Structured detection for simultaneous super-resolution and optical sectioning in laser scanning microscopy

Abstract

Fast detector arrays enable an effective implementation of image scanning microscopy, which overcomes the trade-off between spatial resolution and signal-to-noise ratio of confocal microscopy. However, current image scanning microscopy approaches do not provide optical sectioning and fail with thick samples unless the detector size is limited, thereby introducing a new trade-off between optical sectioning and signal-to-noise ratio. Here we propose a method that overcomes such a limitation. From single-plane acquisition, we reconstruct an image with digital and optical super-resolution, high signal-to-noise ratio and enhanced optical sectioning. On the basis of the observation that imaging with a detector array inherently embeds axial information, we designed a straightforward reconstruction algorithm that inverts the physical model of image scanning microscopy image formation. We present a comprehensive theoretical framework and validate our method with images of biological samples captured using a custom setup equipped with a single-photon avalanche diode array detector. We demonstrate the feasibility of our approach by exciting fluorescence emission in both linear and nonlinear regimes. Moreover, we generalize the algorithm for fluorescence lifetime imaging, fully exploiting the single-photon timing ability of the single-photon avalanche diode array detector. Our method outperforms conventional reconstruction techniques and can be extended to any laser scanning microscopy technique.

A reconstruction method for image scanning microscopy exploits all the information encoded in the four-dimensional image scanning microscopy dataset to achieve optical sectioning and maintain super-resolution and high-signal-to-noise-ratio imaging.

Main

Imaging a three-dimensional (3D) sample requires optical sectioning, namely, the capability to reject out-of-focus light and image a single plane^1,2. Conventional wide-field microscopes cannot separate in-focus light from out-of-focus light, due to the well-known phenomenon of the missing cone^3,4. Some post-processing methods have been proposed to remove the defocused background from conventional images, but they rely on assumptions—such that background has low intensity and low spatial frequencies—which are not general and cannot provide true optical sectioning. Therefore, specific strategies are needed, which can be grouped into three non-mutually exclusive categories. (1) Avoiding the excitation of out-of-focus planes, as in selective plane illumination microscopy⁵, multiphoton excitation microscopy⁶ and photoactivation microscopy⁷. (2) Removing out-of-focus fluorescence before detection, as in confocal laser scanning microscopy (CLSM)⁸, 4Pi⁹ and I⁵M microscopy¹⁰. (3) Modulating the illumination to computationally remove out-of-focus light, as in HiLo¹¹, random illumination microscopy^12,13 and structured illumination microscopy^14–17. Although effective, these approaches either increase microscope complexity, reduce compatibility with super-resolution and other advanced techniques, or introduce constraints on the sample. Among them, CLSM is the most popular for its versatility, robustness and simplicity. Its benefits come from the pinhole: the smaller it is, the less out-of-focus light is collected and the better the lateral resolution—up to twice the diffraction limit¹⁸. However, super-resolution requires a nearly closed pinhole, which severely degrades the signal-to-noise ratio (SNR). Image scanning microscopy (ISM) was introduced as an improvement over CLSM^19,20, replacing the pinhole and single-element detector with a detector array. ISM can be implemented with any pixelated detector^21,22, but single-photon avalanche diode (SPAD) arrays have become the tool of choice owing to their single-photon sensitivity, excellent temporal resolution and absence of read-out noise²³. Each element of the detector array acts as a small pinhole, whereas the entire array guarantees high light collection efficiency. Thus, the ISM generates a set of confocal-like images—one per detector element—which must be computationally fused into a single enhanced image. Such a task is traditionally performed either by adaptive pixel reassignment (APR)^24,25 or multi-image deconvolution²⁶ and derived techniques²⁷. These methods are capable of pushing the SNR and the lateral resolution beyond the diffraction limit but provide no optical sectioning. Thus, the overall array detector size is typically limited to functioning as a pinhole²⁸, which degrades the SNR without fully rejecting out-of-focus light. These limitations prevent ISM from reaching its full potential with thick samples. Still, the axial information required to achieve optical sectioning is inherently encoded into the raw ISM dataset, as reported by a few theoretical publications^29,30 and a recent proof-of-concept study that introduced Focus-ISM³¹. Here we propose a computational reconstruction method that leverages the whole information encoded in the ISM dataset. We aim to achieve the full resolution and SNR benefits of ISM and improve optical sectioning. Our idea stems from the observation that ISM can be intended as part of the general framework of structured illumination³². Indeed, focused excitation provides high-frequency information. Structured detection can leverage it for enhanced resolution and sectioning (Supplementary Note A.1). We invert the ISM image formation model using a maximum likelihood estimation technique akin to the Richardson–Lucy method^33,34, separating the signal into in-focus and out-of-focus components.

Some approaches have already been proposed to enhance the axial sectioning capabilities of ISM, such as refocusing after scanning using helical phase engineering^35,36 and engineered ISM³⁷. They robustly encode the axial information in the ISM dataset through wavefront shaping, enabling volumetric imaging. However, those benefits come at the cost of increasing the experimental complexity and sacrificing some lateral resolution. Conversely, we do not rely on light shaping. Thus, we preserve the simplicity and super-resolution capability of ISM. Since super-resolution and optical sectioning are achieved simultaneously, we named our technique s²ISM (super-resolution sectioning ISM). Furthermore, we retain the capability of ISM to relax the Nyquist sampling criterion by a factor of two, achieving digital super-resolution²⁶. Our method requires no changes in the optical system, maintaining the versatility of the laser scanning architecture. We demonstrate the vast applicability of s²ISM with linear and nonlinear excitation and fluorescence lifetime imaging (FLIM). To simplify the application of s²ISM, we also propose a rigorous strategy to automatically extract the relevant parameters needed to run our algorithm. Finally, we provide the code as an open-source Python package.

Results

Principle of s²ISM

For this work, we developed a custom ISM microscope (Fig. 1a and Supplementary Fig. 1) equipped with a 5 × 5 asynchronous-read-out SPAD array detector³⁸ and controlled by custom software³⁹.

Fig. 1. ISM.

a, Sketch of an ISM device. The inset shows the fingerprints relative to the different axial positions of the sample. b, Simulated PSFs of an ideal ISM system at z = 0 nm (in focus) and z = 720 nm (out of focus) with λ = 640 nm and NA = 1.4. c, Sketch of the ISM image formation. The images of an in-focus sample appear brighter at the centre of the detector coordinate and dimmer at the periphery. The brightness of the images of the out-of-focus samples decays slower along the detector coordinate, encoding the axial information into the ISM dataset. The reconstruction algorithm builds two images from a single-plane dataset, one with the in-focus image and the background discarded. The out-of-focus sections of the sample are projected into a single image, which is subsequently discarded. d, Comparison of a confocal image with the ISM image reconstructed by the s²ISM algorithm on synthetic tubulin filaments.

A laser beam focused at the scan point x_s = (x_s, y_s) excites the fluorescent molecules. Each element of the array detector collects the fluorescence light at location x_d = (x_d, y_d), building a four-dimensional dataset. This can be interpreted as a set of confocal-like images (named scanned images), each blurred by a unique point spread function (PSF) given by

$$\begin{array}{ccc}\hfill h\left({\mathbf{x}}_s,z_s\mid {\mathbf{x}}_d\right)& \hfill =\hfill & h_{\mathrm{exc}}\left(-{\mathbf{x}}_s,z_s\right)\left[h_{\mathrm{em}}\left({\mathbf{x}}_s,z_s\right)*p\left({\mathbf{x}}_s-{\mathbf{x}}_d\right)\right]=\hfill \\ \hfill & \hfill =\hfill & h_{\mathrm{exc}}\left(-{\mathbf{x}}_s,z_s\right)h_{\det }\left({\mathbf{x}}_s-{\mathbf{x}}_d,z_s\right),\hfill \end{array}$$ 1

where * is the convolution operator with respect to the coordinate x_s; z_s is the axial coordinate of the emitter; p is the function describing the geometry of the detector element’s active area; and h_exc and h_em are the excitation and emission PSFs of the microscope, respectively. The detection PSF h_det is the convolution of the emission PSF h_em with the sensor element p. If the latter is small enough, h_det is very similar to h_exc. Thus, the product of the two PSFs is sharper than the individual ones, leading to super-resolution. Conversely, if the sensor size is too large, h_det approaches a constant value and the super-resolution effect is washed out.

PSFs from different detector positions differ not only in shape (Fig. 1b) but also in intensity (Supplementary Fig. 2). Indeed, they are rescaled by the fingerprint

$$f\left({\mathit{x}}_d,z_s\right)={\int }_{{\mathbb{R}}^2}h\left({\mathit{x}}_s,z_s\mid {\mathit{x}}_d\right)\mathrm{d}{\mathit{x}}_s=h_{\mathrm{exc}}\left({\mathit{x}}_d,z_s\right)\star h_{\det }\left({\mathit{x}}_d,z_s\right),$$ 2

where ⋆ is the cross-correlation operator. In general, samples have a 3D structure. Given the linearity of incoherent image formation, the ISM dataset i(x_s∣x_d) is given by the superposition of the fluorescence light emitted from any plane. Assuming that the relevant out-of-focus contributions stem from a finite and discrete number of planes, the forward model of ISM image formation is

$$i\left({\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right)=\sum _{k=1}^N{f}_k\left({\mathbf{x}}_{\mathrm{d}}\right)\left[o_k\left({\mathbf{x}}_{\mathrm{s}}\right)*{\widehat{h}}_k\left({\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right)\right],$$ 3

where o is the object (that is, the specimen’s distribution of emitters), k is the discretized axial position and $\widehat{h}$ is the normalized PSF. The above equations suggest that the light stemming from different axial positions distributes differently on the detector plane, regardless of the lateral sample structure. Following the fingerprint distribution, the images generated by the central and peripheral elements of the detector array collect light mainly from the in-focus and out-of-focus planes, respectively (Fig. 1c). Our goal is to leverage the fingerprint map—uniquely provided by the ISM architecture—to design a reconstruction procedure that builds a super-resolution image starting from a single-plane ISM dataset, excluding the defocused background.

Typically, out-of-focus light stems from multiple planes. However, using a large N would escalate the computational cost of the algorithm and exacerbate the ill-posed nature of the problem we aim to solve. Using only two axial planes (N = 2), we are essentially asking the algorithm if the light collected by the detector array is more likely to have originated from the in-focus or out-of-focus plane. Using a single-photon detector, we assume the shot noise to be dominant. Thus, we write an explicit Poisson likelihood functional (Supplementary Note A.2), whose maximization leads to the following iterative solution:

$$\begin{array}{ccc}\hfill o_1^{\left(m+1\right)}\left({\mathbf{x}}_{\mathrm{s}}\right)& \hfill =\hfill & o_1^{\left(m\right)}\left({\mathbf{x}}_{\mathrm{s}}\right)\int h_1\left(-{\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right)*\frac{i\left({\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right)}{{\sum }_{k=1}^2{o}_k^{\left(m\right)}\left({\mathbf{x}}_{\mathrm{s}}\right)*h_k\left({\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right)}\mathrm{d}{\mathbf{x}}_{\mathrm{d}},\hfill \\ \hfill o_2^{\left(m+1\right)}\left({\mathbf{x}}_{\mathrm{s}}\right)& \hfill =\hfill & o_2^{\left(m\right)}\left({\mathbf{x}}_{\mathrm{s}}\right)\int h_2\left(-{\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right)*\frac{i\left({\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right)}{{\sum }_{k=1}^2{o}_k^{\left(m\right)}\left({\mathbf{x}}_{\mathrm{s}}\right)*h_k\left({\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right)}\mathrm{d}{\mathbf{x}}_{\mathrm{d}},\hfill \end{array}$$ 4

where m is the iteration index. One of the resulting images contains the projection of the out-of-focus light and is discarded. The other is built by fusing and deconvolving the in-focus signal from the scanned images. Indeed, the proposed algorithm can be considered a generalization of the multi-image deconvolution method²⁶, which can be recovered simply by putting N = 1 in equation (3) (Supplementary Fig. 3). Furthermore, dropping the detector dimension x_d recovers the conventional Richardson–Lucy deconvolution equation^33,34. The result of s²ISM is an image with enhanced resolution and optical sectioning compared with its confocal counterpart (Fig. 1d). Importantly, we achieve both benefits without discarding the in-focus light, enhancing the SNR⁴⁰.

To successfully reconstruct an image from the raw ISM data, we need to face two challenges. First, s²ISM shows a semiconvergent behaviour, similar to conventional deconvolution (Fig. 2a,b). Thus, the algorithm should be stopped before amplifying noise⁴¹. The optimum number of iterations is unknown in general, but we can approximate the interval in which the optimum is located by exploiting the photon conservation property of our algorithm. Specifically, the total number of photons in the scanned images equals the sum of the two reconstructed images regardless of the iteration (Supplementary Note A.3). The dynamics of photon exchange between the two planes mostly happen during the initial iterations, later reaching a plateau (Fig. 2b), indicating that convergence has been reached and the algorithm should stop. Second, we need a reliable method to obtain the PSFs of the ISM system. Imaging a subdiffraction source is a viable option, but it requires additional experimental effort and the PSFs will be corrupted by various sources of noise and non-idealities. Therefore, we simulated the PSFs from vectorial diffraction theory⁴² and designed a method to retrieve their key parameters directly from the scanned images, assuming negligible aberrations (Supplementary Note A.6). In detail, we choose the out-of-focus plane as the one that maximizes the diversity of PSFs with respect to the focal plane (Fig. 2c). A more rigorous approach, yet more computationally expensive, consists of choosing the defocus that maximizes the optical sectioning (Supplementary Figs. 10 and 11). Then, we calculate the translation between the scanned images—the shift vectors—generated by the inner 3 × 3 array of the detector. These quantities are uniquely related to the geometrical structure of the array detector. Thus, we use them to retrieve the rotation angle and orientation of the detector (Fig. 2d) and the magnification of the microscope. Imaging of a tubulin network demonstrates that our approach effectively removes the defocused light and improves resolution, revealing details previously hidden by the background (Fig. 2d and Extended Data Fig. 1).

Fig. 2. Data-driven estimation of the parameters.

a, Simulated experiments at λ = 640 nm and z = 720 nm. Comparison of the APR image, s²ISM reconstruction and ground truth of the focal plane. b, Total number of photons per plane (top) and Kullback–Leibler divergence (D_KL) of the reconstruction to the focal ground truth (bottom) at varying iteration numbers. c, D_KL of the out-of-focus PSF dataset to the in-focus one. The maximum position defines the plane used for the s²ISM reconstruction. d, Experimental and fitted shift vectors from the inner 3 × 3 array detector. The fit returns the magnification, orientation and rotation parameters. e, Comparison of APR and s²ISM image of the tubulin network of a HeLa cell (mouse anti-α-tubulin combined with anti-mouse abberior STAR RED).

Extended Data Fig. 1. Tubulin network of a HeLa cell.

Extended images from Fig. 2. Field-of-view: 35 μm × 35 μm. Image size: 875 × 875 pixels. Pixel dwell time: 50 μs. Excitation laser: λ = 640 nm, CW. Average power at the sample plane: 1.2 μW. s²ISM and multi-Image deconvolution iterations: 20.

Experimental validation of s²ISM

To validate s²ISM, we compare it with standard reconstruction methods (Fig. 3a,b, Extended Data Fig. 2 and Supplementary Fig. 18). Summing the scanned images or extracting the central one results in a confocal image with a pinhole size of 1.4 Airy units (AU) and 0.3 AU, respectively. It is well known that reducing the pinhole size trades resolution and sectioning with the SNR. We use confocal reconstructions as references, since they neglect the spatial information from the detector array. APR improves on this by registering and summing the scanned images²⁵, combining resolution enhancement with high SNR. However, APR assumes the scanned images identical but shifted and rescaled—an approximation that leads to suboptimal results. Multi-image deconvolution²⁶ produce better images considering the diversity of PSFs. Nonetheless, like APR, it cannot reject out-of-focus light, limiting its use in thin samples. Focus-ISM^31,43 rejects the background by isolating in-focus components pixel by pixel after reassignment. Although it improves optical sectioning, it is very sensitive to noise and incompatible with multi-image deconvolution. s²ISM combines the strengths of all previous methods. Using both in-focus and out-of-focus PSFs, it achieves enhanced resolution, optical sectioning and SNR without trade-offs.

Fig. 3. Lateral resolution and optical sectioning.

a, Confocal image (left) of the tubulin network of a HeLa cell (mouse anti-α-tubulin combined with anti-mouse abberior STAR RED) compared with the s²ISM reconstruction (right). b, Detail of the image in a (white dashed box) reconstructed using different algorithms. From left to right, the lateral resolution and SNR are improved. From top to bottom, optical sectioning is improved. Both multi-image deconvolution and s²ISM algorithms are stopped at 20 iterations. We excited the specimen using the laser wavelength λ = 640 nm. c, Compared images of a resolution target composed of gradually spaced lines. d, Corresponding modulation transfer function, experimentally measured by calculating the contrast of the dip relative to the two adjacent lines. When no dip is discernible, the contrast is set to zero. e, Compared single-plane images of a 3D stair of rings evenly spaced on the axial direction (Δz = 250 nm). On the bottom, we show the x–z slice of a confocal 3D stack of the same target. The dashed line indicates the axial plane of the images above. f, Corresponding normalized optical sectioning function, calculated by summing the photon counts from each ring. We excited both targets using the laser wavelength λ = 488 nm.

Extended Data Fig. 2. Tubulin network of a group of HeLa cells.

Extended images from Fig. 3a–b. Field-of-view: 80 μm × 80 μm. image size: 2000 × 2000 pixels. Pixel dwell time: 20 μs. Excitation laser: λ = 640 nm, CW. Average power at the sample plane: 2.6 μW. s²ISM and multi-Image deconvolution iterations: 20.

To rigorously quantify the performance of s²ISM, we imaged the fluorescent resolution targets. First, we estimated the resolution gain using a pattern of gradually spaced lines, ranging from 390 nm to 0 nm in steps of 30 nm. This target allows for a reliable assessment of image resolution based on its fundamental definition: the ability to distinguish two separate objects. We reconstructed the target image using APR and multi-image deconvolution, which are state-of-the-art ISM algorithms, and we compared with the confocal image (used as a reference) and s²ISM (Fig. 3c). For each image, we measured the visibility of the dip between adjacent lines at each spacing. The results shown in Fig. 3d demonstrate that our reconstruction method enhances the lateral resolution of the final image, beating the diffraction limit. Then, we quantified the capability of s²ISM to reject out-of-focus light by imaging a 3D stair composed of ring-shaped targets uniformly spaced along the axial coordinate (Fig. 3e, Extended Data Fig. 3 and Supplementary Fig. 22). We reconstructed a single-plane ISM dataset taken from the centre of the stairs using APR, which acts as a reference and has no additional sectioning compared with the open-pinhole confocal image. Then, we applied the popular background removal algorithm known as rolling ball to the APR image. Finally, we applied ISM-specific algorithms for optical sectioning, namely, Focus-ISM and s²ISM. The latter algorithm provides the highest degree of optical sectioning, doubled compared with conventional ISM implementations (Fig. 3f and Supplementary Fig. 23). Indeed, s²ISM allows for sample-agnostic optical sectioning without relying on assumptions on the specimen’s structure. Without the additional information contained in the multiple images of the raw dataset, computational optical sectioning would not be possible (Supplementary Figs. 24–26). Finally, we estimated the SNR enhancement achieved by s²ISM by comparing the reconstruction of multiple noisy realizations of the same ISM dataset (Supplementary Note A.10). The results demonstrate a notable SNR improvement with just a few iterations of the s²ISM algorithm when compared with the initial confocal image (Supplementary Fig. 27). On the other hand, noise can be amplified by an excessive number of iterations. This result underlines once again the importance of an early stop and suggests how to determine a lower bound for the optimal iteration directly from the raw data, without a ground truth.

Extended Data Fig. 3. Gradually spaced lines.

Extended images from Fig. 3a. Field-of-view: 60 μm × 60 μm. Image size: 1500 × 1500 pixels. Pixel dwell time: 50 μs. Excitation laser: λ = 488 nm, CW. Average power at the sample plane: 10.9 μW. s²ISM and multi-Image deconvolution iterations: 20.

Versatility of s²ISM

As recently demonstrated²⁶, the ISM dataset has enough redundancy for twofold lateral upsampling. If the pixel size is chosen to be equal to the demagnified pitch of the array detector, then the scanned images are mutually shifted by half the pixel size. Thus, each pixel in one image aligns with a point between pixels in a neighbouring image (Fig. 4a), doubling the scanned points in the reconstruction. An important implication is that the Nyquist criterion can be relaxed during acquisition. With s²ISM, we can leverage this effect to achieve digital super-resolution without losing the advantages demonstrated so far (Supplementary Note A.4). To demonstrate it, we imaged nuclear pore complexes in a HeLa cell (Fig. 4b and Extended Data Fig. 4) using two pixel sizes: 160 nm and 80 nm. The first respects the upsampling condition but not the Nyquist criterion. Then, we applied s²ISM on both datasets, reaching a target pixel size of 80 nm. Despite having roughly a quarter of the reference photon counts, the upsampled image is correctly reconstructed (Supplementary Note A.8 and Supplementary Fig. 28). Thus, the s²ISM method enables the high-fidelity reconstruction of the undersampled raw data, paving the way for gentler and faster imaging.

Fig. 4. Generalization of s²ISM.

a, Sketch of the upsampling working principle. The images of the ISM dataset are shifted, and the mutual redundancy can be used to fill the gaps and reconstruct an image on a finer grid than that generated by the acquisition process. b, Results of s²ISM reconstruction with and without upsampling at the same target pixel size of 80 nm. The sample is an immunostained HeLa cell for nuclear pore complexes on the nucleus surface (rabbit anti-Nup-153 combined with anti-rabbit abberior STAR 635P). c, Time series of a live HeLa cell with stained mitochondria (MitoTracker Orange). d, Multicolour imaging of a fixed HeLa cell with mitochondria and nuclear membrane immunostained with two different fluorophores (mouse anti-ATP synthase combined with anti-mouse Alexa 647 and rabbit anti-lamin B1 combined with anti-rabbit Alexa 488, respectively). e, 2PE imaging of Purkinje cells in a slice of a mouse’s cerebellum at a depth of roughly 10 μm.

Extended Data Fig. 4. Nuclear pore complexes in a HeLa cell.

Extended images from Fig. 4b. Field-of-view: 25 μm × 25 μm. Image size: 625 × 625 pixels. Pixel dwell time: 100 μs. Excitation laser: λ = 640 nm, CW. Average power at the sample plane: 14.7 μW. s²ISM and multi-Image deconvolution iterations: 20.

The benefits of s²ISM are especially useful in the context of live-cell imaging over a long period of time. We demonstrate this approach on a time series of live mitochondria images (Fig. 4c and Extended Data Fig. 5). We performed the reconstruction frame by frame, obtaining a sequence of images with high resolution and optical sectioning (Supplementary Video 1).

Extended Data Fig. 5. Live-cell imaging of mitochondria.

Extended images from a single frame of the sequence in Fig. 4c. Field-of-view: 60 μm × 60 μm. Image size: 1500 × 1500 pixels. Pixel dwell time: 20 μs. Excitation laser: λ = 561 nm, CW. Average power at the sample plane: 1.8 μW. Framerate: 25 seconds/frame. s²ISM and multi-Image deconvolution iterations: 10.

Similarly, we extend s²ISM to multicolour imaging by applying the reconstruction algorithm to each channel. More in detail, we modelled the image formation of each channel using the corresponding excitation and emission wavelengths. The results demonstrate that s²ISM can easily be applied to multichannel datasets with a simple sequential reconstruction to obtain high-resolution and high-optical-sectioning multicolour images (Fig. 4d and Extended Data Fig. 6).

Extended Data Fig. 6. Multi-color imaging of a HeLa cell.

Extended images from Fig. 4d. Field-of-view: 65 μm × 65 μm. Image size: 1625 × 1625 pixels. Pixel dwell time: 20 μs for both channels. Blue excitation laser: λ = 488 nm, CW. Average power at the sample plane: 1.6 μW. Red excitation laser: λ = 640 nm, CW. Average power at the sample plane: 4.2 μW. s²ISM and multi-Image deconvolution iterations: 20.

The benefits of s²ISM are also particularly useful for investigating thick samples (Supplementary Figs. 29 and 30). Imaging is even more challenging at depths larger than a few tens of micrometres, where the quality is compromised by specimen-induced aberrations and scattering⁴⁴. We demonstrate that s²ISM is helpful in such scenarios by imaging a zebrafish embryo (Supplementary Fig. 31). Despite the fact that the image quality degrades with increasing depth, s²ISM provides a robust and substantial advantage over confocal imaging for the whole depth range we explored, up to 40 μm. To further push the capability to explore tissues, we demonstrate the feasibility of s²ISM with two-photon excitation (2PE), which exploits near-infrared light and a nonlinear excitation process to ease deep imaging. We imaged a mouse cerebellum slice, demonstrating an improvement in the image quality even in the case of multiphoton excitation (Fig. 4e and Extended Data Fig. 7). Indeed, our reconstruction method is general and can be used with any laser scanning microscope equipped with a detector array.

Extended Data Fig. 7. Two-photon excitation imaging of Purkinje cells in a cerebellum slice.

Extended images from Fig. 4e. Field-of-view: 50 μm × 50 μm. Image size: 1250 × 1250 pixels. Excitation laser: λ = 900 nm, pulsed at 80 MHz. Average power at the sample plane: 10.8 mW. s²ISM and multi-Image deconvolution iterations: 20.

s²ISM for FLIM

We extended s²ISM into the time domain for FLIM. Structures at different axial planes may have different lifetimes, and out-of-focus light can distort the lifetime estimation of in-focus structures. We simulated this scenario (Fig. 5a) and reconstructed the time-resolved data using APR, correcting the spatial and temporal shifts to obtain the fluorescence lifetime ISM (FLISM) image⁴⁵. Using the phasor approach⁴⁶, we computed pixel-wise lifetimes. As expected, overlapping out-of-focus light impairs the lifetime estimation. However, the SPAD array captures multiple decays, each with its own impulse response function (IRF) and modulated by the fingerprint, encoding lifetime dependence on the axial position. Therefore, we generalized s²ISM to incorporate the temporal dimension into equation (3), include fluorescence dynamics in the object and IRFs in the PSFs (Supplementary Note A.5). The s²FLISM method uses the data, corrects for IRFs, and separates the in-focus and out-of-focus decays (Supplementary Fig. 32). Furthermore, the simultaneous spatial reconstruction leverages the spatial correlations induced by the PSFs to boost the SNR of each decay. A key feature is that we do not assume an exponential decay model, allowing broader applicability for more complex fluorescence dynamics. We validated this concept on the simulated data (Fig. 5a). The phasor plot and lifetime histogram show the effective rejection of defocused emission with s²FLISM. In particular, no prior knowledge of fluorophore lifetimes is needed and s²FLISM can also remove background fluorescence with lifetimes identical to in-focus signals—something not possible without structured detection.

Fig. 5. FLIM with s²ISM.

a, Simulation of tubulin filaments with different lifetime values (numerical aperture, 1.4, λ = 640 nm). The in-focus filaments have a lifetime value of τ = 3 ns, whereas the out-of-focus (z = 720 nm) filaments have a lifetime value of either τ = 3 ns or τ = 6 ns. b, Experimental image of a rhizome of C. majalis stained with acridine orange, excited with λ = 488 nm. c, Experimental image of HeLa cells with tubulin stained with STAR RED (τ = 3.4 ns) and lamin A on the nuclear membrane stained with STAR 635 (τ = 2.8 ns). Both fluorophores are excited with the same source at λ = 640 nm. The intensity of each image is normalized to its maximum. The phasor plots and histograms are thresholded at 5% of the maximum intensity of the corresponding image. Lifetime values are calculated from the magnitude of the phasors⁴⁶.

Experimentally, we used a multichannel digital frequency domain (DFD) acquisition scheme⁴⁵ to capture fluorescence decays per scan point and detector element. We imaged a Convallaria majalis rhizome stained with a single, environment-sensitive fluorophore (Extended Data Fig. 8). Comparing FLISM and s²FLISM, the latter yielded better resolution and optical sectioning, as well as more robust phasor analysis. Indeed, the phasor cloud and lifetime histogram (Fig. 5b) are narrower, indicating improved SNR and reduced axial cross-talk. These advantages are especially useful in multitarget imaging in which structures are labelled with fluorophores of differing lifetimes but similar excitation spectra. To demonstrate the benefits of our approach in this context, we imaged HeLa cells stained with two fluorophores differing in lifetime (Fig. 5c and Extended Data Fig. 9). In FLISM, the lifetime distributions overlap. By contrast, s²FLISM clearly separates them, making segmentation easier (Supplementary Fig. 33).

Extended Data Fig. 8. Convallaria Majalis rhizome.

Extended images from Fig. 5b. Field-of-view: 100 μm × 100 μm. Image size: 2000 × 2000 pixels. Pixel dwell time: 324 μs. Excitation laser: λ = 488 nm, pulsed at 40 MHz. Average power at the sample plane: 9.1 nW. s²ISM and multi-Image deconvolution iterations: 10.

Extended Data Fig. 9. Nuclei and tubulin network in Hela cells.

Extended images from Fig. 5c. Field-of-view: 50 μm × 50 μm. Image size: 1250 × 1250 pixels. Pixel dwell time: 162 μs. Excitation laser: λ = 640 nm, pulsed at 40 MHz. Average power at the sample plane: 0.7 μW. s²ISM and multi-Image decon- volution iterations: 10.

Discussion

Previous approaches to ISM provided suboptimal reconstructions, failing to extract the whole information contained in the raw dataset. Instead, s²ISM achieves all the improvements of array detection in a comprehensive algorithm without compromises. Although s²ISM is particularly valuable for super-resolved subcellular imaging, the working principle is versatile and can be adapted for imaging at a bigger scale using any choice of numerical aperture and magnification (Supplementary Fig. 34). More specifically, s²ISM can be applied to any LSM equipped with a detector array, as long as the detected light is incoherent (for example, fluorescence, spontaneous Raman and Brillouin scattering, and photothermal imaging). Localization techniques, such as single-molecule ISM⁴⁷, could also benefit from s²ISM, improving localization uncertainty owing to the combined improvement in resolution and reduced background.

Such benefits synergistically translate to any additional dimension contained in the dataset, as we demonstrated in the case of the temporal dimension. Equivalent benefits are to be expected for hyperspectral imaging^48,49. The s²ISM extension to fluorescence lifetime could also be exploited in time-resolved stimulated emission depletion microscopy. In this case, the separation-by-lifetime tuning concept could be embedded into the algorithm for further resolution improvement^50,51. The versatility of s²ISM makes it applicable to more complex time-resolved data, such as those originating from fluorescence fluctuations^52,53 or anti-bunching from single-photon emitters⁵⁴.

With some caution, the concept of s²ISM could also be extended to coherent variations of ISM. One approach is to modify the forward model to account for the coherent image formation process, but it is unclear if such a modality would grant the same benefits as in the incoherent case. An alternative approach is to adjust the microscope to enable interferometric detection^55,56. In this case, s²ISM can be used simply by replacing intensities with fields.

Despite the promising potentialities of s²ISM, one should carefully evaluate when to stop the iterations to avoid noise amplification. A perspective solution involves regularization through statistical denoisers, such as Noise2Noise⁵⁷, integrated into the reconstruction pipeline. This family of denoisers require multiple realizations of the same data, which can be easily provided by SPAD array detectors owing to their excellent temporal resolution.

Finally, we designed s²ISM assuming that the microscope suffers negligible optical aberrations. Still, our algorithm can also be used on each isoplanatic patch as long as the correct wavefront can be measured and used to calculate the corresponding PSFs. Indeed, the combination of wavefront sensing techniques⁵⁸ with s²ISM could dramatically extend its range of usability, pushing the imaging depth.

In conclusion, s²ISM increases the capabilities of any scanning microscope equipped with a detector array without compromising the native features. Therefore, we are positive that s²ISM will be widely adopted by the community of microscopy users and developers.

Methods

Microscope architecture

For this work, we built a custom ISM setup (Supplementary Fig. 1). The excitation beams are provided by three triggerable pulsed (80-ps-pulse-width) diode lasers emitting at 640 nm, 561 nm and 488 nm (LDH-D-C-640, LDH-D-C-560 and LDH-D-C-488; PicoQuant). We control the coarse power of the visible laser using its respective drivers and control software. We performed the fine control of power using acousto-optical modulators (MT80-A1-VIS, AA Opto-Electronic). All laser beams are coupled into a different polarization-maintaining fibre to transport the beams to the microscope. In all cases, we used a half-wave plate to adjust the beam polarization parallel to the fast axis of the polarization-maintaining fibre. The beam for 2PE is provided by a tunable ultrafast laser (Chameleon Vision, Coherent), emitting at 900 nm (140-fs pulse width). The power is controlled using a half-wave plate and a polarizing beamsplitter, which redirects a fraction of the light onto a beam dump, depending on the rotation angle of the half-wave plate. The beam is magnified by a factor of 3 using a telescope. A set of dichroic mirrors (491-nm short pass, 590-nm short pass and 750-nm short pass) allows the combination of all laser beams. The excitation and fluorescence light are separated by a different dichroic mirror (multireflection band 488–560–640–775 nm or 720 nm short pass), depending on the excitation modality (one or two photons, respectively). Two galvanometer scanning mirrors (6215HM40B, CT Cambridge Technology), a scan lens and a tube lens—of a commercial confocal microscope (C2, Nikon)—deflect and direct the entire beam towards the objective lens (CFI Plan Apo VC ×60, 1.4 numerical aperture, oil; Nikon) to perform the raster scan on the specimen. The objective lens is mounted over a nanopositioner (FOC.100, PIEZOCONCEPT), enabling z scanning. The fluorescence light is collected by the same objective lens, descanned and sent towards the detection path. The latter consists of a set of lenses to form a telescopic system that conjugates the sample plane onto the detector plane with an overall magnification of ×450. Spectral filters are installed in the detection path to discard the residual excitation light. Depending on the experiments, fluorescence light is selected by using a dedicated set of filters (red set, ZET633TopNotch and ET685/70M; green set, ZET561NF and ET575LP; blue set, ZET488NF and ET525/50M; two-photon set, 720SP and ET525/50M). The detector is a 7 × 7 SPAD array (PRISM-Light kit, transistor–transistor logic version, Genoa Instruments) with a pixel pitch of 75 μm, but only the inner 5 × 5 array is read due to limitations of the read-out system used in this work. Every photon detected by any element of the SPAD array generates a transistor–transistor logic signal that is delivered through a dedicated channel to a multifunctional field-programmable-gate-array-based input–output device (NI USB-7856R from National Instruments), which acts as a data acquisition system and a control unit. The BrightEyes-MCS software³⁹ controls the entire microscope, including the galvanometric mirrors, the FOC and the acousto-optical modulators. The software also provides real-time image visualization during the scan and saves the raw data in a hierarchical data format (HDF5) file. The saved file contains metadata as a dictionary and data as a six-dimensional array (repetition, axial position, vertical position, horizontal position, time and detector channel).

Time-resolved acquisition system

We used the multichannel DFD method⁴⁵ to measure the fluorescence decay at each scan point and for each detector array element. The DFD strategy enables the acquisition of periodic signals with a timing precision superior to direct sampling through a heterodyne measurement. Laser pulses are emitted at frequency f_exc, and the fluorescence is sampled at frequency f_s. These frequencies are slightly detuned, kf_exc = (k – 1)f_s. Therefore, the sampling accumulates a delay with every cycle, resulting in a sliding window that spans over k – 1 excitation periods until the two signals are back in phase. Each period is more finely sampled in n shorter windows of duration T_w by a frequency f_w = nf_s. Defining the counters w ∈ [0, n) and φ ∈ [0, k), we reconstruct the time index γ as follows:

$$\gamma =\left(mw-\phi \right)\mathrm{mod}k,$$ 5

where $m=\frac{k-1}{n}$, $k\in \mathbb{N}$ and $n\in \mathbb{N}$ such that $m\in \mathbb{N}$. Finally, the photon arrival time is given by t = γT_exc/k.

In our implementation on a field-programmable gate array board (NI USB-7856R, National Instruments), we used a base clock of f₀ = 40 MHz. From this, we derived the frequencies $f_{\mathrm{exc}}=\frac{28}{27}{f}_0=41.48\text{MHz}$, $f_s=\frac{21}{20}{f}_0=42\text{MHz}$ and $f_{\mathrm{w}}=\frac{21}{2}{f}_0=420\text{MHz}$. The DFD parameters are n = 10, k = 81 and m = 8. Therefore, we obtain a timing precision of Δt = T_exc/k = 298 ps and a temporal resolution of T_w = 2.38 ns.

The DFD system builds the fluorescence decay histogram using equation (5) for each detector coordinate x_d. Additionally, the system returns an extra channel that samples the laser trigger signal. This is used as a reference to align different measurements to a common reference frame, whose origin is the instant of emission of the laser pulse.

Numerical simulations

We simulated the phantoms and the PSFs of the ISM microscope using the open-source Python package BrightEyes-ISM⁴². We modelled the SPAD array detector as a 5 × 5 array of pinholes with a pitch of 75 μm and an individual size of 50 μm. For all simulations, we set the magnification to M = 450, the numerical aperture to 1.4 and the refractive index to match that of the immersion oil (n = 1.51). We generate the synthetic datasets using excitation and emission wavelengths of 640 nm and 660 nm, respectively. Finally, we applied Poisson noise to the generated images. In all cases, we assumed that we illuminated the back aperture of the objective lens with a uniform plane wave—that is, we did not apply any aberrations. We modelled the IRFs of the time-resolved synthetic data using a rectangular window smoothed by a Gaussian kernel (w = 2 ns and σ = 0.3 ns). We simulated the fluorescence decay as a single exponential. We used 81 time bins separated by Δt = 298 ps to match our DFD acquisition system. To better distinguish the simulations from the experimental data, we present them using the magma and hot colour map, respectively.

Image processing

Confocal

For each ISM dataset, we generated the corresponding confocal image by summing all the raw images:

$$i_{\mathrm{s}}\left({\mathbf{x}}_{\mathrm{s}}\right)=\sum _{x_{\mathrm{d}}}i\left({\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right).$$ 6

The result is equivalent to a confocal image acquired with a pinhole as large as the detector array.

Adaptive pixel reassignment

We calculated the shift vectors of an ISM dataset as

$$\mathbf{\mu }\left({\mathbf{x}}_{\mathrm{d}}\right)=\underset{{\mathbf{x}}_{\mathrm{s}}}{\mathrm{argmax}}\left\{\mathcal{R}\left({\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right)\right\},$$ 7

where $\mathcal{R}$ is the phase correlation of the raw images to the central one:

$$\mathcal{R}\left({\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right)={\mathcal{F}}^{-1}\left\{\frac{\mathcal{F}\left\{i\left({\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right)\right\}\overline{\mathcal{F}\left\{i\left({\mathbf{x}}_{\mathrm{s}}\mid \mathbf{0}\right)\right\}}}{\mid \mathcal{F}\left\{i\left({\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right)\right\}\overline{\mathcal{F}\left\{i\left({\mathbf{x}}_{\mathrm{s}}\mid \mathbf{0}\right)\right\}}\mid }\right\}.$$ 8

The APR reconstruction²⁵ is calculated as the sum of the aligned images:

$$i_{\mathrm{APR}}\left({\mathbf{x}}_{\mathrm{s}}\right)=\sum _{x_{\mathrm{d}}}i\left({\mathbf{x}}_{\mathrm{s}}+\mathbf{\mu }\left({\mathbf{x}}_{\mathrm{d}}\right)\mid {\mathbf{x}}_{\mathrm{d}}\right).$$ 9

The total computation time is 20 s for a 2,000 × 2,000 × 25 dataset on a computer equipped with an 8-core CPU (3.6 GHz) and 32 GB of RAM.

Focus-ISM

The Focus-ISM algorithm³¹ exploits the APR approach to register the images of the ISM dataset. Instead of summing the result, the algorithm fits each reassigned and normalized micro-image to the following two-components Gaussian mixture model:

$$i\left({\mathbf{x}}_{\mathrm{d}}\right)=\alpha g\left({\mathbf{x}}_{\mathrm{d}}\mid \mathbf{0},{\sigma }_{\mathrm{sig}}\right)+\left(1-\alpha \right)g\left({\mathbf{x}}_{\mathrm{d}}\mid \mathbf{0},{\sigma }_{\mathrm{bkg}}\right),$$ 10

where g(x_d∣0, σ) is a centred Gaussian function and σ_sig is kept fixed following the calibration procedure. Finally, the map of weights α(x_s) is applied to the APR image to remove the background.

The total computation time is 1 h 30 min for a 2,000 × 2,000 × 25 dataset on a computer equipped with an 8-core CPU (3.6 GHz) and 32 GB of RAM.

s²ISM

The first step is to simulate the PSFs of the microscope. To this end, we need to estimate the orientation and rotation of the detector array, the magnification of the system and the position of the out of-focus-plane (Supplementary Note A.6). Other parameters required to simulate the PSFs are easily found from the design of the experiments (excitation wavelength, numerical aperture and so on). Once all the required parameters are known, we numerically simulated the PSFs using the BrightEyes-ISM Python package⁴². We set the size of the simulation box adaptively to contain the full PSFs at every axial plane. We estimated the temporal IRFs h(t, x_d) as the average of multiple (~10⁴) experimental recordings of the scattering of a gold bead. Finally, we combined the PSFs with the IRFs as follows:

$$h_k\left(t,{\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right)=h_k\left({\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right)h\left(t\mid {\mathbf{x}}_{\mathrm{d}}\right)$$ 11

and normalized them such that

$$\sum _t\sum _{{\mathbf{x}}_{\mathrm{d}}}\sum _{{\mathbf{x}}_{\mathrm{s}}}{h}_k\left(t,{\mathbf{x}}_{\mathrm{s}},{\mathbf{x}}_{\mathrm{d}}\right)=1,$$ 12

where k ∈ 1, 2 is the depth index.

The last step consists of the image reconstruction, which is carried out by applying the following iterative rule:

$$o_k^{\left(m+1\right)}\left(t,{\mathbf{x}}_{\mathrm{s}}\right)=o_k^{\left(m\right)}\left(t,{\mathbf{x}}_{\mathrm{s}}\right)\sum _{{\mathbf{x}}_{\mathrm{d}}}{h}_k\left(-t,-{\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right)*\frac{i\left(t,{\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right)}{{\sum }_k{o}_k^{\left(m\right)}\left(t,{\mathbf{x}}_{\mathrm{s}}\right)*h_k\left(t,{\mathbf{x}}_{\mathrm{s}}\mid {\mathbf{x}}_{\mathrm{d}}\right)},$$ 13

where m is the iteration index and * is the convolution operator with respect to the coordinates t and x_s. The out-of-focus reconstruction o₂ is discarded and the in-focus image o₁ is the final result. We stop the algorithm at an arbitrary number of iterations. To avoid noise amplification, we iterate at most 20 times the reconstruction of experimental images.

Using GPU parallelization, the computation time is 1 s per iteration for a 2,000 × 2,000 × 25 dataset on a computer equipped with an 8-core CPU (3.6 GHz), 32 GB of RAM and a GPU with 8 GB of dedicated RAM. Without GPU parallelization on the same hardware, the computation time is 15 s per iteration.

Phasor calibration and analysis

The signal f(t) acquired by the DFD system for each scan and detector coordinate is

$$f\left(t\right)=d\left(t\right)*h\left(t\right),$$ 14

where d(t) is the fluorescence decay and h(t) is the IRF. The corresponding phasor F is given by the complex conjugate of the Fourier transform, evaluated at ω = 2πf_exc. Using the convolution theorem and writing the result in exponential form, we have

$$F=m_{\mathrm{F}}{\mathrm{e}}^{\mathrm{i}{\varphi }_{\mathrm{F}}}=\left(m_{\mathrm{D}}\cdot m_{\mathrm{H}}\right)\exp \left[\mathrm{i}\left({\varphi }_{\mathrm{D}}+{\varphi }_{\mathrm{H}}\right)\right],$$ 15

where m and ϕ are the magnitude and phase of the corresponding phasor, respectively. The phasor of the IRF $m_{\mathrm{H}}{\mathrm{e}}^{\mathrm{i}{\varphi }_{\mathrm{H}}}$ can be estimated indirectly from a sample with a known decay or directly by measuring an almost-instantaneous response, such as that of a quenched fluorophore or a reflective sample. We preferred the latter strategy, being less error prone. We used the backscattering signal from a gold bead, which provides a very good SNR. However, excitation and scattered light have the same wavelength, and we had to measure the signal without removing all the spectral filters. We cleaned the signal from multiple reflections by multiplying the IRFs with a rectangular window centred at the centroid of the IRF and with a length of 4 ns. Finally, we used the DFD acquisition system’s extra channel (laser trigger) to set a common reference frame for all the measurements. In practice, we subtract the phase φ of the reference channel to the phase of the corresponding phasor. Finally, the complete calibration procedure is

$${\varphi }_{\mathrm{D}}\left({\mathbf{x}}_{\mathrm{s}},{\mathbf{x}}_{\mathrm{d}}\right)={\varphi }_{\mathrm{F}}\left({\mathbf{x}}_{\mathrm{s}},{\mathbf{x}}_{\mathrm{d}}\right)-{\varphi }_{\mathrm{H}}\left({\mathbf{x}}_{\mathrm{d}}\right)+{\phi }_{\mathrm{H}}-{\phi }_{\mathrm{F}},$$ 16

$$m_{\mathrm{D}}\left({\mathbf{x}}_{\mathrm{s}},{\mathbf{x}}_{\mathrm{d}}\right)=m_{\mathrm{F}}\left({\mathbf{x}}_{\mathrm{s}},{\mathbf{x}}_{\mathrm{d}}\right)/m_{\mathrm{H}}\left({\mathbf{x}}_{\mathrm{d}}\right).$$ 17

The above procedure is a Wiener deconvolution performed in frequency space. The s²ISM algorithm inherently compensates for the effect of the IRF by performing a temporal deconvolution. Thus, when calculating the phasor from the decays reconstructed by the s²ISM method, there is no need to reconsider the effect of IRF and the calibration is performed only by correcting the phase with the reference channel (ϕ_H = 0 and m_H = 1). Furthermore, the result of s²ISM is a single image, and the dependency from x_d is lost. To calculate the phasor of the corresponding CLSM image, we also removed the dependency of x_d by temporally aligning and summing the decays and the IRFs. Then, we analysed the result as in a single-channel scenario.

Once the magnitude and phase for each pixel are calculated, we can estimate the lifetime map using the following equations, derived using the assumption that the fluorescence dynamics consists of a single-exponential decay:

$${\tau }_{\varphi }=\frac{1}{2\mathrm{\pi }{f}_{\mathrm{exc}}}\tan \left({\varphi }_{\mathrm{D}}\right),{\tau }_{\mathrm{m}}=\frac{1}{2\mathrm{\pi }{f}_{\mathrm{exc}}}\sqrt{\frac{1}{m_{\mathrm{D}}^2}-1}.$$ 18

If the above assumption holds true, the two estimates should match. In practice, the lifetime estimated using the phasor’s magnitude is more robust and less sensitive to miscalibrations. Therefore, we used this to calculate the lifetime values for this work.

Samples

Argolight calibration slide

We used the Argo-SIM v1 slide (Argolight). In detail, we imaged two patterns. The first is the resolution target of gradually spaced lines rotated by 45°. The second is a 3D crossing stair axially spaced by 250 nm.

Cerebellum slice

Thy1-EGFP transgenic mouse brain is fixed in 4% paraformaldehyde in phosphate-buffered saline (PBS; w/v) overnight at 4 °C. Then, 300–350-μm vibratome sections were generated by sectioning tissues embedded in 2% agarose with a vibrating microtome (Leica) and permeabilized in 2% Triton X-100 in PBS (v/v) for 1 day at 35 °C. RapiClear 1.52 (SunJin Lab) was used to clear sections according to the manufacturer’s instructions, and iSpacer (SunJin Lab) was applied to the sample mounting.

Cell culture

We cultured HeLa cells in Dulbecco’s modified Eagle’s medium (Gibco, Thermo Fisher Scientific) supplemented with 10% foetal bovine serum (Sigma-Aldrich) and 1% penicillin–streptomycin (Sigma-Aldrich) at 37 °C in 5% CO₂. The day before the staining, we seeded HeLa cells on coverslips in a 12-well plate (Corning) for immunostaining or a μ-Slide eight-well plate (ibidi) for live-cell imaging.

Fixed cells

HeLa cells were fixed with either ice methanol, when cytoskeletal proteins were imaged, for 20 min at –20 °C, or with a solution of 3.7% paraformaldehyde (Sigma-Aldrich) in PBS (Gibco, Thermo Fisher Scientific) buffer for 15 min at room temperature. Cells were washed three times with PBS buffer and treated with a blocking buffer (5% bovine serum albumin (Sigma-Aldrich) supplemented with 0.2% Triton X-100 in PBS buffer) for 1 h at room temperature. Cells were incubated with primary antibodies diluted in the blocking buffer for 1 h at room temperature. The primary antibodies used in this study were monoclonal mouse anti-α-tubulin antibody (1:1,000, Sigma-Aldrich), rabbit polyclonal anti-lamin B1 antibody (Abcam, ab16048, 1:500), rabbit polyclonal Nup-153 antibody (Abcam, ab84872, 1:500) and mouse monoclonal anti-ATP synthase β antibody (Sigma, A9728, 1:250). After incubation with the antibody, cells were washed three times with the blocking buffer and incubated with a secondary antibody diluted into the blocking buffer for 1 h at room temperature. The secondary antibodies used in this study were anti-mouse IgG-abberior STAR RED (abberior, 1:1,000), anti-mouse IgG-abberior STAR 635P (abberior, 1:1,000), anti-rabbit IgG Alexa 488 (Thermo Fisher Scientific, 1:1,000) and anti-mouse IgG Alexa 647 (Thermo Fisher Scientific, 1:500). We rinsed HeLa cells three times in PBS for 15 min. Finally, we mounted the coverslips onto microscope slides (Avantor, VWR International) with ProLong Diamond Antifade Mountant (Invitrogen, Thermo Fisher Scientific).

Live cells

For the mitochondrial staining in living cells, seeded HeLa cells were incubated with MitoTracker Orange (Thermo Fisher Scientific) at a concentration of 100 nM in Dulbecco’s modified Eagle’s medium supplemented with 10% foetal bovine serum and 1% penicillin–streptomycin for 10 min at 37 °C in 5% CO₂. After incubation, cells were washed three times with PBS and placed in a live-cell imaging solution (Thermo Fisher Scientific) immediately before the measurement.

Zebrafish embryo handling and preparation

The zebrafish line used has a fluorescent protein (eGFP) encoded at the 3′ end of the lap3b gene, which is expressed under the control of the β-acting promoter (β-actin:LAP2B-EGFP). This results into a labelled nuclear envelope. Zebrafish were maintained and raised under standard conditions, and embryos were collected immediately on fertilization. The chorion was chemically removed by incubating the embryos for 3 min in Pronase (1.5 mg ml^–1, Sigma-Aldrich, 107433), diluted in 0.3× Danieau’s buffer, after which the embryos were allowed to develop to a high stage at 28 °C in 0.3× Danieau’s buffer. Embryos were fixed in 4% (w/v) paraformaldehyde in PBST (PBS 1× supplemented with Tween 20 at pH 7.4; Sigma-Aldrich) at 4 °C overnight. Fixed embryos were washed three times with PBST and deyolked manually with forceps. The embryos were kept in a blocking buffer solution (4% bovine serum albumin in PBST) for 1 h at room temperature. Embryos were then dehydrated by incubating them in 50% methanol and then 100% methanol in PBST and incubated overnight at –20 °C. To continue, embryos were rehydrated gradually into the blocking buffer. Embryos were finally mounted in VECTASHIELD Antifade Mounting Medium with 4,6-diamidino-2-phenylindole (Vector Laboratories, VC-H-1200-10) before imaging.

Ethics statement

Zebrafish were maintained and raised under standard conditions according to Swiss regulations (Canton Vaud, license no. VD-H28). Protocols are put in place for the generation of transgenic lines and genotyping of adult individuals (License VDG0003). Embryos were collected immediately on fertilization and fixed with 4% (w/v) paraformaldehyde at the high stage. At the developmental stage of the present work (less than 5 days), the zebrafish embryos did not fall under the Animal Welfare Act.

Online content

Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at 10.1038/s41566-025-01695-0.

Author contributions

A.Z. conceived the idea and designed the study. A.Z. developed the theoretical model. A.Z. and G.G. developed the code for the data analysis. M.D. developed the microscope control software and firmware. A.Z. built the ISM device and performed the experiments. S.Z. and E.P. prepared the biological samples. N.V. provided the zebrafish embryos. A.Z., G.G. and G.V. wrote the manuscript. G.V. supervised the project. All authors discussed the results and commented on the manuscript.

Peer review

Peer review information

Nature Photonics thanks Weisong Zhao and the other, anonymous, reviewer(s) for their contribution to the peer review of this work

Data availability

The experimental data generated for this study are available via Zenodo at 10.5281/zenodo.11284050 (ref. ⁵⁹).

Code availability

The Python code used to perform image processing is available via GitHub at https://github.com/VicidominiLab/s2ISM.

Competing interests

G.V. has a personal financial interest (co-founder) in Genoa Instruments, Italy. The other authors declare no competing interests.

Extended data

is available for this paper at 10.1038/s41566-025-01695-0.

Supplementary information

The online version contains supplementary material available at 10.1038/s41566-025-01695-0.