Localization precision of stochastic optical localization nanoscopy using single frames

Abstract

The Cramer-Rao lower bound (CRLB) on localization precision of unbiased estimators is analyzed for stochastic optical localization nanoscopy that localizes emitters frame by frame independently. It is found that the CRLB is a function of the mean number of detected photons per emitter, signal to Poisson noise ratio, signal to Gaussian noise ratio, point spread function (PSF), pixel size, and relationship of emitter locations. With a slight and practical approximation, effect of Gaussian noise is equivalent to increasing the mean photon count of Poisson noise by a number equal to the variance of Gaussian noise. Numerical examples demonstrate that the CRLB of emitters located on a curve increase fast as the distance of adjacent emitters increases. The mean CRLB of randomly uniformly distributed emitters in both two-dimensional and three-dimensional imaging increases exponentially fast as the emitter density increases. The effects of PSF, standard deviation of PSF, mean number of detected photons per emitter, signal to noise ratio, axial thickness, and pixel size on the CRLB are also numerically investigated. The analytical and numerical results provide a guideline for the design of location estimators and a benchmark for the achievable localization precision of stochastic optical localization nanoscopy.