place a pupil mask on the pupil plane. Amplitude-modulated pupil masks, such as shading [5,6] and single-ring masks [7–9], have been investigated because they can reduce the size of the PSF. Oketani et al. [8] investigated the optimal single-ring mask shape by varying the size of the shielding area of the mask; they reported a mask with the optimal shape that minimized the full width at half maximum (FWHM) of the PSF in the lateral and axial directions. However, this study identified that PSF engineering using conventional amplitude-modulation-type single-ring pupil masks is not suitable for imaging inside biological samples because the mask-modulated excitation light is affected by even slight spherical aberrations. Because of this aberration, the signal-to-noise ratio of the image is lowered, or fluorescence signals from different depth are acquired as false signals.
In this study, we propose an amplitude-modulation-type multi-ring pupil mask comprising multiple light-shielding and transmission areas. As the number of rings increases, the flexibility of the design increases. The multi-ring masks were designed using two different methods. Method 1 minimizes the volume of the PSF via simulation. We also confirmed that the optimal width and arrangement of each ring that minimizes the PSF size depends on the intensity distribution of excitation light. For imaging inside the sample, we examined the effect of spherical aberration when applying the multi-ring mask designed using Method 1. Method 2 reduces the influence of spherical aberration. The multi-ring mask designed using Method 2 is better than the conventional single-ring mask in terms of PSF minimization and was also robust against spherical aberration. Consequently, high-resolution imaging inside the biological samples was achieved. In experiments using fluorescent beads in an epoxy resin and a biological sample, a spatial light modulator (SLM) was used with dynamic PSF engineering to compare the effect of the number of rings for each design method. Moreover, SLM allows simultaneous modification of the amplitude of the pupil mask and the phase for aberration correction, thereby enabling high-resolution observation at greater depths than observation using only the amplitude mask. The improvement in resolution using the masks designed via the proposed method was confirmed by imaging fluorescent beads in epoxy resin and via ex vivo observation of dendritic spines in mouse brain tissue. Furthermore, the proposed method is expected to minimize the PSF in three-photon excitation fluorescence microscopy.
2. Methods
2.1 Multi-ring mask design without considering spherical aberration (Method 1)
Figure 1 shows a schematic of the amplitude modulation using a ring mask. The excitation light beam is expanded using an expander and propagates in the z direction. If amplitude modulation is not performed, the excitation light beam (which has an intensity distribution with a top-hat or Gaussian profile) enters the objective lens. The Gaussian profile is described by
where r and ${I_{ex0}}$ are the radial variable and peak intensity, respectively; ${w_{ex}}$ is the radius when ${I_{ex}}$ = $\frac{1}{{{e^2}}}\; $, and r = 1.0 coincides with the outermost circumference of the pupil of the objective lens. Excitation light focused by the objective lens is irradiated onto a fine fluorescent object with a size below the diffraction limit, resulting in fluorescence. Then, the intensity distribution of the observed fluorescence, i.e., the PSF, is proportional to the square of the intensity distribution of the focused excitation light.
Fig. 1. Amplitude modulation of the excitation light beam using a ring mask and the resulting change in the point spread function (PSF). (a) Schematic of the optical system. (b) The double-ring mask pattern expressed using a grating. (c) The applied ring mask and obtained PSF. (d) Radial parameters for the multi-ring mask design.
Binary amplitude modulation is performed when the ring mask is placed at the conjugate position of the pupil of the objective lens. In Fig. 1(a), an SLM is placed in position as a dynamic pupil mask. When a grating pattern (shown in Fig. 1(b)) is applied to the SLM, some area of the beam is diffracted, while the rest of the beam moves in a straight direction. An excitation light beam with multiple ring-shaped intensity distributions is generated by combining the SLM and an aperture that blocks the undesired diffracted beam. The focal shape changes three-dimensionally because the interference of the excitation light beam is divided in the radial direction (the line profile of the modulated beam is shown in Fig. S1). The intensity balance between the divided excitation lights changes not only the shape of the PSF main lobe that contributes most to fluorescence emission, but also the intensity of the undesired higher-order light called sidelobes (Fig. 1(c)).
In Method 1, we designed a ring mask that allows for the smallest volume of the PSF main lobe within an acceptable intensity of the sidelobe. The flowchart for the mask design procedure is shown in Fig. S2(a). The double-ring mask has two light-shielding regions (Fig. 1(d)). The positions of the inner diameter (r1, r3) and outer diameter (r2, r4) of each light-shielding region are set. Then, the PSF is calculated using the vectorial diffraction formula [10,11]. When the polarization of the excitation light is circular, the focusing shape of the main lobe is an ellipsoid, which is approximately 3.5 times longer in the longitudinal direction (optical axis) than in the transverse direction (perpendicular to the optical axis). The volume V of the main lobe is calculated by fitting the area where the main lobe’s intensity is greater than the FWHM as the ellipsoid:
2.2 Multi-ring mask design considering spherical aberration (Method 2)
While imaging the inside of a sample using a ring mask, spherical aberration occurs due to the refractive index mismatch between the immersion fluid and the sample. Spherical aberration results in a phase difference between the excitation light divided by the ring mask, which changes the shape of the PSF and often introduces side lobes. We refer to these sidelobes as aberration-induced sidelobes. To investigate the changes in the PSF induced by the spherical aberration, the simulated PSF is calculated using the vectorial diffraction formula, which considers spherical aberration [12]. The maximum intensity ratio between the aberration-induced sidelobes and the main lobe, $\Delta {S_2}$, is determined using
where $\; {Q_{ma\_ab}}$ and ${Q_{si\_ab\; }}$ denote the intensity of the PSF main lobe and side lobe, respectively, in the axial direction affected by the spherical aberration. Here, we designed a multi-ring mask in which $\Delta {S_2}$ was kept within a range such that the effect on the output image is sufficiently small.As shown in Fig. S2(b), Method 2 adds the calculation of the aberration-induced sidelobes occurring when the inside of the sample is imaged and $\Delta {S_2}$ to the design procedure of Method 1. Hence, Method 2 is a multi-ring mask design method that is more robust to aberration than Method 1. (The flowchart for the mask design procedure is shown in Fig. S2(b).) We designed a ring mask with the smallest volume of the PSF main lobe under the conditions of $\Delta {S_1} \le 0.05$ and $\Delta {S_2} \le 0.10$ for an excitation light beam with a wavelength of 890 nm and top hat intensity distribution focused by a water immersion objective lens (NA = 1.0) at a depth of 100 µm inside the biological sample. In Method 2, the multi-ring mask was designed according to the refractive index of the observation object and observation depth. Notably, the robustness to spherical aberration and the decrease in the size of the PSF have a conflicting relationship.
2.3 Optical setup
The excitation light beam (890 nm wavelength, 150 fs pulse duration, and 80 MHz repetition rate) from a Ti:sapphire laser (Chameleon vision II, Coherent Inc.) was expanded by a beam expander and projected onto a phase-only modulated-type liquid-crystal silicon type spatial light modulator (LCOS-SLM, Hamamatsu Photonics K.K., 1280 × 1024 pixels, 12.5 µm pixel pitch) with a Peltier system [13,14]. By displaying the multi-ring mask pattern shown in Fig. 1(b) on the SLM, the SLM is used as a variable amplitude-modulation multi-ring mask. The SLM can modulate the amplitude to represent the multi-ring mask and modulate the phase for aberration correction. The zero-order light beam was directed through a telecentric lens system and an x–y galvanometer scanner (6220H, Cambridge Technology) to the objective lens. The expander and telecentric lens systems were adjusted such that the intensity distribution of the excitation light beam was Gaussian with ${w_{ex}}$ = 1.49. The modulated beam was focused by a 20× NA1.0 objective lens (XLUMPLFLN20XW, Olympus), and a fluorescence signal was emitted. The fluorescence collected by the objective lens was detected by a photomultiplier tube (PMT, H10770P-40, Hamamatsu Photonics K.K.). The beam was scanned using a scanner to obtain a two-dimensional image; the objective lens moved to obtain multiple images with different depths. Finally, a three-dimensional image was reconstructed by processing the obtained two-dimensional images using MATLAB (The MathWorks, Inc.).
2.4 Animal samples
Thy1-YFP-h mice that strongly express yellow fluorescent protein (YFP) in their motor neurons [15] were obtained from the Jackson Laboratory (USA). They were kept under specific-pathogen-free conditions on a 12-h dark/light cycle with food and water ad libitum until use. All animal experiments were approved by the Institutional Animal Care and Use Committee of Hamamatsu University School of Medicine (Permission no.: 2019009) and were performed in accordance with relevant guidelines and regulations. A one-year-old male heterozygous Thy1-YFP-H mouse was anesthetized using a mixed anesthetic [16] and then perfusion-fixed with 4% PFA in 0.1 M phosphate buffer (pH 7.4). The brain was isolated and further fixed in the same fixative for 1 h at room temperature. After several washes with PBS, neurons and dendritic spines in the cerebral cortex were obtained for two-photon microscopy.
3. Simulation results
3.1 PSF obtained with the multi-ring mask designed using Method 1
The main lobe obtained when the excitation light beam with a top-hat intensity distribution was modulated by the optimal ring mask is shown in Figs. 2(a)–(d). The white areas are those where the intensity of the main lobe was above the FWHM (without the ring mask), and the red areas are those with the mask applied. Increasing the number of light-shielding regions decreases V, and $\varDelta {L_{axi}}$ becomes greater than $\varDelta {L_{lat}}$. For example, $\Delta V$ was 1.26 when the single-ring mask designed by the method shown in Ref. [8] was applied, whereas it was 1.46 when our 14-ring mask was applied. In particular, the optical axis length of the PSF obtained by the 14-ring mask was 14% smaller than that obtained by the single-ring mask. The actual length is approximately 137 nm shorter.
Fig. 2. Simulation results for the multi-ring masks designed using Method 1. Optimized ring mask for each excitation light intensity distribution and the PSF main lobe. The excitation light beam with top-hat intensity distribution modulated by (a) the conventional single-ring mask designed using the method shown in Ref. [8], (b) a 4-ring mask, (c) an 8-ring mask, and (d) a 14-ring mask. The excitation light beam with a truncated Gaussian intensity distribution whose wex = 0.75 was modulated by (e) the conventional single-ring mask, (f) a 4-ring mask, (g) an 8-ring mask, and (h) a 14-ring mask. White area: intensity of the main lobe above the FWHM (without the ring mask). Red area: with the mask applied. Scale bars: 0.5 µm.
Next, we verified the optimal ring mask for a beam with a truncated Gaussian intensity distribution by changing the size and arrangement of each ring of the multi-ring. The intensity distribution of the beam output from the laser source was Gaussian, and the beam was magnified using an expander. As the beam passes through the pupil of the objective lens, the intensity distribution of the beam becomes a truncated Gaussian as the tails of the Gaussian distribution are cut off. In two-photon excitation microscopy, it is difficult to use a beam with a top-hat intensity distribution because of the low light utilization efficiency; therefore, a beam with a truncated intensity distribution was used as the excitation light beam. The main lobe obtained when the beam with a truncated Gaussian intensity distribution (${w_{ex}}\; = \; 0.75$) was modulated by the ring mask is shown in Figs. 2(e)–(h). It is evident that the optimal ring mask pattern is different for each excitation light intensity distribution, as shown in Figs. 2(a)–(d). Further, the $\Delta V$ obtained with the optimal ring mask for the truncated Gaussian intensity distribution was greater than that obtained with the optimal ring mask for the top-hat intensity distribution. In particular, $\Delta V$ was 2.11 when the 14-ring mask was applied. Interestingly, despite using the beam with a truncated Gaussian intensity distribution (${w_{ex}}\; = \; 0.75$), the main lobe was smaller than that obtained when the beam with a top-hat intensity distribution was focused without the ring mask. This means that even if the beam with a truncated Gaussian intensity distribution (${w_{ex}}\; = \; 0.75$) is used, the PSF below the diffraction limit can be obtained by using the multi-ring mask. Fig. S3 shows the main lobes obtained for the beams with truncated Gaussian intensity distributions of ${w_{ex}}$ = 4.0, 1.5, and 1.0. The optimal shape of the multi-ring mask differs for each intensity distribution of the excitation light, and the improvement ratio increases as ${w_{ex}}$ decreases. From these results, we confirmed that a high improvement ratio can be obtained by optimizing the width and position of each ring of the multi-ring mask according to the intensity distribution of excitation light.
3.2. Behavior of PSF for spherical aberration when multi-ring masks designed using Method 1 are applied
When observations are made inside a sample, the influence of aberrations cannot be ignored. We observed that the excitation light beam modulated by the single-ring mask is strongly affected by even a slight spherical aberration. We numerically studied the effect of a spherical aberration when a medium with a different refractive index from the immersion medium exists in the focusing light path. As shown in Fig. 3(a), in the case of a beam with an 890-nm wavelength and top-hat intensity distribution focused by a water immersion objective lens (NA = 1.0) at a depth of 100 µm inside a sample (average refractive index 1.38), the spherical aberration caused by the refractive index mismatch between the water and the sample was calculated using previously reported methods [12,17–19]. The calculated amount of spherical aberration was expanded by the Zernike polynomial [20], and the coefficient of the fourth-order spherical aberration was 0.08λ.
Fig. 3. Simulation results. The effect of spherical aberration caused by the refractive index mismatch between the immersion water and the biological sample. (a) The PSF affected by the spherical aberration is obtained (b) without the ring mask, (c) with the single-ring mask, (d) with the 4-ring mask (Method 1), (e) with the 14-ring mask (Method 1), (f) with the 4-ring mask (Method 2), and (g) with the 14-ring mask (Method 2). (h) The PSF obtained without a ring mask (no aberration). Scale bar: 2 µm. (i) The relationship between the coefficient of the fourth-order spherical aberration and the intensity of the aberration-induced sidelobe $\Delta {S_2}$. The PSF main lobe obtained with (j) the single-ring mask and (k) the 14-ring mask using Method 2 is also shown. Scale bars: 0.5 µm.
Figure 3(b) shows the PSF obtained without the ring mask. Because the spherical aberration with a coefficient of 0.08λ was not large, the shape of the PSF slightly changed from that of the ideal PSF, as shown in Fig. 3(h). Figure 3(c) shows the PSF obtained with the single-ring mask; two peaks with the same intensity in the axial direction were observed. As spherical aberration occurs, the changes in the PSFs are accompanied by aberration-induced sidelobes. When the single-ring mask was applied, $\Delta {S_2}$ was 0.91. When the 4- and 14-ring masks designed using Method 1 were employed, $\Delta {S_2}$ was 0.48 and 0.31, respectively. When the single-ring mask is applied, the strength of the main lobe and aberration-induced sidelobe is the same, resulting in two focal points. Therefore, because the x–y image simultaneously contains fluorescence from the target depth and depth other than the target depth, it is acquired as if there is an object that does not exist at the target depth.
Figure 3(i) shows the relationship between the coefficient of the fourth-order spherical aberration and the intensity of the aberration-induced sidelobe $\Delta {S_2}$. Assuming that the quality of the acquired image is not significantly affected at $\Delta {S_2} \le 0.1$, the single-ring mask method can be used to observe the sample to a depth at which the coefficient of the fourth-order spherical aberration is smaller than ∼0.02λ. This amount of aberration occurs at a depth of about 20 µm in the biological sample when the water immersion objective lens with NA = 1.0 is used. A similar aberration value occurs as a residual aberration if the aberration correction is not performed strictly. The coefficient of the spherical aberration for $\Delta {S_2}$ < 0.1 was approximately 0.04λ when using the 14-ring mask. In this case, it is possible to observe up to 50 µm inside the sample without being affected by the aberration. However, the observation using the 14-ring mask requires strict aberration correction. Therefore, we attempted to design a multi-ring mask that was even more robust to spherical aberration.
3.3 PSF obtained with the multi-ring mask designed using Method 2
Figures 3(f) and 3(g) show the PSF obtained using the 4-ring and 14-ring masks designed using Method 2, respectively. The observed aberration-induced sidelobes are quite small. The $\Delta V$ obtained with the single-ring masks designed using Method 2 was 1.124 (Fig. 3(i)) while that obtained with the 14-ring masks designed using Method 2 was 1.256 (Fig. 3(k)). Fig. S4 shows the PSF variation when the excitation light beam is affected by astigmatism and coma. From Fig. S4, we confirmed that spherical aberration has the strongest effect on the PSF obtained using the ring mask.
4. Experimental results
4.1 Fluorescent beads in an epoxy resin
4.1.1 Changes in the PSF main lobe
We observed 0.1-µm-diameter fluorescent beads in a transparent epoxy resin (average refractive index n = 1.58) to verify the PSF. First, the images were acquired by switching between the non-modulated pattern shown in Fig. 4(a) and the 14-ring pattern shown in Fig. 4(b) at the same focal depth. The x–y images were acquired at 0.3-µm intervals of objective lens movement. The observed x–y and x–z images obtained with the non-modulated pattern and the 14-ring mask pattern (Method 2) are shown in Fig. 4(a) and (b), respectively. The size of the bead observed in Fig. 4(b) is clearly smaller than that of the bead observed in Fig. 4(a). Figures 4(c) and 4(d) show the line profiles in the lateral and axial directions, respectively; $\varDelta {L_{lat}}$ and $\varDelta {L_{axi}}$ were 1.138 and 1.110, respectively, as obtained via Gaussian fitting. In addition, six beads were analyzed, and the average (±standard deviation) of $\varDelta {L_{lat}}$ and $\varDelta {L_{axi}}$ were 1.097 ± 0.028 and 1.115 ± 0.022, respectively. The theoretical values of $\varDelta {L_{lat}}$ and $\varDelta {L_{axi}}$ were 1.120 and 1.104, respectively. Hence, the experimental and theoretical values were very similar.
Fig. 4. Experimental results. PSF main lobe improvement using the multi-ring mask. The 0.1-µm-diameter fluorescent bead was observed with (a) the non-modulated pattern and (b) the 14-ring pattern (Method 2). Scale bars: 0.5 µm. Line profile and Gaussian fitting results shown in the (c) lateral and (d) axial directions. The intensity of the excitation light under the objective lens was (a) 8.0 and (b) 30.9 mW.
We verified the effectiveness of a multi-ring mask-design method for suppressing the aberration-induced sidelobe. Similar to the simulation results in Fig. 3(i), where the behavior of the PSF for spherical aberration was investigated, $\Delta {S_2}$ exceeds 0.1 when the beam modulated by the single-ring mask pattern is affected by the spherical aberration with a coefficient greater than 0.02λ. Because the refractive index of the epoxy resin is higher than the average refractive index of the biological sample, strong spherical aberrations occur even at shallow depths, thereby resulting in an aberration with a coefficient of 0.02λ at a depth of 7 µm from the surface. Similarly, preliminary simulations predicted that strong aberration-induced sidelobes occur at depths greater than 10 µm for observations using the 4-ring pattern (Method 1) and at depths greater than 27 µm for the 4- and 14-ring mask patterns (Method 2).
Figures 5(a) and 5(b) show the x–z projected images obtained with the non-modulated pattern and the single-ring mask pattern, respectively. Figure 5(c) shows the image obtained with the 4-ring pattern designed using Method 1, and Figs. 5(d) and 5(e) show the images obtained with the 4- and 14-ring patterns designed using Method 2, respectively; the contrast of each image was increased by a factor of 3.4. The observed depth in Fig. 5 ranged from 0–35.7 µm. The range of small aberration-induced sidelobes for each ring mask is shown in Fig. 5(f). In Figs. 5(b) and 5(c), beads that are not originally present (indicated by the light green arrows) were observed because of the strong occurrence of the PSF sidelobes. It is of note that the depth at which the aberration-induced sidelobe appears depends on the number of rings. Figure 5(d) shows that the observed sidelobe was small. In Fig. 5(e), the sidelobe is suppressed even further and is almost not observable because of the higher number of rings.
Fig. 5. Effectiveness of a multi-ring mask design method for suppressing aberration-induced sidelobes. The region where isolated beads and aggregated beads exist was observed. The x–z projected images were obtained using the (a) non-modulated pattern, (b) single-ring mask pattern, (c) 4-ring mask pattern (Method 1), (d) 4-ring mask pattern (Method 2), and (e) 14-ring mask pattern (Method 2). (f) Range of aberration-induced sidelobe suppression. Green: single-ring mask, Orange: Method 1, Red: Method 2. Light green arrows indicate the false signal caused by the aberration-induced sidelobe. Scale bar: 5 µm.
4.1.2 Combination of multi-ring mask and spherical aberration correction patterns
The multi-ring mask designed using Method 2 is less sensitive to small aberrations than those designed by Method 1; however, aberration correction is necessary for observations at a depth where larger spherical aberrations occur. The deeper region is observed by providing the multi-ring pattern and aberration correction pattern (ACP) to the SLM simultaneously. To verify the effect of the aberration correction for a large aberration, we observed the beads at an optical depth of 119–139 µm within the epoxy resin. Under this condition, the interface between the epoxy resin and the immersion fluid (water) is almost perpendicular to the optical axis; therefore, the aberration is dominated by the spherical aberration caused by the refractive index mismatch between the sample and water. This aberration is larger than that considered in Fig. 3.
Figure 6(a), from top to bottom, shows the non-modulated pattern, the 14-ring mask pattern (Method 1), and the 14-ring mask pattern (Method 2). Figures 6(b)–6(d) show the x–z projected images obtained without the ACP, while Figs. 6(e)–(g) show those obtained with the ACP. We performed aberration correction with every 1.0 µm movement of the objective lens. The differences in fluorescent intensity for the measurements performed with the same excitation intensity are shown in the insets of Figs. 6(b) and 6(e). The power density of the excitation light beam was increased by aberration correction, thereby resulting in an improvement in the observed bead elongation and a 2.28-fold increase in fluorescent intensity. Further, Figs. 6(c) and 6(f) were obtained with the 14-ring mask pattern (Method 1), and Figs. 6(d) and (g) show the 14-ring mask pattern (Method 2). As shown in Figs. 6(c) and 6(d), respectively, it was difficult to distinguish the beads due to the spherical aberration. However, by applying the ACP and the multi-ring mask pattern simultaneously, the size of the observed beads was smaller than that obtained using the non-modulated pattern (Figs. 6(f) and 6(g)). Because the multi-ring mask designed using Method 1 has a low tolerance for aberration, strict aberration correction designed by measuring the observation depth more accurately is required to completely suppress the aberration-induced sidelobe. Therefore, in Fig. 6(f), slight aberration-induced sidelobes were observed because of a slight aberration that was not corrected. Because the multi-ring mask designed using Method 2 has a high tolerance for small aberrations, small sidelobes were observed even without strict aberration corrections (Fig. 6(g)).
Fig. 6. Experimental results. Deep-region observations with both the multi-ring masks and aberration correction patterns (ACP) applied simultaneously. The 0.2-µm-diameter fluorescent beads at an optical depth of 119–139 µm were observed. (a) The applied ring mask patterns, from the top: non-modulated, 14-ring (Method 1), and 14-ring (Method 2). The x–z projected images were obtained (b) with the non-modulated pattern and without ACP, (c) with the 14-ring mask pattern (Method 1) and without the ACP, (d) with the 14-ring mask pattern (Method 2) and without the ACP, (e) with the non-modulated pattern and the ACP, (c) with the 14-ring mask pattern (Method 1) and the ACP, and (d) with the 14-ring mask pattern (Method 2) and the ACP. Scale bar: 3 µm.
4.2 Ex vivo observation of nerve fibers and dendritic spines in a mouse brain sample
A fixed mouse brain was sliced, and the observations were made from the surface. The images were acquired from the cut surface of the sample to a depth of 18 µm at intervals of 0.3 µm of objective lens movement. Figure 7 shows the observed nerve fibers and dendritic spines. Figure 7(a), from top to bottom, shows the non-modulated pattern, and the single-ring and 14-ring mask patterns designed using Method 2. Figures 7(b)–(d) show the x–y and x–z images obtained with the non-modulated, single-ring, and 14-ring mask pattern, respectively. From the x–z image shown in Fig. 7(c), the aberration-induced sidelobe was observed with the single-ring mask pattern (green arrow). Owing to the influence of the sidelobe, the observed nerve fiber was elongated in the optical axis compared to that obtained with the non-modulated pattern (white arrow). The aberration-induced sidelobe was not observed in Fig. 7(d). Indeed, the sizes of the dendritic spine and nerve fiber in Fig. 7(d) are smaller than those of the dendritic spine in Fig. 7(b). Figures 7(e) and 7(f) show the line profiles in the lateral and axial directions, respectively, where $\varDelta {L_{lat}}$ and $\varDelta {L_{axi}}$ were 1.128 and 1.148, respectively, as obtained via Gaussian fitting.
Fig. 7. Observed nerve fiber and dendritic spine near the surface of the sample. (a) The applied ring mask pattern, from the top: non-modulated, single-ring mask (Method 1), and 14-ring mask (Method 2). The x–y and x–z images were obtained with the (b) non-modulated, (c) single-ring mask, and (d) 14-ring mask patterns. Scale bar: 2 µm. Line profile and Gaussian fitting results are shown in the (e) lateral and (f) axial directions. The intensity of the excitation light under the objective lens was (b) 27.2, (c) 58.7, and (d) 82.9 mW.
Figure 8 shows the observed nerve fiber and dendritic spines for optical depths of 100–130 µm. By applying the aberration correction, the maximum fluorescent intensity in Fig. 8(c) was 1.34 times higher than that shown in Fig. 8(b). Further, Figs. 8(c) and 8(e) were obtained with the 14-ring mask pattern (Method 2). From the comparison of Figs. 8(d) and 8(e), $\varDelta {L_{lat}}$ and $\varDelta {L_{axi}}$ were 1.085 and 1.130, respectively. Because of aberration correction, the improvement ratio when using the 14-ring mask at a deep region was the same as that when using the 14-ring mask at a shallow region.
Fig. 8. Observed nerve fiber and dendritic spines at optical depths of 100–130 µm. (a) The applied ring mask patterns, from the top: non-modulated, single-ring mask, and 14-ring mask (Method 2). The x–z projected images were obtained (b) with the non-modulated pattern and without the ACP, (c) with the 14-ring mask pattern (Method 2) and without the ACP, (d) with the non-modulated pattern and the ACP, and (e) with the 14-ring mask pattern (Method 2) and the ACP. Scale bar: 2 µm.
5. Discussion
There are two types of pupil masks: amplitude-modulation-type and phase-modulation-type pupil ring masks. When a phase-modulation-type pupil mask is applied, a high depth-of-field observation can be performed because the focusing shape of the excitation light is elongated in the optical axis direction [21–24]. It can also increase resolution in the axial direction, but with large sidelobes [25]. In contrast, as described above, if an amplitude-modulation-type ring mask is applied, a high-resolution observation can be performed because the size of the PSF in both the lateral and axial directions is improved. By switching between amplitude and phase-modulation-type ring masks using SLM, multiple microscope functions can be simply achieved. In particular, wavefront devices such as the SLM are effective for deep-region imaging. Our proposed method increases the resolution for deep imaging without requiring additional devices or changes to the optics of the system. It should be noted that the proposed method is not limited to using the SLM. If the proposed ring-mask pattern was printed on a glass or transparent film, the resolution could be increased at an extremely low cost. At this time, the observation using the multi-ring mask designed by Method 2 maintains high resolution in a deeper region than the observation using the conventional single-ring mask. Our method is superior to STED in cost performance and multi-functional imaging. Of course, our method is inferior to STED in decreasing the size of the PSF, but the size of the main lobe obtained with the multi-ring mask designed using Method 1 is equivalent to the size of that obtained with an objective lens with NA ≥ 0.05 (Fig. S5). The optimal shape of the multi-ring mask depends on the NA of the objective lens and the intensity distribution of the beam. Moreover, the multi-ring mask is effective for observation using three-photon microscopy. Since the PSF is proportional to the cube of the intensity distribution of the focused excitation light in three-photon microscopy, the influence of the sidelobe is reduced, thereby achieving a higher improvement ratio as compared with that obtained by two-photon microscopy imaging (Fig. S6).
The proposed method is effective, not only for imaging inside biological samples, but also for laser processing using multi-photon absorption because it directly improves the focusing shape of the incident light beam. However, as the NA of the objective lens increases, the aberration effect becomes stronger, and therefore, high-accuracy aberration correction becomes more important. Theoretical calculations [17–19,26] and adaptive optics [27–29] could be applied for high-accuracy aberration corrections. In particular, in the case of an oil-immersion objective lens with higher NA, we consider that it is effective to correct aberration caused by the refractive index change due to the temperature of the oil in addition to aberration caused by the sample [30,31].
Because of the amplitude-modulation-type mask, the utilization efficiency of the excitation light is reduced. The transmission of the ring mask designed by Method 1 was approximately 40–55% for a top-hat intensity distribution of the excitation light beam, and approximately 15–25% for a truncated Gaussian (wex = 0.75) distribution. The power density was reduced to approximately 20–60% when applying the ring mask. In general, the laser output power for two-photon microscopy was sufficiently larger than the power for observation, so a decrease in light utilization efficiency does not have a significant effect on observation in a shallow region. For deep observation that requires strong power excitation light, we confirmed from the simulations that slightly reducing $\Delta V$ improves both the transmission of the ring mask and the power density of the excitation light.
Sidelobes may increase background noise in order to generate fluorescence from fluorescent protein other than the observation depth. By adjusting the sidelobe allowance, it is possible to suppress the generation of background noise and prevent the signal-to-noise ratio (SNR) from deteriorating. Figure 9 shows the observed nerve fibers and dendritic spines at an optical depth of 175 µm. The upper side of Fig. 9(a) shows the non-modulated pattern, and the lower side shows the 14-ring mask patterns designed using Method 2 with $\Delta {S_2}$ < 0.07. Figure 9(b) shows the x–z projected images obtained without the ACP, while Figs. 9(c) and (d) show those obtained with the ACP. Figure 9(d) was obtained with the 14-ring mask pattern; the regions of interest were set on the background area and the nerve fiber, which is the signal area. Figures 9(e)–(g) show the histogram obtained from each region. In Fig. 9(e), the signal value is low, and the background noise value is high. Conversely, in Figs. 9(f) and 9(g), the ACP lowered the background noise value and raised the signal value. The SNRs in Figs. 9(e)–(g) were 9:1, 15:1, and 12:1, respectively. The difference between the SNRs in Figs. 9(f) and 9(g) is due to a slight increase in the background noise in Fig. 9(g). On the other hand, using Gaussian fitting, we confirmed that the size of the observed dendritic spine in Fig. 9(g) was 1.100 times smaller than that in Fig. 9(f). The deterioration of image quality due to the influence of the background may be improved by the implementation of the confocal technique [32] and image processing.
Fig. 9. Observed nerve fiber and dendritic spines at optical depth of 175 µm. (a) The applied ring mask patterns; the upper side shows the non-modulated pattern, and the lower side shows the 14-ring mask patterns designed using Method 2 with $\Delta {S_2}$ < 0.07. The x–z projected images were obtained (b) with the non-modulated pattern and without the ACP, (c) with the non-modulated pattern and with the ACP, (d) with the 14-ring mask pattern (Method 2) and the ACP. Scale bar: 2 µm. Histograms of the region of interest in (e) Fig. 9(b), (f) Fig. 9(c), and (g) Fig. 9(d) are shown.
6. Conclusions
It is known that the amplitude-modulation-type single-ring mask decreases the volume of the PSF [5–8]. We clarified that the excitation light beam modulated by the single-ring mask is strongly affected by even a slight spherical aberration that occurs during the observation inside the sample. Then, to increase the PSF improvement ratio, we evaluated the images obtained using the amplitude-modulation-type multi-ring mask [33]. In this study, we clarified the effectiveness of the multi-ring mask: 1) the PSF tends to decrease with the number of rings, 2) the optimum ring pattern that minimizes the PSF depends on the intensity distribution of the excitation light, and 3) the mask that considers the effect of the spherical aberration is effective for the observation inside the sample. We successfully observed nerve fibers and dendritic spines at optical depths of 100–175 µm in a sample using aberration correction and a ring mask designed using Method 2. We believe that our proposed method could provide a cost-effective solution for high-resolution imaging with a wide depth of field for imaging inside biological and other samples that suffer from spherical aberration due to the immersion media.
Acknowledgments
We are grateful to Y. Ohtake and T. Hara for their encouragement and to S. Kataoka, K. Nakamura, T. Miwa, M. Nagata, and Y. Ohbayashi for their invaluable assistance.
Disclosures
N. Matsumoto, T. Inoue, and K. Watanabe: Hamamatsu Photonics K.K. (E, P). S. Okazaki belongs to the endowed laboratory of Hamamatsu Photonics K.K. in Hamamatsu University School of Medicine (F). A. Konno belonged to the endowed laboratory of Hamamatsu Photonics K.K. in Hamamatsu University School of Medicine until April 2020 (F).
There are no other financial and non-financial competing interests to declare in relation to this manuscript.
Supplemental document
See Supplement 1 for supporting content.
References
1. A. Konno, N. Matsumoto, Y. Tomono, and S. Okazaki, “Pathological application of carbocyanine dye-based multicolour imaging of vasculature and associated structures,” Sci. Rep. 10(1), 12613 (2020). [CrossRef]
2. R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat Protoc 6(12), 1929–1941 (2011). [CrossRef]
3. G. Moneron and S. W. Hell, “Two-photon excitation STED microscopy,” Opt. Express 17(17), 14567–14573 (2009). [CrossRef]
4. N. T. Urban, K. I. Willig, S. W. Hell, and U. V. Nagerl, “STED Nanoscopy of actin dynamics in synapses deep inside living brain slices,” Biophys. J. 101(5), 1277–1284 (2011). [CrossRef]
5. M. Martínez-Corral, C. Ibáñez-López, G. Saavedra, and M. T. Caballero, “Axial gain resolution in optical sectioning fluorescence microscopy by shaded-ring filters,” Opt. Express 11(15), 1740–1745 (2003). [CrossRef]
6. C. Ibáñez-López, G. Saavedra, G. Boyer, and M. Martínez-Corral, “Quasi-isotropic 3-D resolution in two-photon scanning microscopy,” Opt. Express 13(16), 6168–6174 (2005). [CrossRef]
7. C. M. Blanca and S. W. Hell, “Axial superresolution with ultrahigh aperture lenses,” Opt. Express 10(17), 893–898 (2002). [CrossRef]
8. R. Oketani, A. Doi, N. I. Smith, Y. Nawa, S. Kawata, and K. Fujita, “Saturated two-photon excitation fluorescence microscopy with core-ring illumination,” Opt. Lett. 42(3), 571–574 (2017). [CrossRef]
9. M. A. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, and V. Sarafis, “Optimized pupil-plane filters for confocal microscope point-spread function engineering,” Opt. Lett. 25(4), 245–247 (2000). [CrossRef]
10. Y. Ohtake, T. Ando, T. Inoue, N. Matsumoto, and H. Toyoda, “Sidelobe reduction of tightly focused radially higher-order Laguerre–Gaussian beams using annular masks,” Opt. Lett. 33(6), 617–619 (2008). [CrossRef]
11. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical vector beams,” Opt. Express 7(2), 77–87 (2000). [CrossRef]
12. P. Török, P. Varga, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: structure of the electromagnetic field. I,” J. Opt. Soc. Am. A 12(10), 2136–2144 (1995). [CrossRef]
13. N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, “Generation of high-quality higher-order Laguerre–Gaussian beams using liquid-crystal-on-silicon spatial light modulators,” J. Opt. Soc. Am. A 25(7), 1642–1651 (2008). [CrossRef]
14. N. Matsumoto, H. Itoh, T. Inoue, T. Otsu, and H. Toyoda, “Stable and flexible multiple spot pattern generation using LCOS spatial light modulator,” Opt. Express 22(20), 24722–24733 (2014). [CrossRef]
15. G. Feng, R. H. Mellor, M. Berstein, C. Keller-Peck, Q. T. Nguyen, M. Wallace, J. M. Nerbonne, J. W. Lichtman, and J. R. Sanes, “Imaging neuronal subsets neurotechnique in transgenic mice expressing multiple spectral variants of GFP,” Neuron 28(1), 41–51 (2000). [CrossRef]
16. S. Kawai, Y. Takagi, S. Kaneko, and T. Kurosawa, “Effect of three types of mixed anesthetic agents alternate to ketamine in mice,” Exp. Anim. 60(5), 481–487 (2011). [CrossRef]
17. M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc. 192(2), 90–98 (1998). [CrossRef]
18. I. Escobar, G. Saavedra, M. Martinez-Corral, and J. Lancis, “Reduction of the spherical aberration effect in high-numerical-aperture optical scanning instruments,” J. Opt. Soc. Am. A 23(12), 3150–3155 (2006). [CrossRef]
19. N. Matsumoto, T. Inoue, A. Matsumoto, and S. Okazaki, “Correction of depth-induced spherical aberration for deep observation using two-photon excitation fluorescence microscopy with spatial light modulator,” Biomed. Opt. Express 6(7), 2575–2587 (2015). [CrossRef]
20. G. D. Love, “Wave-front correction and production of Zernike modes with a liquid-crystal spatial light modulator,” Appl. Opt. 36(7), 1517–1524 (1997). [CrossRef]
21. E. J. Botcherby, R. Juskaitis, and T. Wilson, “Scanning two photon fluorescence microscopy with extended depth of field,” Opt. Commun. 268(2), 253–260 (2006). [CrossRef]
22. H. Guo, X. Weng, M. Jiang, Y. Zhao, G. Sui, Q. Hu, Y. Wang, and S. Zhuang, “Tight focusing of a higher-order radially polarized beam transmitting through multi-zone binary phase pupil filters,” Opt. Express 21(5), 5363–5372 (2013). [CrossRef]
23. G. Meng, Y. Liang, S. Sarsfield, W.-C. Jiang, R. Lu, J. T. Dudman, Y. Aponte, and N. Ji, “High-throughput synapse-resolving two-photon fluorescence microendoscopy for deep-brain volumetric imaging in vivo,” eLife 8, e40805 (2019). [CrossRef]
24. Y. Xu, J. Singh, C. J. R. Sheppard, and N. Chen, “Ultra long high resolution beam by multi-zone rotationally symmetrical complex pupil filter,” Opt. Express 15(10), 6409–6413 (2007). [CrossRef]
25. M. Martínez-Corral, M. T. Caballero, E. H. K. Stelzer, and J. Swoger, “Tailoring the axial shape of the point spread function using the Toraldo concept,” Opt. Express 10(1), 98–103 (2002). [CrossRef]
26. N. Matsumoto, A. Konno, T. Inoue, and S. Okazaki, “Aberration correction considering curved sample surface shape for non-contact two-photon excitation microscopy with spatial light modulator,” Sci. Rep. 8(1), 9252 (2018). [CrossRef]
27. T. J. Gould, D. Burke, J. Bewersdorf, and M. J. Booth, “Adaptive optics enables 3D STED microscopy in aberrating specimens,” Opt. Express 20(19), 20998–21009 (2012). [CrossRef]
28. N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7(2), 141–147 (2010). [CrossRef]
29. K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6(1), 7276 (2015). [CrossRef]
30. S. F. Gibson and F. Lanni, “Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy,” J. Opt. Soc. Am. A 8(10), 1601–1613 (1991). [CrossRef]
31. J. Li, F. Xue, and T. Blu, “Fast and accurate three-dimensional point spread function computation for fluorescence microscopy,” J. Opt. Soc. Am. A 34(6), 1029–1034 (2017). [CrossRef]
32. J. Tanga, J. Rena, and K. Y. Han, “Fluorescence imaging with tailored light,” Nanophotonics 8(12), 2111–2128 (2019). [CrossRef]
33. M. Martínez-Corral, L. Muñoz-Escrivá, M. Kowalczyk, and T. Cichocki, “One-dimensional iterative algorithm for three-dimensional point-spread function engineering,” Opt. Lett. 26(23), 1861–1863 (2001). [CrossRef]
