Beyond the diffraction limit

Abstract

In a comment on resolution in light microscopy¹, Stelzer makes some misleading, if not erroneous, points. His claim to have himself demonstrated the relationship between Abbe's diffraction limit and Heisenberg's uncertainty principle is surprising: this relationship is readily derived from the Fourier theory. The resolution criterion that he seeks to convey is more perplexing: in his description of Dyba and Hell's work², Stelzer ignores the fact that the resolution of any recording system, whether optical or of any other type, is determined by the span of signal frequencies transferred. The higher the transferred frequencies, the finer are the details and the better is the resolution.

Main

A standard way to determine these frequencies and the resolution of a microscope — or of any other signal-recording instrument — is to record the instrument's responses to point- or step-like objects. The responses observed by Dyba and Hell² are clearly of the subdiffraction type, with frequencies beyond the diffraction barrier; they are object-independent by definition. In contrast to Stelzer's view, Dyba and Hell's images, including that of Bacillus megaterium, do not imply a priori information about the sample. The distance between the bacterial membranes is therefore not relevant for proving that the diffraction barrier has been broken.