Abstract
The feasibility of stimulated emission depletion (STED) microscopy using a solid immersion lens was investigated. First, the theoretical feasibility of the considered system is discussed based on a vectorial field algorithm that uses a stratified medium composed of a SIL air-gap and test sample. Using the simulation, we verified that evanescent waves with much higher spatial frequencies corresponding to the high numerical aperture in the air-gap can be utilized to achieve a higher resolution than a confocal fluorescent image without a depletion beam. The simulated expectation was supported by actual imaging on two types of samples: fluorescent beads with a 20 nm diameter and an actin sample with a filamentous structure. The lateral resolution of the system was determined to be 34 nm via the imaging results on the nano-beads. The system was quite promising for achieving nano-scale surface imaging of biological samples; an even higher resolution was achieved by adjusting the wavelength and the intensity of the depletion beam.
© 2017 Optical Society of America
1. Introduction
During the past 20 years, there has been significant research on super resolution microscopy to increase the resolution up to nanoscale by overcoming the diffraction limit that is imposed on conventional far-field optical imaging systems [1–3]. STED [4, 5], which was invented by S. W. Hell, is a type of super resolution fluorescence microscopy that deactivates fluorescence in the focal volume using STED. In this technique, two laser beams of different wavelengths are applied: the first beam is called the excitation beam, which is used to excite fluorophores, and the other beam is a red-shifted beam, called the depletion beam, which induces stimulated emission. Generally, the excitation beam induces normal fluorescence by exciting electrons in a focused area from the ground state to the excited state of a different fundamental energy level. Within several nanoseconds, exited fluorophores spontaneously emit photons after its fast relaxation. If the depletion beam is focused on a specific area before spontaneous emission of the excited fluorophores, it deactivates the fluorescence over the focused area as it forces fluorophores to a higher vibrational state that has a narrow bandgap energy. Therefore, in the focused energy volume, fluorescent emissions can effectively be suppressed. In addition, because a helical phase modulator is used to generate a doughnut-like focus volume by the depletion beam, it is possible to enhance the resolution by imaging spontaneous emissions that have an emission area that is significantly squeezed by the STED.
To obtain a higher STED efficiency and higher fluorescence resolution, a large number of incident photons are needed for the depletion beam to suppress the fluorescence. Therefore, a depletion beam must be of a high intensity. However, as the depletion beam obtains a higher intensity, it is much more likely to induce photobleaching and even photo-toxicity on the fluorophores. In addition to applying a high intensity depletion beam, the optical resolution of the STED microscopy can be enhanced by using a higher numerical aperture (NA) to focus the optics [6, 7]. Fundamentally, it is impossible to obtain a NA for the optics that is higher than the refractive index of the material that light focuses. The widely used method to increase the NA of a microscope is to use immersion liquids between the bottom lens of the objective and the cover glass. However, the specific limit for the NA of oil immersion system is up to 1.4 due to restricted refractive index of medium. Because the absorption and emission spectra of the fluorophore are nearly fixed, there is a specific restriction for enhancing the optical resolution by applying a light source with a lower wavelength to the confocal microscope.
By filling the entire imaging space with a material that has a high refractive index, an extremely high NA can be achieved [8,9]. Practically, it can be constructed by placing a truncated spherical solid immersion lens (SIL) between the focusing objective and sample of interest. SIL-based NF optical systems have been actively studied in the field of optical information storage since it was discovered that detection of the near-field air-gap distance was feasible using the principle of total internal reflection based on Fresnel’s rhomb. Application of the abovementioned principle as the control reference has been used to control the near-field air-gap, even with a disc rotation of thousands of revolution per minute [10,11]. Based on active and robust near-field air-gap control, the application of a SIL to near-field optics has been achieved in the field of information storage systems [12–14].
For application to STED microscopy, innovative work has been performed to address single spins with a resolution of as low as 2.4 nm by applying a SIL to STED microscopy of single nitrogen vacancy (NV) centers [15]. In that configuration, because the STED addresses individual NV centers inside a SIL composed of bulk diamond, an extreme resolution can be achieved with a relatively high intensity of the depletion beam. However, this study only imaged the NV centers inside the diamond SIL, and could not measure the specimen outside the SIL due to the structure of the SIL they used. Therefore, until now, there have been no bio-sample imaging results from a SIL-based STED microscope. To realize this, we design the SIL structure to image the external specimen, and perform simulations and experiments by using designed SIL. Then, we describe the theoretical feasibility of STED microscopy-based vector field diffraction in a stratified medium structure and report some experimental results on imaging bio-samples that agree well with the simulated result. In conclusion, we discuss the feasibility of high resolution imaging with a SIL-based STED, with the use of a near-field air-gap for dynamic gap control between the SIL and cover glass, which protects the bio-sample.
2. Theoretical background of the SIL-based near-field optics
As discussed in [16] and in Fig. 1, when rays are refracted on the spherical surface of a truncated sphere with refractive index ns in a homogenous optical medium with a refractive index n < ns, there are three aplanatic positions at which the spherical aberrations and coma are free. These three positions are the vertex position of the truncated sphere, center of the sphere and position of the super-hemisphere that has thickness from the vertex of the truncated sphere to the position that is equal to (ns + n)/ns times the radius of a sphere. Among these three positions, the center of the sphere is much more tolerant to spherical aberrations due to the thickness error of the truncated sphere, which is a SIL. In addition, for application to STED microscopy, as light sources with different wavelengths are used, the center of the sphere should be used to ensure aberration-free imaging for those two wavelengths. Generally, in SIL-based near-field optics, the bottom surface of the hemispherical SIL is located precisely at the geometric focal position of the pre-focusing lens and the NA of the optics is defined as nSIL·sin(αm). For the SIL, optical materials with a high refractive index exceeding 2.0 are applied. In earlier applications of information storage systems, several materials, such as LaSF35, KTaO3 and diamond, were used [17–20]. For example, by using a hemispherical SIL with KTaO3, it is possible to obtain a high NA of as much as 1.8 by using a high refractive index of 2.23 at a wavelength of 780 nm.
Fundamentally, an optical configuration with a hemispherical SIL obeys Abbe’s sine condition, as shown in Fig. 2. For an aplanatic system that satisfies the sine condition, the electric field at the Gaussian focus is given by the cylindrical coordinates (r, ϕ, z) near the Gaussian focus, which is given by [21]
where rp, ϕp, and zp are cylindrical coordinates on the image plane inside the stratified media and kiz and k1z are the longitudinal components of the propagation vector in ith medium and the first medium, respectively. k0 and k1 are propagation vectors in free space and the first medium, respectively, and kr is the radial component of the propagation vector. The upper limit of the integral, krmax, should be set to k0·sinθmax. The matrices, Πi ± , are the solved forms of the integral over the azimuthal entrance pupil angle, kϕ, with respect to the propagation matrix, which describes the vector rotation and transmittance and reflection coefficients in each medium at the entrance pupil. A detailed derivation of the propagation matrix can be found in [21]. Πi ± for the incident linear, circular, radial, and azimuthal polarizations are defined, respectively, as:where , and JN(rkr) are the Nth Bessel functions of the first type. The detailed derivation of the coefficient, , is given in [21].Generally, in STED microscopy, to achieve an extreme resolution in the lateral plane, a 0–2π vortex phase modulator is placed in the optical path of the left-hand circularly polarized depletion beam [22]. Theoretically, the electric field at the entrance pupil of the imaging optics, after it passes the 0–2π vortex phase plate, can be described as azimuthal polarization. Therefore, the focused electric field of the depletion beam can be calculated using the matrix Π ± i azimuthal defined in Eq. (2). When applying a vortex phase plate to generate a donut-like spot profile for the depletion beam, the theoretical intensity distribution achieved by the STED is defined as Iresultant = Iexcitation * η(Idepletion), where η(Idepletion) = 1/(1 + Idepletion/Isaturation) for continuous wave operation of the STED and η(Idepletion) = exp[-(ln 2)Idepletion/Isaturation] for pulsed operation of the STED [22, 23]. Isaturation is generally defined as the depletion intensity at which the rate of stimulated emission equals the spontaneous decay rate.
For the simulation, we used the commercial calculation software (Matlab, Mathworks Inc., Natick, MA). Using the vectorial field calculation method in the near-focal region in the multi-layered media presented in [21], the diffraction integral for the incident azimuthal angle for each incident polarization condition was derived as Bessel function just as shown in Eq. (6). And to calculate intensity distribution of the depleted electric field, we applied theory in [22].
3. Theoretical study of the feasibility of SIL-based near-field optics for STED Microscopy
In our theoretical study, illumination at 630 nm for the excitation beam and 780 nm for the depletion beam was considered. In addition, we assumed that the STED parameter, Idepletion/Isaturation, was 100 for all cases. In our theoretical study, we considered 3 representative optical configurations just as shown in Fig. 3. Basically, 3 cases of illumination commonly consist of a pre-focusing lens with NA of 0.8 and a KTaO3 SIL whose refractive index is 2.23 at 630 nm and 2.20 at 780 nm. Configuration of Fig. 3 (a) considers image space fully filled with KTaO3. Configurations of Figs. 3(b) and 3(c) consider image space filled with a single material transition and dual material transitions, respectively.
Figure 4 shows the intensity distribution of the electric field for the configuration expressed in Fig. 3(a). We observed that the residual electric field generates focused electric field with 42 nm for its full width at half maximum (FWHM) due to highly focused electric fields for the excitation and depletion beams due to the extremely high NA of the optical system. In addition, the residual electric field gives a high resolution that is almost the same in the FWHM, even on an image plane of z = 200 nm. On the plane of z = 400 nm, the FWHM is enhanced by up to 55 nm as the focused electric field by the excitation beam became larger.
Next, as an approximation of a test sample attached to the rear bottom of a SIL, the configuration expressed in Fig. 3(b) was considered. We used a NA of 1.76–1.78, an image space composed of a KTaO3 SIL and a consecutive material whose refractive index is 1.5. The medium transition was positioned at z = 0 nm. Figure 5 displays the interesting results for the electric field distribution for the 2nd configuration. Due to the index transition at z = 0, the longitudinal electric field of the excitation beam suffered from intensity discontinuity, whereas the pure transversal electric field of the depletion beam maintained a continuous field distribution. Therefore, near the medium transition, the achievable resolution was higher than for the 1st configuration. As shown in Figs. 5(d) and 5(e), the resolution was up to 50 nm inside the medium from the medium transition and the FWHM was less than 40 nm. Just beneath the 2nd medium, FWHM was only 33 nm. Thus, the effect of the electric field of the depletion beam became dominant due to the abrupt decrease in the longitudinal electric field of the excitation beam from the medium transition. In addition, as the focused STED beam is generated by illumination of azimuthal polarized light, there is no electric field along the optical axis due to the vector field characteristic. Thus, when experiencing multi-beam interference in the intermediate transition, it derives a different longitudinal position from the maximum intensity of the excitation beam. Therefore, the intensity of the excitation beam is relatively low compared to the intensity of the STED beam at the position where the resolution of the depleted beam is highest. Conversely, at the position with the lowest resolution of the depleted beam, the intensity of the STED beam is nearly zero. For this reason, variations in the resolution of the reflected depletion field are caused within the SIL.
As mentioned in the introduction, to obtain a high resolution that is enhanced by a SIL, in contrast to the liquid immersion technique, there is an indispensable air-gap to protect the bottom surface of the SIL and the top surface of the sample. Moreover, we already reported previous research that demonstrated an active air-gap control of less than 20 nm even during high-speed movement of a sample or medium. Therefore, by applying the theory described in Section 2, we considered the fundamental 3-layered focal region, which was composed of the SIL, a 20-nm-thick air-gap and the sample. Figure 6 shows the electric field intensity distribution near the focal plane, which was composed of the 3-layered medium structure just as in Fig. 3(c). As shown in Fig. 6(a), similar to the 2nd configuration, the focused electric field of the excitation beam generated a distinctive discontinuous intensity profile at each medium transition due to the discontinuous nature of the longitudinal electric field from Maxwell’s boundary conditions. Different from the circularly polarized illumination of an excitation beam, the pure azimuthally polarized illumination of a depletion beam generates a continuous electric field at each medium transition. Therefore, the intensity decreases along the longitudinal direction more slowly than in the case of illumination of an excitation beam. As the result of the high resolution inside the medium, it maintains the high resolution on and inside the sample, as shown in Fig. 6(c). As plotted in Figs. 6(d) and 6(e), the residual intensity from a SIL STED with a NA of 1.78 yields FWHM of 42 nm on the top surface of the medium and FWHM of 46 nm even inside a medium of z = 70 nm that is 50 nm from the top surface of the medium. On the focal plane of z = 150 nm, the FWHM becomes broader up to 62 nm. Considering a FWHM of 52 nm in the case of a liquid immersion STED with a maximum NA of 1.4, the SIL STED has the potential to the increase the resolution by approximately 20% on the top surface of the medium and by approximately 10% inside the medium.
4. Feasibility via experimental verification
By focusing the beam inside the high refractive index spherical lens, we were able to achieve a higher NA for the optical system than for conventional immersion optics using a high refractive index liquid. To verify the resolution improvement due to the high NA of the SIL optics, a customized STED setup was constructed, as shown in Fig. 7. In this research, as described in the previous section, we employed KTaO3 as the material for the hemispherical SIL. The diameter of the spherical SIL was chosen to be 1 mm, considering the experimental conditions, such as the working distance of the pre-focusing lens and the alignment characteristics. For the pre-focusing lens, a LMPlanFLN 100X from Olympus with a NA of 0.8 was used, and a working distance of 3.4 mm was used to focus the beam inside the SIL.
A Ti-sapphire femto-second laser (Chameleon Ultra II, Coherent Inc., Santa Clara, CA, USA) was used for both the excitation source and STED source, so the pulse delay between the excitation beam and the depletion beam was easily synchronized [24]. The laser beam was split into two beam paths by the HWP and PBS. The lower optical beam path, which passes the PBS, was focused into a photonic crystal fiber (FemtoWHITE 800, NKT Photonics, Blokken 84, Birkerød, Denmark) that induced a super continuum; therefore, white light ranging from ~450 nm to infrared wavelengths was generated. An excitation filter (ET630/20x, Chroma Technology, Vermont, USA) centered at 630 nm with a 20-nm bandwidth was used to adjust the excitation band of the fluorophores. Moreover, it was coupled to the PMF 1 for spatial filtering and to maintain polarization. Then, the excitation beam path was recombined with the depletion beam path in the upper optical branch. The upper optical path reflected at the PBS was used to generate the depletion beam. The beam passes the glass rod to stretch the pulse width to few picoseconds to avoid unwanted nonlinear optical effects in the 100-m-long PMF 2, and it passes the DL to adjust the pulse delay between the excitation and depletion beam. A 100-m-long PMF was used to stretch the pulse width to above 100 picoseconds. The depletion beam was modulated by the VPP-1c (RPC Photonics, New York, USA) to induce a doughnut-shaped beam profile in the focal region on the test sample. After recombining with the excitation beam via two dichroic mirrors (ZT640rdc, Z730sprdc, Chroma Technology, Vermont, USA), both beams pass the galvanometer mirror (GM) and a pair of scanning lenses and tube lens. To generate circular polarization and, consequentially, induce the optimal STED donut-profile, the QWP was placed in front of the pre-focusing lens. Then, the pre-focusing lens focuses the incident light onto the bottom surface of the SIL. The fluorescent signal that was separated from the excitation light and STED light through dichroic mirrors and an emission filter (ET685/56m, Chroma Technology, Vermont, USA) was coupled to the multimode fiber, which has a 105-μm diameter. Because the fiber is connected to a single photon counting APD (SPCM-AQRH-15-FC, Excelitas, Massachusetts, USA), even a very weak fluorescent signal from single molecules can be detected.
To achieve a precise alignment between the SIL and pre-focusing optics, a Twyman-green interferometer was used, as shown in the violet-colored box in Fig. 7. It consists of a non-polarized BS, phase-shifting mirror, tube lens and CCD (XCL-C500, Sony) to detect the reflected irradiance and interferometric fringe. When there is no sample during a test, the focused light flux to the bottom surface of the SIL incident over the regime of a higher incidence angle was completely reflected, whereas the central flux was transmitted ordinarily. As a result, the reflected flux distribution at the exit pupil formed a bright ring-type irradiance pattern. The measured reflected irradiance and interferometric fringe detected by the CDD are shown in Fig. 8. The bright ring shape irradiance shown in Fig. 8(a) was induced by the large amount of total internal reflection on the bottom surface of the SIL. In addition, the optical alignment was confirmed by observing the interferometric fringe, as shown in Fig. 8(b). As shown in the interferometric fringe and in Table 1, the imaging optics were aligned with an acceptably low amount of aberration. In addition, via this experiment, we confirmed the thickness accuracy of the fabricated KTaO3 SIL by observing a low amount of spherical aberration.
To confirm the simulated resolution enhancement by introducing SIL-based optics, samples were attached on the rear bottom surface of the SIL, as shown in Fig. 9. Because the optics were designed to focus on the bottom surface of the SIL, the samples must be in contact with the SIL surface to obtain the image. At first, we imaged 20-nm crimson fluorescent beads (F8782, Molecular Probes, Oregon, USA) in the conventional illumination mode to observe the best lateral resolution for SIL-based STED microscopy. To attach the sample to the rear bottom surface of the SIL, a solution containing the fluorescent beads was coated on the rear bottom surface of the hemisphere SIL after it was coated with a 0.1% poly-L-lysine solution. Additionally, as shown in Fig. 9, the sample was covered with a solution of 2,2'-thiodiethanol (TDE) to preserve the fluorescence quantum yield. This configuration is same condition with Fig. 3(b), 2-layered system. Images were measured over a scan range of 5.5 μm × 5.5 μm with pixel size 17 nm × 17 nm, and these were compared with images from the SIL-confocal setup, which were acquired by simply removing the depletion beam. Measured depletion beam power right before the objective lens was 240 mW.
As observed in Fig. 10, which compares the detected images for both cases, the image from the SIL-based STED shows a significant resolution improvement on the confocal image. As shown in Figs. 10(c) and 10(f), the cross-sectional intensity profiles of the images show a FWHM line width of as much as 34 nm and 78 nm for the SIL STED, and 172 nm and 230 nm for SIL confocal setups, respectively. These values are similar to the calculated FWHM of 33 nm and 176 nm, as shown in Fig. 5. The resolution of the confocal microscopy is approximately 6 times lower than the result given by the proposed SIL STED setup. Considering the non-negligible variation in the size of the beads, the measured FWHM result gives an upper bound for the resolution of the system.
As actin filaments play an important role in determining the cell morphology and regulating many cellular functions such as migration and division, we tried to obtain imaging result of actin filaments as a meaningful approach to bio imaging by SIL STED microscopy. Actin filaments were prepared by polymerizing purified actin monomers in vitro. Lyophilized actin monomers from rabbit skeletal muscle (Cytoskeleton Inc., Denver, CO, USA) were diluted in G-buffer (50 mM Tris-HCl, 20 mM CaCl2, 1% NaN3, 0.2 mM ATP, 0.5 mM DTT, pH 8.0). Actin polymerization was initiated by adding a tenth of the final volume of F-buffer (50 mM Tris-HCl, 500 mM KCl, 2 mM MgCl2, 5 mM ATP, 0.5 mM DTT, pH 8.0). Polymerized actin filaments were fluorescently labeled using phalloidin conjugated with Alexa Flour 647 (A22287, Invitrogen). To minimize photobleaching during imaging, 2 mM Trolox was used as an oxygen scavenger.
Figure 11 shows the imaging results of the actin filaments. Images were measured with pixel size 31 nm × 31 nm, and measured depletion beam power right before the objective lens was 240 mW. At the sharp part of the filamentous structure, the image from the SIL STED setup had a 42-nm FWHM line width, which was approximately 6-fold improved than that of the SIL confocal microscope. This result is similar to the experiment with the image of the fluorescent nano-beads. Therefore, we achieved an approximate 6 times higher resolution using the proposed SIL STED setup.
5. Conclusions
Application of SIL-based near-field optics with an extremely high NA for the imaging head to STED microscopy was investigated via a theoretical analysis and fundamental STED imaging experiment. First, using vector-field calculation theory for the focused electric field near the stratified medium, we proved that an extremely high resolution can be achieved inside a tested medium, even with an air-gap. Therefore, for an air-gap of 20 nm and without an air-gap, compared with the liquid immersion technique, a 20% enhanced resolution is expected inside the test medium. To observe the fundamental actual imaging characteristics, SIL-based near-field optics with a NA of 1.78 were used for STED imaging. Compared with the imaging results that involved on an excitation beam, we achieved an approximate 6 times higher lateral resolution when imaging 20-nm beads and actin filaments. This experimental result was clearly expected from the simulation results on an optical configuration composed of a SIL for a consecutive test medium that has a refractive index of 1.5. As mentioned in the introduction, a near-field active gap control with an air-gap of 20 nm is proven technology. Therefore, we expect that the SIL-based STED technology can be a candidate for achieving an extremely high resolution with an increased detection speed based on the robust active control of the near-field air-gap.
Funding
National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MSIP) (No. 2015R1A5A1037668).
Acknowledgments
The authors would like to acknowledge NTT for supplying the KTaO3 SIL, which is based on their authentic manufacturing process.
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