Single-molecule switching (SMS) microscopy is a super-resolution method capable of producing images with resolutions far exceeding that of the classical diffraction limit. However, like all optical microscopes, SMS microscopes are sensitive to, and often limited by, specimen-induced aberrations. Adaptive optics (AO) has proven beneficial in a range of microscopes to overcome the limitations caused by aberrations. We report here on new AO methods for SMS microscopy that enable the feedback correction of specimen-induced aberrations. The benefits are demonstrated through two-dimensional and three-dimensional STORM imaging. We expect that this advance will broaden the scope of SMS microscopy by enabling deep-cell and tissue-level imaging.
© 2015 Optical Society of America
Single-molecule switching (SMS) microscopes provide super-resolved images of fluorescence-labeled biological specimens, enabling the visualization of structures many times smaller than the classical diffraction limit of the microscope [1–3]. Super-resolution is obtained through the localization of isolated single molecules to a much higher precision than the diffraction limit of the microscope. This process is enabled by the stochastic switching of fluorescent molecules such that only a small proportion of them can emit at any one time and ensures that emission from adjacent molecules does not overlap in the image. With these means, an image with resolution up to 10 times smaller than the diffraction limit of the microscope  can be reconstructed. In the ideal (background-free) case, the obtainable resolution is limited physically by the number of photons that can be detected from each emitter, as the localization precision improves with the square root of the number of photons . In practice, the precision and accuracy of any given localization is also affected by optical aberrations, such as those introduced by the refractive index structure of the specimen, which degrade the imaging properties of the microscope . In this paper, potential localization errors and subsequent image artifacts arising from optical aberrations have been investigated and a novel adaptive optics (AO) scheme has been developed to negate these effects. The implementation of AO in SMS microscopes will broaden the range of possible applications of these microscopes by enabling deep-cell and tissue-level super-resolution imaging.
In considering the effects of aberrations, we note that the optics of a SMS microscope are equivalent to those of a conventional wide-field fluorescence microscope and the detector is usually a pixelated EMCCD or sCMOS camera . In a wide-field microscope, aberrations cause an enlargement of the point-spread function (PSF), particularly along the optic axis, coupled with a decrease in the peak value of the PSF. These effects cause a blurring and loss of contrast in the resulting images. When the object is a single molecule, free to rotate , the spatial probability distribution for photon detection is proportional to the PSF and the probability at a particular pixel is proportional to the integral of the PSF over the pixel area. An essential step in SMS microscopy is the estimation of the emitter position based on the distribution of detected photons. This localization process usually involves the fitting of a model PSF (often approximated for mathematical convenience as a two-dimensional Gaussian) to the measured pixel data . If a particular fit meets certain quality criteria—such as having an estimated precision better than a chosen threshold—the fit will be accepted and will contribute to the final image.
Inevitably, the precision of the fitting process is affected by the compatibility of the model and the data. In an imaging configuration where aberrations are negligible—for example, when using a well-aligned microscope to image just beyond a coverslip—the Gaussian PSF model is realistic . However, when imaging deeper into the specimen through varying refractive indices, the actual PSF deviates significantly from the Gaussian model [6,9].
There are two possible approaches to solve this problem. If the aberrations can be determined, then this information may be incorporated into the PSF model, so that it more accurately represents the recorded data [10–12]. However, this can add significant complexity to the fitting calculations, which then has to accommodate the uncertainty in aberration measurement and include more degrees of freedom. Conversely, AO can return the operation of the system to near the diffraction limit , hence permitting the use of the Gaussian PSF model. AO aims to correct wavefront aberrations by deforming an optical element by an equal and opposite amount to that of the aberrations present in the system .
Following the AO approach, we have implemented a SMS microscope incorporating a deformable mirror (DM) for aberration correction. DMs have previously been applied to SMS microscopy to correct for instrumental aberrations, depth-dependent spherical aberration from a known refractive index mismatch, and to enable astigmatic three-dimensional (3D) SMS imaging . Here, we demonstrate a new feedback AO scheme that enables for the first time the correction of complex specimen-dependent aberrations. This is achieved by a DM in a sensorless AO feedback correction loop using a novel image-based metric, which is computed directly from raw images of blinking emitters. This AO approach does not rely on the presence of artificial guide stars, as is the case in several other AO microscopes, but can be used with regular specimen labeling. We show that the correction of specimen aberrations significantly improves the performance of the microscope over correcting only for instrumental aberrations. Furthermore, it is shown that additional spherical aberration is present, which would not be corrected if assuming a depth-dependent spherical aberration model.
In this study, we show that AO extends the imaging capability of SMS microscopy down to several micrometers in cells. Specifically, the AO scheme is applied to two-dimensional and 3D SMS microscopy.
2. MICROSCOPE LAYOUT AND DATA ACQUISITION
The adaptive microscope layout is shown in Fig. 1. Wide-field illumination was provided by a 500 mW, 655 nm wavelength laser (MLL-III-655-500, Changchun New Industries), which was brought to focus in the back aperture of a 1.4 NA oil immersion lens (Olympus UPLSAPO 100XO). A second, 100 mW laser of wavelength 405 nm (Cobolt MLD 0405-06-01-0100-100) was coupled into the system as an activation laser. Fluorescence emission was separated from laser excitation using a dichroic filter (Chroma T660LPXR) and an emission filter (Chroma ET690/50M). Images were acquired at up to 100 frames per second using an electron-multiplied CCD camera (Andor iXon DV887). This provided an effective field of view of approximately 30 μm using binning pixels, each of unbinned effective projected size of 61.7 nm. A 140-actuator micromachined DM (Boston Micromachines Corporation, multi-DM) was placed in the imaging path at a plane conjugate to the objective lens pupil. A lens system, with magnification of 0.86, imaged the 5.04 mm diameter pupil of the objective lens onto a region of 4.28 mm diameter on the DM. The DM was set up using the method explained in the next section, to ensure that any instrumental aberrations were removed before the imaging experiments were begun.
Sample and stage drift were negated by generating a super-resolution optical fluctuation imaging  image from every 200 frames, then estimating and removing the relative image shifts via their cross correlation .
Single-molecule emitters were identified in each frame using the maximum likelihood estimation (MLE) procedure described in [6,18]. Each frame was split into many small subregions, each containing a single-emitter signal. An iterative routine calculated the MLE for the and (and, where relevant, ) positions of each emitter along with the estimated localization precision, photon count, and the background fluorescence level. Out-of-focus single-molecule emission events and unconverged fits were rejected using a rejection algorithm based on a log-likelihood ratio .
Image representations were generated by placing a two-dimensional Gaussian profile at the estimated position of each located emitter. The standard deviation () of the Gaussian was set to the estimated localization uncertainty . For each reconstructed image, the resolution was estimated using the Fourier ring correlation (FRC) method .
3. ADAPTIVE OPTICS SCHEME
The microscope employed an image-based wavefront-sensorless adaptive optical scheme for aberration correction, whereby the necessary aberration correction is inferred from a sequence of images acquired with different bias aberrations applied to the DM . Such a scheme requires an appropriate choice of aberration modes, an image quality metric, and an optimization scheme. The various specifications for the implementation are outlined below.
A. Aberration Modes
The AO scheme used Zernike polynomials as the aberration modes. The DM was controlled using a matrix that encoded the actuator signals required to generate Zernike modes. For an initial set of input basis functions, the DM control matrix was obtained by estimating the wavefront produced by the DM via phase retrieval on images of a 40 nm red fluorescent bead [21,22]. A combination of defocused bead images permitted the recovery of the phase introduced by the DM when particular amounts of each basis function were applied . Rather than determining each actuator influence function separately, we took the more robust method of using numerically derived orthogonal mirror modes as the initial basis functions . These modes provided a better-conditioned starting point for the determination of the Zernike modes.
For each modeled basis function, a combination of the first 21 Zernike polynomials, , ignoring the piston mode, were fitted to the retrieved phase functions and the resulting coefficients were placed in a matrix. Repeating this decomposition for the first 21 modeled mirror modes, , resulted in an matrix of Zernike mode coefficients. Multiplying the pseudo-inversion of this matrix with the original DM control matrix provided a DM control matrix capable of generating Zernike aberration modes. It is important to ensure that image shifts are not introduced by the DM. For this reason, the lowest-order Zernike modes—tip, tilt, and defocus, which correspond to shifts in , , and , respectively—were removed from the control loop. This ensured that the use of the remaining aberration modes would not cause translation of the images .
B. Image Quality Metric
One of the challenges in the specification of an image-based AO scheme is finding an image quality metric that allows aberration estimation that is independent of the specimen. By the nature of microscopy, the specimen structure is always to some degree unknown. However, in SMS methods, there is an important property of the raw images that provides useful a priori information about the images. The blinking images consist of a pseudorandom combination of point-like emitters, even when the underlying specimen contains extended objects. The way in which aberrations affect each of the blinking images is therefore very closely related to the effect of the aberrations on the PSF of the microscope. Even though each image acquisition will see a different combination of emitters—and so could be considered an image of a different specimen—there are strong spatial correlations between the properties of subsequent images. In practice, there are differences in numbers of emitters and their individual intensities between frames. Therefore, an image sharpness metric was chosen as being insensitive to the intensity and number of emitters; it was therefore ideal for optimization in this microscope. The sharpness metric, , was defined in terms of the second moment of the image Fourier transform (FT) as 27]. This mask ensures that high-frequency noise does not adversely affect the calculation of . Qualitatively, sharp images lead to a broad image Fourier spectrum. Therefore a large value relates to a sharp image arising from a narrow PSF.
C. Aberration Correction Procedure
Each Zernike aberration mode was corrected independently by sequential optimization of the image quality metric. For a chosen mode, a sequence of blinking images was acquired, each with a different amount of the chosen Zernike mode applied to the DM. A Gaussian function was fitted to this sequence of metric evaluations. The position of the maximum of the fitted function was taken as the estimate for the required correction amplitude for that particular mode. The principle of this modal correction is shown in Fig. 2. This procedure was repeated for each mode of interest. For the corrections in this paper, we used a total of typically 11 evaluations per mode for Zernike modes 5–17, following the numbering convention adopted by Noll . A typical correction cycle therefore used a total of approximately 200 captured image frames. However, the number of evaluations per aberration mode was varied empirically from sample to sample depending on the complexity of the measured aberration.
D. Correction of Instrumental Aberrations
Before any imaging experiments were performed, static instrumental aberrations (including any introduced by the DM) were compensated. The instrumental correction was performed as described in the previous section by imaging 40 nm diameter fluorescent beads adhered to a coverslip in conventional wide-field mode. For this particular correction cycle, an alternative image quality metric—the maximum pixel intensity—was used because the maximum intensity of a point source can be related to the amplitude of aberrations in an imaging system .
Before correction, phase retrieval was utilized to estimate the uncorrected phase, which was found to have amplitude of 1.03 rad RMS, corresponding to a Strehl ratio of 0.34. These instrumental aberrations were dominated by astigmatism, although other modes were also present. After correction, phase retrieval estimation showed a residual phase of 0.47 rad RMS, corresponding to a Strehl ratio of 0.81. All aberrations mentioned in this paper are expressed as the additional correction relative to this instrumental correction.
4. LOW-ABERRATION IMAGING
In order to demonstrate the capabilities of the microscope in low-aberration conditions, i.e., conventional SMS imaging, we carried out SMS imaging of microtubules in COS-7 cells immunolabeled with Alexa-647 (Invitrogen A-21236) mounted in an oxygen-scavenging imaging buffer (Fig. 3). For details of the sample and buffer preparation, see Huang et al. . The observed region of the cells was immediately behind the coverslip, where any specimen-induced aberrations should be negligible. The sample was excited with 655 nm laser light, with a measured excitation intensity of . Fifty thousand frames were acquired with an exposure time of 20 ms per frame. Figure 3(a) shows the conventional long-exposure image for these data. The reconstructed super-resolution image is shown in Fig. 3(b). The FRC resolution of the super-resolution image was estimated at with localization precisions of and . These figures are comparable to others reported in the literature .
5. CORRECTION OF SPECIMEN-INDUCED ABERRATIONS
A similar specimen was used to demonstrate the correction of specimen-induced aberrations. The microtubules were imaged through the cells at a depth of approximately 6 μm. Initial images were obtained using only compensation for instrumental aberrations, corresponding to the aberrations experienced when focusing just beyond the coverslip. We acquired 10,000 frames with an exposure time of 20 ms per frame, using an illumination intensity of . Figures 4(a1) and 4(b1) present two examples of reconstructed SMS images.
Aberration correction was performed using the method described in the previous section and new SMS data were acquired. Figures 4(a2) and 4(b2) show the reconstructed SMS images following specimen aberration correction. The specimen aberrations introduced by the DM in each case are represented by the inset figures. It can be noted that the aberrations were different in each case, as the light emitted had to pass through different specimen structures on the way to the objective lens. A spherical aberration component is present—as should be expected when focusing through a refractive index mismatch —but other modes are also seen.
The Zernike coefficients of individual specimen corrections are shown in Fig. 5. At a depth of , the depth-dependent spherical aberration model  predicts of spherical aberration. In both cases presented here, of spherical aberration was measured, which indicates an additional amount of spherical aberration present beyond that predicted from the refractive index mismatch between the mounting and immersion media. The specimen aberration also changed between samples. The nonspherical components of the specimen correction accounted for 0.23 rad RMS of applied phase out of a total of 0.72 rad RMS, for the results in Fig. 4(a2), and 0.26 out of 0.78 rad RMS for those in Fig. 4(b2).
Significant differences can be seen between the uncorrected and corrected SMS images. The compensation of specimen-induced aberrations led to more microtubule structures being reconstructed in some image areas, such as the top left of the specimen [Fig. 4(a2)]. In other regions, e.g., [Fig. 4(b2)], the compensation of specimen-induced aberrations resulted in double the number of emitter localizations.
6. ADAPTIVE OPTICS CORRECTION APPLIED TO 3D LOCALIZATION VIA ASTIGMATISM
Previous work has shown that an astigmatic PSF can be used to enable 3D localization microscopy, as the shape of an emitter image changes dependent upon its position above or below the nominal focus [31–33]. Astigmatism can be introduced by a cylindrical lens or, more controllably, using a DM . We combined the use of the DM as the astigmatic element with image-based aberration correction to show the effects of aberrations and the benefit of their correction on the 3D localization microscope.
The DM provides the ability to tune the amount of astigmatism used to encode axial information. A larger degree of astigmatism will increase the change in the PSF shape relative to the distance to the focal plane. However, a large amount of astigmatism will also distort the PSF shape such that it will become highly asymmetric. This PSF asymmetry will decrease the and localization precisions  and possibly cause borderline fits to fall beneath acceptability thresholds. In order to find the optimum setting, we varied the amount of astigmatism () between while imaging a 40 nm red bead mounted in immersion oil on a coverslip. Empirically, we chose as providing a suitable balance between PSF asymmetry and the determination of the PSF centers . Aberration correction was performed using the same procedure as described previously, without the addition of astigmatism to the DM. Following the aberration correction routine, 3D SMS data were acquired with and, for comparison, without the aberration correction applied.
Figure 6 shows the resulting images of microtubules, imaged in Vectashield buffer , with the coordinate encoded by color over a range of approximately 400 nm. Again, the microtubules were imaged through the cells at a depth of approximately 6 μm. After aberration correction, more of the specimen was visible as more of the emitter fits satisfied the acceptance criteria (particularly in the region at the center of the image). A further example, imaged in oxygen-scavenging buffer, is shown in Fig. 7. The Zernike coefficients of the specimen corrections are shown in Fig. 8. Significant specimen-dependent nonspherical components were present in the applied DM correction. The nonspherical components accounted for 0.51 of 0.71 rad RMS and 0.88 of 1.15 rad RMS for the phase corrections in Figs. 6 and 7, respectively.
In addition to the larger number of acceptable emitter fits following aberration correction, there are regions where the aberrations had caused erroneous estimation of the position. This is further illustrated in Fig. 9, which shows the profile retrieved from three regions of the specimen. For each location, a section through the microtubule is extracted, as indicated by the superimposed box in Fig. 6. The points corresponding to the emitter locations within this box were then projected along the direction to provide a projected distribution. It is clear from these results that the presence of specimen-induced aberrations can have a significant effect on the apparent position of the microtubules, particularly in the coordinate. The number of localizations; the FRC resolution estimate; and the , , and precision estimates for the reconstructed data shown in Figs. 6 and 7 are presented in Table 1. From Table 1 it is clear that correcting specimen-induced aberrations, at a depth of , dramatically increases the number of single-emitter localizations. Even though the , , and precision estimates do not vary significantly with AO correction, as the emitter density increases with AO correction, the FRC resolution estimate improves considerably.
7. EFFECT OF ACCEPTANCE CRITERIA ON IMAGE QUALITY
As aberrations distort the PSF of the microscope, they also affect whether an emitter is accepted as a “good” fit during the analysis of the images of the blinking emitters. The first selection criterion in the estimation process was based on the brightness (total number of detected photons) attributed to each emitter. If the brightness was above a chosen threshold, then the emitter data were passed through to the localization routine, or were otherwise discarded. In the ideal case, the localization precision is inversely proportional to the square root of the total number of photons detected. If the acceptance threshold for emitter brightness were increased, it should therefore be expected that the average localization precision would improve. Similarly, precision should also be enhanced after aberration correction, as the average number of photons in the emitter images above the brightness threshold will increase. Moreover, the fidelity of the PSF would increase and with it the precision of the fit. The shape of the PSF also plays a role in the emitter acceptance criteria, if a further filtering stage based on estimated localization precision is used. A full understanding of the relationship between the final reconstructed image quality and the PSF distortion due to aberrations could be obtained through detailed modeling, which is outside the scope of this work. We can however illustrate the effects of the brightness threshold and the quality of fit criterion on the experimentally acquired data.
Figure 10 shows these phenomena for the , , and precisions estimated from the 3D reconstructed data presented in Fig. 6. In each case, aberration correction provides improved localization precision across the whole range of emitter brightness thresholds. One can also see that apparently equivalent localization precisions could be obtained by adjusting the threshold instead of compensating for the aberrations. This apparent improvement is only brought about by excluding poor-quality fits, thus reducing the number of localizations and leading to inferior quality of the final reconstructed image. In order to illustrate this, the localization data, which generated Fig. 6, were then analyzed again, whereby fits were only accepted if the precisions and were less than 20 nm and was less than 40 nm. As it is more likely that emitter images above the brightness threshold have better-defined peaks after aberration correction, we expect that the total number of acceptable fits for the AO corrected data should be significantly higher than that for the uncorrected data. This is illustrated in Fig. 11.
Due to the strict nature of this acceptance criterion, many more emitters are accepted after the correction of specimen-induced aberrations. For this reason, many specimen features may not appear in the reconstructed uncorrected localization image. Relaxation of the acceptance criteria could lead to more emitters being included without aberration correction, but this would be at the expense of worse effective resolution of the final image.
We have shown that the presence of specimen-induced aberrations detrimentally affects the images obtained in our SMS microscope. Correction of the aberrations using AO improved the quality of the raw images and ensured that the microscope PSF was closer to the model used in the estimation routine. This in turn had a significant effect on the final image representation, particularly in the 3D SMS mode, where aberrations caused the corruption of the estimated coordinate of the emitters. These effects were observed even at modest depths of less than 10 μm into the specimen.
Correction of the specimen aberrations required a new AO method that used raw blinking images as the source for the image-based sensorless adaptive scheme. It is a useful feature of localization microscopes that these images arise essentially from pseudorandom arrays of point emitters. The sharpness metric we employed was therefore independent of the overall specimen structure as it was derived purely from images of point sources. The image-based feedback scheme allowed the correction of aberrations, which would not have been predicted by simpler models based on refractive index mismatch. The magnitude of the additional corrections constituted a considerable fraction of the total applied correction, and nonspherical aberration modes played an important role.
As the images consist of random arrays of PSFs, one might also consider using methods of phase retrieval to determine aberrations in future implementations . Furthermore, it should be noted that the correction of sample-induced aberrations only used a tiny fraction of the total sample exposure time. In general, less than 200 blinking frames were used to achieve AO correction, compared with 20,000–50,000 blinking frames acquired to reconstruct the final data.
The effects of aberrations on the reconstructed localization microscope images were quite different from those in conventional forms of microscopy, where a gradual reduction in resolution and contrast is observed as aberrations increase in magnitude. In localization microscopy, the use of acceptance criteria to separate high-quality emitter fits from poor fits means that emitters are more likely to be excluded from the final image representation when aberrations are present. The resulting images can therefore still appear sharp, as only good fits are ever included. As aberrations increase in magnitude, fewer regions of the specimen will contain acceptable fits, so parts of the specimen will appear dark in the final representation. It is clear that adaptive correction of these aberrations is desirable. However, there are important caveats to be considered when imaging without AO; for example, it is possible that objects that would be visible in an aberration-free image could disappear were aberrations present. This would not be obvious from the final image representation considered alone. It follows that care must be taken in the interpretation of localization images in the presence of aberrations.
Wellcome Trust (095927/A/11/Z, 095927/B/11/Z).
We thank L. Schermelleh and J. Demmerle for providing test samples for the development of the AO scheme, and L. Schroeder for providing the COS-7 samples and for helpful discussions about the buffer and sample preparation.
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