Phase optimisation for structured illumination microscopy.

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.