The importance of the photon arrival times in STED microscopy

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1 he importance of the photon arrival times in SED microscopy Marco Castello a,b, Luca Lanzanó a, Iván Coto Hernández a,d, Christian Eggeling c, Alberto Diaspro a,d,e and Giuseppe Vicidomini a a Nanophysics, Istituto Italiano di ecnonogia, Via Morego 3, 663, Genoa, Italy; b DIBRIS, University of Genoa, Via Opera Pia 3, 645, Genoa, Italy; c MRC Human Immunology Unit, Weatherall Institute of Molecular Medicine, John Radcliffe Department of Molecular Medicine, University of Oxford, OX3 9DS, Oxford, United Kingdom; d DIFI, University of Genoa, Via Dodecaneso 33, 646, Genoa, Italy; e Nikon Imaging Center, Via Morego 3, 663, Italy; ABSRAC In a stimulated emission depletion (SED) microscope the region from which a fluorophore can spontaneously emit shrinks with the continued SED beam action after the excitation event. his fact has been recently used to implement a versatile, simple and cheap SED microscope that uses a pulsed excitation beam, a SED beam running in continuous-wave (CW) and a time-gated detection: By collecting only the delayed (with respect to the excitation events) fluorescence, the SED beam intensity needed for obtaining a certain spatial resolution strongly reduces, which is fundamental to increase live cell imaging compatibility. his new SED microscopy implementation, namely gated CW-SED, is in essence limited (only) by the reduction of the signal associated with the time-gated detection. Here we show the recent advances in gated CW-SED microscopy and related methods. We show that the time-gated detection can be substituted by more efficient computational methods when the arrival-times of all fluorescence photons are provided. Keywords: super-resolved microscopy, stimulated emission depletion microscopy, time-gated detection, image deconvolution. INRODUCION Lens-based or far-field fluorescence microscopy is a very popular technique for revealing the distributions and dynamics of tagged molecules inside living cells. However, the spatial resolution of its standard version is limited by diffraction, impeding the imaging of molecular assemblies at smaller scales. Namely, using lens and focusing light, one cannot discern objects any closer together than a distance d = λ/(2n sin α) given by the numerical aperture of the microscope s objective lens (n sin α, with refractive index n of the embedding medium and α the focusing angle) and the wavelength λ of the light used. he turn of the twenty-first century has witnessed the advent of far-field fluorescence super-resolved microscopy or nanoscopy, a fluorescence microscopy featuring a spatial resolution down to the molecular scales. 4 In common to all the current super-resolved microscopy technologies is that they overcame the diffraction limit by precluding the simultaneous signalling (in general) of adjacent (< d) molecules and thereby recording them sequentially on time. Here, inhibition of signalling is realized by optically driving the fluorescent molecules between states with different signalling characteristics, thus easy to separate. he most used and intuitive states to distinguish are a fluorescent ON- and dark OFF-state. his is exactly the strategy adopted by stimulated emission depletion (SED) super-resolved microscopy. 5, 6 In a SED microscope, stimulated emission (SE) is the optically driven molecular mechanism by which fluorescent molecules are driven between the ON- and OFF-state and (spontaneous) fluorescence signal is precluded. Specifically, a second laser, the SED laser, is added to the microscopes fluorescence excitation laser to drive excited (fluorescent ON-state) molecules into their dark ground OFF-state. hereby, the SED laser features one or more Further author information: (Send correspondence to G.V.) G.V. giuseppe.vicidomini@iit.it, elephone: Single Molecule Spectroscopy and Superresolution Imaging VIII, edited by Jörg Enderlein, Ingo Gregor, Zygmunt Karol Gryczynski, Rainer Erdmann, Felix Koberling, Proc. of SPIE Vol. 933, 933X 25 SPIE Proc. of SPIE Vol X- Downloaded From: on 3/2/25 erms of Use:

2 x sample λ/2 vortex phase plate excitation beam objective lens λ/2 to detector λ/4 band-pass dichroic mirror filter excitation beam b y dichroic mirror 2 SED beam z SED beam effective fluorescence a Figure. Principle of SED microscopy. (a) Schematic drawing of the setup of a SED microscope with the microscope objective which focuses the excitation laser (blue) and the SED laser (red), and collects the fluorescence signal (green) for detection, a phase plate in the SED beam, and a three-dimensional (x, y, z) scanning device for moving the sample relative to the laser light. (b) he excitation laser renders an ordinary diffraction limited focal spot (blue), while the SED laser passes through a phase plate that realizes a focal intensity distribution with a local zero such as a doughnut-like pattern (red), creating an effective excitation volume with dimensions of much below the diffraction limit (green). Scale bars nm. intensity zeroes and thus controls the coordinates where molecules contribute to the overall signal. In the most representative SED microscopy implementation, a regular Gaussian excitation laser beam is co-aligned with a doughnut-shaped SED beam that features a nearly zero-intensity point and a wavelength in the red edge of the emission spectrum of the fluorescence labels (Figure ). Under these conditions, the SED beam transiently de-excites and thus inhibits fluorescence emission of all molecules in the focal laser spots except those located in or at the closest proximity of the zero-intensity point. Most importantly, driving the SED intensity above a certain threshold drives essentially all molecules to their off-state. Increasing the intensity continuously confines the region in which on-state population and thus fluorescence emission is still allowed (the effective observation spot) (Figure ). Scanning the two co-aligned beams across the sample and collecting only the spontaneous emission (stimulated signal is discarded by appropriate spectral filters), yields images whose spatial resolution is given by the size of the effective fluorescence spot. heoretically, the size of the effective fluorescence spot can be decreased to infinitesimal dimensions (and thus the spatial resolution increased to infinity) by increasing the intensity of the SED beam.7 Practically, possible photodamage and phototoxic effects limit the amount of SED laser light that can be focused on the sample, and thereby the ultimate resolution of a SED microscope. hus it is clear that any strategy to decrease the SED beam intensity needed to silence a fluorescent molecule, namely to drive the molecule in the OFF-state, immediately translates in a reduction of photodamage and phototoxicity, similarly, in an increase of the attainable spatial resolution for a given SED beam intensity. A fundamental step toward the reduction of the SED beam intensity was the introduction of the time-gated detection in the SED microscope, or more in general the combination of SED microscopy with time-resolved fluorescence.8 By collecting the fluorescence signal only after a certain time-delay g from the fluorophore s excitation event (t = ) and providing that during this time ( t g ) the fluorophore is subjected to the stimulating photons, reduces substantially the SED beam intensity needed to silence the fluorophore. Indeed, the efficiency of signal depletion, i.e. the probability to silence a fluorophore by stimulated emission, depends on the number of stimulating photons to which the fluorophore is exposed while residing in the excited-state. hus, the time-gated detection ensures that the signal collected stems from fluorophores that have resided into the excited-state for at least a time g and thereby has been exposed to the SED beam at least for the same time. Practically, this allows to spread the stimulating photons across a relative longer time (g ) instead of Proc. of SPIE Vol X-2 Downloaded From: on 3/2/25 erms of Use:

3 a Norm. Fluo. (a.u.) g =/f -2-2 c b Fluo. (/) d g Conf MF g =/f MF g radial freq. (nm - ) radial freq. (nm - ) Figure 2. Calculated effective observation spot in gcw-sed microscope. (a,b) Calculated radial r signal profiles of the normalized (a) and un-normalized (b) E-PSF for increasing time-delay g. (c,d) Calculated radial profiles of the normalized (c) an un-normalized (b) module transfer function (MF) associated to the E-PSF of the gcw-sed microscope. bunching the same amount of photons in a short pulse (acting immediately after the excitation event), with the important consequence that the SED beam (peak) intensity reduces. Not less important, thanks to the time-gated detection, the sophisticate and expensive mode-locked lasers, indispensable to provide the hundreds picoseconds pulses of the SED beam for the first SED microscope implementations, 2, 3 can be substituted by cheaper and turn-key nanosecond pulsed 4, 5, 6 laser or continuous-wave (CW) lasers. he implementations of SED microscopy with SED beams running in CW represent the most straightforward and cheap SED architectures and when combined with the time-gated detection they offer spatial-resolution performance comparable to the most expensive and complex implementations based on pulsed SED beams. hese particular implementations are usually referred as gated CW-SED (gcw-sed) microscopy. In a gcw-sed the spatial resolution can continuously increase with the increase of the time-delay g, namely the volume from which the signal contribute to the image, normally referred as effective point-spread-function (E-PSF), shrinks with the increase of the time-delay g (Figure 2(a)). However, the time-gated detection also introduces a concomitant decrease in the overall fluorescence signal, which imposes an upper limit on the choice of the time-delay g (Figure 2(b)). Indeed, the wanted signal from the center of the doughnut scales as exp( g /), where represents the excited-state lifetime of the fluorophore in absence of stimulating photons. As a consequence, a long time-delay g reduces the signal-to-noise and signal-to-background ratio (SNR and SBR) of the CW-SED image and can cancel-out the gain in spatial resolution. In this report we shows that reduction of the SNR and the SBR is not a limit factor in the case of relative shorter time-delay ( g < /2). Further, we show that, when necessary, an ad-hoc deconvolution algorithm can be used on the gcw-sed dataset to recover optimal SNR and thus maintain the spatial resolution improvement associated to the time-gated detection GAED CW-SED IMAGING he performance of the gcw-sed microscope is well demonstrated by imaging fixed PtK2 cell with the β- tubulin filaments immunolabelled with the organic dye AO647N. Figure 3 shows a side-by-side comparison of confocal, CW-SED and gcw-sed images of a region of interest in the cell cytosckeleton. Following the increase in the effective spatial resolution, as provided by the time-gated detection, the gcw-sed microscopy image is clearly superior in contrast and detail. More importantly, these improvements were obtained at moderate Proc. of SPIE Vol X-3 Downloaded From: on 3/2/25 erms of Use:

4 Confocal CW-SED {,,vir gcw-sed Confocal CW-SED gcw-sed Int. (a.u.) Figure 3. Comparison of conventional CW-SED and gated CW-SED imaging. Upper-left panel, confocal image; upperright panel, CW-SED image; lower-left panel, gcw-sed image ( g = ns); lower-right panel, magnified views of the marked area. Scale bars µm. SED beam intensity (P S ED = 25 mw at 76 nm). A similar spatial resolution on a similar sample was obtained in the classical CW-SED modality with threefold larger SED laser power (P S ED > 6 mw at 592 nm). Recently, it has been demonstrated that the SED laser power can be further reduced (P S ED = 7-9 mw at 577 nm) if a laser with a lower noise level is used (such as a 577 nm OPSL). 5, 8 his level of SED laser power is comparable to the average power used by the more complex pulsed SED implementations (with 8 MHz pulse repetition rates). Note, that we have in this example chosen a moderate time-delay ( g = ns with an excited-state lifetime = 3.9 ns). Much larger time-delay would have reduced the overall signal too much, resulting in rather bad SNR of the image and thereby in a poor effective spatial resolution. In the next section, we show a computational approach based on the time-resolved fluorescence image, which does not reject the early fluorescence photons (before g ), but uses all the fluorescence photon stream and the relative arrival time-information to reconstruct a final high-resolution image. 3. GAED CW-SED IMAGING AND IMAGE DECONVOLUION o generate the final SED image from a time-resolved fluorescent measurement we did not use a time-detection approach but we developed a dedicated deconvolution-based algorithm. 7 In comparison to the time-gated detection, the method produces a final image with higher SNR and thereby an higher effective spatial resolution. In the contest of time-gated detection, the deconvolution-based method takes advantages of the early fluorescent photons (before g ), usually discarded by the time-gated detection. In particular, it recombines the image formed by the early photons with the conventional gcw-sed image (late photons) through a multi-image (MI) deconvolution algorithm. he region from which the early fluorescent photons originated is larger with respect to the counterpart of the late fluorescent photons (after g ), because early fluorescent photons ( g < ) stem from fluorophores which have resided in the excited-state for a shorter time and thus exposed to fewer stimulating photons. hus, the E-PSF associated with this early-photons image (Figure 4(a-b)) (i) is always larger than the gcw-sed microscope s E-PSF; (ii) reduces with increased g from the PSF of the confocal microscope (no SED beam active) to the E-PSF of the CW-SED microscope (no time-gated detection); (iii) increases in amplitude with increased g. In practice, for a long time-delay ( g ), the late-photons image (gcw-sed) has higher resolution but lower Proc. of SPIE Vol X-4 Downloaded From: on 3/2/25 erms of Use:

5 a Norm. Fluo. (a.u.) c g =/f -2-2 b Fluo. (/) d g Conf MF g =/f MF g ,4 radial freq. (nm - ) radial freq. (nm - ) Figure 4. Calculated effective point-spread function for the early-photon CW-SED imaging mode. (a,b) Calculated radial r signal profiles of the normalized (a) and un-normalized (b) early-photon E-PSF for increasing time-delay g. (c,d) Calculated radial profiles of the normalized (c) an un-normalized (b) module transfer function (MF) associated to the early-photon E-PSF. SNR, whilst, the early-photons image has poorer resolution but comparatively higher SNR. From a frequencycontent view (Figures 4(c,d), 3(c,d)) the early-photons image contains only the low frequencies (the cut-off frequency increases with g ), whereas the late-photons image theoretically contains infinite frequencies, though they are mostly dominated by noise. Due to the ill-posed nature of the deconvolution problem, the application of conventional deconvolution algorithms on the late-photons image (gcw-sed image) may amplify noise and introduce artifacts in the restored images. 9 A common method used to compensate for noise-amplification is to introduce, into the deconvolution problem, prior knowledge about the sample (object). hese methods are usually refereed to as constrained deconvolution. 9 he basic idea is to impose some constraints on the solution of the deconvolution problem in order to remove the solutions dominated by artifacts. he most important constraint in fluorescence microscopy is the non-negativity of the solution. Further, typical regularized algorithms employ edge-preserving 2 22 or sparsity-promoting, 23 9, 24 which are usually obtained in a Bayesian framework. o compensate for noise-amplification we did not use a-priori information about the sample, but we used the information provided by the early-photons image. In general, we used the information provided by the temporal dependencies of the E-PSF. We introduced the temporal information through the E-PSFs of a MI 25, 26 deconvolution approach, instead of using a Bayesian framework. In particular we used a MI generalization 27, 28 of the Richardson-Lucy (RL) algorithm x k+ = x k ( L l= H l y l H l x k ), () where: (i) x k denotes the restored images at the k-th iteration; (ii) y l denotes the l-th image associated to the l-th PSF, h l ; (iii) H l is the notation for the discretization of the convolution operator associated to the PSF h l. his strategy was already outlined by Vicidomini et al. and Ingaramo et al., 29 but lacks an extensive study. In the context of this work, we have two images (i.e. L = 2), which represent respectively the early- and late-photons images with the respective PSFs, h early and h late. Figure 5 shows the restored SED image (gcw-sed ++ ) obtained by using the MI deconvolution algorithm. For a fair comparison we report also the restored SED image obtained by using the conventional RL (L=) deconvolution algorithm on the raw gcw-sed image (gcw-sed + ). It is evident that the gcw-sed + restored image suffers severely from the typical artefacts of the RL algorithm. Indeed, it is well known that the RL algorithm converges to a sparse solution (known as the Proc. of SPIE Vol X-5 Downloaded From: on 3/2/25 erms of Use:

6 gcw-sed + CW-SED ++ CW-SED + CW-SED ++ Figure 5. Restored gcw-sed images. Right panel, conventional restored gcw-sed + image ( g = ns); middle panel, multi-image restored gcw-sed ++ image ( g = ns); right-panel, magnified views of the marked area for the different restored images. Scale bars µm. checkerboard effect). interruption of the algorithm can mitigate this problem, but in the case of a low SNR image this does not lead to significant benefits. In our example, the tubulin structures appear as a collection of spots and not as the continuous structures as expected. hese typical artefacts reduce in the gcw-sed ++ multi-image restoration. he information provided by the different E-PSFs allows to the MI algorithm to reach a better solution even though the algorithm deals with images with the same SNR (the CW-SED image is the sum of the early- and late-photons images). 4. CONCLUSIONS he combination of SED microscopy with time-resolved fluorescence offers the unique ability to reduce the SED beam intensity requested to obtain a certain spatial resolution, thus reducing the phototoicity and photodamage in most of the SED imaging applications. Further, it allows to implement SED microscopy with SED beam operating in CW, which effectively reduces cost and complexity of a SED microscope. Improvement in the spatial resolution of a CW-SED microscope can be extracted if the arrival time of each fluorescent photons is known. he most straightforward method consists in the rejection of the early fluorescent photons (before a time-delay g from the triggered excitation events), the so called gated CW-SED implementation. However, by using a time-gated detection approach the improvement in spatial resolution comes along a reduction of the SNR of the image, which in case of dim sample can cancel out the spatial resolution improvement. An alternative to the time-gated detection which is able to preserve the SNR of the final SED image is represented by image deconvolution. We have presented an ad-hoc multi-image deconvolution algorithm which recombines the different CW-SED images obtained at different time-delays without the need of rejecting any fluorescence photons. REFERENCES. Hell, S. W., Far-field optical nanoscopy, Science 36(5828), (27). 2. Hell, S. W., Microscopy and its focal switch, Nat. Methods 6(), (29). 3. Diaspro, A., ed., [Nanoscopy and multidimensional optical fluorescence microscopy], Chapman & Hall (29). 4. Huang, B., Babcock, H., and Zhuang, X., Breaking the diffraction barrier: Super-resolution imaging of cells, Cell 43(7), (2). 5. Hell, S. W. and Wichmann, J., Breaking the diffraction resolution limit by stimulated emission: stimulatedemission-depletion fluorescence microscopy, Opt. Lett. 9(), (994). 6. Blom, H. and Widengren, J., Sted microscopy - towards broadened use and scope of applications, Curr. Opin. Chem. Biol. 2(), (24). 7. Harke, B., Keller, J., Ullal, C. K., Westphal, V., Schönle, A., and Hell, S. W., Resolution scaling in sted microscopy, Opt. Express 6(6), (28). Proc. of SPIE Vol X-6 Downloaded From: on 3/2/25 erms of Use:

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