User:Charleschris/Structured illumination microscopy

Structured Illumination Microscopy (SIM) is a super-resolution imaging technique that enables optical resolution beyond the diffraction limit of light. SIM works by encoding high spatial frequency information of the sample into low frequency signals, which can then be recovered through image processing. This is achieved by illuminating the sample with a patterned light source, typically a sinusoidal pattern generated by the interference of two beams. The resulting interference pattern, known as a Moiré pattern, has a lower spatial frequency than the illumination pattern. By capturing multiple images of the sample with varying pattern orientations, phases and modulation depths, a set of low-frequency images can be obtained that encodes high-frequency information.

The de-facto standard configuration of SIM dates back to Gustafsson (2000), in which a sinusoidal illumination pattern, also known as stripe or fringe pattern, is cycled through three phases and three orientations for a total of nine unique patterns. The techinique has since been widely adopted in biological and materials science research as a powerful tool for studying sub-diffraction structures.

The diffraction limit of an imaging system is described by the optical transfer function (OTF), which represents the transmittable bandwidth of spatial frequency. SIM achieves super-resolution by shifting high spatial frequencies into the accessible passband of the OTF. The OTF is the Fourier transform of the point spread function (PSF), which is the blur kernel in direct space.

The fluorescent response of the sample can then be modelled by the multiplication of the sample structure and the illumination pattern intensity. The final image is formed after blurring by the PSF and addition of white Gaussian noise. By using the convolution theorem, the image formation model can be represented mathematically in the frequency space.

The SIM formalism is relatively standard, and many research studies have been published on various aspects of this technique, such as optimization of pattern design, data processing methods, and applications to various samples. Some examples of these studies include "Superresolution structured illumination microscopy: principles and practice" by Lal et al. (2016) and "Structured illumination microscopy for superresolution imaging in biology" by Gustafsson (2008).

In summary, SIM is a powerful super-resolution imaging technique that enables the study of sub-diffraction structures. By encoding high spatial frequency information of the sample into low frequency signals, SIM overcomes the diffraction limit of light, and has proven to be a valuable tool in biological and materials science research.