Evaluating resolution in live cell structured illumination microscopy

In the last decade, several different structured illumination microscopy (SIM) approaches have been developed. Precise determination of the effective spatial resolution in a live cell SIM reconstructed image is essential for reliable interpretation of reconstruction results. Theoretical resolution improvement can be calculated for every SIM method. In practice, the final spatial resolution of the cell structures in the reconstructed image is limited by many different factors. Therefore, assessing the resolution directly from the single image is an inherent part of the live cell imaging. There are several commonly used resolution measurement techniques based on image analysis. These techniques include full-width at half maximum (FWHM) criterion, or Fourier ring correlation (FRC). FWHM measurement requires fluorescence beads or sharp edge/line in the observed image to determine the point spread function (PSF). FRC method requires two stochastically independent images of the same observed sample. Based on our experimental findings, the FRC method does not seem to be well suited for measuring the resolution of SIM live cell video sequences. Here we show a method based on the Fourier transform analysis using power spectral density (PSD). In order to estimate the cut-off frequency from a noisy signal, we use PSD estimation based on Welch's method. This method is widely used in non-parametric power spectra analysis. Since the PSD-based metric can be computed from a single SIM image (one video frame), without any prior knowledge of the acquiring system, it can become a fundamental tool for imaging in live cell biology.