SUPPLEMENTARY INFORMATION

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1 In the format provided by the authors and unedited. SUPPLEMENTARY INFORMATION DOI: /NPHOTON Background suppression in fluorescence nanoscopy with stimulated emission double depletion Peng Gao, 1,2, Benedikt Prunsche, 2, Lu Zhou, 1,2 Karin Nienhaus, 2 G. Ulrich Nienhaus, 1,2,3,4,* 1 Institute of Nanotechnology, Karlsruhe Institute of Technology, Eggenstein- Leopoldshafen, Germany 2 Institute of Applied Physics, Karlsruhe Institute of Technology, Karlsruhe, Germany 3 Institute of Toxicology and Genetics, Karlsruhe Institute of Technology, Eggenstein- Leopoldshafen, Germany 4 Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA These authors contributed equally to this work. * uli@uiuc.edu NATURE PHOTONICS Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

2 Supplementary Text 1. Experimental setup for STEDD microscopy. A schematic of our home-built STED microscope is shown in Supplementary Fig. 1. Samples are excited by light from a 640-nm pulsed diode laser (LDH-P-C-640B; PicoQuant, Berlin, Germany), featuring pulses of 100 ps length at a frequency of 80 MHz. The beam is spectrally filtered by a 640/14 nm bandpass filter and spatially cleaned by 2 m of polarization-maintaining single-mode fiber (SMF). A quad-band dichroic mirror (zt405/488/561/640rpc; Chroma, Bellow Falls, VT, USA) reflects the excitation beam toward the beam scanner (Yanus V, Till Photonics, Gräfelfing, Germany). The depletion beam is provided by an 80-MHz mode-locked titanium-sapphire (Ti:Sa) laser (Mai Tai HP, Newport Spectra-Physics, Darmstadt, Germany) tuned to nm. The 100-fs pulses of the Ti:Sa laser are stretched to 300 ps by a 60-cm SF6 glass rod followed by 100 m of a polarization-maintaining SMF (PMJ-A3HPC, OZ Optics, Ottawa, Canada). Stretching ensures complete coverage of the excitation pulse to efficiently suppress spontaneous emission of the fluorophores and, in addition, minimizes excitation and photodamage via multi-photon processes. After passing the SMF, the depletion beam is split into three independent beams. To create the 3D STED beam, a vortex and a cylinder phase mask are loaded onto spatial light modulators SLM1 and SLM2 (both LETO, HOLOEYE Photonics AG, Berlin, Germany) to generate the intensity patterns for lateral and axial confinement of the effective excitation, respectively (Supplementary Fig. 2). Both phase masks are superimposed with blazed gratings on the SLMs to exclude non-modulated components of the reflected beam. Careful calibration of the SLM gamma response ensures a diffraction efficiency of 75% in the +1 st order. The +1 st orders are selected by two apertures located in the middle Fourier planes of the telescope system positioned after the two SLMs. Lateral dispersive effects 1 introduced by the phase grating and the pixelation effect are minimized by increasing the pixel number in one period (set to 40 pixels per period) of the blazed grating, defining an angle of 2.4 mrad between the 0 th and 1 st orders. For optimal depletion, the time delay (~200 ps) between the excitation and depletion pulses is carefully adjusted to ensure that most fluorophores are in the excited state at the highest peak intensity 2,3. The third depletion beam is not phase modulated and thus has an approximately 3D Gaussian-shaped intensity profile (Supplementary Fig. 2). It is fed into an optical delay line to generate a variable time delay with respect to the excitation pulse, which defines the period during which signal photons are captured (typically about half the fluorescence lifetime of the fluorophores, see below). After recombining the beam modulated by SLM2 and the 2

3 unmodulated Gaussian beam using a non-polarizing beam splitter, a second polarizationmaintaining beam splitter is used to finally recombine all three depletion beams. The fractional intensities are typically adjusted to 65% and 25% for the beams passing the vortex and the cylinder phase mask, respectively; the Gaussian beam carries the remaining 10% of the total STED intensity. This beam is spatially overlapped with the excitation beam by a 730- nm short pass dichroic mirror (z730sprdc, Chroma). Telescope systems are employed to image the two SLMs onto the beam scanner, and the beam scanner onto the back aperture of the objective (HCX PL APO CS 100 /1.46, Leica, Wetzlar, Germany). In this way, any chromatic dispersion of the blazed grating loaded on the SLMs can be efficiently compensated 4. The combined excitation and depletion beams pass through a quarter-wave plate and are focused into the sample via the objective. The quarter-wave plate induces circular polarization in the excitation and depletion beams to avoid photoselection effects and to ensure a highquality central zero in the depletion intensity pattern 5,6. The spatial overlap between the three depletion beams and the excitation beam is verified by measuring the light reflected off 80- nm gold beads (GC80, BB International, Dundee, UK). The fluorescence emitted by the sample passes through a short pass and a quad-band mirror and is subsequently focused into a multimode fiber serving as a confocal pinhole, with a core diameter corresponding to one Airy unit. Subsequently, the fluorescence is filtered by a 650-nm long pass filter (ET700SP; Chroma) followed by a band pass filter (HC 676/37, Semrock) to block scattered excitation light and STED photons. Photons are counted by an avalanche photodiode ( -SPAD-50; PicoQuant), and a TCSPC card (SPC-150, Becker & Hickl GmbH, Berlin, Germany) records, for each photon, the absolute arrival time as well as the relative time with respect to the trigger signal from the excitation laser. 2. Optimization of the STED microscope. Although STEDD efficiently removes background fluorescence, it is still advisable to minimize background in the first place by optimizing the experimental setup. Importantly, the conventional STED1 pulse should be carefully shaped to minimize the depletion intensity in the centre of the observation volume. Otherwise, uncorrelated background is produced in FCS data from the central spot, in addition to components from peripheral parts of the observation volume. Residual intensity in the centre is mainly due to aberrations caused by imperfect optical elements, beam intensity asymmetries, and improper polarization of the input depletion beam. As a result, upon focusing by an objective, light from different cross-sectional areas of the depletion beam 3

4 cannot interfere destructively to produce a perfect intensity zero in the centre. To minimize the residual intensity, we measure the aberrations due to optical imperfections by using the pupil segmentation technique and then compensate the effects by adding the conjugate phase to all phase masks (Supplementary Fig. 3). Before the depletion beam enters the objective, a beam splitter reflects 10% of the light via a lens onto a CCD camera (Supplementary Fig. 3a). Two small circular phase masks with blazed gratings are loaded onto the SLM; the one in the centre is fixed, whereas the other is moved in both radial and azimuthal directions to select a specific region of the SLM mask. Overall, 54 small, partially overlapping phase masks (with a diameter of 0.62 mm, which corresponds of 1/6 of the overall diameter) are sufficient to reconstruct the large one. The light beams reflected off the two circular areas are directed to the same point on the CCD camera and interfere with one another. Light from regions not covered by the blazed grating does not contribute to the interference pattern. For each position of the moving circular area, three phase biases (0, π/2 and π) are added to the blazed grating, so that the interference patterns recorded by the CCD camera are shifted accordingly. By using a reconstruction algorithm from phase-shifting interferometry 7, the amplitude (Supplementary Fig. 3b) and phase (Supplementary Fig. 3c) of the light from the moving area are determined with respect to the reference light from the fixed central area in the centre. The spatial aberration distribution is obtained by fitting the measured phase (Supplementary Fig. 3c) with a sixth-order two-dimensional polynomial. To compensate for aberration, the phase is reversed and added to the vortex phase and the blazed grating to generate the depletion donut. Donuts generated by loading the vortex phase mask without (Supplementary Fig. 3d) and with (Supplementary Fig. 3e) aberration compensation reveal that the quality of the depletion pattern can be improved substantially by correcting for aberration. Furthermore, intensity asymmetries of the depletion beams can be corrected by suitably modifying the phase masks. An uneven intensity distribution of the depletion beam modulated by the vortex phase mask can be compensated based on the fact that the vortex phase mask has rotational symmetry (Supplementary Fig. 3f). If the intensity of the donut in a certain sector is greater than in the opposing sector, one can cut the phase mask along a chord to remove a peripheral segment of the circle, so as to reduce the area of the respective sector and thus the intensity. Both the sector and the area of the circular segment that is cut off can be adjusted to achieve minimal intensity in the centre of the depletion donut. For the cylinder phase mask, residual intensity in the centre mainly results from uneven intensities from the two regions of phase values 0 and π due to spherical aberrations, which can be caused by variations of the focusing distance or the thickness of the glass cover slide. Residual intensity 4

5 in the centre is minimized by adjusting the ratio of the two areas (Supplementary Fig. 3g). In the ideal case of uniform intensity, the ratio between the radii of the regions with phase values π and 0 is 1/ 2, whereas in our setup, 0.9/ 2 works best. The FCS autocorrelation curves of Atto655 in a glycerol-pbs mixture (72%/28%, w/w) obtained by 3D STED with and without phase mask optimization demonstrate the effectiveness of this approach (Supplementary Fig. 3h). Finally, it is important to select a confocal pinhole that ensures good photon collection efficiency while maintaining a good axial resolution. 3. Choice of the time delay between STED1 and STED2 pulses. The delay time between the 3D STED (STED1) and Gaussian STED (STED2) pulses should be set according to the fluorescence lifetime, τ F, of the fluorophores. To demonstrate the impact of the delay time, we have plotted the fluorescence decay curves of latex beads (immobilized on a surface) that were measured in confocal and STED modes (Supplementary Fig. 4). We varied the delay of the Gaussian pulse with respect to the emission maximum in confocal mode from 0.34 ns to 1.5 ns. By increasing the delay time to about half the fluorescence lifetime (here, τ F = 3 ns), the signal intensity increases and the background is reduced. At even longer delay times, it is no longer possible to describe the background due to uncorrelated noise. In this case, longer voxel dwell times may be used to collect more photons for background determination. Furthermore, 3 3 voxels Wiener filtering may be applied, which generates an evenly distributed background from sparse background photons. 4. Determination of the weight factor γ for background subtraction in STEDD. The detected fluorescence (signal and background) exhibits a temporal decay characteristic of the chosen fluorophores, often appropriately described by an exponential function with a lifetime F. Therefore, the weight factor depends on the probabilities that I STED1 and I STED2 photons are collected in the respective intervals. We measure these probabilities by collecting fluorescence decay histograms after applying only the STED1 pulse. We further note that reexcitation by the additional STED2 pulse is negligible due to its low power and thus does not affect the result. It is advisable to adjust the intensity of the Gaussian STED2 beam so that 2 I sat < I STED2 < 4 I sat at the chosen wavelength. Here, I sat is the saturation intensity at which the rates of spontaneous and stimulated emission are equal. The lower bound ensures that the centre of the excitation focus can be efficiently depleted; the upper bound limits re-excitation. However, if the intensity of the Gaussian STED beam is outside of the preferred range, our approach can 5

6 still be used by adjusting the ratio between I STED1 and I STED2 according to γ = γ [1 exp( ln2 I STED2 /I sat )](1+ χ I STED2 ). Here, χ is a coefficient accounting for re-excitation of the Gaussian STED beam, which can be obtained from measurements of the saturation power, I sat (see Supplementary Fig. 7). Alternatively, instead of using this time-domain procedure, we can also determine in the spatial domain. Background, either due to re-excitation or incomplete depletion, contributes to the I STED1 image with lower spatial frequencies than the signal. Therefore, we analyse the frequency spectrum of the calculated STEDD (I STED1 γ I STED2 ) image and vary so as to minimize low frequency contributions. To this end, we simply compute the function. (1) Here, γ is the magnitude of the Fourier transform of the STEDD image, and the summations extend over all spatial frequencies below a cutoff given by the STEDD resolution limit. The weight factor θ = ( ( max max increases linearly with the spatial frequency so as to give a larger weight to higher frequency components. Accordingly, the function C(γ) displays a maximum for the optimal choice of γ. 5. FCS autocorrelation analysis. We use homemade software written in Matlab (MathWorks, Natick, Massachusetts, USA) for data analysis. For each time lag, τ, the collected photons are re-binned, with the bin width set to 0.5 τ, to calculate intensity traces I STED1 (t) and I STED2 (t). Thus, photon numbers within bins are maximized for each τ to obtain optimal statistics. Twenty data points equally spaced on a logarithmic time scale are calculated for each order of magnitude. The signal intensity trace is calculated according to I sig (t) = I STED1 (t) γ I STED2 (t). We note that it is possible to use time averages of I STED2 (t) at the shortest times (starting from τ = 2 µs, 30 bins, ~26 µs total) to improve statistics. The normalized autocorrelation function is calculated point by point from the backgroundcorrected intensity trace, I sig (t), Isig ( t) Isig ( t ) G( ) 1, (2) 2 I ( t) sig where the angular brackets denote time averages. The autocorrelation curve is fitted with an equation derived for free diffusion through a 3D Gaussian volume 8,9, 1 with N representing the mean number of the fluorescent molecules in the observation volume, 6 1/ ( ) 1 r G 1 2, (3) N D z0 D

7 i.e., their concentration times the effective focus volume, /. The diffusional correlation time τ D represents an average transit time of fluorophores through the observation volume, and r 0 and z 0 are the radial and axial extensions for which the photon detection probability is reduced by 1/e 2 with respect to the centre of the observation volume. From τ D, the diffusion coefficient can be calculated by using 4. To determine the lateral and axial extensions, r 0 and z 0, of the observation volume at different STED beam intensities, we imaged 40-nm fluorescent crimson beads (Molecular Probes, Eugene, OR) immobilized on a coverslip surface with depletion beam intensities varying between 0 95 mw, keeping the intensity ratio between the depletion beams for axial and lateral confinement at 1:2. The intensity profiles of individual fluorescent beads were fitted with Gaussian functions to obtain FWHM values. These data are shown as a function of STED beam intensity in Supplementary Fig. 10. To obtain calibration curves, these data were fitted by using 10 d STED d. (4) conf dconf a ISTED/ Isat Here, d conf denotes the resolution (FWHM) of the confocal microscope in lateral (~1.18 r 0 ) or axial (~1.18 z 0 ) direction, respectively. a represents the parabola coefficient of the STED donut. 7

8 6. Computer simulation of STEDD imaging Description of the model We treat fluorophores as two-level systems with an electronic ground state, S 0, and an excited state, S They are initially in S 0, and are excited to S 1 via photon absorption and de-excited back to S 0 via stimulated emission by applying a sequence of pulsed excitation and STED beams with suitable spatial profiles. We take the time between two consecutive pulses, T, much longer than the excited state lifetime of the fluorophores, F which ensures that all fluorophores have relaxed to S 0 prior to the next excitation pulse. We describe the spatiotemporal intensity distributions (x, y lateral, z axial, t time coordinates) of the excitation pulse, I EXC (x, y, z, t), and the STED pulses, I STED (x, y, z, t), by,,,,, exp, (5),,,,, exp,, exp. (6),,,,,,, and are the three-dimensional intensity distributions of the excitation, (donut-shaped) STED1, and (Gaussian-shaped) STED2 pulses, respectively, calculated by using Debye integration for tightly focused vector fields 12,13. The pulses are taken to be Gaussian in time, t EXC, t STED1 and t STED2 denote their peaks, and T EXC and T STED denote the temporal widths of the excitation and STED pulses, respectively. Our model does not include photoselection and depolarization, which generally affect excitation and depletion efficiencies 6,14. These effect are kept to a minimum by using circular polarization of the pulses. We consider two types of excitation processes. Regular excitation is proportional to I EXC so the rate coefficient is k EXC = ( EXC EXC h c I EXC. There is also re- excitation by the STED beam, which is proportional to I STED, = STED h c I STED. In these expressions, h is Planck s constant, c is the speed of light, EXC and STED are the wavelengths of the excitation and depletion beams, respectively. EXC and STED are the cross sections for the interaction between the fluorophores and the light fields. There are also two de-excitation processes, stimulated emission by the STED beam, with rate coefficient k STED = ( STED h c I STED, and spontaneous emission, with rate coefficient k S1 = 1/ F. The fractional populations in the excited state, P S1, and the ground state, P S0, change with time according to 8

9 , (7). (8) In the absence of photobleaching, the sum of the two fractional populations remains constant, 1. (9) After inserting equation (9) into equation (7), P S1 (x, y, z, t i ) is obtained by integrating equation (7),,,, up,,, exp, (10) with P S1 (x, y, z, 0) = 0 as initial condition. Here, we have simplified the equation by redefining the rate coefficients using and for the overall excitation and de-excitation processes, respectively; is the sum. The emission intensity is proportional to P S1 (x, y, z, t i ),,,,,,,. (11) Here, C is a scaling factor between the number of emitted photons and the population in the excited state. Choice of simulation parameters To simulate the STEDD imaging process as accurately as possible, we took parameters for the simulation similar to those of the experiment. Specifically, we have chosen a fluorophore with F = 3 ns and absorption cross-sections Exc (640 nm) = cm 2 for excitation and (780 nm) = cm 2 for re-excitation by the STED beam. For depletion at 780 nm, the cross section was set to STED (780 nm) = cm 2. These parameters correspond to published values 15,16. A 640-nm laser pulse with Gaussian intensity profile, repetition period T = 12.5 ns and pulse width T EXC = 0.2 ns was used to excite the fluorophores, followed by the 780-nm 3D STED1 beam with a time delay of 0.25 ns and the Gaussian STED2 beam 2.0 ns after the,,,, STED1 pulse. The ratio between the average intensities of and was set as 10:1. The intensity profiles calculated with these illumination parameters are included in Supplementary Fig. 6. The pulse intensities were 787 kw/cm 2, 0.55 GW/cm 2, and GW/cm 2 for the excitation, STED1 and STED2 pulses, respectively, resulting in excitation and depletion rate coefficients k EXC = 1.46 ns 1, k STED1 = 40 ns 1 and k STED2 = 4 ns 1 ; re- 9

10 excitation occurred with k RE (STED1) = 0.03 ns 1 and k RE (STED2) = ns 1. Calculation of fluorescence decays Fluorescence decay curves in confocal, STED, and STEDD mode for 3D imaging were calculated by integrating,,, in the focal volume,,,,,,. (12) Comparison of the three curves shows the efficient depletion induced by the STED1 pulse (Supplementary Fig. 5). The STED2 pulse selectively depletes fluorescence from the centre of the PSF, the residual fluorescence represents emission from molecules in the periphery which were not depleted by the STED1 pulse. Re-excitation by the STED beam was neglected in this calculation. Simulation of STEDD imaging of a 3D phantom of fluorescent beads A 3D phantom, S(x, y, z), was generated by randomly placing 1,280 spherical beads (diameter 40 nm) in a 4 µm 4 µm 4 µm volume. We sampled the phantom in pixels, corresponding to steps of 7.8 nm and 31.2 nm for the lateral and axial directions, respectively. Simulated images of the sample in confocal, STED, and STEDD modes were obtained by 3D convolution of S(x, y, z) with the time-dependent intensity point spread function,,,,,,,,, where IPSF conf is the PSF for confocal mode (here, the intensity-normalized excitation focus profile), P(x, y) is the pupil function of the confocal pinhole (diameter 1 Airy unit), and denotes the 3D convolution operation 17, where,,, was calculated by setting I STED = 0 in confocal mode, I STED = I STED1 for STED and I STED I STED1 + I STED2 for STEDD, respectively. Axial crosssections of the different PSFs are shown in Supplementary Fig. 6. Images at different time points (relative to the excitation and STED pulses) were obtained by integrating S(x, y, z) IPSF(x, y, z, t i ) for different time periods (Supplementary Fig. 6). Photons emitted prior to arrival of the STED1 pulse (t < 0.7 ns) contribute to a confocal image. Photons emitted between the STED1 and STED2 pulses (0.7 < t < 2.7 ns) form a regular, time-gated STED image. Photons emitted after the STED2 pulse (2.9 < t < 6 ns) are collected for the background image. The STEDD image is obtained by weighted subtraction of the I STED2 image from the I STED1 image. The time-gated STED image has markedly higher background than the STEDD image, mainly due to incomplete depletion, especially in the axial direction. 10

11 Supplementary Figures Supplementary Figure 1 Schematic depiction of the experimental setup. L, achromatic lens; M, mirror; BS, non-polarizing beam splitter; PBS, polarization maintaining beam splitter; SLM1 and SLM2, spatial light modulators; SL, scan lens; TL, tube lens; Quad band, quad-band dichroic mirror, SP, 700-nm short pass dichroic mirror; λ/4 and λ/2, quarter-wave plate and half-wave plates; SMF, single-mode fiber; APD, avalanche photodiode. 11

12 Supplementary Figure 2 Intensity profiles of the depletion beams and the emitted fluorescence in the xz plane. I III: beam profiles, generated by a vortex phase mask (I), a cylinder phase mask (II), and a Gaussian phase mask (III, intensity profile of the STED2 beam), respectively. The associated phase patterns are shown on top of the beam profiles. IV: intensity profile of the 3D STED (STED1) beam (overlay of I and II). V: intensity profile of the STEDD beam (overlay of I, II and III). VI: excitation profile. VII: effective excitation spot after depletion by the STED1 beam. VIII: effective excitation spot after depletion by the STED1 and STED2 beams. The focus profiles were calculated by using Debye integration for tightly focused vector fields 12,13. 12

13 Supplementary Figure 3 Optimization procedures for STED imaging. a, Schematic of the setup for aberration compensation via pupil segmentation. b, Amplitude and c, phase of the light from the moving region determined with respect to the reference light from the fixed central region. d, e, Donuts generated by loading the vortex phase mask (d) without and (e) with aberration compensation. f, g, Compensation of uneven intensity distributions of the depletion beam by adjusting the vortex and cylindrical phase masks. h, FCS autocorrelation curves of Atto655 in a glycerol-pbs mixture (72/28, w/w) obtained by 3D STED with and without phase mask optimization. Excitation, 640 nm, depletion, 780 nm. 13

14 Norm. intensity Supplementary Figure 4 Effect of delay time variations between the 3D STED1 and Gaussian STED2 beams. a, Fluorescence decay curves of 40-nm crimson beads (fluorescence lifetime τ F = 3.1 ns), excited by confocal (gray), 3D STED (blue) and STEDD (orange) pulses. Inset: close-up of the area marked by the black frame to highlight the intensity loss upon applying the Gaussian STED2 beam. Vertical arrows indicate different time points for applying the Gaussian STED2 pulse (time delays with respect to the emission maximum in confocal mode: black: 0.34 ns, red: 0.67 ns, blue: 1.16 ns, green: 1.5 ns). b, Intensity profiles of individual beads calculated from the photons emitted before (I STED1, timegated, closed symbols) and after (I STED2, open symbols) the Gaussian STED2 pulse. 14

15 Supplementary Figure 5 Simulated fluorescence decay curves in confocal, STED and STEDD imaging. Excitation (green) and STED (red, STED1 and STED2) pulses are shown as a function of time with normalized amplitudes. The fluorescence decay curves for confocal and STED mode are depicted in orange. The brown curve (filled area below) shows the fluorescence decay in STEDD mode. 15

16 Supplementary Figure 6 Simulated 3D STEDD imaging of fluorescent beads. a d, PSFs in the xz plane. Scale bar in a, 0.5 µm. Images in the xy and xz planes (e, i) were simulated from photons arriving prior to the STED1 pulse at t = 0.7 ns (confocal I prested1 ), (f, j) between the STED pulses (0.7 ns < t < 2.7 ns, I STED1 ), (g, k) after the STED2 pulse at t = 2.7 ns (I STED2, displayed here as 1.67 I STED2 to match the background signal of I STED1 ), and (h, l) by weighted subtraction of I STED2 from I STED1 (I STEDD ). The sum of I prested1 and I STED1 yields the intensity distribution without time gating. m, n Intensity profiles along the dashed lines in e, i. Black dotted: confocal; black: STED1, red: STED2; blue: STEDD. Scale bar in e, i, 1 µm. 16

17 Supplementary Figure 7 Quantification of the STED saturation intensity, I sat. a, b, STED beam power dependence of the normalized emission intensity of 40-nm crimson beads upon 640-nm excitation at 2 µw and (a) 760-nm or (b) 780 nm depletion (red symbols) and with STED beam excitation only (re-excitation, blue symbols). The fluorescence was collected with time-gated detection, starting 0.75 ns after the Gaussian-shaped STED pulse. Red lines: fit of the emission intensity, I em, using em fluor exp ln2 STED sat TED offset, (13) where I STED denotes the depletion intensity of the STED beam. The saturation power of the STED beam, I sat, is defined by the intensity, which reduces the fluorescence intensity to 50% of the initial value (I sat (760 nm) = 0.46 ± 0.02 mw, I sat (780 nm) = 0.73 ± 0.04 mw). denotes a scaling factor to correct for re-excitation by the STED beam. Blue lines: linear fits of the re-excitation data. c, Simulation of the power-dependent emission depletion by a Gaussian-type STED beam. Black, without re-excitation; red, with re-excitation, blue: emission intensity excited by the STED beam only, collected in the time interval ns after the STED pulse. Symbols, simulated data. Lines, fits with equation (13). 17

18 Supplementary Figure 8 3D STEDD imaging of a fixed HeLa cell. Microtubules were immunolabelled with primary (monoclonal anti-β-tubulin antibody produced in mouse (T UL, Sigma-Aldrich, Darmstadt, Germany) and secondary (anti-mouse-iggatto647n antibody produced in goat, ML-F, Sigma-Aldrich) antibodies according to established procedures18 and imaged in confocal, STED and STEDD mode. A volume of µm3, voxels in x, y and z directions, respectively, was imaged with 640-nm excitation (confocal, 2 µw; STED, 3.5 µw) and 780-nm depletion (STED1, vortex phase mask: 50 mw; STED1, cylinder phase mask, 22 mw; Gaussian STED2: 4 mw at the sample plane). Pixel dwell time, 40 µs. a, Confocal overview image of the cell. b, Representative xy projections (8 frames, centered on z = 0.77 µm and z = 1.38 µm) of the 3D stack, depicted as confocal, STED and STEDD images. c, 3D representations, with microtubules colourcoded according to their axial position (0 1.7 µm, red blue, see colour bar). Scale bars, 5 µm (a), 1 µm (c). 18

19 Supplementary Figure 9 3D STEDD imaging of fluorescent beads. a, 3D images of 40- nm polystyrene beads in a 3% (v/v) agarose gel obtained by confocal and STEDD microscopy (640 nm excitation, 780 nm depletion at 72 mw). The 3D images were generated from a stack of 76 images ( pixels, nm 2 per pixel) spanning 4 µm in axial direction. Scale bar, 2 µm. b, 2D images of the beads in the xz plane recorded in confocal, STED1, STED2, and STEDD modes. These images were obtained by integrating a sub-region ( m 3 ) of the 3D images along the y-axis. Colour bar, counts per pixel. Scale bar, 1 µm. c, d, Intensity profiles (symbols) across an individual bead along the dotted lines in (b), yielding (c) full widths at half-maximum of 300 ± 11 nm and 114 ± 7 nm in lateral and (d) 756 ± 51 nm and 327 ± 18 nm in axial direction for confocal and STEDD microscopy, respectively. Intensity profiles of STED1, STED2 and STEDD were rescaled (divided by the maximal value of the STEDD profile), so that the relative intensities were not changed. The confocal intensity profile was scaled to the maximum of the STEDD profile. Lines in (c) and (d) are fits with Gaussian distributions. 19

20 Supplementary Figure 10 Depletion beam phase and intensity profiles generated by using first-order and second-order vortex phase masks. a, Phase patterns and lateral intensity sections in the focal plane, obtained by 3D scanning of 20-nm gold nanoparticles (EM.GC20, BBI solutions, Cardiff, UK). b, Intensity profiles along the dashed lines in panel (a). The donut obtained with the second-order vortex phase mask (black line) is greater than with the first-order phase mask (red line), and there is less residual intensity in its centre. Blue: excitation profile. c, Integrated fluorescence intensity from dark-red fluorescent beads in the axial direction in confocal and 3D STED mode using first-order and second-order phase masks, showing more efficient depletion by the second-order phase mask at larger displacements from the focal plane. d, e, Spatial resolution versus STED beam intensity. 3D STED pulses were generated by superimposing two beams (intensity ratio 1:2) passed through a cylinder phase mask and (d) a first-order or (e) a second-order vortex phase mask. Data were collected on 20-nm crimson beads immobilized sparsely on surfaces coated with poly-l- 20

21 lysine. 32 images (3 3 µm 2, covering 2 µm in axial direction) were recorded, and 3D PSFs were fitted with Gaussians. The FWHM values in lateral and axial directions (symbols), plotted as a function of the STED intensity, were averaged over five beads for each point and fitted with the expression given by equation (3) (lines). 21

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