Resolution and super‐resolution

Abstract

Many papers have claimed the attainment of super-resolution, i.e. resolution beyond that achieved classically, by measurement of the profile of a feature in the image. We argue that measurement of the contrast of the image of a dark bar on a bright background does not give a measure of resolution, but of detection sensitivity. The width of a bar that gives an intensity at the center of the bar of 0.735 that in the bright region (the same ratio as in the Rayleigh resolution criterion) is λ/(13.9×numerical aperture) for the coherent case with central illumination. This figure, which compares with λ/(numerical aperture) for the Abbe resolution limit with central illumination, holds for the classical case, and so is no indication of super-resolution. Theoretical images for two points, two lines, arrays of lines, arrays of bars, and grating objects are compared. These results can be used a reference for experimental results, to determine if super-resolution has indeed been attained. The history of the development of the theory of microscope resolution is outlined.

Optical nanoscopy

“…1. As recently argued by Sheppard [6] "the use of the word "limit" implies a definite and sudden transition from being resolved to not being resolved, in consideration of the original sentence reported by Abbe "Die physikalische Unterscheidungsgrenze dagegen hängt allein vom Oeffnungswinkel ab und ist dem Sinus seines halben Betrages proportional." translated as "The physical limit of resolution, on the other hand, depends wholly on angular aperture, and is proportional to the sine of half the angular aperture."…”

“…translated as "The physical limit of resolution, on the other hand, depends wholly on angular aperture, and is proportional to the sine of half the angular aperture." [6,7]. The lens is the key element of the Abbe's experiment.…”

A joint Richardson—Lucy deconvolution algorithm for the reconstruction of multifocal structured illumination microscopy data

“…A detailed analysis of this approach is presented in [16]. Furthermore, since every single pixel acts as an almost closed pinhole one retains the resolution-doubling potential of confocal microscopy described in [13] and in the previous section, however without inherent loss of signal. Scanning the confocal spot across the whole field of view and repeating this reassignment procedure at all beam positions creates the final super-resolved image.…”

“…In this variant multiple diffraction limited spots, rather than sinusoidal illumination patterns, are used to achieve super-resolution and the pixels on a widefield detector act as tiny pinholes, akin to a parallelised version of confocal microscopy. In fact, MSIM is the parallelised version of image scanning (confocal) microscopy, ISM [12], which uses the inherent super-resolving potential of confocal microscopy to double image resolution, when the detection pinhole is nearly closed [13]. For these reasons, the conventional algorithm for MSIM reconstruction [11] uses a confocal image formation model:…”

A Review of Ghost Imaging via Sparsity Constraints

“…Image resolution is always an important issue in various fields of scientific researches and engineering applications, many great work and discussions of resolution have been made by researchers. For conventional imaging technologies, which is based on the point-to-point correspondence between the object and the image planes, the resolution can be accurately analyzed with the transmission function of the imaging systems [103,104]. However, for imaging systems based on the wavefront random phase modulation [20,64,[105][106][107][108], since the point-to-point correspondence doesn't exist anymore, their resolution ability is difficult to be directly obtained from the transmission function, but can be obtained by analyzing the high-order correlation of light fields.…”