Phase optimisation for structured illumination microscopy

Abstract

Structured illumination microscopy can achieve super-resolution in fluorescence imaging. The sample is illuminated with periodic light patterns, and a series of images are acquired for different pattern positions, also called phases. From these a super-resolution image can be computed. However, for an artefact-free reconstruction it is important that the pattern phases be known with very high precision. If the necessary precision cannot be guaranteed experimentally, the phase information has to be retrieved a posteriori from the acquired data. We present a fast and robust algorithm that iteratively determines these phases with a precision of typically below λ/100. Our method, which is based on cross-correlations, allows optimisation of pattern phase even when the pattern itself is too fine for detection, in which case most other methods inevitably fail. We analyse the performance of this method using simulated data from a synthetic 2D sample as well as experimental single-slice data from a 3D sample and compare it with another previously published approach.

Three-dimensional structured illumination microscopy using Lukosz bound apodization reduces pixel negativity at no resolution cost

“…Apodization with the 3D Lukosz-bound does not require fine-tuning of any free parameters in the apodization function, such as taking it to a power other than one, as is sometimes done with the triangular apodization function [23]. Note that raising the 3D Lukosz-bound to a power smaller than one would violate the non-negativity criteria.…”

“…First, we extracted the spatial frequency bands using the methods developed by Wicker and Heintzmann [22][23][24]. Second, we obtained the final image using the filters described in section 2.1 with the 3D Lukosz-bound based on SO(3) rotations as apodization functionĈ (v).…”

“…The images are linear combinations of shifted band-passed images. These band-passed images can be recovered by an inversion algorithm [22][23][24]:…”

“…(6), v lm = v + R l · q m is the band-shifted spatial frequency vector,B lm (v) = s m w mĤ (v lm ) denotes the ideal or desired response of the imaging system, κ the regularization parameter, A (v) the regularization weight function,Ĉ (v) the apodization function, andĝ (v) a data misfit weight function, that can be used to suppress the hexagonal imprint artifact that is typical for SIM [23]. A Gaussian data misfit function can be chosen:…”

“…A triangular apodization is typically used in practice, which is commonly created using a distance transform [11,23]. In this case the apodization function becomes:…”