1. Introduction

Fluorescence microscopy enables biologists to observe the fine structures of specimens with great contrast and specificity through fluorescent labeling; the extension of spatial resolution beyond the classical diffraction limit is hence of critical importance to reveal the fine structures in increased detail for an improved understanding of their functions and interactions. Optical resolution - the ability of a microscope to distinguish two close objects - depends on either the point-spread function (PSF) or the optical-transfer function (OTF) of the microscopic system; the former corresponds to the image of a point emitting source formed by a microscopic system in real space, whereas the latter is defined as a finite region of spatial frequency that is observable. Accordingly, various super-resolution microscopic techniques related to confocal or wide-field microscopy have been developed to narrow the PSF profile or to extend the OTF region [1–12]. Among them, structured illumination microscopy that uses a structured light pattern to illuminate samples can extend the OTF region of a wide-field fluorescence microscope by a factor approximately two in specific directions, consequently yielding a doubled resolution [4, 5, 6, 9]. Resolution below 100 nm has been realized with a nonlinear structured illumination scheme [13–15] or the incorporation of SIM to total internal reflection fluorescence (TIRF) microscopy [16–18]. In a further advance, three-dimensional resolution was enhanced on either using three mutually coherent light beams to generate an interference pattern varying both laterally and axially [19] or combining SIM with the image-interference and incoherent-interference-illumination microscopy (I⁵M) to implement a new type of wide-field light microscopy, I⁵S (taken from the first letter of I⁵M and SIM, respectively), that uses two, similar, opposing objectives for structured illumination and emission collection coherently [20]. These SIM-based techniques will definitely advance the applications of wide-field fluorescence microscopy in bioimaging research.

The basic concept of SIM is to illuminate samples with a structured light pattern to encode undetectable high-frequency information into detectable smaller frequency. Three individual images are typically taken with the illumination pattern at three phases to reconstruct an image that has an improved resolution in a direction perpendicular to the line pattern; rotations of the illumination pattern to at least three orientations - 0°, 60°, and 120°, are also required to produce a near isotropic resolution in the lateral direction [5, 6, 19]. The phase shifts and rotations of the illumination pattern are, however, time consuming, and require great mechanical precision if a diffraction grating with mechanical motion is used to generate the illumination patterns; additional data processing is also necessary to eliminate the long-time drifts and position offsets.

A liquid-crystal spatial light modulator (SLM) can serve as either a patterned mask for two-dimensional structured illumination or a dynamic grating to generate mutually coherent light beams to form an interference illumination pattern [16,18]. The former application is typically limited to pattern orientations 0° and 90° because of the simplicity of pattern design and data analysis, and also because of large variations in periods and complication of data analysis for other pattern orientations. A high-resolution image reconstructed merely from 0° and 90° pattern orientations is, however, anisotropic as the overlaps of extended frequencies in other directions, particularly 45° and 135°, is small. For an application to interference patterns, the SLM modulates the phases of liquid crystals to shift and to rotate an illumination pattern rapidly and precisely; the use of a SLM can thus overcome the shortcomings of mechanical motion required with a grating. In addition, this application is not hampered by the pixelation of a SLM; a design of special SLM patterns is plausible to generate illumination patterns at various orientations and phases with comparable periods to achieve a laterally isotropic resolution.

In this work, we designed SLM patterns in a set to generate 0°, 45°, 90°, and 135° illumination patterns of high contrast and nearly equivalent periods to decrease the exposure duration and to achieve a near isotropic enhancement in the lateral resolution on our newly launched SI microscopy system. We describe and demonstrate the concept of the design of SLM patterns and the resultant four pattern orientations at three separate phases; the pattern alternations and phase shifts are precise and rapid, at a rate as great as 60 Hz. To demonstrate the improved resolution and advantages of four pattern orientations in image reconstruction, we compared images of 100-nm beads with conventional and SI microscopy that were reconstructed from two (0°+90° or 45°+135°) and four (0°+45°+90°+135°) pattern orientations, with the support of simulations. The sectioned image of 200-nm beads was generated to show the well resolved thin ellipses along the axial direction, and the fine structures of dye-labeled actin filaments was revealed to demonstrate the prospective application of this SI system to biological systems.

2. Structured illumination microscopy

In fluorescence microscopy, the image of dye-stained objects excited with a structured illumination pattern is calculated according to this equation:

in which r is the position, D(r) is the resultant image, S(r) is the object, I(r) is the illumination pattern, P(r) is the point spread function and ⊗ denotes convolution. The spectrum in frequency space is obtained on Fourier transform of Eq. (1):

in which D(k), S(k), I(k), and OTF(k) correspond to the Fourier transforms of D(r), S(r), I(r), and P(r), respectively. As I(r) is a periodic illumination pattern, the excitation intensity on the sample plane is

in which I₀ is the averaged intensity, and k₀ and ϕ are the spatial frequency and phase of the periodic pattern, respectively. Accordingly, the spectrum D(k) is rewritten as

in which D(k) includes S(k) in the original position and two additional components S(k-k₀) and S(k+k ₀) shifted by +k₀ and -k₀, respectively. Because the maximum k₀ is limited by the observable region OTF(k), the addition of two components to extend the observable region thus improves theoretically the resolution by a maximal factor two. For simplicity, let D(k)=S(k)OTF(k), D′(k+k₀)=S(k+k₀)OTF(k) and D′(k-k₀)=S(k-k₀)OTF(k); they can be solved from three spectra D₁(k), D₂(k) and D₃(k) acquired at three separate phases - ϕ₁, ϕ₂, and ϕ₃, according to this equation:

The obtained D′(k-k₀) and D′(k+k₀) are then shifted back -k₀ and +k₀, respectively, to form D(k-k₀) and D(k+k₀) before being added to D(k) to retrieve a high-resolution image by the inverse Fourier transform. Figure 1 shows the shifts of D′(k-k₀) and D′(k+k₀) to D(k-k₀) and D(k+k₀) and their additions to D(k) to form the final spectrum acquired with 0° illumination pattern at three phases. Because the final spectrum extends the observable region in the pattern direction, the resolution is improved accordingly in the same direction. To retrieve an isotropic image, further sets of D(k), D(k-k₀) and D(k+k₀) obtained at other pattern orientations are combined before the inverse Fourier transform. In this work, we use four pattern orientations - 0°, 45°, 90° and 135°, to extend the observable regions in all directions and to simplify the data processing on the pixelation of the SLM.

 

Fig. 1. Shifts of D′(k-k0) and D′(k+k0) to D(k-k0) and D(k+k0) and their addition to D(k) to form the final spectrum acquired with 0° illumination pattern at three phases

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3. Microscope setup and image reconstruction

3.1 Microscope setup

Figure 2 shows the structured illumination microscope setup. The mainframe is an upright microscope (Nikon 80i) with a water-immersion objective (Nikon, Plan Apochromat VC, 60x, NA=1.2) to form an interference pattern on the sample plane with laser beams of orders ±1 diffracted by the SLM and to collect fluorescence on a 12-bit CCD camera (Cooke, sensicam qe) for imaging. The use of a water-immersion objective is because biological samples are generally surrounded by water. Although the oil-immersion objective has a greater NA value (e.g. NA=1.45) that allows generating an interference pattern of narrower linewidths, according to the diffraction limit, to achieve an improved resolution, the sample is required to be surrounded by index-matching fluid to reach the critical incident angle of the objective, which is uncommon for most of biological species. The SLM (Hamamatsu, X10468-04) is a reflective type of pure phase spatial light modulator based on liquid crystal on silicon (LCOS) technology.It comprises 600×800 pixels, with a pixel size 20×20 µm2, a maximal frame-refresh rate 60 Hz, and the phase can be linear modulated with continuous input signal level. The excitation source is a He-Ne laser (Lasos, 1 mW, 543 nm). This laser beam was expanded to illuminate the entire SLM at an incident angle <10°, as suggested by the manufacturer to eliminate the variation in diffraction angles ensuing from distinct SLM patterns, and diffracted mainly into zero and ±1 order laser beams. The zero-order laser beam was blocked using a small black spot marked on a slide to form a high-pass spatial filter. A lens set of four, with their respective focal lengths 25, 5, 10, and 15 cm, were used to collect, to expand and to focus the two ±1 order laser beams on the back focal plane of the objective at positions near the opposite edges to form the illumination period near the diffraction limit; the laser power on the sample is about 150 µW for each ±1 order laser beams. Because of the polarization dependence of the SLM, a λ/4 wave-plate (CVI Laser, ACWP) is also placed after the SLM to alter the laser beam from linear to circular polarization to eliminate the fluorescence variations caused by the illumination patterns at separate orientations. The maximal field of view of this setup is about 13.6×13.6 µm². Twelve images of selected size are acquired with 0°, 45°, 90°, and 135° patterns and at three phases for each pattern to reconstruct a high-resolution image. All imaging processing was conducted with programs written with MATLAB.

 

Fig. 2. SI microscope setup

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3.2 SLM Patterns

SLM patterns in a set were designed to generate the 0°, 45°, 90°, and 135° illumination patterns at three phases. A unit of three pixels is typically the simplest design of SLM patterns to generate three different phases for each illumination pattern. The other advantage of this design is that a smaller period of SLM pattern would cause the two diffracted laser beams to interfere at large angles that simplifies the optical setup to generate an illumination period near the diffraction limit on the sample plane. However, the period of the 0° (90°) pattern is 3 pixels but 3√ 2/2 pixels for that of 45° (135°) due to diagonal; a large difference ~29% in periods would cause unequal resolution enhancement, which in turn produces an anisotropic high-resolution image. To reconstruct an isotropic image, it is hence critical to design SLM patterns in two sets that can generate nearly equivalent periods. One plausible pair is 3 pixels for the 0° (90°) pattern and 4 pixels for the 45° (135°) pattern; their respective period of 3 and 2√ 2 pixels produces a small difference, ~6 %, but the phase shift π of 45° (135°) patterns caused by shifting one pixel (1/4 period) fails to generate patterns at three separate phases. Our new design is a unit 7 pixels for the 0° (90°) pattern and 10 pixels for the 45° (135°) pattern; they correspond to periods of 7 and 5√ 2 (7.07) pixels, respectively, with a difference ~1%. Figure 3 shows the SLM patterns and their corresponding illumination patterns for 0° and 45° orientations at three phases. The periods are 295 and 300 nm for 0° (90°) and 45° (135°) illumination patterns, respectively; a difference ~1.6 % agrees satisfactorily with our current setup. Also shown in the figure are two additional 0° illumination patterns with a separation 4π/7 that are generated on shifting 1/7 and 2/7 periods of the 7-pixel SLM pattern; the separation is likewise 4π/5 for the 45° illumination patterns on shifting 1/5 and 2/5 periods of the 10-pixel SLM pattern.

 

Fig. 3. 0° and 45° SLM patterns at three phases and their corresponding illumination patterns; the black ones in the SLM patterns indicate no phase retardation on the incident beam

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3.3 Imaging reconstruction

For image reconstruction, the three images at each pattern orientation were Fourier transformed and calculated according to Eq. 5 to obtain D(k), D′(k-k₀), and D′(k+k₀), followed by shifting D′(k-k₀) and D′(k+k₀) to the true positions D(k-k₀) and D(k+k₀), respectively. Because the addition of D(k), D(k-k₀), and D(k+k₀) requires sub-pixel precision, their values were derived from the three images that were resampled (from 256×256 to 512×512) by zero-padding their respective Fourier transforms and then renormalized to their original values. As for the period and modulation depth of each pattern orientation, we determined those from the illumination patterns, as shown in Fig. 3. A final parameter is the initial phase φ of each pattern orientation, which was found by complex linear regression of D(k-k₀) or D(k+k₀) against D(k) in the overlap region; i.e. for each orientation, 20 equally spaced φ from 0 to 2π were used to calculate the D(k-k₀), D(k+k₀) and D(k) in the overlap region (~2k₀×2k₀), then the spectra of D(k-k₀) or D(k+k₀) against D(k) are compared; accordingly, the initial phase ϕ is found that promises the best similarity of the spectra. Because the initial phases of the four orientation patterns change significantly with the sample location, we did the calculations for every image reconstruction. Once all parameters for four pattern orientations were determined, we averaged the four D(k) and added the averaged D(k) to the four sets of D(k-k₀) and D(k+k₀) to form a final spectrum of the sample, SD(k), before an inverse Fourier transform to obtain a high-resolution image. Typically, the total image processing time takes about 180 s with a common PC for an image size of 13.6×13.6 µm² (256×256 pixels).

Sometimes, the SD(k) is calculated through a generalized Wiener filter to suppress peripheral regions of small ratio of signal to noise as follows,

in which SOTF(k) is a calculated OTF (the calculated SI spectrum of an infinitesimal object divided by the Fourier transform of the object with NA=0.97 and a pattern period of 300 nm) and w² is the Wiener parameter (a constant that is adjusted empirically). Because the Wiener filter would cause ringing artifacts in a real-space image, a triangle function that serves as an apodization function is also implemented for data processing before the resultant spectrum becomes retransformed. All images shown in this article have resampling four-fold by Amira with the Lanczos algorithm to increase the pixelation for presenting the images at high resolution.

4. Results

For our wide-filed microscopy, the Rayleigh resolution limit is ~285 nm calculated with NA=1.2 and emission at 560 nm; experimentally, the full width at half maximum (FWHM) is 290±5 nm averaged from ten 100-nm beads with their intensity distributions fitted to a Gaussian function. The simulations and experimental results of images of 100-nm fluorescence beads (Molecular probes, F8800) for conventional wide-field and SIM reconstructed from two (0°+90° and 45°+135°) and four (0°+45°+90°+135°) pattern orientations are shown in Figs. 4 and 5 to demonstrate the improvement and difference in resolution and image.

In the simulation, the simulated conventional image was obtained from the convolution of the calculated PSF with several randomly distributed 100-nm beads. PSF was calculated from the first-order Bessel function of first kind, J ₁(r), according to the equation PSF=[2J ₁(r)/r]², where r=2πρNA/λ, ρ is a cylindrical coordinate and λ is the emission wavelength; each bead was modeled as a disc of uniform brightness. Because the Gaussian-fitted FWHM of the simulated 100-nm bead is ~240 nm; we readjusted NA to 0.97 to obtain the experimental FWHM 290±5 nm for comparison of the structured illumination images with experimental results. We also set a pixel size 53 nm for image data and used a cosine function with a period of 300 nm in the simulation of SI images to fit the experimental parameters. The conventional image and intensity distribution of the marked bead are shown in Fig. 4(a); Figs. 4(b), 4(c) show the images and intensity distributions reconstructed from 0°+90° and 45°+135° pattern orientations, and Fig. 4(d) shows those reconstructed from four (0°+45°+90°+135°) pattern orientations. All image brightness and contrasts were adjusted intentionally to show the side lobes clearly. As seen in Fig. 4(b), the 100-nm bead is diamond-like with side-lobes in four diagonal directions; moreover, the fitted FWHM, without the side-lobes taken into account, are 151 and 149 nm in 0° and 90° directions, slightly greater than 134 nm in both 45° and 135° directions. This result is contrary to an expectation of resolution improvement in the pattern orientations, ensuing from the extension of the observable region. Similarly, the 100-nm bead reconstructed from 45°+135° patterns has a square shape with a slightly superior resolution in the 0° and 90° directions, 137–134 nm compared to 152–154 nm in 45° and 135° directions (Fig. 4(c)). The advantages of reconstruction of a high-resolution image from four pattern orientations - near isotropic and increased resolution enhancement - are clearly demonstrated in Fig. 4(d), which shows round beads with smaller side lobes of ring shape and nearly equivalent FWHM 134–136 nm in four directions.

 

Fig. 4. (a-d) Simulations of images and intensity distributions of 100-nm beads for conventional and structured illumination microscopy reconstructed from 0°+90°, 45°+135° and 0°+90°+45°+135° pattern orientations; the solid lines represent Gaussian-fits and the brightness and contrasts were adjusted to show side lobes clearly

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Experimentally, the spectra of spatial frequency, conventional image and intensity distribution of the marked bead are shown in Fig. 5(a); Figs. 5(b), 5(c), and 5(d) show those reconstructed from 0°+90°, 45°+135°, and 0°+45°+90°+135° pattern orientations, respectively. The spectra of spatial frequency confirm the extension of the observable region under structured illumination; moreover, an isotropic resolution enhancement requires four pattern orientations. In Figs. 5(b) and 5(c), the diamond-like and square shapes of the 100-nm beads reconstructed from 0°+90° and 45°+135° pattern orientations agree satisfactorily with the simulations; accordingly, an anisotropic resolution improvement with a difference ~14–15 nm is observed between the averaged FWHM of directions in the two sets - 0°+90° and 45°+135°. In Fig. 5(d), the intensity distribution and the resolution improvement is near isotropic and superior, with an averaged FWHM 144±3 nm of five 100-nm beads. This result shows a resolution improvement of a factor ~2, as compared to the averaged FWHM 290±5 nm in the conventional image; moreover, with this improvement, the beads that can not be differentiated in the conventional image are well resolved in the structured illumination.

 

Fig. 5. (a-d) Experimental spectra of spatial frequency, images and intensity distributions of 100-nm beads for conventional and structured illumination microscopy reconstructed from 0°+90°, 45°+135° and 0°+90°+45°+135° pattern orientations, without additions of a Wiener filter and an apodization function; the solid lines represent Gaussian-fits

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In Fig. 6, the performance of our SI system on 200-nm beads (Molecular probes, F8809) at varied depths is compared with conventional microscopy to verify the improvement of lateral resolution and to reveal the axial intensity distribution. Figures 6(a) and 6(b) show the in-focus images of beads for conventional and SI microscopy, respectively; Figs. 6(c) and 6(d) show the corresponding axial (xz) images of the blue region in Figs. 6(a) and 6(b). The axial images were constructed from 30 sections separated by 100 nm with the brightest point projection method of ImageJ program. The well separated thin ellipses in the SI confirm the improvement of lateral resolution, but not in the axial resolution. As seen in Fig. 6(e), the axial intensity distributions along the red dotted lines have FWHM ~800 and ~900 nm for conventional and SI, respectively; moreover, the asymmetry of both curves is likely due to the spherical aberration of the objective. This result is expected because the OTF does not extend in axial direction with this two-beam SI method; three-beam interference is required to double the resolution in both the lateral and axial dimensions, as demonstrated previously by Gustafsson et. al [19]. Despite that concern, the improved contrast of the thin ellipse in SI indicates decreased crosstalk between individual beads at separate axial positions; this technique hence enables improving the image contrast of a thick sample.

 

Fig. 6. (a, b) In-focus images of 200-nm beads for conventional and structured-illumination microscopy, respectively, (c, d) corresponding axial images of the blue region in Figs. 6(a) and 6(b), taken at a step 100 nm for each section, and (e) intensity profiles along the red dotted lines

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For biological applications, Fig. 7 shows the reconstructed images of a dye-labeled actin cytoskeleton near the edge of a HeLa cell. The actin filaments were labeled with Rhodamine phalloidin that emits fluorescence at 565 nm upon excitation at 540 nm; twelve images were acquired in ~30 s at four pattern orientations and three phases for each pattern orientation for image reconstruction. Figures 7(a) and 7(b) demonstrate that actin fibres aligned with the illumination patterns have improved resolution; as indicated by red arrows, the fibres in the 45° direction are narrower with 45°+135° reconstruction than with 0°+90° reconstruction, and vice versa. Hence, to reveal fine structures of biological specimens in more details, particularly for randomly orientated structures, achieving an isotropic resolution with completed pattern orientations is important. Figures 7(c) and 7(d) show images reconstructed with four pattern orientations and additions of a Wiener filter and an apodization function, respectively; the nearly isotropic resolution extension signifies the advantage of SIM and the suppression of background noise associated with a decrease of resolution slightly in Fig. 7(d), unlike for the beads, is essential to retrieve an image of satisfactory quality for biological specimens.

For a test of the biological resolution, Figs. 8(a) and 8(b) show a comparison of conventional and SI images of a dye-labeled actin cytoskeleton. Four fibres, entirely unresolved in the conventional image, are well resolved in the SI image with a minimal separation 186 nm; their intensity distributions are shown in Fig. 8(c). In addition, the Gaussian-fitted FWHM 110 and 281 nm were obtained from one actin fibre in the SI and conventional images, respectively. This result indicates a resolution enhancement greater than a factor two; the cause might be image contrast that was enhanced by the interference of the emissions of labeled actin fibres at various locations.

 

Fig. 7. SI image of a dye-labeled actin cytoskeleton at the edge of a HeLa cell with (a) 0°+90°, (b) 45°+135°, (c) 0°+90°+45°+135° reconstructions, and (d) a Wiener filter and an apodization function on image (c) to show the differences in resolution resulting from the reconstructions of separate pattern orientations

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Fig. 8. (a) Conventional image of a dye-labeled actin cytoskeleton, (b) the corresponding SI image after Wiener filter and apodization treatment for comparison, and (c) the intensity distributions along the dotted lines to show the well resolved structures separated by 186 nm in SI image

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5. Conclusions

The use of a SLM in SIM allows rapid and precise pattern alternations at varied phases and orientations, without mechanical calibration, but the resolution enhancement might be limited by the complexity of pattern generation at other orientations than 0° and 90°. In this work, we used a SLM as a phase grating to generate illumination patterns of great illumination contrast and nearly equivalent periods at four orientations - 0°, 45°, 90°, and 135°, and demonstrated the differences in resolution and image on comparison of the images of 100-nm beads that were reconstructed from two (0°+90° and 45°+135°) and four (0°+45°+90°+135°) pattern orientations both experimentally and simulatedly. The experimental results agree satisfactorily with simulations; both confirm that the resolution enhancement is anisotropic with two pattern orientations, but near isotropic with four pattern orientations in the lateral direction. Calculated from the averaged FWHM 144±3 nm, this SIM setup achieves a nearly isotropic lateral resolution to 0.25 wavelengths.

The method by interfering two coherent beams to generate an illumination pattern directly on the object being imaged is expected to have an improved resolution because the generation of a high-frequency structured illumination pattern is unlimited by the NA of the objective[9]. However, with large spatial frequency of the structured illumination pattern, the overlap between the original frequency region and the shifted frequency region, such as the D(k) and D(k+k₀) (or D(k-k₀)) spectra shown in Fig.1, will become small or even missed due to the constraint of optical transfer function of the system. A small overlap will cause the frequency distribution anomalous that could consequently generate some unexpected side-lobes in the reconstructed image to deteriorate the resolution and image quality. The use of multi-beam interference method through a lensless focusing scheme to generate a move complex aperiodic illumination pattern can overcome the problem of small overlap of the spectra and increase the resolution by a factor of more than two; however, this method is currently only demonstrated on low NA objectives [21].

That there is no improvement in the axial direction of our system is confirmed from the sectioned images of 200-nm beads at various depths; nevertheless, the improved contrast of thin ellipses in the axial direction indicates decreased crosstalk between individual beads at separate axial positions and plausibly allows improved differentiation. The addition of a zero diffraction order to generate three-dimensional interference illumination patterns definitely doubles the axial resolution, as well as the lateral resolution, as demonstrated previously [19]. We also demonstrated high-resolution images of actin filaments inside HeLa cells to show the advantage of the enhancement of isotropic resolution and the prospective biological applications of this new system.