Resolution and super‐resolution

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.

[1]  Colin J. R. Sheppard,et al.  Information capacity and resolution in an optical system , 1986 .

[2]  W. Talbot.  Facts relating to optical science , 1836 .

[3]  W. Lukosz.  Optical Systems with Resolving Powers Exceeding the Classical Limit , 1966 .

[4]  Lord Rayleigh,et al.  On the Theory of Optical Images, with Special Reference to the Microscope , 1903 .

[5]  C. Sheppard,et al.  Image Formation in the Scanning Microscope , 1977 .

[6]  T Wilson,et al.  The theory of the direct‐view confocal microscope , 1981, Journal of microscopy.

[7]  D. W. Rosebrugh.  Notes on Resolving Power , 1949 .

[8]  C. Sheppard.  Optical resolution and the spatial frequency cut-off , 1984 .

[9]  Tony Wilson,et al.  SUPER-RESOLUTION BY CONFOCAL FLUORESCENT MICROSCOPY , 1982 .

[10]  Y. Ichioka,et al.  Influence of Light Coherence at the Exit Pupil of the Condenser on the Image Formation , 1976 .

[11]  Lester Curtis.  The Limits of the Optical Capacity of the Microscope , 1877, The American journal of dental science.

[12]  Colin J. R. Sheppard,et al.  Equivalent of the point spread function for partially coherent imaging , 2015 .

[13]  L. Rayleigh.  Investigations in optics, with special reference to the spectroscope , 1880 .

[14]  Colin J. R. Sheppard,et al.  Information capacity and resolution in three-dimensional imaging , 2003, International Commission for Optics.

[15]  J. NelsonDugarte.  Die Lehre von der Bildentstehung im Mikroskop von Ernst Abbe , 1911, Nature.

[16]  M. Davidson,et al.  Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics , 2015, Science.

[17]  C. Sheppard,et al.  Resolution of aplanatic solid immersion lens based microscopy. , 2012, Journal of the Optical Society of America. A, Optics, image science, and vision.

[18]  H. H. Hopkins,et al.  The Influence of the Condenser on Microscopic Resolution , 1950 .

[19]  Zengbo Wang,et al.  Optical virtual imaging at 50 nm lateral resolution with a white-light nanoscope. , 2011, Nature communications.

[20]  Colin J. R. Sheppard,et al.  Image Formation in Scanning Microscopes with Partially Coherent Source and Detector , 1978 .

[21]  H. Fripp.  On the Limits of the Optical Capacity of the Microscope , 1876 .

[22]  Colin J. R. Sheppard,et al.  Imaging by a high aperture optical system , 1993 .

[23]  R. Sec..  XV. On the theory of optical images, with special reference to the microscope , 2009 .

[24]  Richard Barakat,et al.  Line Spread Function and Cumulative Line Spread Function for Systems with Rotational Symmetry , 1964 .

[25]  W. J. Bates.  The Theory of the Microscope , 1968 .

[26]  H. Köhler,et al.  On Abbe's Theory of Image Formation in the Microscope , 1981 .

[27]  P. Marquet,et al.  Marker-free phase nanoscopy , 2013, Nature Photonics.

[28]  Lord Rayleigh.  On the Theory of Optical Images, with Special Reference to the Microscope , 1903 .

[29]  H. Hopkins.  On the diffraction theory of optical images , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[30]  C W McCutchen,et al.  Superresolution in microscopy and the Abbe resolution limit. , 1967, Journal of the Optical Society of America.

[31]  Alan Boyde,et al.  Tandem scanning reflected light microscopy: a new method for in vitro assessment of dental operative procedures and restorations , 1987 .

[32]  R. K. Luneburg,et al.  Mathematical Theory of Optics , 1966 .

[33]  Laura Waller,et al.  Standardizing the resolution claims for coherent microscopy , 2016, Nature Photonics.

[34]  Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung , 1873 .

[35]  W. Lukosz,et al.  Optischen Abbildung Unter Überschreitung der Beugungsbedingten Auflösungsgrenze , 1963 .

[36]  Nonvolatile two-color photorefractive holographic recording in In:Ce:Cu:LiNbO3 , 2003 .