1. Introduction

Single molecule microscopy and single particle tracking are versatile tools for analyzing dynamic interactions in biophysical and biological systems in three dimensions (3D) without averaging over molecular ensembles [1]. Reduction of background fluorescence is of key importance to achieve a sufficiently high signal-to-noise ratio (SNR) of the intrinsically weak single-molecule signals. The use of high numerical aperture lenses and low fluorescent particle concentrations is mandatory, because otherwise the fluorescence of out-of-focus particles complicates the detection of single particles in the focal plane.

A further reduction of out-of-focus fluorescence can be achieved by using an illumination of the object plane perpendicular to the optical axis of the detection objective lens instead of the commonly used epi-illumination (Fig. 1). This principle of an orthogonal illumination was already used in the so-called ultramicroscope for the investigation of colloidal particles at the beginning of the 20^th century [2]. Meanwhile, the principle of a selective illumination of the focal plane was very successfully adopted to fluorescence microscopy in various ways (abbreviated here as SPIM for selective plane illumination microscopy) [3–7]. The fundamental principle of SPIM is the exclusive illumination of a thin spatial region around the focal plane of the detection objective lens. Its combination with fluorescence produces an intrinsic optical sectioning effect, because fluorescent molecules are only excited and visualized within the illuminated focal plane. Unlike in a conventional epi-fluorescence microscope, no out-of-focus fluorescence is contributing to the image. In light-sheet based microscopy the sample is illuminated with a laser beam, which is shaped by a cylindrical lens telescope into a strongly elliptical beam profile. An illumination objective lens focuses this profile into the sample thereby creating the light sheet. The sample is usually moved by a scanner through this plane, which is imaged by a CCD camera. This elegant optical sectioning microscope combines the improved contrast and resolution of a confocal laser scanning microscope with the speed and sensitivity of a video microscope. Also, photobleaching is reduced, because only the imaged sample region is illuminated. Finally, due to the fact that the image is acquired in a parallel manner the imaging rate can be greatly increased compared to optical sectioning microscopes based on point or line scanning. All these features make SPIM the ideal imaging technique for the visualization and tracking of single molecules, particles or vesicles in biological or other microsystems.

In this work we present the construction of a SPIM with a very thin light sheet and high axial resolution. The imaging properties of this microscope were calculated both by theory and ray tracing, and matched perfectly the experimental results. We characterized the improved contrast of our SPIM and its capability of tracking fast fluorescent particles by measuring the diffusion coefficient of single quantum dots in aqueous solution.

 

Fig. 1. Comparison of epi-illumination and SPIM. In contrast to (A) epi-illumination microscopy the emission path in (B) SPIM is perpendicular to the excitation beam path. By selective illumination of the focal plane, no out-of-focus fluorescence is generated. This results not only in a strongly reduced background signal and higher resolution, but also in the optical sectioning capability of the instrument.

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2. Microscopic setup

Figure 2 shows a sketch of our microscopic setup. The fluorescent object is positioned within a water-filled chamber, and illuminated by a laser beam along the x axis, while the fluorescence emission imaged along the z axis. By translating the sample along the z axis, imaging of different optical slices in the xy-plane is possible.

The laser beam is expanded and shaped by a cylindrical Galilean beam expander. Out of the incoming circular-symmetrical Gaussian beam with a wavelength of 633 nm we produce a beam with an elliptical intensity profile with a 1/e² diameter of 7.2 mm along the z-axis and of 1.6 mm along the y-axis. For green laser light (λ₀=543nm) we obtain 6.6 mm for the z-direction and 2.2 mm for the y-direction, respectively. The strongly elliptical Gaussian beam is then focused by a custom-designed long distance objective lens with high numerical aperture (NA 0.33) into a water chamber [8]. In this manner we achieved a sufficiently high irradiance of 1 to 10 kW/cm² even when using a low power laser (2 mW) for fluorescence excitation, and also limited the illumination region in order to avoid unnecessary photobleaching in the sample. The custom-made lens was designed to optimize the illumination sheet geometry for our specific sample chamber layout. Positioning of the thus created light sheet is done by a gimbal-mounted scanning mirror, which is placed in a plane conjugated to the back-focal plane of the illumination objective lens.

The fluorescent sample is mounted on a three axis sample scanner. It consists of three orthogonal stacked translation stages, where the z-axis is motorized (M105.1B translation stage with DC-Mike linear actuator M232-17 with 7 nm minimum step size from PI, Karlsruhe, Germany), and the x- and y-axis are manually adjustable (100 nm minimum step size). Usually, the sample is mounted in an open water chamber by a refractive index matched agarose cylinder (0.5%–1.0% agarose gel) pushed several millimeters out of a glass capillary [4]. Rotating and tilting of the sample for optimal imaging conditions is realizable. For dynamic measurements, e.g. mobility measurements of diffusing particles, the liquid is filled into a hollow agarose cylinder, which is sealed with silicone paste.

The fluorescence is collected by a water-dipping objective lens (Nikon, 60× NA 1.0) and imaged onto a cooled slow-scan CCD-camera (Photometrics, SenSys KAF-1401E with 1317×1035 pixels, pixel size 6.8 µm²). For dynamic measurements an electron multiplying CCD-camera (EMCCD) is used (iXon BI DV-860, Andor Technologies, Belfast, Ireland). To eliminate any scattered laser light a suitable long pass filter is placed in front of the camera. As laser sources we use a green 2 mW HeNe laser (LHGR-0200, Laser2000) emitting at 543 nm, and a 633 nm HeNe laser (Spectra Physics, Model 127, 35 mW). For most measurements 1 to 5 mW were more than sufficient.

 

Fig. 2. Schematic view of the high-resolution SPIM setup. Laser light is guided into a Galilean cylindrical beam expander by mirrors M1 and M2 and a dichroic beam splitter (DB). The beam expander transforms the circular-symmetrical Gaussian beam into an elliptical one. The illumination objective lens focuses the beam into a water chamber (WaCh), and creates a light sheet in the focal plane of the detection objective lens. Positioning of the light sheet can be done with the scanning mirror (SM), which is placed in a conjugated plane of the back focal plane of the illumination objective lens. The sample is moved by a three axis sample scanner, the z-axis is motorized. Fluorescence is collected by a water-dipping objective lens and imaged via a tube lens (TL) onto a CCD-camera. Scattered laser light is blocked by an emission filter (EF). By introducing a dichroic beam splitter into the detection beam path it is possible to use a standard wide-field illumination (dashed box).

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3. Theory

An essential feature of SPIM is its axial resolution, which is determined by the thickness of the incident light sheet, the NA of the imaging objective lens and the wavelength of the fluorescence light. The objective lens in the excitation beam path focuses the laser beam into a hyperbolic light pattern with a Gaussian intensity distribution perpendicular to the propagation direction. The lateral dimensions of the Gaussian beam are defined by the≥1/e² intensity profile. The thickness of the profile increases with increasing distance to the focus. Twice the Rayleigh range defines the depth-of-focus (Fig. 3). Within the depth-of-focus, along one axis a focused Gaussian beam can be approximated by a rectangle [9]. Therefore, an object positioned in this region is sectioned by a light sheet of almost constant thickness.

3.1 Extension of the light sheet

To discuss the slicing thickness and the resolution of the SPIM, a respective definition has to be chosen. The Rayleigh criterion corresponding to the distance between the central maximum and the first-order-minimum of a diffractive limited intensity distribution is often used. However, it is experimentally inconvenient to determine the first-order-minimum due to a high background or low signals. Other commonly used criteria to specify the width of an intensity profile are the full-width-at-half-maximum (FWHM) and the distance between the maximum intensity I_max and the distance, at which it decayed to 1/e² I_max. For characterizing the focal thickness and the resolution we use the respective FWHM values.

 

Fig. 3. Illumination light sheet for λ₀=633nm in water (n=1.33). (A) Dimensions (1/e² distance) and orientation of the light sheet along the illumination axis (x-direction) over a distance of 300 µm. The axial distance, in which the beam width is not greater than a factor of √2 of its focal value is known as the depth-of-focus. All units in µm. (B) A cut through the elliptical Gaussian intensity distribution of the light sheet at the focus of the detection objective lens. (C) and (D), experimental data and fit (red line) of the Gaussian beam width in the XZ-and XY-plane [9]. All data points were obtained by knife edge measurements (see section 4.1).

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In our microscopic setup we produce the illumination pattern approximating a light sheet by coupling an elliptical beam created by a cylindrical lens telescope into the illumination objective lens. The final thickness of the light sheet is depending on the width of the incident beam, the optical parameters of the objective lens, the wavelength and the surrounding medium. The thickness of the light sheet can be determined by ray tracing software or analytically [6, 10]. Since the light sheet is formed by an (elliptical) Gaussian beam, the focal thickness can be calculated by the well-known ABCD-law of Gaussian beams in a very straightforward manner [11]. The ABCD-law is essentially a matrix description of beam propagation in optical systems. We were able to calculate all required parameters such as e.g. effective focal length, position of the back focal plane, outgoing beam width for our custom made objective lens by the ray tracing software OSLO Light (Lambda Research Corporation, Littleton, MA, USA). Then we used the ABCD-law to determine the thickness of the light sheet (z-extension), and obtained a FWHM of 1.7 µm and 2.0 µm for the excitation wavelengths 543 nm and 633 nm, respectively. The FWHM values of the light sheet height (y-extension) were 5.3 and 8.3 µm for 543 and 633nm, respectively. Additionally, we determined the focal thickness by the ray tracing program OSLO Light. Both approaches yielded identical results (Table. 1), and agreed well with the experimental results (see below).

Table 1:. Calculated and measured values for the focal height and focal thickness of the light sheet

View Table

FWHM values for the focal height (y-direction) and focal thickness (z-direction) of the light sheet for two different illuminating wavelengths. The first two lines show the theoretical values, which were either analytically calculated or determined by a ray tracing software. The last line shows the experimental results (Fig. 3, N=10), measured by a knife edge test (section 4.1). The light sheet is focused by our custom made objective lens (NA_ill=0.33) in water (n=1.33).

3.2 Calculation of the point spread function

Like in a confocal microscope, the point spread function (PSF) of a SPIM is determined by the product of the illumination intensity distribution g(x,y,z) and the imaging lens blurring function d(x,y,z):

The illumination intensity distribution is given by the elliptical Gaussian beam profile of the light sheet. Hence, it can be written as follows:

σ_y and σ_z represent the standard deviations of the Gaussian intensity distribution along the respective axes. The lens blurring function within focal plane of the imaging objective lens is given by the well known Airy formula:

Here, ν is given by

J ₁ is a first order Bessel function, n the refractive index, λ₀ designates the vacuum wavelength of the image forming light, and 2α is the opening angle of the imaging objective lens. Also, the axial extension of d(0,0,z) along the imaging axis is well known [12]:

Here, the axial optical coordinate u is written in the form valid for objective lenses with high numerical apertures.

With these equations (Eqs. 1–6) the PSF can be written as:

The height of the light sheet is much greater than the lateral extent of d(x,y,z), and therefore the exponential term in Eq. (7b) can be neglected. Hence, the PSF in x- and y-direction are approximately identical, and are defined solely by the lens blurring function of the detection objective lens.

These Eqs. (7a)–(7c) allow us to calculate theoretical estimates for the lateral and axial FWHM of the PSF of the SPIM setup as a measure of its optical resolution. For an imaging wavelength of λ₀=680 nm and an imaging objective lens with a NA of 1.0 we determined a FWHM of the PSF of 347 nm for the lateral and 1120 nm for the axial resolution, respectively, by a Taylor expansion of Eqs. (7a)–(7c).

4. Experimental results

4.1 Light sheet characterization

To measure the true extension of the light sheet in the water chamber a knife edge test was used [13]. In the knife edge test a razor blade is moved by the sample scanner across the beam path, and the unblocked intensity is measured with a power meter. In this manner the integral of the intensity profile is obtained. For Gaussian intensity profiles the data can be fitted with an error-function to determine the actual beam widths. In this manner we measured the beam widths along the illumination beam path (x-axis), and fitted the data with the function for the Gaussian beam propagation [9]. The results of this procedure were plotted in terms of the 1/e² diameters of the small and wide waist of the elliptical beam in Figs. 3(c) and 3(d), respectively. From these data the FWHM values of the beam extensions were deduced, and listed in Table 1. The experimentally determined values are in excellent agreement with the theoretical estimates. Most importantly, we succeeded in obtaining a very small extension of the light sheet along the imaging axis.

The field-of-view with optimal contrast is suggested by the dimensions of the light sheet, which we define by the Rayleigh length along x- (21 µm) and the FWHM values of the y- (5.3 µm) and z-direction (1.7 µm) for 543 nm excitation light. For the red HeNe laser emitting at 633 nm, these dimensions were 29 µm×8.3 µm×2.0 µm.

4.2 Optical resolution

The 3D extension of the SPIM-PSF was measured with red fluorescent microspheres using excitation with 633nm He-Ne laser light. Microspheres with diameters of 40 nm and 200 nm (Invitrogen, Karlsruhe, Germany) were used for lateral and axial resolution measurements. The microspheres were embedded in agarose and acted as point-like light sources, which were moved in 100 nm steps along the optical detection axis while being imaged by the CCD camera. The intensity distribution within the focal plane and along the detection axis was plotted, and the data were approximated by Gaussian functions to determine the FWHMs of the lateral and axial resolution (see Fig. 4).

 

Fig. 4. Comparison of calculated and measured PSF. Experimentally determined (A) lateral and (B) axial point spread functions. Fluorescent microspheres were illuminated with a 633 nm He- Ne Laser, and imaged with a water-dipping objective lens (NA 1.0). The data were fitted with a Gaussian function to determine the FWHM (red, dashed lines). The theoretical curves were calculated with Eqs. (7a) and (7c) for the lateral and axial PSFs, respectively.

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We obtained 350±40 nm and 1.13±0.02 µm for the lateral and axial FWHM, respectively, for an emission wavelength of 680 nm. These results were in excellent agreement with the theoretical estimates (347 nm and 1120 nm, see above). We achieved an increase in axial resolution of more than 50% compared to previously presented results [6, 10].

4.3 Contrast improvement by SPIM

One of the beneficial consequences of optical sectioning microscopy, and hence the perpendicular illumination-imaging configuration, is a significantly improved image contrast compared to a standard epi-illumination microscopy in thick specimen. We verified this feature by imaging a sample containing fluorescent microspheres on a homogeneous fluorescent background with both illumination geometries. To this end we prepared a sample of diluted fluorescent microspheres (Invitrogen, dark red, diameter 210 nm), which were fixed and mounted in 1% agarose containing varying concentrations of dextran molecules (500 kDa), which was covalently conjugated to Atto633 (Atto Tec, Siegen, Germany). The dye concentrations were determined by reference measurements in a confocal laser scanning microscope (LSM510 Meta, Zeiss, Jena, Germany). The specimen could be illuminated for extended time periods without any significant photobleaching. Switching between SPIM and epi-illumination was achieved by inserting a dichroic beam splitter into the detection beam path (see Fig. 2). Imaging was performed in both cases with the same NA 1.0 objective lens. Thereby we could image the same specimen region with both illumination configurations. Laser power was adjusted such that in both imaging modes approximately identical maximum fluorescence signals were obtained.

 

Fig. 5. Contrast improvement in SPIM versus epi-illumination microscopy. (A) Contrast values of dark red fluorescent 210 nm microspheres were determined using SPIM and epifluorescence microscopy as a function of homogeneous dye (Atto633) concentration in sample. SPIM images showed a strong background reduction, leading to a distinct contrast improvement. The maximum fluorescent intensity was kept at the same level for both cases. (B) Example frames showing the beads upon SPIM and epi-illumination microscopy at a background dye concentration of 460 nM.

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Contrast, C, is defined by the maximum fluorescent intensity of the signal, I_max, above background, I_min, divided by the sum of both values, or C=(I_max-I_min)/(I_max+I_min). Datasets were acquired by moving the specimen axially trough the focal plane. Maximum intensities were determined at the beads’ brightest pixels, I_min was the averaged intensity of the background. For each data point at least 8 beads and background values were determined. The contrast values for both illumination types were plotted in Fig. 5 as a function of dye concentration up to 1 µM. Obviously, the image contrast was clearly superior when SPIM was used. At high fluorophore concentration, where imaging with epi-illumination becomes problematic, obtaining distinct signals with SPIM is still feasible. Two images demonstrating this effect for a dye concentration of 460 nM were shown in Fig. 5(b). Here, the contrast improvement by SPIM was especially striking.

It should be noted that background fluorescence is strongly dependent on the sample characteristics. Consequently, the quantitative impact of the illumination geometry varies strongly with the specimen. In general, however, SPIM allows observation of single particles at higher concentrations, where in an epi-fluorescence microscope the single particle signals would be dominated by out-of-focus background fluorescence.

 

Fig. 6. Diffusion of single quantum dots in aqueous solution (A) Single frames illustrating the diffusion of a red fluorescent quantum dot (λ_em=655nm). The frames were acquired with an integration time of 4 ms. In each frame the position of the dot was determined, and assembled into the trajectory (shown in red). (B) A jump distance histogram was fitted (red) with the probability density function for determination of the diffusion coefficients. The histogram comprised two components, which were due to Qdot monomers (green) and Qdot aggregates (blue).

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4.4 Imaging and tracking of quantum dots in aqueous solution

Previous realizations of SPIM focused onto the special imaging properties with regard to the obtainable resolution. We see an especially great potential in applying the technique to single particle tracking in 3D-extended samples, which suffer from inherently low SNR when epi-illumination is used. 3D particle tracking is based on three requirements, namely high resolution, high contrast and high imaging rates. To demonstrate the capabilities of our SPIM setup to meet these requirements we visualized the diffusion of nanometer-sized quantum dots in aqueous solution. As a sample we used streptavidin-conjugated red fluorescent quantum dots (λ_em=655nm; Invitrogen) in 0.5% BSA buffer solution at a concentration of 200 pM. The liquid sample was mounted in a hollow agarose cylinder as described in section 2. For excitation we used the 633 nm He-Ne laser. Imaging was performed with a fast, electron-multiplying CCD camera (128×128 pixels, iXon DV 860 BI, Andor Technologies, Belfast, Ireland) supplemented with a 4× magnifier yielding a pixel size of 100 nm in the object plane. Movies from mobile quantum dots were acquired using SPIM with a single frame integration time of 4 ms at a frame rate of 243 Hz. Several example frames from a movie were shown in Fig. 6(A). To extract the diffusion coefficient from the image data we traced the diffraction-limited quantum dot signals using a commercial ImageJ plug-in for particle tracking (IL Tracker Version 1.01b), and analyzed the jump distance distribution of the quantum dots from frame to frame [16]. In Fig. 6(B) we plotted the normalized frequency distribution in a histogram, and subsequently fitted the data by the following equation [16]:

The equation describes the jump distance probability density function for i diffusive species, where A_i is the fractional amount of each component. D_i is the respective diffusion coefficient and r the jump distance covered in the time interval Δt. In this manner we determined the diffusion coefficients of Qdots655 as D₁=17.5±3.2 µm²/s, which was in perfect agreement with earlier results [17]. It is well known that Qdots tend to aggregate in solution. Therefore, we detected a slow diffusing fraction with D₂=5.5±0.3 µm²/s besides the fast diffusing Qdots, which was presumably due to larger quantum dot aggregates. This experiment demonstrated the capability of the SPIM setup for single particle tracking in a very direct manner. Usually in single molecule tracking experiments in wide-field microscopy require very low sample concentrations, otherwise the background fluorescence inhibits detection of single particles.

5. Conclusions

We constructed an optical sectioning microscope based on selective focal plane illumination featuring an especially thin illumination slice. We used the ABCD-law of Gaussian beams and ray-tracing to calculate the characteristics of our illumination sheet, which were verified by quantitative measurements. Thus we demonstrated various improvements compared to previous reports, for instance an axial slicing FWHM of 1.7µm at λ₀=543nm and 2.0 µm at λ₀=633nm only, as well as a lateral resolution of 350 nm and an axial resolution of 1.13 µm, both at λ₀=680nm. The striking enhancement of the contrast suggests that SPIM is a valuable tool to observe the dynamics of single particles and molecules under critical conditions such as weak signals and high particle concentration. This was demonstrated by imaging and analyzing the rapid diffusive motion of single streptavidin-conjugated quantum dots in aqueous solution at a time resolution of 4 ms. Altogether, the development of this highresolution SPI-microscope eliminated major problems in single molecule microscopy in 3D-extended specimen. Last not least, this instrument will allow the direct tracking of single particles within living cells in full three dimensions by keeping a selected particle in focus and adjusting the axial sample position using a feed-back loop.