## Parallelized STED microscopy using tailored speckles

[N. Bender et al., arxiv, 2007.15491 (2020)]

Super-resolution fluorescence microscopy techniques, such as stimulated emission depletion (STED), rely on depleting fluorescence around a region smaller than the limit of diffraction. This can be achieved with a doughnut-shaped beam that is then scanned to produce an image. Such a process is time-consuming. Structured illumination techniques were proposed to parallelize the process by having multiple zeros of the field in the same image, for example with an array of doughnut beams. However, it typically limits optical sectioning as the field conserves its shape for quite large distances along the axial direction. One way to overcome this limitation is to use speckle patterns. Speckle exhibits numerous singularities, allowing parallelization of the technique, and they rapidly and non-repeatably change along the axial direction, guarantying the optical sectioning while being robust to aberrations. The issue is that speckle singularities (optical vortices) are not isotropic, leading to distortions of the image. In the present paper, N. Bender and co-authors use wavefront shaping to design ideal speckle patterns for non-linear microscopy to achieve isotropic and uniform super-resolution.

In a nutshell, STED microscopy relies on the local depletion of fluorescence when the optical intensity reaches a given threshold. If the threshold is reached everywhere but in a small region, once we switch off the depletion beam, we know that fluorescence can only come from this particular region. This can be achieved using a doughnut-shaped beam.  Because the thresholding effect is intrinsically non-linear, this region can be made smaller than the diffraction limit. By scanning the beam, we add up the image information from small areas and recreate a super-resolution image.

In order to parallelize the process without deteriorating the image, we need:

1. to have multimode dark spots in a globally brighter field,
2. to have the distance between these spots greater than the diffraction limit,
3. to have isotropic shapes of these dark spots.

Typical speckle patterns are the result of random interferences and follow a typical Rayleigh distribution of the intensity :

$$p(I) \propto e^{{I}/{\left\langle I\right\rangle}}$$

with $$p(I)$$ the probability of having an intensity $$I$$ and $$\left\langle I\right\rangle$$ the mean intensity.

As the probability of the intensity decrease with the intensity, we globally have few bright spots over a globally dark pattern (the highest probability is for $$I=0$$). This is not optimal for STED microscopy as we want only a few regions not to be depleted. To avoid high exposure times or high depletion beam intensities, it is better to have a globally high intensity with few dark spots. In Fig 1. the authors show the photoconversion strength (fluorescence efficiency) after illumination with a Rayleigh speckle pattern for two exposure times. Due to the high probability of low intensities, the regions where fluorescence is not depleted have snake-like shapes connecting the optical vortices.

Figure 1. Rayleigh speckle. Intensity pattern of the depletion beam (left) and photoconversion efficiency for increasing exposure times (center and right).

In [Y. Bromberg and H. Cao, Phys. Rev. Lett., 112 (2014)], Y. Bromberg and H. Cao previously demonstrated that using a phase-only spatial light modulator, one can create speckle patterns that do not follow the Rayleigh statistics. It is, for instance, possible to create speckles with a high probability of having an intensity close to the average one and a low probability for low intensities. The intensity distribution of the tailored speckle is shown in Fig 2. (left). Interestingly, such speckle patterns also have the property of having a smaller correlation width in the transverse direction (Fig 2. right) and also in the axial direction, which could lead to better optical sectioning.

Figure 2. Distribution of speckle intensity (left) and spatial correlation (right).

For the same parameters as for the Rayleigh speckle, tailored speckles lead to smaller and more isotropic areas where the fluorescence has not been depleted, as shown in Fig 3.