Light Lattice Structured Illumination Microscopy

Abstract

Structured illumination microscopy (SIM) is a super resolution technique that bypasses the traditional diffraction limit. This is achieved by shining a spatially periodic illumination pattern onto a sample, which reveals finer details because high spatial frequencies can be downshifted within the optical transfer function (OTF) support of the imaging system. During the image reconstruction process, it is the convention to neglect the so-called noise matrix. The noise matrix describes the amount of cross-talk between Fourier orders, however, the simplification ignores the cross-talk by assuming that this matrix can be approximated by M=I. This assumption is made to reduce the computational load and processing time, but it comes at the potential cost of image quality.

This thesis studies the validity of the suboptimal filter assumption for a range of light lattice configurations, including conventional SIM, plus shaped light lattices and unit cell grid layouts. By comparing analytical bounds, such as the Kantorovich inequality and the Bounding Theorem, against exact spectral signal-to-noise ratio (SSNR) numerical calculations, this research has concluded that analytical bounds are often too loose to properly represent the physical system. Consequently, numerical analysis is done. The numerical results are that for sparse lattice configurations, such as 2D conventional SIM and plus shaped light lattices, the simplification is highly valid since the noise matrix is strongly diagonally dominant. This means there is minimal penalty and the SSNR ratio remains above 0.8 across all spatial frequencies. However, for dense lattices, such as high pitch unit cell grids, significant cross-talk occurs between orders. This invalidates the simplification with image quality penalties of upwards of 50% to 60% near cutoff. Furthermore, as the lattice pitch approaches infinity, the system converges to the image scanning microscopy (ISM) limit, where using the exact noise matrix becomes essential to obtaining image clarity.