Unified resolution bounds for conventional and stochastic localization fluorescence microscopy.

Superresolution microscopy enables imaging in the optical far field with ~20 nm-scale resolution. However, classical concepts of resolution using point-spread and modulation-transfer functions fail to describe the physical limits of superresolution techniques based on stochastic localization of single emitters. Prior treatments of stochastic localization microscopy have defined how accurately a single emitter's position can be determined, but these bounds are restricted to sparse emitters, do not describe conventional microscopy, and fail to provide unified concepts of resolution for all optical methods. Here we introduce a measure of resolution, the information transfer function (ITF), that gives physical limits for conventional and stochastic localization techniques. The ITF bounds the accuracy of image determination as a function of spatial frequency and for conventional microscopy is proportional to the square of the modulation-transfer function. We use the ITF to describe how emitter density and photon counts affect imaging performance across the continuum from conventional to superresolution microscopy, without assuming emitters are sparse. This unified physical description of resolution facilitates experimental choices and designs of image reconstruction algorithms.