In this paper, we report the enhancement of resolution of continuous wave (CW) stimulated emission depletion (STED) microscopy by a novel method of structured illumination of an excitation beam. Illumination by multiple excitation beams through the specific pupil apertures with high in-plane wave vectors leads to interference of diffracted light flux near the focal plane, resulting in the contraction of the point spread function (PSF) of the excitation. Light spot reduction by the suggested standing wave (SW) illumination method contributes to make up much lower depletion efficiency of the CW STED microscopy than that of the pulsed STED method. First, theoretical analysis showed that the full width at half maximum (FWHM) of the effective PSF on the detection plane is expected to be smaller than 25% of that of conventional CW STED. Second, through the simulation, it was elucidated that both the donut-shaped PSF of the depletion beam and the confocal optics suppress undesired contribution of sidelobes of the PSF by the SW illumination to the effective PSF of the STED system. Finally, through the imaging experiment on 40-nm fluorescent beads with the developed SW-CW STED microscopy system, we obtained the result which follows the overall tendency from the simulation in the aspects of resolution improvement and reduction of sidelobes. Based on the obtained result, we expect that the proposed method can become one of the strategies to enhance the resolution of the CW STED microscopy.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
To overcome diffraction limit in resolution of the conventional fluorescence microscopy, stimulated emission depletion (STED) microscopy was introduced by S. W. Hell a quarter century ago . STED microscopy allows to achieve resolution in the range of several tens of nanometers by focusing temporally and spatially controlled depletion beam to suppress the spontaneous emission of the excited fluorophores . In a STED microscope, as a periphery of the excited spot region is superimposed by the donut-shaped depletion spot, spontaneous emission in the outer region of the point spread function (PSF) is suppressed because of stimulated emission induced by the depletion beam, resulting in the reduction of effective PSF below the diffraction limit. As a result, even though both the excitation PSF and the depletion PSF are governed by the optical properties of the diffraction, the effective PSF of the STED microscope breaks the diffraction limit.
It is well known that depletion of spontaneous emission greatly depends on the amount of photons in the depletion beam that are encountered by excited fluorophores before a possible spontaneous emission . Thus, even if operated at the same time-averaged power, pulsed systems yield higher resolution with 4–6 times higher depletion efficiency than continuous wave (CW) mode systems [3,4]. Although studies on a pulsed STED microscopy have shown that sophisticated temporal pulse control became possible in many laboratories, the disadvantages of applying expensive pulsed visible lasers and complex pulse preparation have hampered wider use of STED microscopy. On the other hand, CW STED microscopy has a merit that a temporal pulse control is not required, and hence, a compact STED optical system can be implemented. Moreover, the use of CW lasers makes CW STED microscopes more cost-effective than pulsed STED microscopes . In addition, relatively low resolution of the CW STED microscopy can be greatly improved by using gated CW STED method that has been actively researched in recent years [5–8]. Therefore, if the size of the effective PSF can be further reduced using the optical systems of conventional CW STED microscopes, it is expected that even higher resolution can be realized through the gated STED method.
Generally, the resolution of STED microscopy can be improved by applying higher power of depletion beam. K. Willig et al. achieved high resolution applying near infrared depletion beam with very high power of 825 mW . However, in the case of imaging real biological specimens in STED microscopes, multi-color STED is required to observe living cells, for example respiratory syncytial virus particles, more accurately. Multi-color STEDs inevitably require multiple wavelength bands for excitation and depletion. Visible depletion beam with the wavelength of 592 nm has been broadly applied in precedent researches for multi-color STED. When the depletion beam with 592 nm is used, the depletion power is applied in the regime of 200-370 mW to prevent photobleaching of the specimen, and the obtained FWHM of detected PSF is ranged from 95 to 115 nm [9,10]. Therefore, to achieve better resolution, it is much more effective to reduce the spot diameter of the excitation beam in the case of the CW STED microscopy.
In this paper, we report on the improvement of the resolution of the CW STED microscopy by standing wave (SW) illumination, namely the SW-CW STED microscopy. It is generally known that a very sharp interference pattern is achieved by illuminating the light flux through opposite lens or through only high aperture angle of the objective lens with the use of, e.g., dipole-shaped or quadrupole-shaped apertures [11–15]. The first method, illuminating the light flux through opposite lens, is known as 4pi microscopy, which improves axial resolution of confocal microscopy. Although there is image degradation due to side lobe generation by interference in the early days, as the research such as image processing for side lobe elimination progressed, 4pi microscopy has become a technology that can successfully improve the axial resolution . Similarly, the second method, which we applied to CW-STED microscopy, generates sharpen interference pattern in lateral axis. However, in most of the cases, with modulation in the entrance pupil of the optical system, significant level of sidelobes in the focal region is induced. For this reason, this method cannot be applied widely in the conventional fluorescence microscopy, except Structured Illumination Microscopy (SIM) and some applications [12,15,17], which have their unique way to eliminate the influence of side lobes. On the other hand, it is expected that suppression of spontaneous emission around the sidelobes of the excitation beam by the donut-shaped depletion beam can compensate the effect of the sidelobes on the effective emission PSF. The schematics of the conventional STED and SW-CW STED microscopy are shown in Fig. 1. Compared to the conventional STED microscopy setup, the incident light flux of the excitation beam of the SW-CW STED microscope is separated into multiple localized light fluxes passing through the aperture to induce interference at focal point. Thus, the excitation PSF is spatially modulated, resulting in thin interference fringe. Theoretically, if the sidelobe region with high intensity is perfectly matches to the peak intensity region of the depletion beam, the sidelobe effect can be minimized. Therefore, shrinkage of the excited area by SW excitation beam and depletion beam can improve the resolution of the CW STED microscopy.
2. Theoretical backgrounds
To calculate the electric field and the resultant PSF near the focal plane of the proposed SW-CW STED microscopy, the optical configuration, which obeys Abbe’s sine condition, is considered as shown in Fig. 2. For the system illuminated by the rotationally symmetric incident light flux, it is preferred to use cylindrical coordinate basis to calculate the electric field near the focal plane. In such case, the diffraction integral over the azimuthal angle of the exit pupil can be simplified to the Bessel function, and therefore, the electric field in the near-focus region can be easily calculated [18,19]. However, for the SW-CW STED microscopy, it is hard to take account of the effect of the light flux passing through the dipole-shaped or quadrupole-shaped aperture in cylindrical coordinate basis because of its rotational asymmetry. Therefore, in this study, to consider the effect of arbitrary shaped aperture, the diffracted electric field at the specific position (xp, yp, zp) near the focal plane is defined in the Cartesian coordinates just as follows [18,19]:20]. In addition, E0 represents the plane wave in the entrance pupil of the incident light including polarization status. For example, the linearly polarized light in the x-direction can be described as E0 = [1, 0, 0] for [Ex, Ey, Ez].
In the case when light flux is modulated in either amplitude or phase, plane wave potential vector E1 can be described as20].
In this study, it is important to make the one-dimensional spot profile sharp in the sample imaging plane. Therefore, the analysis was performed for only two types of apertures as shown in Fig. 3. An analysis of these examples will be presented in the next section. The considered apertures in the entrance pupil for the SW-CW STED microscopy are shown in Fig. 3. In case of applying a dipole-shaped aperture without phase modulation as shown in Fig. 3(a), Am(kx,ky) has the same state as E0 for kx and ky satisfying the condition
For another aperture example as shown in Fig. 3(b), Am(kx,ky) has the same state with E0 for kx and ky satisfying the condition
In both cases, Am(kx,ky) = 0 in the pupil region that does not satisfy the corresponding condition, Eq. (3) or (4). The effective fluorescent PSF at the sample plane considering the effect of depletion of spontaneous emission is defined as IEffective = IExcitation·η(IDepletion), where η(IDepletion) = 1/(1 + IDepletion/ISaturation) for the CW STED and η(IDepletion) = exp[-(ln 2)·IDepletion/ISaturation] for the pulsed STED [4,21]. ISaturation is generally defined as the depletion intensity at which the rate of stimulated emission equals to the spontaneous decay rate. In addition, in the confocal microscopy, a spatial pinhole is used to increase optical resolution and the contrast of image by blocking out-of-focus light in image formation; hence, the resultant PSF at the detection plane should be calculated considering resolution enhancement by spatial filtering pinhole. The confocal PSF modulation is expressed as [15,22–24]:
3. Simulation Results
In this section, the excitation PSFs in the image plane induced by illumination of excitation beam and the effective emission PSF induced by the depletion beam on the fluorescent sample are analyzed considering the amplitude modulation according to various aperture shapes in the entrance pupil. Next, through the analysis of the resultant detection PSF, the resolution enhancement of the STED system achieved by simple amplitude modulation is investigated. For this purpose, we have analyzed imaging characteristics in various cases with different types of apertures. However, we only discuss cases with apertures shown in Fig. 3(a) and 3(b), as those cases yield representative result on improvement of resolution. Generally, in the high-resolution STED microscopy, as the exit surface of an objective lens contacts the liquid with the refractive index appropriately matched to the refractive index of the measurement sample, the NA of the optical system is capable of exceeding 1.0. In our simulation, the system NA was fixed at 1.4 with NA0 of the objective lens taken as 0.933 and the refractive index of the measurement sample equaled to 1.5. Linearly polarized light in the y-direction with the wavelength of 488 nm and circularly polarized light with the wavelength of 488 nm were considered for the cases of SW excitation and of the conventional excitation, respectively. Circularly polarized light was considered for the illumination of depletion beam. Obviously, it was assumed that a pupil aperture is placed in the path of the excitation beam only. In addition, in most CW STED experimental researches which apply the excitation beam and the depletion beam with wavelengths of 488 nm and 592 nm, respectively, ~200-370 mW of depletion power has been used to cope with phototoxicity of the fluorescent sample. And the obtained resolution of the CW STED microscopy is ranged ~95-115 nm. Therefore, we set the wavelengths of 488 nm and 592 nm for the excitation beam and the depletion beam, respectively, and we obtained simulation parameter which yields 108 nm of FWHM for the case of conventional CW STED, and it was applied to whole simulations to analyze effect of SW-CW STED. For calculation, it corresponds to 2.25 of IDepletion when the saturation intensity ISaturation is set to be 1. For the simulation, we used the commercial calculation software (Matlab, Mathworks Inc., Natick, MA).
Figures 4 and 5 show the excitation PSFs and effective emission PSFs in the image plane on the surface of the measurement sample for various values of blocking ratio ρ in the cases shown in Fig. 3(a) and 3(b), respectively. In the case with the dipole aperture in the entrance pupil, as the light flux transmitted through the low ky region in the entrance pupil is imaged, the resolution in the y-direction on the image plane of the sample is very low compared to the x-direction. This tendency becomes worse with the increase of ρ. In addition, in the region beyond 300 nm from the optical axis in the image plane where the intensity of the depletion beam is greatly reduced, the fluorescence emission by the excitation beam is not sufficiently suppressed. Therefore, as shown in Fig. 4(c) and 4(d), the effective emission PSF gets higher sidelobes, especially in the profile in the y-direction.
In the case when the aperture blocks the central region of the incident light flux in the entrance pupil as shown in Fig. 3(b), the light flux having axially confined intensity in the x-direction perpendicular to the polarization direction of the incident light flux is induced by the diffraction of light with high values of kx, as it can be observed in Fig. 5(a). As a result, it provokes huge sidelobe along the x-direction. However, as shown in Fig. 5(c), the STED effect induced by the depletion beam effectively suppresses the fluorescence emission in the large sidelobe region along the x-direction. On the other hand, as shown in Fig. 5(b), the spatial resolution of y-direction is lower than that of x-direction. This is mainly originated from the diffraction of light flux with low values of ky together with high values of ky. Moreover, unlike the PSF in the x-direction, the resolution is further reduced by the contribution of the longitudinal Ez component, which has significant optical path difference along the y-axis. However, the analysis of the FWHM of the PSF reveals that because of the STED effect the effective area of the fluorescence emission from the sample does not broaden remarkably compared with the case where the aperture is not applied. Therefore, based on the results shown in Figs. 4 and 5, we concluded that central flux blocking aperture in the entrance pupil yields superior imaging characteristics to the other case with the dipole shaped aperture in the aspects of achievable resolution in both x- and y-direction s on the image plane of the detector.
To obtain the PSF on the detection plane, we considered spatial filtering effect by the pinhole based on Eq. (4). Figure 6 shows confocal PSFs and the effective emission PSFs in the x- and y-directions on the detection plane for various values of blocking ratio, ρ, in the configuration of the central flux blocking aperture. From the results of PSF calculation, it is clearly observed that the FWHM of the PSFs and the amount of sidelobe is reduced by spatial filtering effect in the pinhole at the detection plane. Evidently, by applying the linearly polarized light in the y-direction, it is impossible to obtain higher resolution in the y-direction on the detection plane parallel to the direction of polarization than in the case without pupil modulation. However, in the case with central flux blocking aperture, it can be noticed that degradation in resolution in the y-direction is appropriately minimized.
Figure 7 shows the dependences of the FWHM of the PSF in x- and y-directions at the detection plane on the blocking ratio ρ of the central flux blocking aperture compared with that of the conventional CW STED microscopy with circularly polarized incident light flux without aperture. In case of the conventional CW STED microscopy, the beam spot profile is the same in both x- and y-directions because of the circular polarization of light. The FWHM of the PSF in the x-direction remarkably decreases by more than 25% when the blocking ratio is higher than 0.6, and the increase of the FWHM of the PSF in the y-direction is appropriately suppressed by less than 10% compared to the conventional CW STED case. The ratio of the height of the sidelobe to the height of the main-lobe is plotted on the right y-axis according to the blocking ratio ρ. Although the sidelobe height increases as the value of ρ increases, it is less than 6% of the ratio value used in this paper.
It is necessary to compare results with the dipole aperture and the central blocking aperture to results with the quadruple aperture and the crossed area flux blocking aperture. In Appendix, we represent the shape of apertures, and calculation results are compared with the result with the proposed aperture.
4. Experimental results and discussion
To verify the resolution enhancement experimentally, we constructed the optical system of the SW-CW STED microscopy as shown in Fig. 8. Generally, it is a standard CW STED microscopy setup, except for the additional excitation path for SW illumination. A Ti:sapphire femto-second (FS) laser (Chameleon Ultra II, Coherent Inc., Santa Clara, CA, USA) was used as an excitation source. Laser beam at 780 nm from the FS laser source passed through the super-continuum device (FemotoWHITE 800, NKT Photonics, Birkerød, Denmark) and a color filter to generate a pulsed excitation beam at 488 nm. After passing a half-wave plate (HWP), the excitation beam was divided into two paths, conventional illumination path and SW illumination path, via flip mirror (FM1). Then, both paths were coupled to polarization maintaining fibers and collimated by lenses. In conventional illumination path, the polarization of the beam was maintained circular by the quarter wave plate (QWP). In the SW illumination path, collimated light flux was modulated by an aperture after it passed Glan-Thompson polarizer (GTH10M-A, Thorlabs Inc., NJ, USA) to enhance degree of polarization. Then both paths were merged by the flip mirror FM2. By flipping both FM1 and FM2, the illumination mode could be switched between conventional and SW. The depletion beam was generated by 592 nm CW laser (2RU-VFL-P-1000-592-B1R, MPB Communications Inc., QC, Canada) and then converted to donut-shaped by the vortex phase plate (VPP-1a, RPC Photonics, NY, USA). Refractive index was matched between the objective lens and the measurement sample by applying the index matching oil with the index of 1.5. Fluorescence light from the sample was spectrally filtered by dichroic mirrors and emission filters (ZT561rdc-UF3, ZT594dcrb-UF3, and ET525/50m, Chroma Technology Corp., VT, USA, respectively). Then, it was focused by a tube lens onto the multi-mode fiber with core diameter of 62.5 μm, which also worked as a pinhole of the confocal microscopy. Finally, it was detected by an APD module (SPCM-AQRH-15-FC, Excelitas Technologies Corp., MA, USA).
To confirm the simulated resolution enhancement by the SW-CW STED microscopy, we investigated imaging characteristics of fluorescent beads with several central blocking apertures with different blocking ratio ρ as shown in Fig. 9. Prior to fluorescent beads imaging, 80 nm gold nano-beads were imaged to check the STED microscope system and the resolution at each wavelength used in the microscope. As gold nano-beads are not fluorescent, it is generally used to confirm extent of the optical alignment and the maximum resolution without STED effect.
Figure 10 shows 80 nm gold nano-beads images of different beam condition. Each images is obtained in xy-plane under the imaging condition of 10 × 10 μm2 with 20 nm pixel resolution. Each images are, respectively, cases of the depletion beam, the conventional circularly polarized excitation beam, and the proposed SW excitation beam with blocking ratios of ρ = 0.4, 0.5, 0.6, and 0.7. Figures 10(a) and 10(b) confirm that focal spots with conventional confocal of excitation beam and the donut-shaped depletion beam are well formed. In addition, as it is expected through the simulation result shown in Fig. 6(a), confocal images by the SW excitation beam enhances the resolution in x-direction compared with the confocal microscope image by conventional excitation beam. In addition, as the blocking ratio increases, the resolution of the main-lobe is enhanced and the sidelobe increases. To confirm this aspect, the profile of the enlarged spot of each image is shown in Fig. 10(g). The values of FWHM for several images listed in Figs. 10(a)-10(f) are summarized in Table 1. As listed in Table 1, experimental results are very close to those of simulation results. We judged that small deviation from the simulation results is caused by the effect of actuator drift during scanning by PZT and aberration due to possible misalignment of the optical axis.
Figure 11 shows experiment results of fluorescent bead imaging using SW-CW STED microscopy and CW STED microscopy for various depletion power condition to investigate the resolution improvement by STED effect. For SW cases, the central blocking aperture with ρ = 0.6 is used. We attached yellow-green fluorescent beads with diameter of 40 nm (FluoSpheres, F8795, Molecular Probes, Thermo Fisher, MA USA) to poly-L-lysine coated cover slips and mounted them in 2,2'-Thiodiethanol (Sigma-Aldrich, MO, USA). During the measurement, it was feasible to avoid serious photobleaching problem by selection of appropriate depletion beam power under 300 mW at pupil of the objective lens. In Fig. 11, images are taken by scanning the sample with conditions of 16 × 16 μm2 of 20 nm pixel resolution, and dwell time of 16 μs. In both cases of the conventional STED and SW-CW STED, the same sample area is scanned with different depletion power conditions. Figure 12(a) shows the FWHM values for several conditions of illuminations according to the depletion beam power from 0 to 3 W. Basically, from the theoretical point of view, as the depletion beam power becomes stronger, the resolution greatly increases for all cases. Even though the value of SW-CW STED is steadily smallest, the difference of the values becomes very small, as the depletion beam power increases. However, in the effective range of the depletion beam power dominantly applied in CW microscopy, there is more than 20 nm difference compared to the conventional CW STED. Figure 12(b) summarizes the FWHM values of Fig. 11. Each FWHM value was obtained by calculating the average value of the 30-60 spot profiles excluding aggregated beads of each image through the numerical detection using the circular Hough transform method. As shown in this, it can be seen that measured FWHM values similar to those of the simulation are measured, and the changes in resolution (x-axis, y-axis) versus depletion power were verified through simulation and experiments.
In Fig. 13, by showing confocal images with 0 mW and STED images with 300 mW, both the conventional CW STED method and the proposed SW STED method are directly compared. When we performed this experiment, the same area of the same fluorescent bead sample is imaged, and the scanned area was 5.2 × 4 μm2. Please note that depletion power 0 mW corresponds to confocal mode for each case. In Fig. 13(a), the visualized images apparently show that the SW-CW STED microscopy enhances lateral resolution of fluorescence image when the depletion power is the same in the short axis (x-axis). Intensity profiles of comparing spots with white arrows are shown in Fig. 13(b). Measured FWHM values along x-axis for the cases of the conventional confocal, the conventional STED, the SW confocal and the SW-CW STED were 178 nm and 102 nm, 104 nm, and 80 nm, respectively. In the case of the SW-CW confocal method, as expected from the simulation, the measured profile yields smaller FWHM value with considerable amount of sidelobe. However, when the depletion beam is applied, the resolution is greatly improved with suppressing sidelobes due to STED effect.
In the light of experimental confirmation of the resolution enhancement, it is clear that integration of SW illumination into the CW STED microscopy could compensate low depletion efficiency of conventional CW STED microscopy.
In this paper, to overcome inherent limitation of the conventional CW STED microscopy originated from low depletion efficiency, we proposed SW-CW STED microscopy with the SW in focused excitation spot based on STED microscopy. Even though forming of an image with SW by amplitude modulation of excitation beam in the entrance pupil yield highly confined spot profile along the optical axis, it naturally generates sidelobes. SW-CW STED microscopy in this study was motivated by the facts that fluorescence emission induced by sidelobes of SW excitation beam can be properly suppressed by depletion beam and that spatial filtering in the confocal system additionally cuts the contribution of emission from sidelobes off. In this paper, a sequential process to obtain the PSF in the image plane of the detector is suggested. Our core concept was supported by the results, which yield the improvement of resolution by as much as 24% in the best case. Among various types of apertures generating SW imaging, the central flux blocking aperture was selected, as it yields the best resolution improvement in the x-direction, which is perpendicular to the direction of polarization, and weak resolution degradation in the y-direction, which is parallel to the direction of polarization.
In the experimental part of the study, first, the influence of the amplitude modulation on the detection of the PSFs of the confocal microscopy was examined by the analysis of non-fluorescent gold nano-beads images. To verify the resolution enhancement using SW-CW STED imaging, imaging of fluorescent beads with a diameter of 40 nm was performed. The predicted ratio of the resolution enhancement in the direction perpendicular to the polarization direction was achieved by more than 25% in a single direction.
On the other hand, we anticipate that further efforts will be needed to evolve the results of this study into superresolution fluorescence imaging for complex structures. First, it is expected that the weak sidelobe effect, as confirmed by simulation and experiments, will cause a slight image quality degradation. We expect to be able to overcome complex imaging structures such as biological imaging or aggregated beads through methods such as image processing based on repeated imaging data to achieve perfect superresolution imaging. As reported in , the shape of the aperture can be continuously changed in a single optical path by using a spatial light modulation element, and the polarization direction of the incident light beam can be changed by utilizing a simple electro-mechanical actuator such as a step motor. As this method requires acquisition of numbers of images by changing incident polarization state and the shape of aperture, influence of photobleaching can be a technical issue. Therefore, we conclude that the resolution of the CW STED microscopy can be greatly improved in either direction on the image plane by applying sequential spatial light modulation with the aperture shape proposed in this study. Second, the axial resolution achievable using the proposed microscope system is similar to that of confocal microscopy, which does not have STED effects. The measurement results for the axial direction PSF are given in the appendix. Therefore, the SW-CW STED microscopy proposed through this study can be used directly to improve the 2D resolution of biological imaging. In addition, the SW-CW STED microscopy can further improve 3D resolution by incorporating many previous studies that can improve axial resolution. For example, by scanning multiple images while modulating the excitation beam, reconstructing the axial image of each axial section  or applying depletion beam modulation by phase mask can improve resolution both horizontally and axially [21,25]. Furthermore, in prospect, the application of the time-gated detection method, which was successfully employed to improve the resolution of the CW STED microscopy, to the SW-CW STED system will allow to provide resolution comparable to that of the pulsed STED system, and more enhanced resolution will be possible. To obtain ideal resolution improvement compared to CW STED microscopy, our subsequent research will focus on resolution improvement in either direction on the image plane by applying sequential spatial light modulation. eliminating the effects of sidelobes completely by image processing.
In the case of applying the aperture with the symmetrical shape as shown in Fig. 14, if the circular polarization with the rotationally symmetric polarization state is illuminated, the resolution improvement effect in both directions can be obtained. However, in these cases, the resolution improvement effect is much weaker than the case of illumination with the illumination by y-linearly polarization. Also, in the case quadrupole illumination, when the incident light beam linearly polarized in y-direction is applied, the one dimensional resolution improvement effect is reduced by diffraction of light flux with lower wave vectors. In the case of applying cross area flux blocking aperture, resolution in the x-direction is slightly lower than the proposed central flux blocking aperture. This study was intended to ensure obvious resolution improvement in one direction, minimizing deterioration of resolution in the vertical direction. The two representative aperture shapes as shown in Fig. 3(a) and 3(b), increase the resolution of 1D to similar level. However, as described in the paper, two cases yield very large difference in the resolution of the vertical axis. Therefore, we selected the central blocking aperture to obtain higher resolution in one direction and to minimize deterioration in resolution in its vertical direction.
For both types of aperture, ρ was set to 0.5, and resultant PSFs are compared with the PSFs by the proposed central block aperture with ρ = 0.5. Simulation results for various illumination conditions are shown in Figs. 15 and 16.
In order to check the resolution in the axial direction, the gold beads image in the xz-plane is measured as can be seen from the results shown in Fig. 17. The axial resolution achievable using the proposed microscope system is similar to that of confocal microscopy, which does not have STED effects. This is because, as can be seen in Fig. 17(c), the intensity of the depletion beam along the axial direction in the focus area follows the Gaussian profile and resultantly there is no increase in resolution due to depletion beam. In the end, the axial resolution of the STED microscope is similar to the axial resolution of the confocal microscope, unless an additional depletion modulation is introduced that leads the axial intensity profile of the depletion beam to be similar to the depletion beam intensity profile of the lateral direction. See Table 2 for a list of FWHM of PSFs in the x-direction on several observation plane considering various conditions of illumination and types of apertures.
National Research Foundation of Korea (NRF) (2015R1A5A1037668, 2017R1D1A1B03036114).
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