# Super-resolution with lattice illumination

Microscopy is fundamentally limited in terms how small the details we can observe in a sample are. However, scientist have not stayed sit and much effort has been done into pushing this limit. This means fighting the very same properties of the light that both allow imaging as well as limit the smallest detail observable. Therefore, new microscopy techniques have been developed exploiting different tricks.

The pattern is created using lattice illumination on the sample and then an image is obtained using MUSICAL.

One of them is Structure Illumination Microscopy, referred most of the time as SIM [1]. This technique is based on illuminating the sample with a known periodic pattern (normally something simple as a sinusoidal one which looks like a series of parallel lines) at several positions and rotations without moving the sample. While every single image is limited in resolution as the imaging principle is the same, they contain different details of the sample. By combining the whole set and solving a set of equations using the illumination as one of the known variables, a new image is generated. In order for being able to keep the mathematics solvable, the illumination pattern is preferred to be simple. In it, details up to two times smaller to what is conventionally possible can be correctly visualized. But, can we do better? This is the challenge we set out to solve.

In SIM, the resolution improvement comes from the fact that every illumination pattern allows to capture a combination of the different details, even smaller than diffraction. And while the problem is then, decode them, these patterns themself are also limited in terms of how much details we can use in them as they are projected in the sample using optical elements such as lenses. So, there are essentially two problems: the patterns are limited by the system, and to solve the equations we need a precise knowledge of these patterns.

In a recent work conducted collaboratively between the nanoRIP team at UiT and the photonics team at Indian Institute of Technology, Delhi and reported in [2] these two problems are addressed. In the illumination side, interference of light was used to directly create the pattern (for example, a sinusoidal one) into the sample using a technique called lattice illumination. This allows projecting smaller details than in conventional SIM. Once these images were acquired, an alternative computational approach to decode the small features was used: they used MUSICAL [3] as the solver, an algorithm conventionally used in fluctuation-based microscopy. This algorithm does not require any knowledge of the pattern itself, which in practice means it allows blind reconstruction. By combining these two concepts the team demonstrated an increase of 6 times in resolution using beads (a sample composed by small particles), which shows the potential of lattice illumination as a way of achieving super-resolution.

**References**

- M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
- K. Samanta, S. Sarkar, S. Acuña, J. Joseph, B. S. Ahluwalia, and K. Agarwal, “Blind Super-Resolution Approach for Exploiting Illumination Variety in Optical-Lattice Illumination Microscopy,”
*ACS Photonics*8, 9, 2626–2634 (2021) - K. Agarwal and R. Macháň, “Multiple signal classification algorithm for super-resolution fluorescence microscopy,” Nat. Commun. 7(1), 13752 (2016)