Since the 1990s, new fluorescence microscopy methods have been developed and offered spatial resolution over diffraction resolution limit (Abbe’s resolution limit, typically 250 nm [1]) for far-field optical microscopy. Among those methods, single-molecule localization microscopy (SMLM), such as fPALM/PALM and dSTORM/STORM, are based on detection and localization of single molecular fluorescent blinking events and achieves 20–30 nm lateral resolution and 60–70 nm axial resolution [2–5]. Typically, a SMLM measurement needs to record 1000–100,000 frames at a speed of 10–1000 frames/s, and takes several minutes or longer [5–7]. Since SMLM aims to obtain 10–30 nm resolution, sample drift (typically 1–10 nm/s [7]) becomes a critical problem due to inescapable mechanical relaxation or temperature changes in long recording time [8]. Sample drift can reduce resolution of the reconstructed image, or even distort fine structures of the image.

To overcome this problem, several methods have been developed [4,5,7–14] and can be sorted into three groups. The first group is real-time three-dimensional (3D) drift correction by detecting and compensating sample drift using expensive feedback equipments during measurements [9,10]. The second group use fiduciary markers and track their movements. Fiduciary makers can be gold nanoparticles [4] or fluorescence beads [5,11], but that may influence the targeted fluorescence signals. Another method is to use pre-prepare pattern on coverslip as fiduciary markers then exploit the position of the pattern in bright field. However pattern fabrication on coverslip is complicated and asks for extra expense (using electron beam exposure and needs high marker density) [7], and pattern also can be sheltered by sample structures. The third group is to calculate the cross-correlation between the fluorescence images [12–14] or reconstructed super-resolution images [8,15] and can achieve 5 nm precision of 3D drift correction if there is no fluorescent signal intensity decay during measurement [8]. However, fluorescence photobleaching is unavoidable, especially when high-power excitation laser is applied that is often the case in SMLM measurement, and in this case, anti-drift precision is significantly reduced.

These methods inspired us to develop a new anti-drift method by recording both fluorescent and bright field images. In this method, bright field images of sample itself are used for anti-drift tracking. Compared to fluorescent recordings, bright field images have significant higher signal-to-noise ratio and the signal intensities do not decay while measuring. Photobleaching of the fluorophores is totally avoided, and no external fiduciary markers or structures are needed, which makes its implementation simple and straightforward for most SMLM imaging. Normalized root-mean-square errors (NRMSEs) [13,14] between bright field images are calculated to get sample drifts between frames. The method was tested with simulated data; better than 0.3 nm drift correction precisions were achieved for $x$ and $y$ directions, respectively, and also applied on dSTORM imaging of cells, and the quality of reconstructed images was significantly enhanced.

To implement this method, two optical configurations are presented in Fig. 1. In the first configuration, one camera is used for recording bright field images and fluorescence images alternately [Fig. 1(a)]. In the second configuration, two cameras are employed, bright field images and fluorescence images are recorded separately at the same time [Fig. 1(b)]. The first configuration is optically less cost but takes double the recording time.

 

Fig. 1. Schema of optical setups for super-resolution imaging with drift correction. (a) Laser and LED illuminations are switched alternately, fluorescence and bright field images are recorded with the same EMCCD camera; (b) laser and LED illuminations are switched simultaneously, and fluorescence and bright field images are recorded with an EMCCD and a CCD camera separately. DM denotes dichroic beamsplitter and M denotes mirror.

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Assume $d=(\mathrm{\Delta }x,\mathrm{\Delta }y)$ is the drift translocation between image $\mathbf{g}(x,y)$ and reference image $\mathbf{f}(x,y)$ in $x$ and $y$ directions. The solution corresponds to maximal similarity between the anti-drift image ${\mathbf{g}}^d(x,y)=\mathbf{g}(x-\mathrm{\Delta }x,y-\mathrm{\Delta }y)$ and reference image $\mathbf{f}(x,y)$, so the objective function can be defined as NRMSE between ${\mathbf{g}}^d(x,y)$ and $\mathbf{f}(x,y)$ [13,14]:

To solve this nonlinear optimization problem (Eq. 1), first we implement a Gaussian smooth ($3\times 3$ mask, standard deviation 0.5 pixels) on $\mathbf{f}(x,y)$ and $\mathbf{g}(x,y)$ to reduce noise. Then the FFT approach is used to find the maximal cross-correlation (Eq. 2) between $\mathbf{g}(x,y)$ and $\mathbf{f}(x,y)$ to within 1/10 of a pixel [14]: (i) upsample the image $\mathbf{g}(x,y)$ and $\mathbf{f}(x,y)$ by a factor of 10, and get the upsampling image ${\mathbf{g}}_{\text{up}}(x,y)$ and ${\mathbf{f}}_{\text{up}}(x,y)$; (ii) compute ${\mathbf{G}}_{\text{up}}(u,v)=\mathcal{F}[{\mathbf{g}}_{\text{up}}(x,y)]$ and ${\mathbf{F}}_{\text{up}}(u,v)=\mathcal{F}[{\mathbf{f}}_{\text{up}}(x,y)]$; (iii) compute the product ${\mathbf{F}}_{\text{up}}(u,v){\mathbf{G}}_{\text{up}}^{*}(u,v)$; (iv) compute the inverse FFT of ${\mathbf{F}}_{\text{up}}(u,v){\mathbf{G}}_{\text{up}}^{*}(u,v)$ to get the upsampling cross-correlation; (v) locate the peak of the upsampling cross-correlation to obtain $(\mathrm{\Delta }x,\mathrm{\Delta }y)$, the corresponding value of $(\mathrm{\Delta }x,\mathrm{\Delta }y)$ with $\alpha =1$ as the initial estimation of Eq. (1). Last, a Levenberg–Marquardt nonlinear optimization [17,18] is implemented to solve Eq. (1).

To evaluate the performance, the method was applied on an artificially drifted bright field image data set. We simulated a frame sequence of 4000 images by adding random drift on one bright field image of a COS-7 cell with a scale of 66.7 nm per pixel. Step lengths of drifts between two sequential frames were randomly generated and followed normal distribution with mean $\mu$, and variance ${\sigma }^2$ (here, $\mu =0\mathrm{nm}$, $\sigma =1,2,3,\dots ,20\mathrm{nm}$) on two directions independently. The drifted frames were calculated by Eq. (3). Then, Poisson noise, the intrinsic noise of photon detection (also called shot noise [19]), was superimposed on each pixel independently. Results of anti-drift applied on drift simulation with $\mu =0\mathrm{nm}$ and $\sigma =10\mathrm{nm}$ are shown in Fig. 2. Sample drift traces of $x$ and $y$ directions are shown in Figs. 2(a) and 2(d). Anti-drift errors, the differences between estimated drifts and real drifts, are shown in Figs. 2(b) and 2(e) for $x$ and $y$ directions. The precision of drift corrections are $-0.0621\pm 0.0877\mathrm{nm}$, $0.0702\pm 0.0969\mathrm{nm}$ for $x$ and $y$ directions, respectively, and shown in Figs. 2(c) and 2(f). Further, we simulated different drift step lengths followed by normal distribution with standard deviation from 1 to 20 nm and with mean 0 nm: the results are shown in Fig. 3. Drift correction precisions were better than 0.3 nm in all cases indicating this method is robust for different drift situations.

 

Fig. 2. Anti-drift for artificially drifted bright field image sequence for 4000 frames on two directions, respectively: (a), (d) sample drift traces; (b), (e) anti-drift error and its histogram and precision (c), (f).

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Fig. 3. Means and standard deviations (SD) of drift correction errors for 20 simulated image sequences (4000 frames) with different drift step lengths. The precisions of drift corrections are better than 0.3 nm in all cases for both $x$ and $y$ directions.

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This method was then applied on dSTORM imaging of F-actins of 3T3 cell. Details of the dSTORM imaging experiment were described as following.

Cell Culture: NIH 3T3 cells were maintained in Dulbecco’s modified Eagle’s medium (DMEM, GIBCO-BRL) supplemented with 10% (v/v) fetal calf serum (FCS) at 37° in a humidified ${\mathrm{CO}}_2$-controlled (5%) incubator.

Immunocytochemical staining: All solutions were sterile filtered before application, and all steps were performed at room temperature. For fixation, cells were washed 3 times with phosphate buffered saline (PBS, pH 7.4), then incubated with 4% paraformaldehyde (PFA) in PBS for 10 min. After fixation, cells were washed 6 times with PBS for 5 min, stored at 4° over night; then cells were washed 3 times with PBS for 5 min, and blocked with 5% (wt./vol.) Albumin Bovine V (Solarbio, A8020) in PBS for 60 min to avoid nonspecific binding, then stained with $1.0\times {10}^{-5}\mathrm{\mu g}/\mathrm{\mu l}$ Phalloidin-ATTO 488 (Sigma, 49409, dilution 1:30000) solution in PBS for 60 min, washed 3 times with 0.1% Tween-20 for 5 min, and washed 3 times with PBS for 5 min again before measurement.

Anti-drift super-resolution fluorescence microscopy: Optical configuration Fig. 1(a) is demonstrated on a self-built super-resolution microscopy based on Olympus IX-81 inverted microscopy (Olympus) with objective UApoN $150\times$ Oil NA 1.45 (Olympus). A 488-nm laser (Sapphire 488-150CW, Coherent) is switched by an acousto optic tunable filter (AOTFnC-$\mathrm{VIS}·\mathrm{TN}450–700\mathrm{nm}$, AA Opto-electronic Inc.) for fluorescent excitation. Fluorescent emission is filtered with a dichroic mirror (FF509-FDi01, Semrock), in combination with a longpass filter (BLP01-488R, Semrock). A red LED (Luxeon 5027-PD12, Philips, center wavelength: 627 nm) replaces the halogen bulb for conventional bright field illumination light source since it can be fast regulated with a power amplifier. Due to the intrinsic property of LED, it can be switched on and off with nanosecond time resolution and well satisfied this application. Two-way illuminations are synchronized with EMCCD exposure. The relative light intensity of LED was well adjusted compared to fluorescent intensity to achieve high signal-to-noise ratio bright field image meanwhile not saturating the detector, since gain setting of EMCCD camera (iXon DU897E, Andor) is optimized for fluorescent imaging.

dSTORM imaging: In dSTORM measurements, 6,000 frames bright field and 6000 frames super-resolution fluorescence images were recorded alternately. For bright field illumination, the voltage of power supply for LED was 3.0 V and exposure time was 2 ms; for fluorescence excitation, 488 nm laser power was 100 mW and exposure time was 20 ms; one pixel size was mapped to 66.7 nm. Reading frequency of EMCCD was 10 MHz, and the whole measurement lasted about 10 min.

The results of dSTORM imaging are shown in Fig. 4. Figure 4(d) reveals that the sample stage drifted linearly with a constant speed while recording. Reconstructed super-resolution image [Fig. 4(a)] are much more blurry compared with anti-drifted results [Fig. 4(b)]. Profiles of a representative region with and without anti-drift are shown in Fig. 4(e). It shows that without anti-drift, the width of cell membrane is artificially enlarged, and a pseudo double-peak is presented.

 

Fig. 4. dSTORM imaging of F-actins of the 3T3 cell. Scale bar is 2 μm. (a) Super-resolution image without drift correction. (b) Super-resolution image with drift correction. (c) Bright field image. (d) Sample drifts of $x$ and $y$ directions, respectively. (e) The profiles of selective region (yellow window) projected on a base line (yellow line) in original and drift-corrected super-resolution images.

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Since SMLM measurement needs to acquire a great number of frames and takes considerable recording time, sample anti-drift became a critical concern. In this Letter, we developed an anti-drift method used in SMLM-based super-resolution imaging, and two optical implementations are suggested. This method is based on the calculation of NRMSE of bright field images that have much higher signal-to-noise ratio compared with fluorescence images, and photobleaching problem is totally avoided. It also does not ask for extra labelling or markers. Structures of sample itself are used as native fiduciary markers. Biological samples, e.g., cells have rich structures in bright field imaging and make this method applicable. Beside post-measurement application, combining a nanopositioning sample stage, this method in principle also can be used as a real-time feedback anti-drift method. This method does not relay on complicated and expensive equipments and can be applied easily for most PALM/(d)STORM setups. The quality of super-resolution image is greatly improved, and a more objective super-resolution image is reconstructed after anti-drift.