1. Introduction

Localization based super-resolution microscopy [1–3] is reaching a significant state of maturity enabling important biologically relevant discoveries [4–6]. Recent work has shown techniques directed at maximizing the information acquisition via optical system design [7–9] and estimation algorithms [10–13], improving probes [14,15] and throughput [16]. However, currently the acquisition of single-molecule data to construct meaningful images typically requires molecule localizations from thousands of images. During this long acquisition time, the sample tends to move relative to the objective and the image plane, with typical drifts ranging from few hundred nanometers to a few microns in three directions. In highly controlled setups such as used for super-resolution microscopy, the displacements are typically under a few hundreds of nanometers, but they are significant to cause smearing of the final image, reduce resolution, and possibly lead to misinterpretation of the results. Another concern is that drift may cause the sample to move out of focus, - due to limited depth of field - causing the peak signal intensity to drop and leading to precision degradation.

Current prevalent techniques require a posteriori drift correction, which precludes the implementation of most real-time imaging experiments. For instance, experiments cannot be easily optimized in situ in terms of power of activation/excitation light. Further, the tracking of moving particles or molecules with respect to a super-resolved background cannot be performed in real time, often resulting in the object leaving the field of view due to drift. Significant axial drift also causes a drop in peak signal to noise ratio affecting localization precision.

Early attempts at real-time drift control for localization microscopy used a separate feedback channel with an infrared beam totally internally reflected from the cover glass-water interface through the objective and detected by a photodiode [17]. This method only compensates for drift along the axial direction, maintaining microscope focus within ~20 nm, while drift in the lateral direction is corrected during post processing. Some commercial microscopes also offer a feedback mechanism for keeping the sample focused on the camera within the depth of field of the objective [18]. These systems are good at keeping the sample focused but their precision is lower than the requirements for localization microscopy. Moreover, they only apply real-time correction in the axial dimension, neglecting lateral drifts, which can be significant for long acquisition times.

Likewise, recently proposed active image correlation techniques still provide drift correction precisions of the same order as the single-molecule measurements, have a slow response time because of the need to integrate information over many image frames, or require fixed samples [19]. In addition, these sytems provide feedback from an external CCD camera, which can drift with respect to the EMCCD cameras used for single-molecule localization. Further, even the latest video-rate super-resolution techniques [16] will require drift strategies for long lasting live dynamic biological experiments.

In the past, closed-loop feedback techniques have been used in biophysical studies [20–24]. In [24], nanopatterning of coverslips is used for feedback generation to stabilize a microscope within 1 nm in x-y and 5 nm in z. However, this method requires slight defocus for tracking in z which would be detrimental to imaging precision if applied to super-resolution microscopy.

Therefore, in this paper we address the above mentioned issues demonstrating super-resolution localization microscopy without any substantial long-term three-dimensional drift [25], i.e. the drift can be lower (even up to one order of magnitude) than the typical precision of super-resolution systems [7]. The paper is organized as follows: First we discuss prevalent methods used to compensate relative sample drift in localization-based super-resolution microscopy. Next, we introduce a solution based on feedback signals generated by gold nanoparticles and 3D imaging using a double-helix (DH) point spread function (PSF) interleaved with single molecule signals. We also present an experimental validation of long-term as well as short-term stability along with a discussion of the advantages and disadvantages with respect to the current methods. In the following section, results of a super-resolution experiment conducted with the proposed method are presented, validating the use in high-resolution microscopy. In the last section, we discuss the results and the applicability of the method to other 2D and 3D localization-based super-resolution techniques.

2. Prevalent methods for a posteriori drift correction in three dimensions

An illustrative example of the dramatic importance of drift correction is depicted in Fig. 1 showing a typical localization microscopy image reconstructed with and without drift correction. One of the most prevalent techniques to address this problem is to place fluorescent fiduciary markers on the coverslip in random or periodic arrays, including fluorescent beads [1–3], quantum dots or gold nanoparticles [26]. The precise position of the fiduciary markers is estimated in post processing and used for adjusting the estimated single-molecule positions. The disadvantage of the technique is that these bright beads can compromise the much weaker single molecule fluorescence signal. Furthermore, sample preparation is complicated because of the need to place markers with the right density and at the proper locations. Typically it is preferred to have the fluorescent fiduciaries away from the cellular region of interest to reduce any background light, a strategy that reduces the available field of view. Also, fluorescent markers often bleach or move from their original position with respect to the coverslip, adding challenges to sample drift estimation using this method.

 

Fig. 1 The effect of 3D drift on super-resolution localization microscopy reconstruction of microtubules. (a) Map of localizations without correcting for drift. In this experiment the stage drifted about 400 nm in x, 800 nm in y and within a range of 300 nm in z with manual feedback to avoid the sample from leaving the focal region. (b) Reconstruction map after correcting localizations for drift estimated using fluorescent bead fiducials.

Download Full Size | PDF

A second popular method is to perform time correlations of post processed localization data to calculate drift [17,27–29]. The method has been shown to perform corrections down to ~5 nm for 3D super-resolution imaging. One important advantage is that no fiducial markers are needed. In practice, this method’s precision depends on the number of localizations, the imaged structures, and the labelling density.

3. Closed-loop real-time adaptive 3D drift correction

We implemented a closed-loop feedback system that detects drift in the sample with respect to its original position and commands the sample positioning stage to compensate for that drift. The key features of this process are that sample drift of few nanometers is detected and compensated in a very short time as compared to the time scale of the experiment, creating a virtually drift-less setup within the spatial and temporal resolutions of the experiment. Therefore, the system is capable of maintaining localization imaging within time scales from a few seconds to hours. The adaptive drift correction method we report here is based on the following key mechanisms:

The feedback signal is obtained periodically via a bright-field image of gold nanoparticles randomly located in proximity to the sample. An LED source is introduced to illuminate the sample in transmission and generate the scattering signal from the gold nanoparticles. The fiducial markers are embedded and immobilized on the coverslip with a 100 nm layer of SiO₂. No significant aberrations are added to the images due to this layer because of negligible refractive index mismatch with the coverslip. Further, we have not observed any increase in the background of the single-molecule signal due to fluorescence or scattering of the gold nanoparticles.

A key advantage of the method is that it does not require any modification to the imaging side of the microscope. The gold-particle bright-field images encode 3D position information in their spatial distribution via an engineered PSF, in this case a DH-PSF [7]. Real time processing algorithms estimate the precise location of the gold particle from these images and calculate the instantaneous 3D drift. The 3D nano-positioning stage uses the drift information to apply compensatory motion. The closed-loop system uses a proportional-integral-derivative (PID) controller via a custom data processing and device control algorithm implemented in MATLAB, thereby controlling both the camera and the sample stage with the same software program.

3.1 Setup and imaging scheme

In this section we describe the super-resolution localization microscope used to demonstrate super-resolution localization imaging without a posteriori dirft correction. A DH-PSF system is implemented for 3D super-resolution localization microscopy using a phase mask etched in glass. A schematic of the custom setup is shown in Fig. 2. The specific DH-PSF is designed to achieve high precision in the presence of background noise and to reduce the PSF cross-section (see [7]). The same DH-PSF mask that modulates the single molecule fluorescent signal also modulates the bright-field signal scattered by the gold nano-particles. Towards this goal, we choose an LED matching the pass band of the emission filters to reduce wasteful heating of the sample. The LED is directly modulated in sync with the excitation laser signal (see inset in Fig. 2). In the experiments reported here, we use Alexa 647 dye; in order to match its emission band of approximately 670 nm to 720 nm, we select an LED at 690 nm (ELJ-690-629 Roithner Lasertechnik, Austria, bandwidth 25 nm). In addition, we place a band pass filter in front of the LED to cut-off shorter wavelengths and avoid any single molecule excitation.

 

Fig. 2 Setup for super-resolution imaging with closed-loop active drift correction. A 641 nm laser is used for excitation in epi-illumination and an LED (690 nm) for bright-field transmission imaging. A switching circuit controls the laser and LED. A closed-loop feedback processes the EMCCD data and delivers signals to the nano-positioning stage holding the sample. The acquisition scheme on the top right shows the switching of the excitation laser and the LED synced with the camera.

Download Full Size | PDF

The setup consists of a 1.45NA 100X Nikon objective and an Andor electron multiplying charge coupled device (EMCCD) for detection (Andor iXion DU897E CS0 #BV, South Windsor, CT, USA). A nano-positioning stage (Physik Instrumente PZ 164E, Irvine, CA, USA) holds the sample and moves it to counteract drift. A coverslip containing stained cells is mounted in a rose chamber and locked down on the nano-positioning stage. A 4F-system implements the DH-PSF [30,31] with the phase mask placed at a plane conjugate to the pupil plane of the objective.

For Alexa 647 dye, the 641 nm diode laser (Coherent Cube) is used for excitation. The laser and LED are used in synchronization with the EMCCD camera as shown in the inset of Fig. 2. A polychroic mirror from Semrock (Di01R405/488/561/635) is used to separate the excitation and emission light. The emission is further filtered by two stacked dual-band pass filters (Semrock DBP FF01-538/685-25 and Omega XF3470 540-700DBEM, Brattleboro, VT, USA).

Gold nanoparticles are widely used in microscopy for their useful optical properties such as fluorescent markers, scatterers, etc [32]. In this work, they are imaged in bright-field illumination mode so that their emission light does not interfere with the epi-fluorescent signal of single molecules. Single molecule localization based super-resolution normally requires alternate switching of laser pulses between activation and excitation or just pulsing of the excitation illumination. The bright-field channel is added intermittently into the switching sequence with minimal loss of acquisition time and photodamage.

For the samples used in this experiment, no activation illumination is required as the dye molecules spontaneously and stochastically activate [33]. In the switching scheme, the LED pulses are interlaced with the excitation laser. If an activation laser is required, two different switching schemes are possible. The first option is to have both the activation and the bright-field pulses illuminate the sample simultaneously, with the activation emission usually blocked by the emission filter. The second option is to have the LED pulse switched on in between the excitation and activation pulses (in that order). The pulsing frequency of the bright-field mode can also be reduced in some cases according to the dynamics of the drift. Hence, depending upon various experimental conditions and requirements, it is possible to adjust the bright-field detection.

3.2 Drift estimation and correction

The drift correction method implements a simple PID controller where the bright-field images of the gold beads are processed to find the x-y-z location of the gold nanoparticles and hence drift of the sample with respect to its original position. This control is continuously active during the localization imaging process. In our experiments, it was observed that a proportional controller suffices to attain the target dynamic response.

The algorithm estimates the drift and implements the correction in two parts. First it takes the most recent camera image and determines whether it is a bright-field image or a single-molecule image based on a criterion of image average and peak value. This simple and fast method enables asynchronous operation with the camera and was found to be flawless. The bright-field image is added to a buffer that collects N images (N is user determined via a GUI input). The N images are averaged and used for drift estimation. M user preselected regions containing images of the gold beads are selected and the 3D position of each of the gold beads is estimated. The current estimated position of each bead is subtracted from its initial position and M drifts calculated. Under the assumption of only translational sample motion, a weighted average (based on the bead intensity) of M drifts is calculated to estimate the sample drift.

In the second part of the algorithm, the estimated drift is scaled down by the chosen proportionality constant and fed back to the stage to shift appropriate distances in x, y and z for compensation. The estimated drift is scaled down (proportional component of the PID control) to maintain stability.

The drift estimation is improved by averaging N images (increasing the gold particle localization precision) and by taking a mean of the M different beads. It was found that values of N = 8-10 images and M = 3-5 gold beads were suitable in our super-resolution experiments with acquisition rates of 20 frames per second. The stage settling time is 100 ms. A good value of the proportionality factor was empirically found to be in the range 0.4 – 0.7. For different experimental conditions such as fluorophore yield, imaging speed, frequency of gold-bead imaging, and settling time of the nanopositioning stage, the optimal values of N and M can be changed. For instance, setups prone to fast and large drifts will require smaller N and larger M. Another user adjustable parameter to control the stability of the system is the frequency of correction. Likewise, more complex PID controllers can be implemented for faster or more robust control.

For illustration purposes, bright-field images of a gold bead at different defocus positions are shown in Fig. 3(a). The angle estimator in conjunction with the z-calibration curve [Fig. 3(b)] determines the x-y-z location of the gold particles. In this imaging modality, the two lobes are darker than the background, so the angle estimator [31] algorithm is modified accordingly.

 

Fig. 3 Bright-field imaging of gold beads used for drift estimation. (a) Images taken for z calibration, at different defocus positions in the DH-PSF microscope. (b) The rotation vs. z calibration curve.

Download Full Size | PDF

3.3 Precision of real-time adaptive drift correction

To measure the precision of the adaptive control, a measurement that is more precise and accurate than the feedback signal is needed. Very bright fluorescent beads can provide precision within a few nanometers and were therefore used to test the performance of drift correction. For this experiment, a coverslip with 100 nm gold nanoparticles was prepared (as discussed in the Appendix). We deposited a dilution of 200 nm fluorescent beads (660/680 from Invitrogen) on the coverslip prepared with gold beads and left it to dry for 2 hours. The fluorescent beads and gold nanoparticles were then imaged with the switching scheme where the fluorescent beads are imaged 3 times for every image of gold beads. The camera acquisition rate was set at 20 Hz and the feedback signal was acquired at 5 Hz. For the drift correction algorithm, we chose N = 9 and M = 5. In the GUI, the user is allowed to select M regions where the selected gold beads are located. Both the fluorescence signal and gold particle scattering were set to use the full dynamic range of the camera.

First an experiment was done without adaptive drift correction to measure the localization precision for the fluorescent beads. Approximately 5000 images of 4 fluorescent beads were taken and the sample was found to drift a total of ~40 nm in each of the three dimensions during the 4 minute experiment. The positions of these beads were estimated. To calculate the precision of localization, this data had to be corrected for drift. The drift was estimated from the bead positions themselves using the boxcar moving average filter. After drift correction, the 3D localization precision was measured to be σ_bead(x,y,z) = (2.1, 2.1, 3.5) nm.

In the second experiment, adaptive drift correction was applied and the localization precision of the fluorescent beads was measured again. The raw data of the fluorescent bead was used to calculate the precision without any a posteriori correction of the data, producing σ_bead-adapt(x,y,z) = (3.4, 3.4, 5.4) nm. Histograms of precision for both experiments are shown in Fig. 4.

 

Fig. 4 Experiment to evaluate the precision of adaptive drift correction. A bright fluorescent bead is localized with and without adaptive drift correction. The plots show precision histograms for a fluorescent bead with a posteriori correction but without adaptive correction (left) and with adaptive correction (right) and no a posteriori correction.

Download Full Size | PDF

The measured localization uncertainty in the adaptive experiment results from the uncertainty of the feedback signal and inherent uncertainty in the fluorescent bead localization used to evaluate the precision. By comparing the fluorescent bead localization precisions in the two experiments, we find the precision of the adaptive drift correction. The precision σ_bead-adapt incorporates the compound uncertainty in fluorescent bead localization (estimated to be σ_bead) and the uncertainty in the drift correction per se σ_adapt. Therefore, the latter precision of 3D drift correction can be found as the geometric difference of the two experiments. As a result, the precision of drift correction can be estimated to be σ_adapt(x,y,z) ≈(2.7, 2.7, 4.1) nm, which is marginally better than the more conservative estimate of σ_bead-adapt. Thus, with either estimate, we conclude that in this experiment the adaptive drift correction is achieved with 3-5 nm precision in all dimensions. For most fluorescent molecules currently in use, the number of emitted photons is generally in the range 500-2000 and the precision is limited to 20-50 nm. Hence, the added error being down to one order of magnitude lower is more than appropriate to generate virtually drift-less images.

If brighter fluorophores are used and therefore more precise single molecule measurements achieved, adaptive drift correction under 1 nm precision is possible by proper control parameter selection. In this experiment, for instance, the gold-bead image acquisition rate was 5Hz and correction motion was applied approximately at the rate of 0.5 Hz. A correction rate slower than 0.5 Hz would work well for experiments where the drift rate is under 0.5 nm/sec. Such drift rate is typical in super-resolution experiments such as shown in Fig. 1. Therefore, by optimizing the correction rate, increasing N or M, and determining appropriate PID constants, the drift correction precision can be further improved.

3.4 Long and short term microscope stability

The proposed method is capable of achieving short as well as long term stability. An experiment demonstrating adaptive drift correction including sudden (externally produced) large motions of the sample was carried out (Fig. 5). The plot shows adaptive stabilization, when manual translations of the sample along one of the axes are introduced, bringing the stage and the sample back to its original position. The blue, green and red curves show the measured x-y-z positions of the gold beads and the ability to bring the sample back to initial position. The spikes in the plot illustrate instances when the stage was forced to a new position in one direction and the control brought the sample back to its initial position. This can be seen for all the three axes. The experimental parameters are the same as described in the previous section.

 

Fig. 5 An experiment demonstrating adaptive drift compensation and stabilization. (a) Blue, green and red curves are for the estimated x, y and z positions of the sample. The spikes are instances when the stage was purposely moved away and the control system brought the sample back to the original position. (b-d) Details of a few instances of stage perturbation.

Download Full Size | PDF

We tested the long-term stability in a d-STORM experiment as described in the next section. The system was stabilized for 26 minutes without any external monitoring or control. No post correction of the single molecule localizations was required to obtain a super-resolution reconstruction shown in Fig. 7. Figure 6 shows the localization of gold beads used in this experiment when N = 10 (averaged images) and M = 5 (# of gold beads) were used with EM gain set to maximum (300) and exposure time set to 0.049 secs. The setup can be used for longer acquisition because the gold bead signal does not bleach. In this experiment the stabilization precision achieved was sufficient [σ(x,y,z) = (11,14,23)nm] because it was better than the localization precision of the single molecules. However, it could have been increased by taking larger N or M or by dynamically changing the gain of the EMCCD to adjust to the higher signal of the fiducials relative to the single molecules. In other words, the control quality is determined by the feedback signal quality chosen in the particular experiment.

 

Fig. 6 Long term stability achieved using the adaptive drift compensation during a d-STORM experiment. Blue, green and red curves show the estimated x, y and z positions of the sample using 5 gold beads and 10 averaged images.

Download Full Size | PDF

4. Experimental demonstration of 3D super-resolution imaging

A super-resolution localization microscopy experiment was performed with the real-time adaptive drift correction method. Imaging was performed on fixed PtK1 cells (Rat-kangaroo kidney epithelial cells) tagged with a tubulin antibody labeled with Alexa 647 [33]. The cells were cultured on cover slips prepared with gold beads as described in the Appendix. In this method, direct on/off switching of Alexa 647 dye takes place without the assistance of an activator dye. We used the setup of Fig. 2 with the camera acquiring at 20 Hz. For bright-field imaging, the illumination was set to use the full dynamic range of the camera with values N = 9 and M = 5. The single-molecule signals and bright field imaging frames were multiplexed as shown in the inset of Fig. 2.

Figure 7(a) shows a 3D super-resolution reconstruction of the data acquired using adaptive drift correction. Note that no post correction of the localizations was done; the plot shows the raw position estimations. The depth of field was ~1.2 µm for the entire field of view. To verify the precision for this experiment, the diameter of a microtubule was calculated from its transverse positions and the corresponding histogram is shown in Fig. 7(b). The diameter of labeled microtubules was found to be 88 nm. In evaluating this width, we need to consider the dye size and the localization uncertainty, which significantly expand the measured microtubule diameter that is known to be about 25nm. Hence, this result is in good agreement with previous measurements [7].

 

Fig. 7 3D super-resolution localization imaging with adaptive drift correction. (a) Super-resolution image of microtubules in PtK1 cells. (b) A histogram of transverse localizations of a microtubule with FWHM = 88 nm. (c) Zoomed-in super-resolution and (d) normal fluorescent images of a region in (a). The colomap represents the depth.

Download Full Size | PDF

5. Discussion

Drift in super-resolution microscopy experiments leads to inaccurate and low precision single molecule localizations. Most methods recover the accuracy of localizations by monitoring this drift and a posteriori correction of the single molecule localization data. However, the lost precision due to drift in the axial dimension cannot be recovered by these methods. Thus, it is important to actively stabilize the microscope in all three dimensions. In this paper, we have demonstrated an adaptive drift correction system able to compensate drift in three dimensions and in real time with high precision, enabling super-resolution localization imaging without a posteriori drift correction of the localization data. The advantage of the active correction method over post-processing based on fiduciary fluorescent particles is that (1) there is no interference between the weak single-molecule signal and the strong fiducial signal, (2) the microscope focus is maintained during acquisition; (3) avoids potential drift of the fiducials with respect to the sample; (4) enables use of the whole microscope field of view; (5) enables long-duration live cell experiments; (6) provides fast response to sudden bumps to the system. Further, with respect to systems based on image correlations [19], the system demonstrated here can adaptively change its precision to be below the single-molecule localization precision, while also being amenable to imaging of dynamic samples such as live cells for which correlations would, in principle, not function. With this method, the setup, the sample preparation, and the imaging protocol require minimal changes and can be implemented with any localization microscopy approach such as PALM and STORM. Any of the 3D localization methods used for 3D single-molecule imaging can be used for localization of fiduciary gold beads as reported here. Because the same imaging path is used for the single-molecules and the feedback signal, there is full correlation between the motion of the gold beads and the molecules. As a result, it avoids the problem that may arise from the independent motion among separate optical imaging channels [19]. The optical system optimization for 3D localization with engineered PSF enables not only high precision localization but also extends the depth range and recovery from potential sudden shifts of the sample due to vibrations or bumps to the system. Interestingly, this real-time adaptive imaging method can be readily applied to other imaging modalities where drift or perturbation problems exists, such as in live cell imaging or biophysical measurements.

The real-time drift correction system demonstrated here enables experiment-dependent optimization of parameters such as integration time, number of bead localizations, and update frequency to achieve the target precision, which has to be better than the single-molecule localization precision. The problems of fluorescent fiducials are overcome by the use of fixed gold beads that do not interfere with the single molecule signal (multiplexed in time to avoid crosstalk), do not bleach, and do not move with respect to the sample. However, the spacing of gold beads is still random as in the case of fluorescent beads; which can be overcome by increasing the density without compromising the single molecule signal unlike in the case of fluorescent beads. While gold nanoparticles have been used as fluorescent fiducial markers, here they are used as absorbers and imaged in bright-field transmission. As an alternative to gold beads, scattering centers can be created on the coverslip by lithography [24] or direct-laser writing [34,35].