Generalized low-pass filtering in structured illumination microscopy and spatial domain reconstructions with high signal-to-noise ratio.

Structured illumination microscopy (SIM) is a technique that employs non-uniform illumination to shift spatial frequencies that are normally unobservable into the non-zero region of the optical transfer function (OTF). Several differently illuminated images are combined to reconstruct these high spatial frequencies, yielding an up to two-fold increase in resolution beyond the diffraction limit. The reconstruction quality is affected by the noise level which depends on the specific procedure. In this work, we show that least-squares Fourier domain reconstruction results in the best possible theoretically achievable SSNR and thus can serve as a metric for reconstruction quality. We consider, in a general manner, how the choice of low-pass filtering in the reconstruction procedure affects the spectral signal-to-noise ratio (SSNR) in the reconstructed image. Finally, we present fast real-space reconstruction procedures that demonstrate near-optimal noise performance.