Adaptive optics enables 3 D STED microscopy in aberrating specimens

Stimulated emission depletion (STED) microscopy allows fluorescence far-field imaging with diffraction-unlimited resolution. Unfortunately, extending this technique to three-dimensional (3D) imaging of thick specimens has been inhibited by sample-induced aberrations. Here we present the first implementation of adaptive optics in STED microscopy to allow 3D super-resolution imaging in strongly aberrated imaging conditions, such as those introduced by thick biological tissue. ©2012 Optical Society of America OCIS codes: (180.2520) Fluorescence microscopy; (180.6900) Three-dimensional microscopy; (110.1080) Active or adaptive optics; (350.5730) Resolution. References and links 1. D. Toomre and J. Bewersdorf, “A new wave of cellular imaging,” Annu. Rev. Cell Dev. Biol. 26(1), 285–314 (2010). 2. S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6(1), 24–32 (2009). 3. S. W. Hell and J. 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Lett. 36(17), 3389–3391 (2011). #171616 $15.00 USD Received 29 Jun 2012; revised 31 Jul 2012; accepted 2 Aug 2012; published 29 Aug 2012 (C) 2012 OSA 10 September 2012 / Vol. 20, No. 19 / OPTICS EXPRESS 20998 18. M. Schwertner, M. J. Booth, and T. Wilson, “Characterizing specimen induced aberrations for high NA adaptive optical microscopy,” Opt. Express 12(26), 6540–6552 (2004). 19. T. J. Gould, J. R. Myers, and J. Bewersdorf, “Total internal reflection STED microscopy,” Opt. Express 19(14), 13351–13357 (2011). 20. G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, “Macromolecular-scale resolution in biological fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 103(31), 11440–11445 (2006). 21. K. I. Willig, R. R. Kellner, R. Medda, B. Hein, S. Jakobs, and S. W. Hell, “Nanoscale resolution in GFP-based microscopy,” Nat. Methods 3(9), 721–723 (2006). 22. E. Auksorius, B. R. Boruah, C. Dunsby, P. M. Lanigan, G. 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Introduction
The recent development of sub-diffraction microscopy -or nanoscopy -is revolutionizing fluorescence imaging [1].Through either targeted or stochastic switching of fluorophores, resolution on the order of tens of nanometers or better is now achievable [2].In thick samples, the targeted switching approach of stimulated emission depletion (STED) microscopy [3] has the advantage over widefield-based stochastic single-molecule switching techniques [4][5][6] that background fluorescence is suppressed through the inherent optical sectioning of a confocal laser scanning geometry.After initial successes in imaging thin samples such as single cells, STED microscopy has successfully been demonstrated to image tissue sections [7,8], nematodes [9], and even living mice [10].STED microscopy overcomes the diffraction limit by superimposing a conventional excitation focus with a second laser focus of high intensity -the depletion-focus -which is red-shifted with regard to the peak of the fluorescence spectrum and features a central intensity minimum (ideally an intensity zero).The depletion laser forces excited fluorophores back to the ground state by stimulated emission and thereby suppresses fluorescence at the periphery of the excitation focus.Increasing the intensity of the depletion beam reduces the effective point spread function (PSF) to a size that is in principle diffraction-unlimited.However, in practice, the obtainable resolution in STED microscopy depends strongly on the quality of the intensity minimum in the center of the depletion focus: for non-negligible minimum intensities, fluorescence is also depleted in the center of the focus and resolution improvement is countered.Both system-and sample-induced aberrations of the depletion laser beam can dramatically decrease the beam quality and create non-negligible minimum intensities.STED microscopy deep in aberrating samples is therefore far from trivial.Fortunately, the most commonly used depletion profile, which is created by a helicoidal phase mask, is strongly resistant against beam aberrations [11].All previous STED applications in thick samples have taken advantage of this fact [7][8][9][10].Indeed, except for the straightforward adjustment of the objective correction collar [8], no aberration correction has been necessary in these applications.On the downside, however, the helicoidal phase mask creates a toroidal depletion-focus, that results in a highly anisotropic effective PSF that is confined in the lateral (xy) plane but still diffraction-limited in the axial (z) direction.Consequently these STED images are superresolved in the lateral direction, but not along the optical axis.To image the intrinsic 3D organization of tissue at the finest detail, STED microscopy must exhibit 3D resolution enhancement.
For thin samples, two 3D STED methods have been demonstrated thus far.The highest resolution has been achieved with a complex setup utilizing two opposing objective lenses [12] which is not compatible with thick sample geometries.Alternatively, using a single objective, an annular phase filter featuring a central circle with a phase step of π radians (λ/2) has been applied [13].This phase mask creates a ring-shaped focus with additional highintensity lobes above and below the central minimum and thereby allows suppression of fluorescence emission in all directions around the center.Unfortunately, this approach is far more susceptible to aberrations than the helicoidal phase mask approach [11] and, not surprisingly, no 3D STED imaging has been demonstrated to date in thick samples.
To realize 3D STED microscopy with the central λ/2 phase filter deep in samples, two approaches are conceivable.First, the tissue could be 'cleared' by embedding it in a refractive index-matching medium, but this approach is not compatible with living specimens.Second, adaptive optics (AO) could be employed.Adaptive elements such as deformable mirrors or spatial light modulators have been successfully implemented in a variety of microscopes to correct specimen-induced aberrations [14][15][16][17].As aberrations are not predictable, but rather vary across different regions and depths in the specimen, the key to a successful implementation of AO is the use of feedback from the measured microscope focus quality into the aberration correction procedure.This approach distinguishes adaptive aberration correction from simple static correction methods, such as adjustment of the objective lens correction collar [8].These static methods cannot correct the complex aberrations that are actually encountered in biological microscopy [18].Here we demonstrate the first implementation of AO in 3D STED microscopy using a novel image quality feedback metric and demonstrate resolution well below the diffraction limit in all three dimensions when imaging through optically aberrating specimens such as tissue.

Setup
In order to achieve 3D super-resolution, we adapted a custom-built STED microscope described previously [19] by implementing a central λ/2 phase mask in the depletion beam path.Figure 1 illustrates the AO STED setup.The output from an 80 MHz mode-locked Ti:Sapphire laser (Chameleon Ultra II, Coherent) was passed through a Faraday isolator (Newport) and a half-wave plate before being split into two beam paths by a Glan laser polarizer (Newport).The transmitted beam was used for STED illumination.This beam was passed through a 19 cm long glass block, a delay stage for pulse delay adjustment, and an acousto-optical modulator (AA Optoelectronics) for laser power adjustment before it was coupled into a 100 m long polarization-maintaining single mode fiber (Fibercore).The glass block and single mode fiber served to stretch the pulses to a few hundred picoseconds.To generate synchronized excitation pulses, the beam reflected at the Glan laser polarizer was focused into a photonic crystal fiber (SCG-800, Newport).The white light spectrum output from this fiber was passed through an acousto-optical tunable filter (AOTF; AA Optoelectronics) for wavelength selection and power control and then coupled into a second polarization-maintaining single mode fiber (Thorlabs).At the output of each single mode fiber, the beams were collimated and reflected off of a liquid crystal spatial light modulator (SLM) placed in a plane conjugate to the objective pupil.Half-and quarter-wave plates were used to produce circular polarization of each beam in the sample.Additionally, a polarizing beam splitter cube was used in the STED beam path to clean up the beam polarization.The beams were then merged to a common path by a dichroic mirror before being focused by a 100x/1.4NAoil immersion objective lens (UPLSAPO 100XO/PSF, Olympus) mounted in a commercial microscope stand (IX71, Olympus).Samples were mounted to an xyz piezo stage (PINano, Physik Instrumente) for scanning.The fluorescence signal was collected by the objective, separated from laser light by the dichroic mirrors (FF01-740-Di01 and FF662-FDi01, Semrock), filtered by two bandpass filters (FF01-685/40, Semrock), and focused into a 62.5 µm core diameter (~0.64 Airy units) 50:50 signal-splitting multimode fiber (OZ Optics).Each output of the multimode fiber was attached to a single photon counting avalanche photodiode (ARQ-13-FC, Perkin Elmer).Image acquisition and instrument control was achieved using custom software written in Labview (National Instruments).For imaging, the Ti:Sapphire laser was tuned to 770 nm for depletion and an excitation line at 633 nm was selected from the output of the photonic crystal fiber using the AOTF.Laser powers measured at the objective back aperture were 84-132 mW and 0.2-2 µW for depletion and excitation, respectively.Images (128x128 pixels) were acquired with a scan rate of 100 lines/s, a pixel size of 40 nm, and 1-3 frame accumulations (corresponding to 1.28-3.84s/image).Lines were scanned unidirectionally using a sinusoidal velocity profile which resulted in a pixel dwell time of 21.5 µs at the scan center and approximately twice this value at the edges.Recorded pixel values were therefore normalized according the pixel dwell times such that the center pixel was divided by unity.Fitting of line profiles was performed using the software Imspector (Andreas Schönle, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany).Fits were performed either using a Lorentzian (for images taken after aberration correction) or a Gaussian function (for images taken without aberration correction since in this case the observed data did not fit a Lorentzian profile).3D volume renderings were generated using the software Volocity (Perkin Elmer).
The STED phase mask as well as aberration correction were realized using the SLM (Hamamatsu X10468-02) placed in the depletion beam path (SLM1 in Fig. 1).The 800x600 pixels of the SLM can be addressed individually by connecting the SLM as an additional display device to the instrument PC.Phase modulation from 0 to 2π radians (and more) at the wavelengths used is achieved by varying the gray scale of the phase image fed to the SLM.Phase modulations significantly larger than 2π radians can be produced through phasewrapping, whereby larger phase values are translated into the range 0 to 2π radians.Although aberrations affect the illumination, emission and depletion beam paths, the achievable resolution is dominated by the quality of the depletion focus.For this reason, aberration correction by the SLM solely in the depletion path is sufficient to significantly improve the image quality.Aberrations in the illumination and emission paths, however, influence the level of fluorescence excitation (by reducing the illumination intensity in the focus), the detection efficiency (by blurring the fluorescence focus on the confocal pinhole) and the background signal (through excitation and detection of fluorescence outside of the depletion region).Therefore, we included a second SLM (Hamamatsu X10468-01) to perform additional aberration correction in the excitation beam path (SLM2 in Fig. 1).Further improvement could in principle be attained with aberration correction in the emission path.However, the polarization dependence of the SLM limits its suitability for correction of fluorescence emission.
SLMs have been used previously in STED microscopy in a direct reflection configuration [20,21].However, this implementation requires near-perfect phase modulation of the light by the SLM.Instead, here we use an off-axis hologram which is beneficial because it separates the phase-modulated light from any directly reflected, unmodulated light [22].In our setup an active pupil was defined on the SLM by creating such an off-axis hologram (Fig. 1 insets) -a blazed grating of circular outline that diffracts light off the principal reflection axis into the first diffraction order -and the diffracted light was focused into the sample.The remaining small non-diffracted fraction of the incident light (as well as light reflected from parts outside the active pupil) were simply reflected along the principal reflection axis and formed a secondary focus in the sample, much weaker than the depletion spot, approximately 3 µm away from the primary focus.This approach ensured that any residual light stemming from imperfect phase modulation could not interfere with the desired depletion focus and reduce its quality.We note that the non-diffracted light could also be blocked at an intermediate focal plane if necessary.Phase masks for creating the depletion focus were produced by adding the corresponding function to the SLM phase pattern.In this manner, phase masks can be added, modified and exchanged with considerable ease, compared to systems where manufactured phase plates are physically placed in the optical path.
The microscope employed an oil immersion lens of numerical aperture (NA) 1.4.Specimens were mounted in either aqueous media (phosphate buffered saline, PBS) of refractive index n = 1.34 or glycerol (n = 1.47).For the aqueous mounting media, the limiting system NA is restricted to the refractive index of the mounting medium due to total internal reflection at higher angles of incidence of the focusing beam.We therefore restricted the active aperture defined on the SLM to a size corresponding to an objective NA of 1.325.This enabled us, in effect, to mimic the performance of a water immersion objective lens of NA = 1.325, which is higher than commercially available objectives.

Aberration correction
The SLM enables adaptive aberration correction through the addition of further phase functions to the SLM [22].In the system described here we employed a sensorless AO scheme to determine the aberrations induced by the system and specimen [23][24][25].In sensorless AO, aberrations are estimated through analysis of a set of images that is obtained using a sequence of predetermined bias aberrations.This process requires 1) expansion of the aberrations using an appropriate set of modes, and 2) definition of an image quality metric that is maximized to find the optimal aberration correction.
We chose to model aberrations using a Zernike polynomial expansion modified to remove small image shifts introduced by displacement (tip, tilt, and defocus) modes [25,26].Table 1 lists the Zernike modes (following the numbering convention used by Neil et al. [27]) used for aberration correction in this work.Zernike polynomial modes are widely used to model aberrations in adaptive optics.One reason for this is the orthogonality between the modes, which has useful practical consequences, such as the separation of displacement of the focus (by tip, tilt and defocus modes) and distortion of the focus (through higher order modes such as astigmatism, coma and spherical aberration).However, this separation of effects is only strictly true in the paraxial approximation and with a uniform pupil function.When using phase masks and high NA lenses in STED microscopy, these approximations are no longer valid.We observed experimentally that the zero intensity point of the depletion focus can shift laterally when, for example, Zernike coma is applied using the SLM.Similar axial shifts were observed when applying Zernike spherical modes.This behavior has been confirmed through theoretical modeling (data not shown).In order to remove these displacement effects, we measured the induced focal shifts for each Zernike mode using images of gold beads.Using a linear approximation of the zero shift, a proportionate amount of the tip, tilt, or defocus mode (as appropriate) was added to each applied Zernike mode to ensure that the intensity zero did not shift position.This procedure defined a modified set of "displacement-free" Zernike modes that was used for the subsequent experiments.Table 2 lists the coupling between displacement and aberration modes used to generate displacement-free Zernike modes.Subsequent references to Zernike modes will hereafter represent displacement-free Zernike modes.Previously published sensorless AO microscopes (e.g.confocal, two-photon) have used simple image quality metrics, such as total image brightness (sum of pixel values) [24].The response of these metrics to suitably chosen aberration modes provided a well-defined maximum, which was typically quadratic, thus optimization could be readily performed using simple algorithms.However, in the STED microscope, these simple metrics prove to be of limited use.A heavily aberrated STED microscope does not effectively confine the fluorescence to a narrow region, but permits emission from fluorophores across a larger volume.If from this state the aberrations are corrected, there is an inherent drop in total image intensity as the depletion becomes more effective and the effective PSF encompasses fewer fluorophores.Furthermore, we have observed that close to the optimum correction the adjustment of certain aberration modes caused a decrease in image intensity, whereas others led to an increase (Fig. 2).The brightness metric alone is therefore inappropriate in the STED microscope.Metrics related to image sharpness might in principle seem better suited, but optimization purely on this basis is susceptible to degradation of the STED focus as the metric is misled by the background noise (noise tends to be "sharper" than the imaged specimen).It was further found that the response of the sharpness metric to some aberration modes was very flat near optimum correction, exhibiting a variation that was closer to quartic than quadratic (Fig. 2).In practice, the characteristics that we desire from a STED image are high brightness combined with high resolution.We have therefore introduced a new metric that seeks to optimize both image brightness and image sharpness in a combined approach, which succeeds where either separate approach can fail.The combined metric was defined as where B and S are the brightness and sharpness metrics, respectively.The expression in brackets in Eq. ( 1) is a logistic function that, in effect, introduces the contribution of the brightness metric B only when the sharpness metric S is above a particular threshold S T (typically chosen to be 90% of the peak sharpness).The parameter β was chosen empirically to balance the contributions from S and B and the parameter k was used to adjust the rate of transition of the logistic function in the region of S≈S T .The constant σ was + 1 or −1 dependent upon whether the aberration mode in question produced a minimum or maximum in B for zero aberration magnitude.The image brightness metric B was calculated as the sum of the pixel values in the confocal or STED image.The sharpness metric S was defined as the second moment of the image Fourier transform (FT) and calculated as where , ˆn m I is the discrete FT of the image, where w is a radius (in units of pixels of the image FT) defined as the size of the field of view divided by an upper bound on the expected resolution (assumed to be 200 nm).This mask is used to cut off higher spatial frequencies that would otherwise cause S to be dominated by noise.The motivation for this choice of metric lies in the inverse relationship between the width of image features and the width of the corresponding image's spatial frequency spectrum -sharp images lead to a broad image FT.As the second moment calculation of Eq. ( 2) is a measure of width of the image FT, it follows that a large value of S corresponds to a sharp image arising from a narrow PSF. Figure 2 shows comparisons of the three metrics B, S and M for selected Zernike modes for STED imaging (using a λ/2 phase mask) of 200 nm crimson beads (F8806, Invitrogen) attached to a coverglass and mounted in glycerol.Images were acquired in the xy (focal) plane.We demonstrate here the suitability of the metric M using images of fluorescent beads, however, the definition of M should mean that it is readily applicable to any sample that features structures smaller than the diffraction limit.
It is important to note that the 2nd and 3rd spherical modes lead to decreases in image brightness while the 1st spherical mode leads to a brightness increase when imaging with the central λ/2 phase mask (Fig. 2).These results reveal that manual adjustment of the objective correction collar to maximize image brightness cannot necessarily be applied to 3D STED microscopy as the collar adjusts a combination of these spherical aberration modes.
For our sensorless adaptive optics scheme, images (single accumulation) were acquired in either confocal (for excitation path correction) or STED (for depletion path correction) mode while adding a bias aberration, bZ i , of a given mode Z i where b was a suitably chosen bias amplitude.Typically, b was chosen to cover the range of −1 to + 1 radian while acquiring a total of 5 to 7 images for each Z i (corresponding to ~6.4-9 s for each iteration of correction for each mode).For each image the appropriate metric was calculated (B for excitation path correction; M for depletion path correction) and then plotted as a function of the bias amplitude b as shown in Fig. 2. The correction aberration, a corr , was then estimated as the peak of the curve, which was calculated by fitting a quadratic function to the data.In cases where a quadratic approximation did not represent the data, peaks could be identified manually.The aberration a corr Z i was then added to the SLM phase pattern, and this measurement and correction cycle was then repeated for each of the modes of interest.Aberrations due to coma, astigmatism, and trefoil could be assessed using a single iteration of our correction routine.Spherical modes were typically the dominant aberrations in the experiments conducted here and typically required 1-4 correction iterations to converge to optimal values.However, when results for correcting the excitation beam path were used as a starting point for correction of the depletion beam path 1-2 iterations were typically sufficient to assess the spherical aberrations.All AO STED images shown are of the same field of view used to perform aberration correction.Fig. 2. Metric curves as a function of the SLM-applied aberration for correction in the depletion beam path when using a central λ/2 phase mask.Example curves are shown for Zernike modes 5 (astigmatism), 7 (coma), 9 (trefoil), 11 (1st spherical), 22 (2nd spherical), and 37 (3rd spherical) including sharpness (S; green lines), brightness (B; black lines), and combined (M; red lines) metrics.A prime (e.g.Z '11) indicates that a particular mode was corrected to be displacement free.Insets show corresponding normalized (-π to + π) phase distributions in the objective back aperture.Data was obtained by imaging 200 nm fluorescent beads in STED mode.

AO STED microscopy
As an initial implementation, system aberrations were corrected using images of fluorescent beads.For this purpose, a fluorescent bead sample was prepared by attaching 100 nm diameter crimson beads (C47248, Invitrogen) to a coverglass coated with poly-L-lysine and mounting the coverglass to a microscope slide with glycerol as the mounting medium.Optimization was performed first for the excitation beam path using the brightness metric (in confocal imaging mode) and then for the STED beam path using the combined metric defined in Eq. ( 1) (in STED imaging mode).Figure 3 shows xz-images of fluorescent beads before and after aberration correction.It can be clearly seen that the aberrated depletion focus (PSF shown in Fig. 3(a)) had a detrimental effect on both the image intensity and resolution.By correcting system aberrations, the axial STED resolution could be improved by a factor of 2 from ~280 nm to ~140 nm while at the same time the signal intensity increased by a factor of ~1.6.This quality improvement can also be seen when measuring the depletion focus directly: Figs.3(a) and 3(b) show the intensity distribution of the depletion focus measured in reflection mode by scanning a 150 nm diameter gold bead through the focal region without and with the obtained aberration correction, respectively.As shown in this figure, aberration correction leads to a far more symmetric depletion focus with a more pronounced intensity minimum.
To demonstrate correction of aberrations induced by a strongly aberrating sample, we next imaged fluorescent beads through a layer of glycerol (n = 1.47).Samples with fluorescent beads were prepared by attaching 100 nm crimson beads to the microscope slide coated with poly-L-lysine and beads were imaged through a #1.5 coverglass and ~55 µm of glycerol which was used as the embedding medium.Figure 4 shows the bead images before and after aberration correction in regular confocal and in STED imaging modes.The aberration correction routine began by correcting the excitation beam path using the image brightness B as the metric in confocal imaging mode.The resulting correction values were then used as the starting point for correction of the depletion beam path using the combined metric defined in Eq. ( 1) in STED imaging mode.Figures 4(a   To further test the correction procedure using aberrations encountered in biological specimens, 200 nm crimson beads were added on top of zebrafish retina sections attached to #1.5 coverglass and then mounted in PBS (to mimic the aqueous embedding conditions of live sample imaging) onto a microscope slide.Figures 5(a)-5(l) show xy and xz images of an individual bead after focusing ~14 µm or ~25 µm through the retina sections.In this application all aberration correction was performed solely on the STED beam path to demonstrate that correction of the depletion beam path is possible without prior knowledge of corrections made to the excitation path.These data also demonstrate that the quality of the depletion focus is the dominating factor in achieving sub-diffraction resolution in the STED images.While correction of relatively few aberration modes was sufficient to obtain ~200 nm and ~250 nm axial resolution for imaging depths of ~14 µm and ~25 µm, respectively, we expect that including higher order aberrations in the correction routine should further improve the STED resolution.We note that the STED images shown in Figs.3-5 before and after aberration correction are of the same beads on which the correction routine was performed, thus demonstrating that photobleaching was not significant in these experiments.Labeling conditions in biological imaging applications are likely to use less photostable fluorophores, which in some instances may not tolerate the acquisition of 5-7 STED images per aberration mode.However, it has been demonstrated that only 2N + 1 images are required to correct for N aberration modes [25] and we expect this approach to be compatible with methods presented here.Furthermore, applications otherwise inhibited by photobleaching may benefit from the implementation of triplet-state-relaxation during STED imaging [20] either by increasing scan rates or using lower repetition rate lasers.

Summary
In summary, we have implemented for the first time adaptive correction of aberrations in a STED microscope using image-based feedback that enables compensation of both system and specimen-induced aberrations.Moreover, through aberration correction we have performed STED microscopy through thick tissue samples using a central λ/2 phase mask to enhance resolution in 3D.This achievement contrasts with the 2D enhancement shown in previous applications of STED microscopy in tissue imaging in which helicoidal phase masks were used.In a previous report an SLM was used to correct for system aberrations in the depletion beam path through direct observation of the depletion focus [22].However, this method is not practical for correction of aberrations introduced in microscopy of real specimens, where one usually has access only to the fluorescence images.Our developments permit aberration correction using the super resolution image itself, which is a significant step towards making automated AO practical for biological superresolution microscopy.
The SLM provides a convenient way to combine a STED phase mask and adaptive aberration correction in the same microscope.The alternative approach of using deformable mirrors would have the advantage of being able to correct all three (depletion, excitation, and emission) beam paths with the same device.However, unlike the SLM, the continuous reflective surface of mirror devices does not permit the generation of the STED phase masks, which require discontinuous phase jumps.
Aberrations were corrected using a sensorless AO scheme in which aberration modes were sequentially corrected through a process of image optimization.The definition of a new image quality metric, combining both image sharpness and brightness, was necessary to account for the way in which aberrations affect STED images.We have implemented the correction using images of beads through tissue specimens.We expect, however, that our correction scheme is applicable to any arrangement of fine scale objects.
The implementation of AO in STED microscopy is a critical step towards achieving 3D super-resolution inside strongly aberrating samples.This is especially important when imaging living samples where matching the refractive indices of immersion liquids and mounting media is not practical.In addition to the demonstrations of superresolution STED microscopy in tissue, there have recently been applications of stochastic switching-based nanoscopy approaches to the imaging of multi-cellular structures [28].AO has also recently been used in this branch of nanoscopy to correct for instrument-induced aberrations [29].We expect that AO will be instrumental in extending correction of sample-induced aberrations to all superresolution modalities using an approach similar to that presented here.This implementation of AO has the potential to advance 3D diffraction-unlimited microscopy to a new imaging frontier in (living) tissue and intact specimens.
,and n and m are the coordinates ranging from 0 to N-1 or M-1, respectively.The function , ) and 4(b) illustrate the benefits of using a second SLM to correct aberrations in the excitation beam path (for confocal imaging).As shown in Fig.4(c), the non-corrected STED image exhibits moderately improved resolution compared to the confocal image, but at the expense of a significant decrease in the signal level as the non-zero central intensity depletes the fluorescence.On the other hand, correction of aberrations significantly enhances both the intensity and resolution of the STED image (Fig.4(d)).Comparing the axial profiles of the STED and AO STED images (Fig.4(e)) reveals a ~5-fold increase in the peak signal as well as a ~3.2-fold improvement in resolution.

Fig. 3 .
Fig. 3. Adaptive correction of residual system aberrations.(A, B) STED PSF using the central λ/2 phase mask before (A) and after (B) correction for system aberrations with corresponding phase patterns used on SLM2.(C, D) xz STED images of 100 nm fluorescent bead attached to coverglass and imaged (C) before and (D) after correction of system aberrations.(E) Axial line profiles of pixels summed across horizontal dimension of dashed boxes in (C) and (D).Fitted curves give FWHM of 280 nm (Gaussian fit) for the uncorrected STED image and 140 nm (Lorentzian fit) when adaptive optics is used to compensate for system-induced aberrations in the STED beam path.

Fig. 4 .
Fig. 4. Images of 100 nm fluorescent beads through ~55 µm layer of glycerol.xz images were acquired in confocal mode (A) before and (B) after correction of sample induced aberrations, and STED mode with (C) correction to the excitation beam only and (D) correction to excitation and depletion beam paths.(E) Axial line profiles of pixels summed across horizontal dimension of dashed boxes in (C) in (D) show improvement in both resolution and signal when aberrations are corrected in the STED beam path.
Figures 5(m)-5(o) show volume renderings of the data depicted in Figs.5(a)-5(f) and represent the first 3D super-resolution STED image recorded through scattering tissue.

Fig. 5 .
Fig. 5. AO STED images of fluorescent beads through zebrafish retina sections.(A-F) Results for beads imaged though ~14 µm of retina.Lateral and axial sections of a single fluorescent bead imaged in (A, D) confocal, (B, E) STED, and (C, F) AO STED show improvement in signal and resolution when adaptive aberration correction is applied to the depletion beam path.(G-L) Similar image sequences for beads imaged through ~25 µm of retina.Axial profiles of beads in AO STED images were ~208 nm and ~249 nm for (F) and (L), respectively.Color bar in (E) also applies to (B), (C), and (F).Color bar in (K) also applies to (H), (I), and (L).(M-O) Volume renderings for data shown in (A-F) for (M) confocal, (N) STED, and (O) AO STED data.(N) and (O) plotted on same color scale for comparison of signal.