The reduction of out of focus signal is a general task in fluorescence microscopy and is especially important in the recently developed super-resolution techniques because of the degradation of the final image. Several illumination methods have been developed to provide decreased out of focus signal level relative to the common epifluorescent illumination. In this paper we examine the highly inclined and the total internal reflection illumination techniques using the ray tracing method. Two merit functions were introduced for the quantitative description of the excitation of the selected region. We studied the feasibility of illumination methods, and the required corrections arising from the imperfections of the optical elements.
© 2014 Optical Society of America
Epi-fluorescence (EPI) illumination is the most common excitation method applied in laser based wide-field fluorescence microscopy . This illumination provides homogenous excitation of the sample in the Region of Interest (ROI), but can also introduce a major out of focus signal that significantly reduces the image quality. The depth of field in the EPI illumination mode is determined by the numerical aperture of the applied microscope objective and can be below one micron. However, the out of focus signal generated by the excited volume beneath and above the imaged ROI reduces the overall image quality. One of the general aims in the development of wide-field illumination methods is to achieve appropriate sectioning with a reduced out of focus signal. The sectioning property is determined by the Depth of Field (DOF = 2λ/NA2 where λ is the excitation wavelength and NA is the numerical aperture of the objective). Its typical value is ~500 nm in the visible range when a high numerical aperture objective is applied. However, the out of focus signal depends on the quality of illumination. To ensure a lower out of focus signal new modified illumination methods have been developed, such as objective type total internal reflection fluorescence microscopy TIRF , variable angle epifluorescence microscopy VAEM , highly inclined and laminated optical sheet microscopy HILO  and oblique selective plane illumination microscopy, oblique SPIM . These techniques can be used in an upright or an inverted microscope with a single objective. Techniques such as prism type TIRF microscopy  and SPIM [6, 7] require a separate optical system for illumination. In the super-resolution localization based methods, such as STORM , dSTORM  and PALM  the reduction of the out of focus signal is more critical because the precision of localization strongly depends on the magnitude of the out of focus signal .
The modified wide-field illumination techniques such as TIRF, VAEM and HILO are becoming more and more popular, but their practical implementation into microscope systems is a challenge that has yet to be studied in detail. These illumination techniques are widely used in super-resolution localization based microscopy, therefore we have examined them in a modeled inverted microscope with a high numerical aperture objective.
In case of TIRF illumination (first proposed by Axelrod et al. ) the incoming beam suffers total internal reflection and hence a thin (~50-150nm) evanescent field emerges in the sample. This illumination method is widely applied in cell biology to reduce out of focus signal .
VAEM illumination was proposed and studied by Konopka et al . In this approach the angle of incidence is close to the critical angle. The incoming beam is refracted on the interface of the cover slide and the specimen. Considering a relatively high incoming angle (which is still below the critical angle), the resulting illumination will be highly inclined. With this method the deeper regions of the specimen can be imaged with reduced out of focus signal.
HILO illumination was presented by Tokunaga et al . They demonstrated a method similar to VAEM, but they applied additional correction in the illumination path to ensure centered sample illumination with a higher inclination angle. This correction is required because of the imperfection of the objective (e.g. spherical aberration) especially when deeper regions are imaged at a higher inclination angle.
In practice two important cases can be distinguished: the imaged region is located (i) near the cover slide or (ii) deeper inside the sample. Figure 1 depicts the feasible illumination methods in these cases. In the first case [Fig. 1(a)] besides the conventional EPI illumination (red), TIRF (purple) and VAEM (green) can also be used. To achieve the VAEM and TIRF illumination the incoming beam must be focused into an off-axis point in the back-focal plane of the microscope objective. This shift introduces an inclination in the image plane according to the laws of geometrical optics (assuming a perfect focusing lens: the angle of inclination equals the shift in the back-focal plane/focal length). If the angle of inclination reaches the critical angle on the boundary of the cover slide and the sample, the beam suffers total internal reflection. If a deeper region is imaged [Fig. 1(b)] HILO illumination can be used for effective out of focus signal reduction instead of the conventional EPI illumination. To achieve HILO illumination, in addition to the shift of the focused incoming beam a tilt is also required in the back-focal plane . The main difference between VAEM and HILO is this additional correction tilt, which is necessary because of the imperfection of the optical system (the center of inclination is not exactly in the focal plane, which causes decentralized ROI illumination). The deeper the focal plane and the larger the desired inclination angle, the higher the required correction. The properties of the sample such as its thickness or docking ability to the surface of the cover plate are the key factors in the selection of the most appropriate illumination method.
This paper describes a ray-tracing analysis (OSLO optical design software)  of the mentioned illumination geometries using a realistic high NA objective . This model takes into consideration the imperfection of the objective in contrast to the simple geometrical optics approach, where the inclination introduced by the shift in the back-focal plane was assumed to be ideal and centered. We studied the possible illuminations at several depths in the sample (50 nm, 1µm and 5µm). We gave an overview of the realization of these illumination modes specifying the effect of imperfect inclination and the possible solution thereto. We also describe these illumination modes based on their effectiveness (out of focus signal, effective ROI illumination). Calibration curves for appropriate illumination and correction were also addedbased on the ray tracing simulations. We focused on issues which could not be trivially solved using a simple geometrical optical approach.
2. Materials and methods
The methods described above require the manipulation (shift and inclination) of the illumination beam in the back-focal plane. The illumination port of the optical system must be ready for such manipulations, which can be carried out with tilted mirrors in the appropriate conjugate planes or with translated lenses. In this paper we demonstrate an optical system that applies tilted mirrors in the conjugate planes. Such a system is able to be operated in the TIRF, VAEM and HILO illumination modes. The mirrors were placed in the conjugate plane of the focal plane (INCL mirror) and the back-focal plane (CORR mirror) of the objective [Fig. 2(a)]. By tilting the INCL mirror one can change the position of the focus in the back-focal plane and hereby the angle of inclination in the focal plane. By tilting the CORR mirror an inclination can be introduced in the back-focal plane, and the position of the illuminated area can be changed in the focal plane. Our system included a modeled oil immersion objective (a lens system with 1.41 NA, 100 × magnification and a focal length of 1.8 mm ), perfect lenses (with a focal length of 180 mm) and mirrors. A collimated incoming beam with a wavelength of 647 nm was used to illuminate the sample (this is an excitation wavelength of Alexa Fluor 647, one of the most widely used fluorescent dyes used in super-resolution microscopy). The refractive index of the sample was assumed to be 1.33 mimicking a water-based fluorescent biological sample . The center of rotation of the mirrors (marked with O in Fig. 2(a)) was on the surface of the mirrors so tilting did not introduce any additional translation of the beam. In practice this kind of tilt can be carried out with Gimbal type mirror mounts. Afocal evaluation mode of OSLO was chosen. In the simulations the coordinates of the incoming rays were captured in several planes. Further analyses and visualization were made in MATLAB. The Region of Interest (ROI) was chosen to be 20.48 µm × 20.48 µm × 0.67 µm, corresponding to the imaging of a 128 × 128 pixel region on a camera with a pixel size of 16 µm and an overall magnification of × 100. The Depth of Field (DOF) was 0.67 µm determined by the emission wavelength (~670 nm) and the numerical aperture: 2λ/NA2.) These parameters are typical in a localization based microscope system. To describe the analyzed oblique illuminations two measures were defined: ILLROI and ILLOUT. ILLROI is the portion of the ROI which is illuminated [Fig. 2(b)]:
ILLOUT is the illuminated volume out of the ROI, relative to the size of ROI [Fig. 2(b)]:
It was assumed throughout the simulations that the initial EPI illumination was homogenous and the beam illuminated the entire ROI. In other words the beam was matched to the ROI. The incoming rays were distributed equally on the incoming aperture except for one case in the final section, where Gaussian illumination was applied.
3.1 Illumination in case of “sample scanning”
In case of “sample scanning”, the position of the lenses and the objective was static, and only the sample was moved. In this approach the thickness of the oil layer was set so that the ROI was aligned into the object plane.
First we studied the illumination in the case when the focal plane was located at 50 nm above the surface of the cover slide inside the sample. The best illumination method is typically TIRF at this distance. We analyzed the EPI-TIRF transition by tilting the INCL mirror [Fig. 3(a)-3(d)]. The angle was varied from 0° (EPI) to 0.3868° (TIRF). The angles were measured from the initial position in all cases. In the course of inclination the perfectly collimated beam became slightly divergent. This artifact was introduced by the imperfection of the objective (the rays have a highly oblique optical path through the lens, and the effect of optical aberrations rises). The transition to total internal reflection is continuous and starts at ~0.3862°. Because of the slight divergence of the beam the rays have different incidence angles on the surface of cover slide. As a result, the rays reach the critical angle on the boundary of the cover slide and the sample at different INCL angles. According to the laws of geometrical optics, the critical angle for refraction between the cover slide and the sample is θc = 61.73°. Taking into consideration the angle magnification and the effect of tilting the mirror, the presumed INCL position related to the critical angle would be θc/(2 × magnification) = 0.3087°. However, full TIRF illumination (when the entire beam is back-reflected) was achieved at ~0.3868° [Fig. 3(d)] in the simulation. This value was 25.3 percent higher than the presumed value, and the discrepancy was caused by the imperfection of the objective. The range of the transition was 6 × 10−4 °, i.e. equaled the sensitivity of a typical mirror mount (6-10 × 10−4 °). However, the illumination became decentered (3.123 µm in the focal plane) during the transition due to the imperfect inclination. The illuminated area could be centralized by slightly (0.05°) tilting the CORR mirror [Fig. 3(e)]. This issue is critical when a relatively small ROI has to be applied such as in localization microscopy. If the ROI is not illuminated entirely and centrally (which is even more critical in the case of not perfectly homogenous illumination), the final image quality can degrade. Conclusively, the effect of imperfect inclination significantly occurs in case of the TIRF illumination of a relatively small ROI by the decentration, which can be compensated by the appropriate tilting of the CORR mirror.
Secondly we investigated the illumination of the ROI where the focal plane was located at 1µm deep in the sample. At this depth the TIRF illumination cannot be applied. Instead of the normal EPI illumination two other illumination methods can be used to reduce the out of focus signal. At first we studied the VAEM illumination [Fig. 4(a)]. The INCL mirror was tilted by 0.32205°. In this case the quality factors were: ILLROI = 1 and ILLOUT = 14.384. Over this INCL angle the ROI is not illuminated entirely. If the focal plane is located deeper in the sample the VAEM illumination becomes less effective in the reduction of the out of focus signal because the maximum INCL angle which can be applied without the decentration of ROI illumination decreases. If a larger scale out of focus signal reduction is desired, HILO illumination can also be applied. We analyzed illumination at an INCL angle of 0.3862°. HILO illumination requires a calibration process. The appropriate CORR angle must be found for the given INCL angle taking into consideration the quality factors ILLROI and ILLOUT [Fig. 4(b)]. In the presented case it was 1.903 [Fig. 4(c)]. Spline curve fitting was applied during the calibration. We studied a case at a higher INCL angle (0.3864°) [Fig. 4(d)-4(g)], where we accomplished the calibration process [Fig. 4(d)], and the optimum case was found at a CORR angle of 0.2929° [Fig. 4(g)]. At a lower CORR angle a portion of the incoming beam suffers total internal reflection as it can be seen in Fig. 4(e) and 4(f), but at a higher CORR angle the entire beam is back-refracted due to the combination of a slight divergence and imperfect inclination in the back-focal plane. In conclusion, when the focal plane is located deeper in the sample, VAEM and HILO illumination can be applied. With HILO illumination a higher out of focus signal reduction can be achieved due to the correction of decentration at a higher inclination angle.
Thirdly we studied the HILO illumination of ROI, where the focal plane was located at 5 µm deep in the sample. This situation typically occurs for instance when a thicker cell culture or a brain tissue section is imaged. The calibration method described above can be repeated as seen in Fig. 5(a) in the case of an INCL angle of 0.385°. The actual illuminations are presented in Fig. 5(b)-5(d) at several CORR angles. As the CORR angle increases, the illumination of the ROI improves until the optimum is achieved.
This calibration was carried out for several INCL angles. The CORR angle and ILLOUT values found in the optimum cases were fitted with the spline fitting method. Thus a calibration curve was received for a CORR angle with ILLOUT values [Fig. 5(e)]. Increasing the INCL angle the ILLOUT factor is decreasing and the CORR angle is increasing.
The intensity distribution was also studied in the optimum case at an INCL angle of 0.385° [Fig. 5(f)], where the incoming beam had a Gaussian distribution with a so called Gauss factor of 2. (The standard deviation of the Gaussian distribution was twice larger than the lateral size of ROI in the focal plane). The intersection points of the rays were captured in the focal plane and plotted in a 2D histogram. The histogram was fitted with a 2D Gaussian surface depicted in Fig. 5(f). The illumination of the focal plane was slightly inhomogeneous and decentered. However, the achievement of a perfectly homogeneous ROI illumination is a challenge, especially in localization based microscopy, where the magnitude of intensity is essential in the photoactivation or photoswitching processes .
3.2 Illumination in case of “objective scanning”
In practice the image plane is sometimes set by moving the objective and keeping the sample at a fixed position, which is referred to as “objective scanning”. In this section we study the effect of moving the objective under HILO illumination. With the objective moving, the common focus of the last perfect lens and the objective [Fig. 2] is dislocated. An optimum ROI illumination was chosen where the initial focal plane was at 5 µm deep in the sample [Fig. 6(a)]. The INCL and CORR angles were set to 0.385° and 0.515°, respectively, according to the calibration process described above. The positions of the focal plane (3 µm and 7 µm deep in the sample) were set by means of moving the objective. Due to the focus dislocation, the ROI was not illuminated entirely after defocusing, thus an additional correction with a CORR mirror was needed. The calibration process was carried out for several defocus values for this additional correction, and after cubic curve fitting a calibration curve was achieved for the additional correction values for CORR mirror tilting [Fig. 6(b)].
In this paper we demonstrated an analysis of illuminations applied in wide-field microscopy, especially focusing on localization based microscopy issues. We studied the possible illumination methods of a ROI at depths of 100 nm, 1 µm and 5 µm in the sample. We found that a correction was required after the EPI-TIRF transition for centered illumination in the TIRF mode. A calibration curve was added for the CORR angle in case of HILO illumination. We investigated the effect of the positioning process of ROI in the sample by moving the objective. Due to focus dislocation, the ROI was not illuminated entirely, therefore additional correction was needed. A calibration curve was given for this additional correction too. TIRF, VAEM and HILO illumination can also be realized with movable lenses. By moving the lenses the required inclination and shift can be introduced according to the laws of geometrical optics. In the future we will study the issues mentioned above in such a system. We plan to carry out measurements in connection with the described issues using a standard layered sample. Another challenge in fluorescence microscopy is multicolor illumination. We made preliminary simulations with our modeled system at 405, 488 and 532 nm. It can be clearly seen that an illumination system optimized for a given wavelength is not appropriate for another one because of the high divergence of the beam caused by chromatic aberration.
ME acknowledges support from the Marie Curie Integration Grant (PCIG13-GA-2013-618273) and the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. We acknowledge Lambda Research Corporation for providing the OSLO optical system design software for the simulations. The research was partially funded by “TÁMOP-4.2.2.A-11/1/KONV-2012-0060 – “Impulse lasers for use in materials science and biophotonics” supported by the European Union and by the European Social Fund, by “TÁMOP-4.2.2.C-11/1/KONV-2012-0010” and by the Hungarian Brain Research Program (KTIA_13_NAP-A-I/14).
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