1. Introduction

Super-resolution optical microscopy innovates physics, chemistry, and biology fields by revealing microscopic structures of various samples at a spatial resolution beyond the diffraction limit, and this has been recognized with the award of the Nobel Prize in Chemistry in 2014. Among the super-resolution optical microscopic techniques, localization microscopy [1–4] achieves super-resolution via stochastically exciting and precisely localizing individual molecules that are apart from each other. Stimulated emission depletion (STED) [5–9] achieves super-resolution by superimposing a red-shifted, doughnut-shaped depletion light with Gaussian-shaped excitation light. Once the depletion light switches off the fluorophores except for its intensity minima, the fluorophores in the fluorescing state will be confined in a reduced region. In parallel with these developments, structured illumination microscopy (SIM) was developed as an alternative means to achieve optical super-resolution [10,11]. SIM utilizes moiré patterns that are generated when projecting on a sample periodic fringes, which downshift high-frequencies of the object wave into the frequency support of the microscope and eventually enhance the resolution of the microscope. Compared to the other two approaches, SIM is a fast (wide-field), minimally-invasive technique and hence it is most suitable for live sample imaging [12–14]. Structured illumination can also enhance the spatial resolution of quantitative phase microscopy that images transparent samples in a label-free manner [15], but the enhanced resolution is still below the diffraction limit [16].

Nowadays, SIM usually uses a digital micromirror device (DMD) or spatial light modulator (SLM) to generate and switch structured illumination patterns for different orientations and phase shifts at a speed of tens of frames per second (FPS) [17]. In DMD/SLM-based linear SIM, 90 nm resolution can be achieved with 180nm-period structured illumination. Yet, due to the limited pixel number of SLM or DMD (e.g., 1920 × 1080), the number of the fringes generated is often below 500, confining the field of view (FOV) of SIM below 90 × 50 µm². Such a small FOV is not sufficient for many applications, such as SR imaging of tissues or pathological slices. As one of the solutions, a large-field SR image can be synthesized by mechanically translating a sample in 2D through the FOV of SIM, taking raw images for a SR image, and later synthesizing a large SR image using an image mosaic algorithm [18,19]. This method is straightforward but time-consuming due to the involved mechanical translation of the sample. The projection of a physical grating on samples was employed to generate thousands of fringes in a large FOV [20]. Mechanical translation and rotation of the grating limit the method to only static samples. Large-field SIM can also be achieved by using interference of the beam pairs from a radially-opposite fiber array [21] or two scanners [22]. Recently, we demonstrated the combination of a physical grating and a SLM can realize fast fringe selection and phase shifting in SR SIM imaging [23].

In aside to using 1D periodic structured illumination, lattice illumination was proved for its application to SIM super-resolution imaging [24]. Calvarese utilized optical waveguides to generate lattice patterns [25]. Zeiss utilized a 2D grating to generate quadratic lattice patterns for super-resolution imaging and achieved a 60-nm spatial resolution together with an advanced deconvolution procedure [26]. In Zeiss’s lattice SIM configuration, phase shifting of the lattice patterns is performed by rotating two glass plates with galvanometric scanners. Schropp demonstrated 2D lattice SIM for optically-sectioned imaging using seven-step coherent hexagonal structured illumination [27]. In 2014, lattice patterns generated by two SLMs were applied to light-sheet microscopy, providing super-resolution, 3D images of biological samples of different scales [28]. In essence, the above-mentioned lattice patterns are spatially periodic interference patterns resulting from the coherent superposition of a finite set of plane waves [29]. There are more interference terms involved in these patterns, and hence seven or even more phase-shifted images are required to reconstruct a SR image.

In this paper, we present a large-field, five-step lattice structured illumination microscopy (Lattice SIM). The lattice pattern is generated by incoherent addition of two orthogonal 1D fringes. Consequently, the lattice SIM needs only five raw intensity images to reconstruct a super-resolved SIM image, enhancing the imaging speed and reducing the photo-bleaching both by 17%, compared to linear SIM with two directions and three shifts [23]. The grating projection also allows for three-fold spatial bandwidth product (SBP) enhancement compared to classic SIM based on SLM/DMD for fringe projection. We demonstrate the proposed large-field, five-step SIM by imaging fluorescent beads and lily stigma.

2. Methods

2.1 Concept of lattice pattern generation

The concept of lattice SIM is shown in Fig. 1(a). 2D lattice patterns are generated by projection of a 2D grating. The interference of the ±1 diffraction orders in the -x and -y directions yields 2D grid patterns. Phase shifting of the lattice patterns is performed by phase modulating the +1^st orders of the generated lattice field on a plane close to the Fourier plane, where the spectra of the ±1 diffraction orders are separate from each other, as shown in Fig. 1(b). We mean to set a defocusing distance d between the Fourier plane and SLM plane, so that the broadly-extended defocused spectrum can be well sampled by hundreds of SLM pixels, avoiding the injury of the SLM by the laser light.

 

Fig. 1. Schematics of large-field lattice pattern generation. (a) Scheme of lattice pattern generation utilizing a 2D grating, a SLM, and polarization mask. (b) Phase and polarization modulation on the spectra of illumination light. (c) Spatial filter mask for selecting the ±1st diffraction orders of the 2D grating. (d) Schematics of genratred lattice pattern

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Two polarizers with their polarization azimuth of 90° and 0° (i.e., -s and -p polarizations) are respectively placed on the spectra of the ±1st orders along the -x and -y directions and these polarizations can be maintained during the whole imaging process. In the middle Fourier plane of the projection system, the spectrum of the lattice field is further filtered by four circular holes, which block the spectra of the illumination light except for the ±1^st orders (Fig. 1(c)). Hence, the generated lattice pattern is incoherent addition of two orthogonal 1D-fringes along the -x and -y directions, as is shown in Fig. 1(d). It is worth pointing out that the number of the lattice patterns is solely determined by the period and size of the 2D grating. Nowadays, advanced manufacturing techniques can fabricate larger-scale gratings with small periods to generate thousands of lattice patterns of which the number is tens of folds of the SLM/DMD-generated patterns.

2.2 Experimental setup of lattice SIM

The schematic diagram of the proposed high throughput lattice SIM is shown in Fig. 2. A 532 nm, non-polarized diode laser (1875-532L, Laserland, Wuhan, China) is used as the light source. A polarizer P₂ is located on the beam path to convert the illumination into horizontally polarized light, ensuring the maximum modulation efficiency of SLM. The intensity of the illumination beam can be adjusted by rotating the polarizer P₁ that sits between the polarizer P₂ and the laser. The beam is further expanded by a telescope system L₁-L₂, so that the uniform illumination is generated to cover a 22 × 22 mm² 2D grating, which is, in practice, composed of two 1D gratings (80 lines/mm, #46-070, Edmund Optics, Barrington, New Jersey, America) with their grating lines orthogonally orientated. The 2D grating diffracts the illumination beam into multiple plane waves in different directions. The ±1^st diffraction orders with 45°/225° (-45°/135°) azimuths have the highest diffraction efficiency and are used to form lattice patterns. For simplicity, the beam pair with 45°/225° azimuths are denoted with s- beams and those with 45°/135° azimuths are denoted with t- beams. Here we use s- and t- (instead of s- and p-) to indicate two beams with orthogonal polarizations in general. Noting that the above angle setting ensures all the ±1^st order spectra fall into the SLM target.

 

Fig. 2. The schematic setup of high-throughput lattice SIM. The bottom and top of the inset show the phase-shifted lattice patterns,and a chematic morie pattern generation when projecting lattice patterns on cellular structures. DM, dichroic mirror; L₁-L₆, achromatic lens; M, mirror; MO, micro-objective; NPBS, non-polarizing beam splitter; P₁-P₄, polarizer; QW, quanter-wave plate, TL, tube lens.

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Both the s- and t- beams are Fourier transformed by the lens L₃, and their spectra appear on a plane with a distance d from a SLM (1920×1200 pixels, pixel size 8 µm, HDSLM80R, UPOLabs Co., Ltd., China). After being phase modulated by the SLM, these spectra are further imaged by a telescope system L₄-L₅ to a spatial filter mask. The mask contains four circular holes (diameter 350 µm, spacing 5.5 mm), which blocks the spectra of the illumination light except for the ±1^st orders. A quarter-wave plate (QW) located in the back focal plane of the lens L₄ converts both the -s and -t beams into circular polarization. Two polarizers P₃ and P₄ with their polarization azimuths 0° and 90° are placed on the spectra of the s- and t- beams, avoiding the interference between the s- and t- beams. After the filtered spectrum is further Fourier transformed by the lens L₆, lattice patterns are generated and are further relayed to the sample plane using two telescope systems L₅-L₆ and TL-MO. In essence, the generated lattice pattern is incoherent superimposition of two groups of interference patterns with their grating lines in the ±45° directions. It is worth mentioning that here the 90° and 0° polarization setting on the -s and -t beams preserves the orthogonal linear polarizations for the s- and t- beams during the imaging process. In case a larger SLM is available, it is preferable to set the propagation azimuths of the grating vectors along 0° and 90° (currently, they are along the diagonal directions of the SLM) to have optimized fringe contrast [30]. Alternatively, we can use two dichroic mirrors arranged perpendicularly in 3D to compensate for such unwanted polarization conversion by dichroic mirrors [30].

When a sample is illuminated by the lattice pattern, a 2D Moire pattern will be generated, as shown in the inset of Fig. 2. The Morie pattern is imaged by a telescope system MO-TL to a CMOS camera (4096×3000 pixels, pixel size 3.45 µm, Basler ace acA4112-20um, Basler Vision Technology (Beijing) Co., Ltd., China). A dichroic mirror DM (FF545/650-Di01-25×36, Semrock, USA) is placed to separate the excitation light and fluorescence. In addition, a filter (FF01-562/40-25, Semrock, USA) is placed in front of the CMOS to block the excitation beam and the stray light from the background.

To reconstruct a super-resolution lattice SIM image, the lattice patterns are phase shifted by loading five different quadrant phase masks to the SLM, and the generated intensity images are recorded in sequence. For each phase mask, the third and the fourth quadrants have the fixed phase value of 0, while the phases of the first and the second quadrants, indicated with φ_s,i and φ_t,j, are changed in pairs. The indices i and j indicate the phase-shifting index performed in the s- and t- directions, respectively. Specifically, the combination of φ_s,i and φ_t,j of [0, 0], [0, 2π/3], [0, 4π/3], [2π/3, 0], and [4π/3, 2π/3] were used in our experiment. After five intensity images of a sample are recorded in sequence, a super-resolved SIM image can be reconstructed using the approach described in section 2.3. The framerate of the SLM is 60 frames per second (FPS), and the maximal framerate of the CMOS camera is 23 FPS in full-frame exposure mode. Therefore, the super-resolution imaging speed of the proposed lattice SIM is 23/5 = 4.6 FPS.

Figure 3(a) shows one frame of the phase-shifted lattice patterns recorded when placing a mirror on the sample plane and recording the intensity pattern without the fluorescence filter. Figure 3(b) and 3(c) show three phase-shifted lattice patterns generated with the phase shift combination of [0, 0], [0, 2p/3], [0, 4p/3]. The intensity distributions along a line crossing the same location in three phase-shifted intensity patterns in the -s direction were extracted and shown in Fig. 3(d). It is found that the period of the periodic modulation is 0.69 µm under a microscopic objective (20×/0.75NA, MRF00200, Nikon). The sinusoidal fit of the three intensity curves indicates that the phase shifts are [0, 2.05, 3.92] rad, which is close to the theoretical values of [0, 2π/3, 4π/3] rad.

 

Fig. 3. Phase-shifted lattice patterns in lattice SIM. (a) exemplary lattice pattern recorded when placing a mirror on the sample plane. A sub-region indicated with the yellow box is magnified and shown as a closeup in the right panel. The schematic images (b) and real-images (c) of the phase-shifted lattice patterns. (d) Intensity distributions along the dotted line in (c)

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2.3 Reconstruction of lattice SIM

In lattice SIM, the lattice pattern is generated by an incoherent superimposing of two groups of 1D periodic fringes, as shown in Fig. 3(a). Hence, the intensity of the lattice pattern can be written as:

Under the illumination of the lattice pattern ${I_{i,j}}({\vec{r}} )$, a fluorescently labelled sample S($\vec{r}$) is imaged by the telescope system MO-TL to the CMOS camera, and the recorded intensity image corresponds to the convolution of $S{I_{i,j}}({\vec{r}} )$ with the intensity point spread function ${h_D}$ ($\vec{r}$) of the system:

Here $\vec{k}$ is the spectrum coordinate in the Fourier domain, ${\tilde{D}_{i,j}}({\vec{k}} )$, ${\tilde{h}_D}({\vec{k}} )$, $\tilde{S}({\vec{k}} )$, and ${\tilde{I}_{i,j}}({\vec{k}} )$ are the frequency spectra of ${D_{i,j}}$($\vec{r}$), ${h_D}$($\vec{r}$), S($\vec{r}$), and ${I_{i,j}}({\vec{r}} )$, respectively. After we bring Eq. (1) into Eq. (3) and use the convolution theorem, the spectrum of the acquired raw image ${\tilde{D}_{i,j}}({\vec{k}} )$ is given by [31]:

Here, the constant factor I₀ acts trivially as to scale the intensity of the captured imaged and thus may be assumed to be 1. Eq.(4) can be written in a matrix form for five different phase shift combination [φ_s,i, φ_t,j]:

It is found from Eq.(6) that ${\tilde{C}_0}({\vec{k}} )$, ${\tilde{C}_{s,1}}({\vec{k}} )$, ${\tilde{C}_{s, - 1}}({\vec{k}} )$, ${\tilde{C}_{t,1}}({\vec{k}} )$, and ${\tilde{C}_{t, - 1}}({\vec{k}} )\; $ can be solved from five raw intensity images acquired under five lattice-illuminations with different [φ_s,i, φ_t,j], only if the rank of the coefficient matrix in Eq.(6) is five. In our experiment, we keep using [0, 0], [0, 2π/3], [0, 4π/3], [2π/3, 0], and [4π/3, 2π/3] for [φ_s,i, φ_t,j] in the five-step phase shifting of lattice illumination, with which the rank of the coefficient matrix is five. Note that this phase shift combination is not unique and can even be optimized later on for higher robustness.

The carrier-frequency of ${\tilde{C}_{s,1}}({\vec{k}} )$, ${\tilde{C}_{s, - 1}}({\vec{k}} )$, ${\tilde{C}_{t,1}}({\vec{k}} )$, and ${\tilde{C}_{t, - 1}}({\vec{k}} )$ can be determined by identifying the point with maximal intensity in the spectrum or, more preferably, analyzing the autocorrelation of ${\tilde{D}_{i,j}}({\vec{k}} )$ with its shifted variant ${\tilde{D}_{i,j}}({\vec{k} - {{\vec{k}}_m}} )$ [31]. We show as an example the frequency spectrum of ${\tilde{C}_{s,1}}({\vec{k}} )$ in Fig. 4(a), where the point with the maximal intensity has the coordinates κ_x =6.0 × 10⁴ µm^-1 and κ_y =5.2 × 10⁴ µm^-1, respectively. Then, ${\tilde{C}_0}({\vec{k}} )$, ${\tilde{C}_{s,1}}({\vec{k}} )$, ${\tilde{C}_{s, - 1}}({\vec{k}} )$, ${\tilde{C}_{t,1}}({\vec{k}} )$, and ${\tilde{C}_{t, - 1}}({\vec{k}} )$ are moved to their correct position in Fourier space, added up, and deconvoluted with ${\tilde{h}_D}({\vec{k}} )$ [32]:

 

Fig. 4. Carrier-frequency determination and spectrum synthesis. (a) The spectrum of ${\tilde{C}_{s,1}}({\vec{k}} )$. (b) Spectrum synthesis. The blue circle denotes the support area of the imaging system’s optical transfer function (OTF). The yellow circles denote the spectra of ${\tilde{C}_{s,1}}({\vec{k}} )$, ${\tilde{C}_{s, - 1}}({\vec{k}} )$, ${\tilde{C}_{t,1}}({\vec{k}} )$, and ${\tilde{C}_{t, - 1}}({\vec{k}} )$ after deconvolution.

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Eventually, after we perform an inversed Fourier transform on the synthesized spectrum, a super-resolution SIM image can be obtained. In addition, using the terms I_s,1($\vec{r}$), I_s,-1($\vec{r}$), I_t,1($\vec{r}$), and I_t,-1($\vec{r}$), the optically sectioned image can be obtained by I_section(x,y) = [|I_s,1($\vec{r}$)|+ |I_s,-1($\vec{r}$)|+ |I_t,1($\vec{r}$)|+ |I_t,-1($\vec{r}$)|]/4, with which the out-of-focus background is removed [27,34].

The above lattice SIM reconstruction has been programmed with Matlab, which can be freely found in Code 1 (Ref. [35]). The program can reconstruct a super-resolution image from five raw images of 1024 × 1024 pixels within 2.3 seconds in a computer with 3.7 GHz CPU and 64G RAM. The reconstruction can be further enhanced by using an end-to-end, physics-driven deep residual neural network, such as ML-SIM [36], which has the potential to reconstruct a super-resolution image with four or even fewer raw images once being trained with five raw images.

3. Experiments and results

3.1 Lattice SIM imaging of fluorescence beads

The first experiment was performed to demonstrate spatial resolution enhancement and high throughput of the proposed lattice SIM. In this experiment, fluorescent beads (RF240C, excitation-peak wavelength 535 nm, Shanghai Huge Biotechnology Co., Ltd, China) with a diameter of 240 nm were immobilized on a cove slip and used as the sample. Lattice SIM equips a low-magnification objective (20×/0.75), providing a FOV of 690×517 µm². The numerical aperture (NA_detect= 0.75) of the objective limits the lateral resolution under epi-illumination to δ=λ_em/(2NA) = 370 nm, where λ_em= 554 nm is the emission-peak wavelength of the fluorophore used. Considering the periods of the lattice illumination along the two orthogonal directions are both P_lattice= 0.69 µm, the theoretical enhancement on the lateral resolution of SIM is [λ_em/(2NA)]/[λ_em/(2NA+λ_em/P)] = 1.6 [37], implying a theoretical resolution of 231 nm (defined with the above-mentioned Abbe criterion) for SIM.

In the experiment, we loaded, in sequence, five phase masks with the phase shift combination of [0, 0], [0, 2π/3], [0, 4π/3], [2π/3, 0], and [4π/3, 2π/3], and recorded accordingly five phase-shifted intensity images. The acquired five raw images are shown in Fig. 5(a), of which a sub-region is selected and magnified in Fig. 5(b). Figure 5(c) shows the further-magnified view of a ROI in Fig. 5(b), from which periodic lattice patterns can be seen. In addition, the frequency spectrum of the intensity image acquired with the first lattice illumination is shown in Fig. 5(d). Apparently, there are two groups of spectra, distributed along the ±45°directions, respectively.

 

Fig. 5. Intensity images of 240 nm-diameter fluorescent beads under lattice illumination. (a) Intensity images of fluorescence beads obtained under the lattice illumination with the phase shift combination of [0, 0], [0, 2π/3], [0, 4π/3], [2π/3,0], and [4π/3, 2π/3]. (b) The magnified views of the ROI indicated with the box in (a). (c) The further magnified view of the box in (b). (d) The frequency spectrum of the first intensity image in (a). Scale bars in (a), (b), and (c) indicate 100 µm, 8 µm, and 2 µm, respectively.

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Eventually, the super-resolved image of the sample can be obtained with the reconstruction algorithm explained in Section 2.3 and is shown in Fig. 6(a)-right, in comparison with the conventional wide-field image in Fig. 6(a)-left. The comparison of the SIM images and wide-field images from five different regions of interest (ROI) in Fig. 6(b) tells that the SIM images have significantly enhanced spatial resolution. And, this conclusion is further confirmed by analyzing the intensity profiles along a line crossing two adjacent beads in Fig. 6(c). To quantitatively evaluate the lateral resolution, twenty fluorescent beads were randomly chosen from Fig. 6(a). The intensity distributions along the line crossing the bead centers were extracted and fitted with Gaussian functions. And the statistics results are shown in Fig. 6(d). The results show that the averaged FWHM is 560 ± 30 nm (mean ± half-width of the box) for the conventional wide-field image and 313 ± 24 nm for the lattice SIM image, which means a resolution enhancement factor of 1.78. It should be mentioned that the experimental spatial resolutions of both imaging modes are lower than the theoretical resolutions due to the existence of the system’s aberration. The experimental resolution enhancement factor is higher than the theoretical one due to the constructive contribution of deconvolution operation. The spatial resolution obtained here is somehow worse than that obtained in Fig. 7. This might be due to the diameter of the fluorescent particles (240 nm) is too large compared to the resolution.

 

Fig. 6. Wide-field and SIM imaging on 240 nm-diameter fluorescent beads. (a) Wide-field (left) and SIM (right) images of the fluorescent beads. (b) five enlarged regions-of-interest (ROIs) indicated with five boxes in (b). (c) intensity profiles along the two dash lines in (b). (d) The statistic of spatial resolution defined with the averaged FWHM of the intensity profiles crossing individual bead centers. The boxes indicate the 25%∼75% distribution of the data.

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Fig. 7. Comparison of reconstruction quality of lattice SIM and stripe-SIM. (a) wide-field, lattice SIM, and stripe SIM image on 100 nm-diameter fluorescent particles. (b) the intensity profiles along three dash lines in (a), where symbols are the experimental data and lines are gaussian fit. (c) statistics of spatial resolution in term of the FWHM of individual particles. (d) structural similarity index metric (SSIM) of reconstructed image at different brightness with respect to the one with 880 photons per particle. Scale bar in (a), 5 µm.

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In aside to resolution enhancement, the lattice SIM also has three-fold SBP enhancement compared to SLM/DMD-based SIM. The SBP of lattice SIM can be assessed with the division of 2D FOV by a minimally-resolvable disc area: (4112×3.45 µm/20) × (3008×3.45 µm/20)/[π×0.313² µm²] = 1.2 Million. For a classic SIM based on a programmable device [38], the effective FOV is limited by the area covered with fringes, which is in turn limited by the pixel number of SLM/DMD. A SLM/DMD with 1920 × 1080 pixels can only cover a FOV of 442×248 µm² with fringes that have a period of P_lattice= 0.69 µm, considering each fringe period is sampled with three pixels. Therefore, the effective SBP of SLM/DMD-based SIM can be calculated with (442 µm × 248 µm)/[π×0.313² µm²] = 0.36 Million. It is meant that lattice SIM has a 3.2-fold SBP enhancement compared with the classic SIM.

The proposed lattice SIM was compared with stripe SIM [23] on SR imaging, for which fluorescent particles (RF100C, excitation-peak wavelength 535 nm, diameter: 100 nm, Shanghai Huge Biotechnology Co., Ltd, China) were used as the sample. The wide-field, lattice SIM, and stripe SIM images on the sample were obtained and are shown in Fig. 7(a). For stripe SIM, six raw images were recorded under the fringe illumination along two orthogonal directions and three phase shifts for each direction. For lattice SIM, five raw images were recorded with the phase shift combination of [0, 0], [0, 2π/3], [0, 4π/3], [2π/3, 0], and [4π/3, 2p/3]. Compared to the wide-field image, both lattice SIM image and stripe SIM image have significantly enhanced spatial resolution The line profiles crossing the same particle in the wide-field, lattice SIM, and stripe SIM images were extracted and compared in Fig. 7(b). For quantitative comparison of spatial resolution, statistic on the FWHMs of ten individual particles was carried out. The results in Fig. 7(c) reveal that the spatial resolution of wide-field, lattice SIM, and stripe SIM are 470 ± 21 nm, 262 ± 15 nm, and 246 ± 10 nm, respectively. The comparison confirms the stripe SIM can provide slightly higher spatial resolution than lattice SIM. We speculate that this attributes to the advanced deconvolution operation involved in the open SIM [31] that was used to reconstruct the stripe SIM image.

Furthermore, both lattice SIM and stripe SIM were tested for SR imaging at different exposure time, which in turn leads to different particle brightness, ranging from 27 to 880 photons per particle. The structural similarity index metric (SSIM) of the reconstructed images at different exposure time with respect to the one obtained with the highest brightness (i.e., 880 photons per particle) was calculated and shown in Fig. 7(d). The comparison reveals that stripe SIM is superior to lattice SIM for the reconstruction with low photon does. This is mainly due to stripe SIM utilizes six raw images versus five raw images in lattice SIM, and the prior one has, in total, more photons to depict the sample structures.

3.2 Lattice SIM imaging of microtubules in fixed mouse stem cells

In the second experiment, both wide-field and lattice SIM imaging were performed on the microtubules in fixed mouse stem cells. Mouse stem cells were labeled with primary antibody (β-Tubulin antibody, #2146, produced in rabbit) and secondary antibody (Goat anti-Rabbit IgG (H + L)-Alexa Fluor 532). We imaged the microtubules in the fixed cells in both wide-field and lattice SIM mode, and Fig. 8(a) shows the resulted wide-field image (left) and lattice SIM image (right). The wide-field and lattice SIM images of a sub-regions indicated with five yellow boxes in Fig. 8(a) are magnified and compared in Fig. 8(b). The comparison shows that lattice SIM image has more resolvable structures and much clearer backgrounds. Furthermore, a cut-line was extracted from the same position in the wide-field and lattice SIM images, and the intensity distributions along the lines are shown in Fig. 8(c1). The comparison of the two lines confirms that lattice SIM can resolve finer structures of microtubules than the wide-field microscopy. Deconvolution based spatial resolution analysis [38] has also been conducted on the wide-field and lattice SIM images shown in Fig. 8(b), and the results are shown in Fig. 8(c2) and 8(c3), respectively. The deconvolution analysis reveals that the wide-field and lattice SIM images have a cut-off frequency of 3.0 µm^-1 and 6.4 µm^-1, meaning a spatial resolution of 0.67 µm and 0.31 µm, respectively. The deconvolution analysis predicts a spatial resolution enhancement beyond a factor of 2, which is apparently higher than the actual value. This is mainly due to the fact that the decorrelation analysis method quantitatively assesses the resolution by balancing the signal and noise contribution. In lattice SIM, the phase-shifting operation works to suppress the out-of-focus noise, yielding a signal-to-noise ratio (SNR) of 0.46 and 0.50 for the wide-field and lattice SIM, respectively.

 

Fig. 8. Wide-field and lattice SIM image of the microtubules in fixed mouse stem cells labeled with Alexa fluor 532. (a) wide-field image (left) and lattice SIM image (right) of the sample. (b) magnified view of a region indicated with a white box in (a): upper panel: wide-field images and lower panel: lattice SIM images. (c) comparison of spatial resolution of wide-field and lattice SIM microscopy. (c1) the intensity profiles along the dash lines in (b). (c2) and (c3) decorrelation based resolution analysis of the wide-field image and lattice SIM image [39].

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4. Conclusion

In this paper, we present a large-field, five-step lattice structured illumination microscopic technique. This method utilizes a 2D grating for lattice projection and a spatial light modulator (SLM) to perform fast phase shifting. Mechanically rotating and shifting the pattern is no longer necessary. Unlike the conventional lattice SIM that utilizes coherent lattice patterns, the proposed technique utilizes the lattice patterns produced by incoherent superimposition of two groups of 1D fringes, avoiding other cross-interference. Consequently, only five phase-shifted intensity images are acquired to reconstruct a super-resolution SIM image. Compared to stripe SIM with two directions and three phase shifts (six raw images are needed) [23], the proposed lattice SIM has 17% imaging speed enhancement and 17% photo-bleaching reduction. The proposed lattice SIM can contribute to long-term and high-speed imaging of live samples.

5. Discussion

In classic SIM, a programmable device, such as SLM or DMD, is used to project periodic fringes, and hence the fringe number is limited and is often below 500. By contrast, in lattice SIM, the projection of a 2D physical grating projection allows for the generation of thousands of patterns to provide a large-field, super-resolved image if the generated raw image can be appropriately recorded by a camera. We verify with the experiment that the proposed lattice technique has a three-fold enhancement on lattice number (or SBP) above classic SIM. Using physical grating instead of pixelated SLM/DMD avoids additional unwanted diffraction orders that deflect illumination laser power and form a jagged edge in the illumination pattern [17,30]. In conventional lattice SIM, phase shifting was performed by mechanical rotating a glass plate with two galvanometric scanners [26] or using a piezo-transducer [40]. By contrast, the proposed lattice SIM uses a SLM to perform phase-shifting, and hence it is much faster and has a higher reproducibility.

Once using a 2D amplitude grating that has the same transmittance for different illumination wavelengths, the lattice SIM also allows multi-color SIM imaging, avoiding the pixelation and dispersion effect of DMD [36]. Furthermore, the lattice SIM can be extended to 3D lattice SIM, when using three diffraction beams of a 2D grating to create a pattern with both lateral and axial components [41]. In this case, the SLM can still modulate their separate spectra to perform phase shifting. The lattice illumination can also be combined with the single-molecule localization microscopic (SMLM) method to provide additional resolution enhancement, similar to interferometric SMLM [42].

The proposed method also has disadvantages: first, the period of the fringe/lattice patterns can not be varied digitally like what in SLM/DMD-based SIM. Second, this method has a relatively complex configuration due to the involvement of both a physical grating and a SLM. What’s more, the resolution enhancement achieved with this method is less isotropic than the standard 3-angle 2-beam SIM [17]. The abrupt drop in spectral power (due to insufficient illumination angles) in Fourier-space will cause ring-shaped artifacts in real space. An apodization can be applied to reduce this effect [24], but it will also reduce the resolution enhancement somehow. More preferably, the current lattice patterns can be extended to hexagonal SIM patterns of three-fold symmetry [24] by using a specially-designed diffractive optical element (DOE) and recording more raw images under different phase-shift combinations.