Tomographic STED microscopy

Abstract

Stimulated emission depletion (STED) microscopy is a versatile imaging method with diffraction-unlimited resolution. Here, we present a novel STED microscopy variant that achieves either increased resolution at equal laser power or identical super-resolution conditions at significantly lower laser power when compared to the classical implementation. By applying a one-dimensional depletion pattern instead of the well-known doughnut-shaped STED focus, a more efficient depletion is achieved, thereby necessitating less STED laser power to achieve identical resolution. A two-dimensional resolution increase is obtained by recording a sequence of images with different high-resolution directions. This corresponds to a collection of tomographic projections within diffraction-limited spots, an approach that so far has not been explored in super-resolution microscopy. Via appropriate reconstruction algorithms, our method also provides an opportunity to speed up the acquisition process. Both aspects, the necessity of less STED laser power and the feasibility to decrease the recording time, have the potential to reduce photo-bleaching as well as sample damage drastically.

Fig. 1.

Schematic diagram of the setup. The depletion beam is phase-modulated by a spatial light modulator (SLM), imprinting either a helical phase-retardation for a doughnut-shaped depletion pattern or a phase step of $\pi$ to obtain a 1D depletion focus. Correspondent voltage levels are illustrated by the respective blazed holograms (gray box). (Exc: excitation laser, STED: depletion laser, QWP: quarter-wave plate, PPC: pair of Pockels cells, DM: dichroic mirror, BS: beam scanner, OL: objective lens, S: sample, APD1, APD2: detectors, MMF: multimode fiber with integrated fiber splitter)

Fig. 2.

One-dimensional resolution increase for the 1D/2D depletion patterns: (a) Intensity distribution at the focal plane and phase pattern in the pupil plane (inset) for 2D STED. (b) The corresponding quantities for the 1D case. (c) Depletion patterns $h_{\text{STED}}(x,y=0)$ for 1D (blue) and 2D STED (red), drawn along white lines in (a) and (b). The power in the focal plane is the same for both cases. (d) Second derivatives of $h_{\text{STED}}(x,y=0)$. (e) Exemplary bead measurements for ${\zeta }_{\text{1DSTED}}=25$ and ${\zeta }_{\text{2DSTED}}=65$ and corresponding intensity profiles. Scale bar: 100 nm. (f) Same quantities as in (e) for ${\zeta }_{\text{1DSTED}}=210$ and ${\zeta }_{\text{2DSTED}}=450$. (g) Dependence of the resolution on $\zeta$ for 2D STED (red dots) and for the 1D depletion pattern (blue dots), data corrected to the bead size of 25 nm. The data points that correspond to (e) and (f) are indicated. Error bars denote the standard error of the mean.

Fig. 3.

Two-dimensional resolution enhancement and image reconstruction: (a) Description of the required number of different 1D depletion pattern orientations in real space. (b) Profiles of OTFs along a spatial frequency coordinate: 2D STED OTF ($k_{\text{2D}}=5$), tomoSTED OTF for the SV method ($k_{\text{1D}}=8$) when rotating continuously, tomoSTED OTF for the MFV method ($k_{\text{1D}}=8,N_{\text{opt}}=12$) in the optimal direction. Spatial frequency coordinates corresponding to a period of ${\mathrm{\Delta }}_{\text{conf}}/i$ for $i=1,5,8$ are emphasized by dotted vertical lines. (c) Image reconstruction methods shown on a simulation of a test object of concentric rings with increasing diameters (bottom row on the left). The differences of the diameters range from 30 nm (inner rings) up to 55 nm (outer rings). For 2D STED (left column, $k_{\text{2D}}=5$) the raw data and the RL estimate is shown. For tomoSTED ($k_{\text{1D}}=8,N_{\text{opt}}=12$) and $N=N_{\text{opt}}$, $N=N_{\text{opt}}/2$, $N=N_{\text{opt}}/4$, the MFV method images are shown as well as the APRL reconstructions (2000 iterations). Circles indicate the area where the test object cannot be resolved. A radial add-up of the RL estimation for 2D STED and the APRL estimation for tomoSTED ($N_{\text{opt}}$ sub-images) is shown in the bottom row on the right. The numbers indicate the distances between neighboring rings of the test object. Scale bar: 0.2 $\mu$m.

Fig. 4.

Exemplary measurements of vimentin network in fixed Vero cells. (a) RL reconstruction for confocal (left) and 2D STED data (right). Scale bar: 5 $\mu m$. (b) APRL reconstruction for tomoSTED. In (a) and (b), the intensity is scaled to the respective maximum. (c) Fourier Correlation indicates the same resolution enhancement for 2D and tomoSTED. The white circle marks the FC threshold of 0.2 in the 2D STED case. (d) Zoom-ins, as highlighted by the white box in (a) and (b). Upper row: Data acquired with 2D STED is compared to MFV reconstructions of tomoSTED ($N_{\text{opt}}=6$) measurements ($N=N_{\text{opt}}$ (center) and $N=N_{\text{opt}}/2$ (right)). Lower row: Results of the APRL reconstruction (number of iterations and value of regularization parameter as indicated), intensity scaled to maximum. The scale bar represents 1 $\mu$m. A profile (highlighted by the white lines) is illustrated in (e). Here, a profile for the confocal case (data not shown) is included.

Fig. 5.

Bleaching experiments for Abberior STAR 635P-stained vimentin network in fixed Vero cells. (a) Ten consecutive frames displayed for 2D STED and for tomoSTED (MFV reconstruction with $N=N_{\text{opt}}=6$). Total pixel dwell time (30 $\mu s$) and pixel size (15 nm) are equal for both methods compared (scale bar: 1 $\mu m$). (b) Normalized fluorescence intensity vs. number of frames. The data for tomoSTED with $N=N_{\text{opt}}/2=3$ depletion pattern orientations is derived by allocating the $N=N_{\text{opt}}=6$ data into two separate data sets. Error bars denote the standard error of the mean.

Fig. 6.

Live cell measurement of microtubule filaments in 2D STED and tomoSTED microscopy. For visualization of the movement, the first, the fifth and the tenth frame are superposed with different color tables. Measurements are performed with $P_{\text{exc}}=0.5\mu$W and a pixel size of 20 nm. (a) RL reconstruction for 2D STED. Here, $P_{{\text{STED}}_{\text{2D}}}=10$ mW and the pixel dwell time is set to $60\mu$s. (b) Intensity profile taken from 2D STED data along marked line in (a), and correspondent Gaussian fits. (c) APRL reconstruction for tomoSTED with $N=N_{\text{opt}}/2=3$ depletion pattern orientations. Here, $P_{{\text{STED}}_{\text{1D}}}=5$ mW and the pixel dwell time per 1D super-resolved frame amounts to $10\mu$s. (d) Intensity profiles taken from the respectively oriented sub-image along marked line in (c), and correspondent Gaussian fits. Note that the intensity profiles are averaged over 5 pixels perpendicular to the profile orientation. Scale bars 1 µm.

Fig. 7.

Determination of saturation power $P_{\text{sat}}$. Fluorescence intensity of 25 nm sized crimson fluorescent microspheres is measured as a function of the applied STED power $P_{\text{STED}}$ and normalized to the intensity that corresponds to $P_{\text{STED}}=0$ mW. The exponential fit (black curve) provides a decay constant of $t_1=0.4$ mW. The blue line indicates the saturation power $P_{\text{sat}}=0.28$ mW, for which the fluorescence intensity is suppressed by a factor two. Error bars denote the standard error of the mean.

Fig. 8.

Finite bead size correction. Simulations show influence of finite bead size on image size and relative peak intensity. (a) Relative PSF FWHM (PSF FWHM/ bead diameter) as a function of relative Image FWHM (Image FWHM/ bead diameter) for 2D STED (red dots) and tomoSTED (blue dots). For rel. Image FWHM between 1 and 2, the determined resolution is corrected according to a polynomial model (green, dashed line). The black line, indicating the same size of rel. PSF FWHM and rel. Image FWHM, is approached for rel. Image FWHM $>$ 2. (b) Relative peak intensity vs. factor of resolution enhancement k, simulated for a bead size of 25 nm. Cubic fits of simulation results for 2D STED (red dots) and tomoSTED (blue dots) are used for correcting the respective measurement.

Fig. 9.

Relative peak intensity for 2D and 1D depletion patterns. (a) Relative peak intensity vs. saturation factor $\zeta$: The 1D and the 2D implementation show a similar behavior. Lines are drawn as guides to the eye. (b) In dependence of the factor of resolution enhancement $k$, the relative peak intensity decreases faster for 2D STED. The experimental data shown in (a) and (b) are corrected to a bead size of 25 nm. Error bars denote the standard error of the mean.

Fig. 10.

tomoSTED reconstruction by Radon transform back projection. (a-i) Simulated images of a tubular structure for orientations of the 1D depletion pattern of 0, 20, 40, 60, 80, 100, 120, 140 and 160 deg, respectively. Integrating a series of such images over lines being oriented in the direction of the confocal resolution yields the super-resolved Radon transform of the structure (j). The two-dimensionally super-resolved image can be derived by filtered back-projection of this sinogram (k). Here, the iradon function from Matlab with a shape-preserving piecewise cubic interpolation and a Ram-Lak filter multiplied with a Hann window has been used. The resolution is 250 nm and 31 nm in the confocal and super-resolved direction respectively. Scale bars 1 µm.

Fig. 11.

Comparison of image reconstruction methods. (a) 2D STED $k_{\text{2D}}=5$ raw data (PSF as inlay) of the test object in Fig. 3(c). (b) SV image for tomoSTED $k_{\text{1D}}=8,N_{\text{opt}}=12$ for the same object. Corresponding PSF (average of sub-images' PSFs) shown in inlay. (c) MFV image for tomoSTED (same conditions as in (b)). (d),(e) RL deconvolution (2000 iterations) of the data in (a) and (b), respectively. (f) APRL reconstruction (2000 iterations) of the sub-images. Circles indicate the area where the test object cannot be resolved. Total acquisition time is the same in each case. Scale bar 0.2 $\mu$m.

Fig. 12.

Measurement of fluorescent beads with same STED laser power in tomoSTED and 2D STED configuration. The pixel dwell time in the 2D STED case is 160 $\mu$s. Since $N=8$ pattern orientations are considered, the pixel dwell time per sub-image in tomoSTED microscopy is set to 20 $\mu$s. In either case, $P_{\text{STED}}=17$ mW, $P_{\text{exc}}=2.5\mu$W and the pixel size amounts to 20 nm. (a-h) Sub-images recorded under pattern orientations of 0°, 22.5°, 45°, 67.5°, 90°, 112.5°, 135°and 157.5°. The scale bar represents 1 $\mu$m. (i) 2D STED image, the lower left corner displays the RL image. Scale bar: 1 $\mu$m. (j) MFV image. The APRL estimate is depicted in the lower left corner. Intensity profiles shown in (k) and (l) are drawn along the lines indicated in (a), (e), (i) and (j).

Fig. 13.

tomoSTED raw data of the vimentin measurement shown in Fig. 4(d). (a) Overview of the recorded area, exemplarily depicted for a depletion pattern orientation of $0^{\circ }$. The depletion pattern orientation is indicated by the arrow in the upper right corner. The scale bar represents 2 $\mu$m. Zoom-ins are indicated by the white rectangle and shown in (b-g): tomoSTED raw data for depletion pattern orientations of $0^{\circ }$, ${30}^{\circ }$, ${60}^{\circ }$, ${90}^{\circ }$, ${120}^{\circ }$ and ${150}^{\circ }$. The excitation power is set to $5\mu$W and a STED laser power of $35$ mW is chosen. Per pattern orientation, the pixel dwell time amounts to 5 $\mu$s. Scale bar: 1 $\mu$m.

Fig. 14.

Long-term tomoSTED measurement of mictrotubule filaments in living fibroblasts ($P_{\text{STED}}=5$ mW, $P_{\text{exc}}=0.5\mu$W). Over a temporal course of 38 minutes, 50 frames are acquired, of which the first is shown. (a-c) tomoSTED raw data for depletion pattern orientations of 0, 60 and 120 deg., respectively. Each sub-image is recorded with a pixel size of 20 nm and a pixel dwell time of $5\mu$s. Scale bar: 4 $\mu$m. (d) APRL result ($N=3$, 50 iteration steps, $\alpha =0.005$). Scale bar: 2 $\mu$m. See Visualization 1 for a movie of all frames, in which each sequence of frames is scaled to the maximum intensity in the first frame, respectively.