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A novel high-resolution stage scanning confocal microscope for fluorescence microscopy and spatially resolved spectroscopy with a high numerical aperture (NA≈1) parabolic mirror objective is investigated. A spatial resolution close to the diffraction limit is achieved. As microscopic fluorescent test objects, dye-loaded zeolite microcrystals (diameter approx. 0.4 µm) and single fluorescent molecules were used. Confocal fluorescence images show a spatial resolution of Δx=0.8·λ both at room temperature and at 1.8 K. Imaging of a quasi-point light source and focusing by the parabolic mirror were investigated experimentally and theoretically. Deviations between the theoretical results for a perfect parabolic mirror and the experimental results can be attributed to small deviations of the mirror profile from an ideal parabola.
©2001 Optical Society of America
1. Introduction
The electromagnetic field distribution in the focal region of a high NA parabolic mirror has been investigated recently [1–4]. In a previous theoretical paper [5] we have examined in detail an ideal parabolic mirror with respect to confocal microscopy and characterized its fundamental imaging properties. The numerical calculations showed that electromagnetic waves can be focused to a highly confined diffraction limited optical field around the focal point. Making use of the high numerical aperture the electric field vector in the focal spot can be oriented parallel and perpendicular to the optical axis. Confocal images of the radiation field of a dipole (e. g. from a molecule) reveal its three dimensional orientation.
These properties make a parabolic mirror an ideal optical element for focusing and light collection in a stage scanning confocal microscope where the focal spot rests on the optical axis. While high NA parabolic mirrors have been used as efficient light collectors in highly resolved laser spectroscopy of single molecules [6–10], however, for imaging they have been avoided due to their poor off axis imaging performance.
Here we experimentally verify some features of a parabolic mirror as focusing and imaging element in a stage scanning confocal microscope. First we examine the image of a quasi-point light source which is initially placed in the focal spot and then gradually moved away from the optical axis. Second we explore the focal depth of a highly confined optical field which can be created by illuminating the mirror with circularly polarized light. In order to characterize the microscope as a whole we have recorded confocal images of dye-loaded zeolite L microcrystals and single fluorescent dye molecules as microscopic test objects.
2. Experimental
The optical path of the system is sketched in Fig. 1. The output of an optical single mode fiber fed by a laser followed by a beam expander serves as a light source in order to produce a parallel optical beam. It illuminates a wedge plate (wedge angle 0.75°) with an antireflection coating on the backside which acts as a beam splitter. The light reflected off this wedge plate is guided by two flat mirrors into the parabolic mirror, which focuses the incoming light onto the sample. The two flat mirrors are necessary to match precisely the optical axis of the parabolic mirror and the direction of the exciting beam, because smallest deviations from the optical axis cause strong coma in the field distribution around the focal region [5]. Fluorescence emission excited in the focal spot and backreflected light are collected by the same parabolic mirror and guided backwards through the beam splitter via the two flat mirrors to be focused into the image plane by a photo objective (Sonnar T* 135 mm, Carl Zeiss, Germany). Wavelength selective optical filters e.g. for suppressing the excitation light in fluorescence microscopy can be installed into the parallel beam between the beam splitter and the photo objective.
The microscope head, containing the parabolic mirror and the scanning stage for the sample, can be placed in a liquid helium cryostat (SVT-200 Model 10 CNDT, Janis Research Company Inc., USA), that can be operated both as a bath or flow cryostat in a temperature range from room temperature down to 1.8 K. The mechanical design of the cryostat insert has been adopted from the atomic force microscope for low temperatures by Hug et al. and the reader interested in low temperature micromechanical design is referred to their work [11]. With such a stage scanning setup the focal spot can always rest on the optical axis of the parabolic mirror and the sample is scanned in a raster-like fashion. Therefore the off-axis aberrations of a parabolic mirror, which are much stronger compared with a corrected objective, are not disturbing. For coarse focusing, the parabolic mirror can be translated some millimeters along its optical axis. Fine focusing is achieved by the piezo-tube scanning stage carrying the sample.
Fig. 1. Layout of the optical path of a confocal microscope with a parabolic mirror objective. A parallel beam generated by the output of an optical single-mode fiber and a beam expander lens is focused onto the sample by a parabolic mirror. The light from the focal region is collected by the same mirror and is focused backwards into the image plane.
For recording an image the sample is scanned through the focal spot line by line. The detector (e.g. an avalanche photodiode) records either the reflected light intensity or the emitted fluorescence intensity if a suitable set of filters is used. The detector output is registered point-by-point by a computer. For detailed examination, single objects can be positioned in the focal spot of the parabolic mirror e.g. for recording spectra or time resolved measurements.
Fig. 2. (a) Photograph of the mounted parabolic mirror. (b) Arbitrary cross section through one half of the mirror. The diagram shows the deviations Δz(r) of the mirror surface from an ideal parabola. The dotted line indicates the smoothed curve which is used for the calculations.
Figure 2a shows the diamond turned parabolic mirror (Optische Werke Rodenstock, Germany) in its mount. The half opening angle is 87° and the focal length is 4.5 mm. The center hole allows to access the focal region with a tip for possible future scanning probe microscopy experiments. The notches at the rim allow to view the focal region and the sample from the side. Figure 2b shows the deviation of the mirror surface from a parabola along an arbitrary section through one half of the mirror. We see that the deviations are mostly smaller than 150 nm. Hence we must expect some phase errors with the angular wave components reflected from the mirror surface. High quality optical elements have been used throughout the remaining optical path to avoid additional phase errors. In the next section we will see that the experimental results come close to the theoretically expected ideal situation.
3. Results
Two different experiments were performed in order to characterize the confocal imaging properties of the parabolic mirror. First, a quasi-point light source was positioned in the parabolic mirror and its image was analyzed. In a further experiment the parabolic mirror was illuminated along its axis with a plane wave and the emerging intensity distribution was measured in the focal region. The experimental data are compared with theoretical intensity distributions in each case.
3.1 Imaging a quasi-point light source in the focal region
As a microscopic light source we used an illuminated well characterized sub-wavelength circular aperture, 100 nm in diameter, at the end face of an aluminum coated fiber tip of the kind which is used for near-field optical microscopy. The aperture was carved by a focused ion beam (FIB). The tip was further characterized by SEM and optical microscopy. The technique to prepare such tips is described in the literature [12,13]. The tip is mounted on the scanning stage of the microscope along the optical axis such that the aperture faces the mirror surface. The tip can be positioned in all three directions by the scanning stage. The light of a frequency doubled Nd:YVO4-Laser (λ=532 nm) is fed into the fiber such that the far-field of the light emerging from the aperture is linearly polarized.
Fig. 3. Images of a quasi-point light source (λ=532 nm): (a) experimental results, (b) simulations with an ideal parabolic mirror, and (c) simulations with a parabolic mirror with phase errors. From top to bottom the light source is shifted away from the optical axis to the right by 0, 7, 14 and 20 µm. Every picture is normalized to its intensity maximum. The length bar corresponds to 5·M·λ (M=magnification, λ=wavelength).
In our experiments (Fig. 3a) the aperture is initially in the focal point of the parabolic mirror such that the image of the focal spot is as small and as intense as possible. Afterwards the tip is moved perpendicularly to the optical axis away from the focal spot. For recording the images a CCD camera (LN/CCD-512TKB/1, Princeton Instruments Inc., USA) was placed directly into the image plane. The polarization of the emitted light is parallel to the baseline of the pictures and thus parallel to the displacement direction of the tip.
When the aperture is in the focal spot the image consists of a bright center spot surrounded by a weak circular halo. As the aperture moves away from the optical axis an extended tail develops. The bright center spot decays into several bright interference maxima having the shape of an arrow tip that points away from the optical axis.
Column b) in Fig. 3 shows the respective calculated images generated by a point light source near the focal point of an ideal parabolic mirror. The optical far field of a sub-wavelength aperture was approximated by an electric dipole and a perpendicularly oriented magnetic dipole in the ratio 1:2, both parallel to the aperture surface [14]. Similar to the experimental data, an extended tail develops when the source is moved away from the focal spot. The main difference between the calculated and the measured images is a superimposed elliptical structure in the experimental images.
As can be seen in Fig. 3c, parts of this structure can be explained by an additional phase factor Φ(r) in the representation of the electromagnetic wave reflected from the mirror surface (see Eq. 3 in reference [5]):
In Eq. 1 Δz(r) is the deviation of the mirror surface from an ideal parabola, Θ is the polar angle in the mirror and λ is the wavelength. The calculations are based on the deviations given by a single scan (see Fig. 2b) and assumed to be rotationally symmetric.
3.2 Focusing with a parabolic mirror
A section through the calculated intensity distribution of the electromagnetic field in the focal region of an ideal parabolic mirror is depicted in Fig. 4a for an incident circularly polarized Gaussian beam. Fig. 4b depicts the intensity distribution if the same deviations of the mirror surface from an ideal parabola are assumed as in Fig. 3c. Clearly the phase errors spread out the intensity of the side maxima along the mirror axis in expense of the main intensity maximum. Notice that Fig. 4 is a logarithmic representation and thus less intense sections appear enhanced in comparison with a linear scale.
Fig. 4. Logarithmic representation of the calculated intensity distribution in the focal region of a parabolic mirror illuminated with circularly polarized light (λ=532 nm). The cross section is oriented along the optical axis (z-direction). The optical axis is located in the center of the illustration. (a) Focal region of an ideal parabolic mirror and (b) focal region of a mirror which produces phase errors due to its imperfect surface profile (see Fig. 3c). In both cases the intensity distribution through the focal spot in x-direction has a FWHM of 0.30 µm. Along the mirror axis the ideal mirror yields a FWHM of 0.54 µm whereas the imperfect mirror yields a FWHM of 0.50 µm for the most intense maximum. The central intensity maximum for the ideal mirror is approximately twice as high as the maximum for the imperfect mirror.
The intensity distribution was measured by scanning the cleaved end of a single-mode optical fiber covered with the fluorescent dye rhodamine-6G through the focal region along the mirror axis. Fluorescence photons which are generated near the fiber axis and match the acceptance angle of the core (diameter 5 µm) can propagate with low loss through the fiber and are registered by a photomultiplier (H 5702-02, Hamamatsu, Japan). The collection efficiency decays rapidly when the fiber axis is displaced laterally with respect to the mirror axis and has the shape of a Gaussian distribution with a halfwidth (FWHM) of 0.16 µm. For the measurement of the intensity distribution the tip was positioned on the mirror axis. Each data point in the experimental curve of Fig. 5 corresponds to the fluorescence intensity collected by the fiber core at a certain position along the mirror axis. To eliminate the excitation light we used a holographic notch filter (optical density 6 for the excitation wavelength) in front of the detector.
Fig. 5. Experimental and calculated intensity distribution in the focal region of the parabolic mirror along the axis. The origin corresponds to the location of the focal spot for an ideal mirror. The width of the intensity distribution along the mirror axis (FWHM) is 0.80 µm in the experiment, 0.53 µm in the calculation for a mirror with phase errors and 0.62 µm for the ideal mirror.
The theoretical intensity distributions perpendicular to the optical axis in the focal region were calculated for this experiment along the lines of ref. [15] for a vacuum-glass interface with n=1.46. The theoretical curves in Fig. 5 resulted by weighting these field distributions with a radial Gaussian shaped collection efficiency (FWHM 0.16 µm) centered at the mirror axis.
The intensity distribution along the axis of our parabolic mirror can rather well be reproduced by a parabolic mirror with the same minor radial phase errors. Both the calculated and the measured data show a distinct intensity maximum about 0.75 µm beneath the focal spot of the ideal parabolic mirror. Residual deviations originate from the fact that the phase errors of our mirror are not really radially symmetric.
3.3 Confocal imaging
3.3.1 Single microcrystals
In order to characterize the imaging properties of the confocal microscope at room temperature, we have recorded fluorescence images of single dye-loaded zeolite L microcrystals dispersed on a flat quartz glass surface. These microcrystals are excellent objects for this purpose, because their size (100 nm up to 2 µm) has the dimensions of the confined optical field in the focal spot and they have a good fluorescence stability with a sizedependent high fluorescence yield. These crystals as well as the sample preparation are described in detail in [16]. The dye (oxonine) is excited with circularly polarized light at 532 nm and the maximum emission lies around 610 nm. Circular polarization is used to avoid polarization effects generated by the orientation of the microcrystals. For recording confocal fluorescence images, the excitation light is suppressed by a holographic notch filter at 532 nm and the fluorescence is collected by an avalanche photodiode (SPCM-200-PQ, EG&G, Canada). The active area with a diameter of≈170 nm is located in the image plane of the microscope and serves as detection pinhole.
Fig. 6. (a) Confocal fluorescence image of dye-loaded zeolite L microcrystals dispersed on a quartz glass surface. The brightest crystallite has an intensity maximum of 1.5·103 counts per 5 ms. (b) Line sections through one of the crystals. The excitation light is circularly polarized. Differences in brightness correspond to the size of the crystals. (c) Scanning electron micrograph of the same section of the sample as in (a).
In Fig. 6a a confocal fluorescence image is shown with (Fig. 6b) line sections along the x- and y-axes through one of the crystals together with (Fig. 6c) a scanning electron micrograph of the same sample section. The length of the examined crystals is about 0.4 µm as can be seen in the scanning electron micrograph. The fluorescence image can be fitted by a two dimensional convolution of a rectangular function for the crystals with a Gaussian function for the intensity distribution in the focal region. The fit yields a FWHM of (0.43±0.06) µm for the intensity distribution around the focal spot. This value is about 1.4 times larger than the expected theoretical value for an ideal parabolic mirror (see Fig. 4a). This deviation can be attributed to the neglected non-rotationally symmetric geometrical errors of the parabolic mirror or a slightly imperfect adjustment of the optical path.
3.3.2 Single molecules
Single organic dye molecules are objects much smaller than the dimensions of the confined optical field in the focal region. A single molecule can be approximated by a point dipole which in our case has no influence on the electromagnetic field distribution in the focal region. We used the well known dye terrylene embedded in the Shpol’skii matrix octadecane. The bright, almost circular spot in Fig. 7a is the spatially resolved fluorescence emitted by one single molecule. The measurements were carried out at a temperature of 1.8 K in a pumped helium bath. The sample was prepared according to reference [17]. For excitation a single-mode ring dye-laser with a nominal linewidth of 1 MHz (CR-699-29, Coherent Inc., USA) is tuned to the resonance of a molecule at 571.6 nm. Color glass filters (RG 610, Schott, Germany) are used to separate the fluorescence light from the excitation light.
A two-dimensional Gaussian fit to the data of the fluorescence image yields a FWHM of 0.46 µm, which corresponds to the diameter of the intensity distribution in the focal plane and is in good accordance with the previous results obtained with the zeolites. The structures around the molecule in the fluorescence image can be attributed to microcrystalline formations of the Shpol’skii matrix (see [17]). Refraction at rough sections at the surface or at boundaries between different domains leads to a modified intensity distribution of excitation light inside the matrix and to an indifferent imaging of the emitted fluorescence. All fluorescence disappears after a spectral jump of the molecule.
Fig. 7. (a) Confocal fluorescence image of a single terrylene molecule embedded in the Shpol’skii matrix octadecane, immersed in superfluid Helium at 1.8 K. The lines through the fluorescence spot indicate the cross sections in graph (b). A two dimensional Gaussian fit yields a FWHM of 0.46 µm. The excitation light is circularly polarized with a wavelength λ=571.6 nm.
Detailed excitation spectroscopy shows that we deal in fact with single molecules. We observed reversible spectral jumps as well as homogenous line widths of about 40 MHz in agreement with the literature for comparable hosts [18–20]. An examination of the fluorescence emission spectrum permits a clear identification of the so called “fingerprint”- region of terrylene [21]. Overall, the molecule is sufficiently stable for two-dimensional imaging.
4 Conclusion
We have characterized the focusing and imaging properties of a high-NA parabolic mirror objective in a stage scanning confocal microscope. The formation of a confined optical field in the focal region and the imaging of a point light source were investigated experimentally and modelled by vector field theory.
We found that a parabolic mirror objective is perfectly suited for high-resolution confocal microscopy. With our mirror objective a spatial resolution of 0.8·λ was achieved both at room temperature and at 1.8 K when the mirror was immersed in super-fluid helium. The high resolution obtained in fluorescence imaging and spectroscopy of single molecules comes close to the theoretical limit predicted by vector field theory. A small improvement in resolution could still be achieved by an ideal parabolic mirror surface.
The high NA of the mirror objective, which covers a solid angle of almost 2π around the focal spot, allows to generate an optical field in the focal region with a strong electric field component along the mirror axis which allows to collect the polarization component along the z-axis of light scattered by an object in the focal spot. The polarization features of the parabolic mirror objective are the topic of ongoing research and will be presented in a forthcoming publication.
Acknowledgments
We gratefully acknowledge Prof. Dr. G. Calzaferri, Dept. of chemistry and biochemistry, University Bern, Switzerland for the oxonine loaded zeolite L microcrystals and Prof. Dr. K. Müllen, Max-Planck-Institute for polymer research, Mainz, Germany for providing us the terrylene molecules. One of the authors (G.T.) acknowledges financial support from FONDECYT for Project No. 1971191.
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