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Abstract
Stimulated emission depletion (STED) microscopy theoretically provides unlimited resolution. However, in practice the achievable resolution in biological samples is essentially limited by photobleaching. One method which overcomes this problem is tomographic STED (tomoSTED) microscopy. In tomoSTED microscopy, one-dimensional depletion patterns facing in different directions are successively applied in order to acquire a highly-resolved image in two dimensions. In this context, the number of addressed directions depends on the desired angular homogeneity of the point spread function or the optical transfer function and thus on the resolution increase as compared to diffraction-limited imaging. At a reasonable angular homogeneity the light dose and thus bleaching can be reduced, as compared to conventional STED microscopy. Here, we propose and demonstrate for the first time, to our knowledge, that the number of required depletion pattern orientations can be reduced by combining tomoSTED microscopy with the concept of image scanning microscopy (ISM). With our realization of an ISM-tomoSTED microscope, we show that approximately a factor of $\sqrt {2}$ lower number of orientations are required to achieve the same resolution and image quality as in tomoSTED microscopy.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fluorescence nanoscopy has become an indispensable tool in the life sciences, since it allows non-invasive imaging of three-dimensional structures with an optical resolution far beyond the diffraction limit [1]. Thus, it is ideally suited to investigate not only the spatial distribution of proteins, nucleic acids and lipids on the nanoscale, but also to gain insights into dynamic molecular processes in living cells and tissues [2,3].
Stimulated emission depletion (STED) microscopy [4,5], which was the first methods to fundamentally overcome the diffraction limit, nowadays achieves an optical resolution of $20 - 60$ nm in biological samples [6,7] and has been successfully applied to various fields in the life sciences such as physiology, immunology, virology, bacteriology and cancer biology [2,8,9]. It belongs to the scanning-based family of super-resolution techniques and uses an additional laser beam to discern adjacent fluorophore ensembles. To this end, a typically doughnut-shaped STED focus is superposed with a Gaussian-shaped excitation focus and confines the fluorescent area to the doughnut center through saturated depletion. In principle, the higher the applied STED power, the smaller this area and the better the resolution [10,11]. In practice, however, the maximum achievable signal-to-noise ratio and thus the resolution is limited due to photo-bleaching of the fluorophores [10,12]. In the context of live-cell imaging, an additional challenge arises since the required light dose may compromise cell health, which must be avoided to retain the validity of live-cell studies [13,14].
So far multiple strategies for STED microscopy have been developed to address these issues. New, more photostable, dyes [15], protectedSTED [16] and the optimization of the temporal distribution of the local light dose (via longer STED pulses [12], low repetition-rate lasers or fast scanners [17]) aim at optimizing the fluorescence yield per molecule, but do not necessarily lower the overall light dose. Smart-scanning techniques such as RESCue [18], FastRESCue [19], DyMIN [20] and MINFIELD [21], on the other hand, directly reduce the light dose applied to the sample.
Our group has recently introduced tomographic STED (tomoSTED) microscopy [22], which has the same objective and allows for STED imaging at reduced light dose. Unlike the other methods mentioned above, tomoSTED microscopy is based on the modification of the depletion pattern. Importantly, the light dose reduction is therefore intrinsic to the tomoSTED concept, implying that all the above mentioned methods can be combined with the advantages the tomoSTED approach provides.
Contrary to the doughnut-shaped depletion pattern used in the classical STED implementation, tomoSTED microscopy employs a one-dimensional (1D) pattern, which confines the fluorescent area only in one direction. A two-dimensionally (2D) super-resolved image is then reconstructed from a series of individual images, each exhibiting sub-diffraction resolution in a different direction. The number of orientations required for reconstruction depends on the desired angular homogeneity of the point spread function (PSF) or the optical transfer function (OTF) and thus on the ratio between the resolution in the diffraction-limited direction and the resolution in the high-resolution direction.
TomoSTED microscopy therefore offers an interesting possibility for further improvement, since an increase in resolution in the diffraction-limited direction would reduce the required number of orientations, which has the potential to translate into a further reduction of the overall light dose. For this reason, we combine tomoSTED microscopy with image scanning microscopy (ISM) which is known to allow for an up to $\sqrt {2}$-fold resolution increase in confocal microscopy without loss of signal [23,24]. We show that ISM-assisted tomoSTED microscopy achieves the same image quality as tomoSTED microscopy at a reduced number of orientations and validate its performance in technical as well as biological samples. The reduction factor for the number of required orientations corresponds to the factor of resolution enhancement in the diffraction-limited direction due to ISM.
2. Basics of ISM-assisted tomoSTED microscopy
Both tomoSTED microscopy and ISM are based on confocal laser-scanning microscopy, in which the PSF can be written as [25]
2.1 Tomographic STED microscopy
Being a variant of STED microscopy, tomoSTED microscopy relies on the spatial narrowing of the fluorescence-allowed area, which can be considered as an effective narrowing of the excitation PSF:
The suppression factor $\eta$ reflects the remaining fraction of fluorescence after having applied the STED light to the sample and is a function of the focal intensity distribution of the STED light, the so-called depletion pattern. For temporally separated excitation and STED pulses, $\text {PSF}_{\text {eff,ex}}$ can be well approximated by a 2D Gaussian function [11].Contrary to classical 2D-STED, tomoSTED utilizes 1D depletion patterns [22], which are generated e.g. by 0-$\pi$ phase masks instead of the well-known helical phase mask used for the doughnut-shaped depletion pattern. The corresponding effective excitation PSFs are therefore asymmetric, exhibiting a direction in which the full width at half maximum (FWHM) is narrowed to $\Delta _{\text {high}}$ due to STED (high-resolution direction) and a corresponding orthogonal direction in which the resolution remains diffraction-limited (low-resolution direction, $\Delta _{\text {low}}$).
Assuming a sufficiently large pinhole, its influence can be neglected and the 1D-PSF can be written as [22]
For data acquisition, $\text {PSF}_{\text {1D}}$ is scanned through the region of interest in the sample. The fluorescence signal is detected by a point-detector (Fig. 1 top row, left) and assigned to the respective scan position. This is repeated for different orientations of $\text {PSF}_{\text {1D}}$, resulting in a set of tomoSTED sub-images, each exhibiting a different high-resolution direction (Fig. 1 top row, center).
Fig. 1. Illustration of tomoSTED microscopy, ISM, and ISM-assisted tomoSTED microscopy, visualizing the shape of the detector as well as the incident signal for several scan positions (left), the (sub)-PSFs for (virtual) confocal detection as well as pixel reassignment (center) and the PSFs after tomoSTED-reconstruction (right). (top row) TomoSTED microscopy employs an asymmetric effective excitation PSF, featuring a low-resolution and a high-resolution direction. For different PSF orientations and for each scan position, the fluorescence signal is recorded by a point-detector, which results in a set of tomoSTED sub-images with different orientations of the high-resolution direction. A final tomoSTED image is reconstructed therefrom. (middle row) In ISM, an array detector, in which each pixels acts as a very small pinhole, detects the signal for each scan position. From this series of array recordings, a confocal image, adding up the signal of the central pixels, as well as an ISM image, using pixel reassignment, can be obtained. ISM increases the resolution up to $\sqrt {2}$-fold. (bottom row) ISM-assisted tomoSTED combines both methods. For each orientation of the high-resolution direction and for each scan position, the signal is recorded with an array detector. Therefore a set of confocal as well as pixel-reassigned sub-images can be generated. The final ISM-tomoSTED image is reconstructed from the set of pixel-reassigned sub-images.
After data acquisition, the final tomoSTED image is reconstructed from the set of sub-images via appropriate reconstruction algorithms (Fig. 1 top row, right) [22]. The light dose advantage of tomoSTED as compared to classical 2D-STED is based on the following effects: First, the employed 1D depletion patterns feature a larger pattern steepness than the doughnut pattern which allows to achieve the same $\Delta _{\text {high}}$ at about half STED power. Second, the fluorescence signal recorded in the sub-images is $k = \Delta _{\text {low}}/\Delta _{\text {high}}$ times higher due to the resolution improvement in only a single direction, allowing to reduce the acquisition time for each individual sub-image accordingly. Typically, half or the same total acquisition time as compared to the classical STED implementation is used in tomoSTED for recording the complete set of sub-images [22]. Therefore, only a quarter or half of the light dose is applied to the sample.
2.2 Image scanning microscopy
In confocal microscopy, an infinitesimal small detection pinhole theoretically leads to a resolution improvement of $\sqrt {2}$ as compared to widefield microscopy [25], as fluorescence from the edge of the excitation focus is detected less effectively. Unfortunately, this is not practicable since closing the pinhole leads to a reduction of the detected signal and therefore to a poor signal-to-noise ratio [27].
The ISM principle allows to overcome this problem and to reach a $\sqrt {2}$-fold resolution improvement while maintaining the signal [23,24,28–30]. Here, the image is recorded not only with a single point-detector, but instead with many closely spaced ones [23]. In practice, a detector array (for example a camera [24] or a single-photon avalanche diode (SPAD) array [29]) is used for that purpose and each array pixel acts as a point-like detector [31].
For data acquisition, the excitation focus is scanned through the region of interest in the sample, and for each scan position the fluorescence is imaged onto the detector array, resulting in a series of array recordings (Fig. 1 middle row, left). Each detector array pixel thus records an image of the sample (not shown in Fig. 1). These images are shifted with respect to each other due to the different positions of the individual detector pixels on the array [31]. By an appropriate re-combination of these images [24,28,29], which aims at reassigning the signal of each detector pixel to its most likely origin in the sample, the final ISM image is obtained (Fig. 1 middle row, center). Note that the pixelation of the reassigned image is determined by the pixelation of the scanning process and not by the size of the detector array pixels. Compared to confocal imaging with an open pinhole, the resolution is improved while the signal is maintained. Under the assumption of Gaussian-shaped symmetric excitation and detection PSFs, the expected resolution in the final ISM image is [32]
2.3 ISM-assisted tomoSTED microscopy
The unique property of tomoSTED microscopy (as opposed to classical STED microscopy), namely that one direction remains diffraction-limited, enables its combination with ISM. The corresponding workflow of ISM-assisted tomoSTED microscopy is illustrated in the bottom row of Fig. 1. Similar to ISM, the fluorescence signal is recorded with a detector array for each scan position and for several orientations of $\text {PSF}_\text {1D}$. Pixel reassignment is then performed for each orientation independently, leading to a set of ISM-tomoSTED sub-images (Fig. 1 bottom row, center). These correspond to the sub-images in tomoSTED microscopy, however they exhibit an improved resolution in the low-resolution direction due to the pixel reassignment step. The final ISM-tomoSTED image is then generated from the sub-images employing the tomoSTED reconstruction algorithm.
Due to the elliptical shape of the 1D-PSFs, the optimum pixel reassignment factor differs for the low-resolution and for the high-resolution direction. In order to ensure an optimum resolution in both directions, a theoretical pixel reassignment factor can be derived similarly to [32] under the assumption of a symmetrical detection PSF:
3. Material and methods
3.1 Experimental realization
The ISM-tomoSTED measurements were performed using the setup illustrated in Fig. 2. For fluorescence excitation and depletion, a 640 nm-excitation laser diode (LDH-P-C-640B, PicoQuant, Germany) with a pulse length of 100 ps and a STED laser (Katana 08 HP, Onefive GmbH, Switzerland) with a wavelength of 775 nm and a pulse length of 600 ps are used. Both run at a repetition rate of 80 MHz and are coupled via polarization maintaining single-mode fibers (PMC-630-4.1-NA012-3-APC-560-P and PMC-E-780-5.1-NA012-3-APC.EC-500-P, Schäfter + Kirchhoff GmbH, Germany) into the setup. For intensity modulation of the laser beams, an acousto-optic modulator (AA.MT110-1.5-VIS and AA.MT110-A1.5-IR, AA Opto Electronic, France) is installed in front of each fiber coupling. The excitation laser diode is triggered by the STED laser and the time delay between excitation and STED pulse is adjusted electronically for maximum depletion efficiency.
Fig. 2. Schematic illustration of the experimental setup (STED: STED laser unit, Ex: excitation laser unit, SLM: spatial light modulator, LCR: liquid crystal retarder, APD: avalanche photo diode, GT: Glan-Thompson-prism, HWP: half-wave plate, QWP: quarter-wave plate, DM: dichroic mirror, f: focal length, BS: pellicle beam splitter, BF: emission band pass filter, S: sample)
To generate the 1D depletion patterns, the phase and the polarization of the STED beam need to be adjusted. For phase modulation, a spatial light modulator ($\text {SLM}_{1}$, Meadowlark Optics, USA) is placed in a plane conjugated to the objective’s backfocal plane. Via an appropriate voltage-pixel mask on the SLM, a 0-$\pi$-phase step is imprinted on the STED beam. To filter out phase-unmodulated STED light, the voltage-pixel mask for the phase step is combined with one for a diffraction grating and only the light diffracted into the first order is directed to the sample. Note that the setup features a second SLM ($\text {SLM}_{2}$, Hamamatsu Photonics Deutschland GmbH, Germany) which is merely used as a mirror within the scope of this article. The polarization of the STED beam is set parallel to the phase step line in order to optimize the zero-intensity line of the depletion pattern. To this end, a combination of two liquid crystal retarders (LCR, LRC-200-IR1-TSC, Meadowlark Optics, USA), whose fast axes enclose an angle of $45^{\circ }$, and a quarter-wave plate is used. The fast axis of the quarter-wave plate is aligned parallel to the first LCR’s fast axis. They allow to set any linear polarization state via mere adjustment of the LCRs’ control voltages.
To scan the excitation spot as well as the STED depletion pattern beam through the sample, a galvanometric scanner (Abberior Instruments GmbH, Germany) is built into the setup. The focussing is done by an oil objective lens with a numerical aperture of $1.4$ (UPLSAPO 100XO, Olympus, Japan). The fluorescent light, which is collected by the same objective lens, is separated with two dichroic mirrors (F43-643 and F73-750T, AHF analysentechnik AG, Germany) from the excitation and the STED light. To prevent residual excitation and STED light to reach the detectors, an emission band pass filter (F49-691, AHF analysentechnik AG, Germany) is placed into the beam path. For fluorescence detection, two options are available: an sCMOS camera (Zyla 4.2 Plus, Andor Technology, UK) and two avalanche photo diodes (APD) (SPCM-AQRH-13-FC, Excelitas Technologies Corp., USA). The APDs were only used for alignment purposes, while both the tomoSTED and the ISM-tomoSTED measurements were performed with the camera to ensure the comparability of the methods in terms of the signal-to-noise ratio.
During an (ISM-)tomoSTED measurement, laser pulse delay and scanning are controlled via the software Imspector (Abberior Instruments GmbH, Germany) with the help of a multifunction I/O-device (PCIe-7852, National Instruments corp., USA), which also provides pixel and line trigger signals. Camera detection and sample illumination are synchronized to the scanning with the help of the pixel trigger in such a way that, first, at each scan position exactly one frame is acquired via the camera software Andor Solis (Andor Technology, UK), and second, the sample is only illuminated during the frame exposure time. The phase and polarization of the STED beam are controlled via a custom written Python script, such that the depletion pattern is rotated after each line acquisition. Since each line is scanned with each depletion pattern orientation before the next line is addressed, tomoSTED sub-images with differently oriented high-resolution direction are obtained. All measurements presented in this article were performed with a pixel size of 20 nm with respect to galvanometric scanning, in order to satisfy Nyquist’s sampling theorem. The frame exposure time was 150 µs, the camera pixel size corresponds to (69±1) nm in the sample plane and a frame consists of 16 x 16 pixels, thus corresponding to a sample region of 1104 nm x 1104 nm. In order to reject camera pixels with low information content, a circular evaluation region is defined that is centered around the optical axis. Its radius of 359 nm corresponds to three times the standard deviation of a Gaussian with FWHM = 282 nm, which is the mean FWHM of the experimentally determined detection PSF. For the following, only camera pixels are used which fall into this circular area. The set of tomoSTED sub-images was obtained by summing up the camera pixel counts for each scan position and by registering this value at the corresponding scan position. The set of ISM-tomoSTED sub-images was generated by pixel reassignment, as described in section 3.2. Before the tomoSTED reconstruction step (see section 3.3), a background correction was performed on the individual (ISM-)tomoSTED sub-images, for which the background signal was estimated from a square object-free region within the sub-images.
3.2 Pixel reassignment
For the pixel reassignment step, which results in the ISM-tomoSTED sub-images, the phase correlation approach is applied as presented in [29]. This approach has the advantage that it estimates the shifts and therefore the pixel reassignment factors directly from the data. First, those camera frames (compare Fig. 1) are identified which belong to a specific orientation of the depletion pattern. The result is a series of frames, with one frame for each scan position in the sample plane. For each camera pixel, an image ($\text {I}_{n_x,n_y}$ with $n_x$, $n_y$ denoting the pixel position on the camera chip) is obtained by registering the respective pixel count of each frame at the corresponding scan position. Then, the shift of each of those images relative to the image recorded by the central pixel ($I_{c_x,c_y}$) is determined [29]. The central pixel is located on the optical axis and thus exhibits an overlapping excitation and detection PSF. For each image $\text {I}_{n_x,n_y}$, the inverse Fourier transform of the cross power spectrum with respect to $I_{c_x,c_y}$ is calculated: [29,34]
3.3 TomoSTED reconstruction
The final, 2D highly-resolved (ISM-)tomoSTED image is reconstructed from the set of (ISM-) tomoSTED sub-images, each exhibiting a different orientation of the high-resolution direction. For this, a Matlab-based reconstruction algorithm is used. First, a shift correction is performed by applying the phase correlation method (see section 3.2) to correct for slight misalignments between the differently oriented 1D-PSFs. Then, the ’maximum Fourier value’-reconstruction method is applied, which is performed in Fourier space [22]. To this end, each sub-image is Fourier transformed using the Matlab function fft2. For each spatial frequency, only the amplitude with the largest magnitude is kept from the set of Fourier-transformed sub-images and the result is inverse Fourier transformed to obtain the final (ISM-)tomoSTED image in real space. As also mentioned in [22], this final image contains negative values, due to the background correction of the sub-images as well discontinuities in the assembled synthetic Fourier transform. Therefore, we want to note, that all presented line profiles show the full data range. Only for better visualization of the images, the negative values are set to zero there.
3.4 Simulation of tomoSTED as well as ISM-tomoSTED imaging
The performance of tomoSTED and ISM-tomoSTED is not only compared via experimental data, but also in simulations. These were performed in Matlab. In the case of tomoSTED, the 1D-PSFs were simulated assuming a 2D-Gaussian function with a FWHM of 268 nm and 70 nm in the low-resolution and the high-resolution direction respectively, which corresponds to the values in the experiment. For tomoSTED imaging of an object, sub-images were generated by convolving the 1D-PSFs with the object for a scan pixel size of 5 nm. In the case of ISM-tomoSTED, the camera frames were simulated for a symmetric Gaussian-shaped detection PSF with an FWHM of 282 nm, a camera pixel array of 15 x 15 pixels and a camera pixel size, which corresponds to 70 nm x 70 nm in the sample plane. Additionally, the above mentioned 1D-PSFs were used as effective excitation PSFs. ISM-tomoSTED imaging of an object was simulated by convolving the respective PSF for each camera pixel with the object for a scan pixel size of 5 nm. The pixel reassignment for these frames was performed as described in section 3.2. To obtain the final (ISM-)tomoSTED images, the tomoSTED reconstruction method presented in section 3.3 was applied.
3.5 Samples
The performance of ISM-tomoSTED microscopy is experimentally compared to that of tomoSTED microscopy by imaging fluorescent microspheres as well as fluorescently-labelled fixed cells. For imaging of fluorescent microspheres, 48 nm-sized fluospheres (FluoSpheres carboxylate-modified microspheres, crimson fluorescent (625/645); Life Technologies, USA) were attached to the surface of a cover slip, which is coated with Poly-L-lysine (0.1$\%$(w/v) in $\text {H}_{2}\text {O}$, Sigma-Aldrich, USA). For imaging of fixed cells, methanol-fixed vero cells, which are seeded on a cover slip, were stained for their $\alpha$-tubulin according to standard immunofluorescence protocols using a primary (rabbit anti-$\alpha$-tubulin, Abcam, UK) and a secondary antibody (Abberior Star 635P anti-rabbit, Abberior, Germany). Both sample types were embedded in self-prepared mowiol for imaging.
4. Results
4.1 Application of the ISM-concept to tomoSTED 1D-PSFs
To validate that the ISM concept can successfully be applied to tomoSTED microscopy, simulated as well as experimentally measured ISM-tomoSTED 1D-PSFs are compared to the corresponding tomoSTED 1D-PSFs. Figure 3(a) exemplarily shows simulated 1D-PSFs with $0^{\circ }$-orientation and their respective line profiles along the low-resolution and the high-resolution direction. The position and the orientation of the lines along which the line profiles were determined are indicated by arrows which are colored according to the respective profiles. A resolution improvement of 1.37 along the low-resolution and of 1.03 along the high-resolution direction is obtained, which is close to the theoretical expected values according to Eq. (7) (1.38 for the low-resolution direction and 1.03 for the high-resolution direction). The slight deviations from the theoretically expected values are most probably caused by the finite pixelation within the simulations.
Fig. 3. Application of the ISM-principle to individual tomoSTED PSFs. (a) Simulated tomoSTED and ISM-tomoSTED 1D-PSFs for an orientation of $0^{\circ }$ with respect to the y-axis and corresponding line profiles along the directions indicated by the respectively colored arrows. Orange and purple indicate the low-resolution direction (here denoted as y’) while light blue and red indicate the high-resolution direction (here denoted as x’). (b) Examples of experimentally determined tomoSTED and ISM-tomoSTED 1D-PSFs for different orientations (approximately $0^{\circ }$, $45^{\circ }$ and $90^{\circ }$) measured on 48 nm-sized fluorescent microspheres. The raw data is visualized with symbols, while the Gaussian fits are drawn as solid lines. Due to background correction of the camera images, the data contain negative values. Whereas negative values are set to zero for visualization of the 1D-PSFs, the profiles show the full data range.
To quantify the resolution improvement also for experimental data, (ISM-)tomoSTED imaging of fluorescent microspheres with a diameter of 48 nm was performed. Exemplary 1D-PSFs for an orientation of approximately $0^{\circ }$, $45^{\circ }$ and $90^{\circ }$ are shown in Fig. 3(b). Here, the line profiles are determined by averaging over three neighbouring pixels and subsequent fitting with a Gaussian function. By averaging over five beads as well as over two orientations, namely the $0^{\circ }$- and $90^{\circ }$- orientation, weighted with the respective error of the fit, a mean FWHM in the low-resolution direction of (268±1) nm for the tomoSTED 1D-PSF and of (201±1) nm for the ISM-tomoSTED 1D-PSF is determined. Thus, the width is reduced on average by a factor of $1.33 \pm 0.01$ in the low-resolution direction. In the high-resolution direction, a mean FWHM of (${70\pm 1}$ nm) was determined for both ISM-tomoSTED and tomoSTED, resulting in a ratio of $1.00 \pm 0.02$. Please note that because of the non-negligible bead size, this mean FWHM serves as an upper estimate for the resolution in the high-resolution direction. When comparing the experimental results with the simulations (Fig. 3(a)), it can be stated that the experimentally observed resolution improvement due to ISM is slightly lower than expected, which may be due to optical aberrations in the experimental setup. Nevertheless, a clear resolution improvement in the low-resolution direction can be observed.
4.2 Analysis of required number of PSF orientations for ISM-assisted tomoSTED
To determine the number of 1D-PSF orientations which are required to achieve virtually isotropic resolution for ISM-assisted tomoSTED in comparison to tomoSTED, the coverage of spatial frequencies for both methods is first analyzed in Fourier space. For this purpose, final tomoSTED and ISM-tomoSTED PSFs with an FWHM of 70 nm in the high-resolution direction of the individual 1D-PSFs were simulated as described in section 3.4. Analogue to the PSF and image notation, their OTFs are denoted as final (ISM-)tomo OTF in the following. Figure 4 (a) exemplarily shows the modulus of these OTFs that are reconstructed from $\text {N} = 4$ ($0^{\circ }$, $45^{\circ }$, $90^{\circ }$, $135^{\circ }$) and $\text {N} = 6$ ($0^{\circ }$, $30^{\circ }, \ldots, 150^{\circ }$) orientations, respectively. It is obvious that the OTFs exhibit an angular symmetry which reflects the number of orientations used for the tomoSTED reconstruction.
Fig. 4. Analysis of final (ISM-)tomoSTED OTFs. (a) Normalized modulus of simulated final tomoSTED OTFs (left) and final ISM-tomoSTED OTFs (right) for four (top) and six (bottom) orientations ($\Delta _\text {high,tomo} = {70}{\mathrm {nm}}$). (b) Profiles over the circles indicated in (a). $\alpha$ denotes the polar angle with respect to the $v$-axis. Note that due to the symmetry, only the range from $\alpha =0^{\circ } - 180^{\circ }$ is shown. The circle radius $\omega _0 = {39.6}\,{\mathrm{\mu m}}^{-1}$ is the same for all profiles. (c,d) Averaged minimum amplitude of a profile, normalized to the averaged maximum amplitude within the same profile, for tomoSTED (blue symbols) and ISM-tomoSTED (red symbols) as a function of N. Simulated data are shown in (c), and experimental data in (d). The solid lines in (c) and (d) represent Eq. (9) for tomoSTED (red) and ISM-tomoSTED (blue).
To compare the OTFs’ angular coverage, profiles along a semi-circle with diameter $\omega _0$ are shown in Fig. 4 (b). The diameter of that circle of $2\omega _0$ corresponds to the FWHM of a Fourier-transformed Gaussian function with a FWHM of $\Delta _\text {high}$. The ISM-tomoSTED profiles (red) exhibit slightly higher maximum amplitudes than the tomoSTED profiles (blue). This is expected because, first, the maximum amplitudes are given by the amplitude of the single OTFs at frequency distance $\omega _0$ along their high-resolution direction (see section 3.3) and, second, the resolution in the high-resolution direction is slightly improved due to ISM. Figure 4 (b) also illustrates that the number of maxima and minima of each profile equals the number of orientations used. For either method, the minimum amplitude increases when more orientations are used. For the same number of orientations, the minima are less pronounced for ISM-tomoSTED than for tomoSTED due to the ISM-resolution improvement in the low-resolution direction. Notably, for the chosen parameters, ISM-tomoSTED exhibits similar minimum amplitudes for N = 4 as tomoSTED does for N = 6, not only in absolute terms but also relative to the respective maximum values.
In the following, this is analyzed in more detail for a general number of orientations. To this end, the minimum amplitude normalized to the maximum within the same profile is considered as a measure for the OTF’s angular homogeneity. As the amplitudes slightly vary within the same profile due to the pixelation in the simulations, the average over all respective minima and maxima, $\text {<|OTF|}_{\text {min}}\text {>}$ and $\text {<|OTF|}_{\text {max}}\text {>}$, is considered. Figure 4 (c) shows the normalized $\text {<|OTF|}_{\text {min}}\text {>}$ for an extended range of N. For any number of orientations, larger normalized $\text {<|OTF|}_{\text {min}}\text {>}$ and therefore a better angular homogeneity can be observed for ISM-tomoSTED as compared to tomoSTED.
To validate the simulations experimentally, 48 nm-sized fluorescent microspheres were measured with 12 suitably chosen orientations of the 1D-PSF. From all these orientations subsets of N = 3, 4, 5 and 6 equally-spaced orientations were selected and for each subset, a final tomoSTED as well as a final ISM-tomoSTED OTF was reconstructed. Figure 4 (d) shows the experimentally determined, normalized $\text {<|OTF|}_{\text {min}}\text {>}$, which were averaged over six microspheres. The comparison with Fig. 4 (c) reveals that the experimental data agree well with the simulations.
Assuming Gaussian-shaped PSFs, an analytical expression can be derived for $\text {OTF}_{\text {min}}$, which allows for a further generalization of the angular homogeneity with respect to N and the FWHMs of the 1D-PSFs. As derived in the Appendix, the normalized minimum amplitude of the (ISM-)tomoSTED OTF along a circle with radius $\omega _0$ is given by:
Eq. (9) now allows to find a relation between those $\text {N}_\text {tomo}$ and $\text {N}_\text {ISM-tomo}$ that result in the same angular homogeneity ($\Vert \min \left [\text {OTF}_{\text {tomo}}\right ]\Vert = \Vert \min \left [\text {OTF}_{\text {ISM-tomo}}\right ]\Vert$):
Fig. 5. Resolution comparison of ISM-tomoSTED and tomoSTED in real space. (a) Number of ISM-tomoSTED orientations $\text {N}_ \text {ISM-tomo}$, for which the final OTF exhibits at least the same angular homogeneity as tomoSTED with $\text {N}_\text {tomo}$ orientations, according to Eq. (10) (black solid line) and to the upper estimate Eq. (12) (black dotted line). (b) Simulated final tomoSTED (left) and final ISM-tomoSTED images (right) of an object consisting of five concentric rings with increasing distance. In each case, four (top) and six (bottom) orientations were used for the reconstruction. (c) Averaged radial profiles of (b), normalized to the respective maximum of the tomoSTED (blue) and the ISM-tomoSTED (red) image for six (solid line) and four (dashed line) orientations. $r$ denotes the radial coordinate and $r = 0$ is the ring center.
Next, to analyse whether ISM-tomoSTED with $\gamma$-less orientations than tomoSTED leads to a comparable isotropic resolution in real space, final (ISM-)tomoSTED images of an object consisting of five concentric rings were simulated (Fig. 5 (b)). The distances between the rings increases by 12 nm from the inside to the outside, starting from 84 nm. Following [22], $\text {N}_{\text {i}} = 6$ was used as the starting point (with $k_{\text {tomo}}\approx 3.83$). Since the N$_{\text {i}}$ must be integers, $\text {N}_{\text {i}}$ was also set to 4, thereby using slightly less orientations than theoretically suggested ($\gamma = 1.5$ instead of $\gamma = 1.42$). Figure 5 (b) shows that for identical $\text {N}_{\text {i}}$, the final ISM-tomoSTED image looks more isotropic than the respective final tomoSTED image reflecting the better angular homogeneity of the OTF. To quantify the resolving capability in more detail, averaged radial profiles are displayed in Fig. 5 (c). As expected, the rings can be separated best for ISM-tomoSTED and six orientations. Noteworthy, the profiles for ISM-tomoSTED with N = 4 and for tomoSTED with N = 6 are almost congruent which means that, on average, the same resolving capability is achieved. This indicates, that the comparable angular homogeneity in Fourier space for $\gamma$-less ISM-tomoSTED orientations is indeed transferred to a comparably isotropic resolution in real space.
4.3 Experimental validation of ISM-tomoSTED
So far, the properties of ISM-tomoSTED have been mainly analyzed by simulations, which assumed Gaussian-shaped PSFs and neglected the influence of noise. Therefore, in the following, ISM-tomoSTED is compared to tomoSTED experimentally by imaging 48 nm-sized fluorescent microspheres, which serve as point-like objects, and tubulin-labelled fixed vero cells, i.e. a biological sample with filamentous structures running in various directions.
The measurements were performed with eight orientations of the 1D-PSF, such that six and four equally-spaced orientations were available for the tomoSTED and ISM-tomoSTED reconstruction respectively. Note that in each case, the disregarded sub-images did not contribute to the final images. Figure 6 (a) shows a section of the final images of the microsphere sample on the left and exemplary line profiles, which were averaged over three pixels, on the right. The range within the images corresponding to the specific line profile is marked with the respective color. To quantify the resolution more precisely, line profiles along the x-direction were determined through the center of seven different microspheres and each fitted by a Gaussian function. The resulting average FWHM of $81.3 \pm 0.4$ nm for tomoSTED and $82.1 \pm 0.4$ nm for ISM-tomoSTED agree within the error range. Figure 6 (b) presents the final tomoSTED and ISM-tomoSTED images for the cell sample on the left and an exemplary line profile on the right. For both samples, the tomoSTED image and the ISM-tomoSTED image exhibit a similar brightness and a similar resolution (respectively structure sizes). This indicates that the final ISM-tomoSTED, which is reconstructed from 1.5-times less orientations as compared to tomoSTED, exhibits indeed a comparable image quality.
Fig. 6. ISM-tomoSTED imaging with a 1.5-times lower number of orientations for (a) 48 nm-sized fluorescent microspheres and (b) fluorescently-labelled fixed vero cells. Left: The final tomoSTED image (reconstructed with N = 6 orientations) and the final ISM-tomoSTED images (reconstructed with N = 4 orientations) have a comparable image quality. Right: Exemplary line profiles along the lines indicated in blue and red on the left show that the structure size observed in the ISM-tomoSTED image is similar to the one in the final tomoSTED image.
5. Discussion and conclusions
We have demonstrated for the first time, to our knowledge, that the performance of tomoSTED microscopy can be improved by combining it with ISM. The ISM-enabled resolution improvement in the low-resolution direction allows us to reduce the number of orientations required for the tomoSTED reconstruction by a factor of approximately $\sqrt 2$ while maintaining the angular homogeneity of the PSF or OTF. To ensure the same measurement conditions for ISM-tomoSTED as well as tomoSTED, eight orientations of the 1D-PSF were used in the experiments, although only four or six were used for the respective reconstruction. For routine imaging, only the orientations that are required for reconstruction have to be recorded.
We have shown that pixel reassignment applied on experimentally measured, asymmetric PSFs with different orientations of the high-resolution direction leads to an FWHM improvement which agrees with the theory and our simulations. Because we used an adaptive pixel reassignment method [29], in which the pixel reassignment factor and, more generally, the shift vectors are obtained directly from the data, neither the orientation nor the FWHM of the high-resolution direction need to be known. Therefore, despite that the STED-enabled resolution improvement in the high-resolution direction is an experimental variable parameter and depends e.g. on the STED power and the fluorophore, the pixel reassignment can be readily performed without any prior knowledge.
The improvement in the low-resolution direction of the individual tomoSTED PSFs due to ISM could be further improved for example by additionally applying a Fourier filter during the ISM pixel reassignment step [24]. This would likely enhance the advantage of ISM-tomoSTED over tomoSTED further. Moreover, multi-image deconvolution [29] may also be beneficial.
Because of the ISM-enabled improvement of the low-resolution direction, final ISM-tomoSTED OTFs of simulated as well as experimental data feature an improved angular homogeneity of spatial frequencies for equal orientation number. Assuming Gaussian PSFs, we have derived an easy relation for those orientation numbers $\text {N}_\text {tomo}$ and $\text {N}_\text {ISM-tomo}$ that lead to the same angular homogeneity. The proportionality factor $\gamma$ depends mainly on the resolution improvement due to ISM in the low-resolution direction, which can usually be estimated from the optical setup and the Stokes shift of the used fluorophores. Therefore, we believe that $\gamma$ can serve as an easily accessible estimate, with which $\text {N}_\text {ISM-tomo}$ can be determined before the actual imaging is performed.
We have shown for one set of orientation numbers (N = 4 and N = 6), using simulated as well as experimental data, that 1.5-less orientations lead to the same resolution and image quality for ISM-tomoSTED as compared to tomoSTED. This ratio is reasonably close to (and even higher than) the calculated $\gamma$-value of 1.42, which is why we believe that the theoretic estimate is indeed applicable.
In terms of instrumentation, only a small modification of the tomoSTED experimental setup is needed to incorporate the ISM concept, as the point detector conventionally used for (tomo)STED microscopy has just to be replaced by an array detector. In this study, we used a cooled sCMOS camera for this purpose. Its frame rate and noise characteristics were sufficient to compare the performance of ISM-tomoSTED with that of tomoSTED. However, to enable faster imaging, the camera should be exchanged e.g. by a SPAD array [29,39]. So far, the orientation of the 1D-PSFs has been changed line by line. To access fast dynamics, this could be changed to a pixel-wise rotation. Thereby, applications beyond imaging, such as tracking and tracing, are conceivable.
For tomoSTED reconstruction, we used a simple method, which does not require any knowledge about the 1D-PSFs. According to [22], the number of required pattern orientations can however be reduced by a factor of two, when using a Richardson Lucy deconvolution. In this way, tomoSTED microscopy reduces the light dose by a factor of four as compared to the classical 2D implementation. It is highly probable, that this is also valid for ISM-tomoSTED microscopy. Thus, the advantage of ISM-tomoSTED microscopy over classical 2D-STED microscopy has the potential to amount to a factor of approximately six provided that sufficiently sensitive array detectors are used.
Appendix: Normalized minimum of the angular profile of tomoSTED OTFs
According to Eq. (3) the 1D-PSF is given by
If the ’maximum Fourier value’-reconstruction is used, the final (ISM-)tomoSTED OTF is given by the point-wise maximum of the set of 1D-OTFs, each rotated by an angle $\phi _n = n\pi / \text {N}$ with $n=0,\ldots,\text {N}-1$. Note that $\alpha = 0$ points in the direction of the v-axis.
Funding
Niedersächsisches Ministerium für Wissenschaft und Kultur (13-76102-11-1-15); Bundesministerium für Wirtschaft und Technologie (03THW05K07).
Acknowledgments
The authors thank K. Soliman for providing the cell samples.
Disclosures
CG: Institute for Nanophotonics Göttingen (P), AE: Institute for Nanophotonics Göttingen (P), Abberior Instruments GmbH (I,C).
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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