Resolving Power and Information

Francia, G. Toraldo di

doi:10.1364/josa.45.000497

Cited by 287 publications

(93 citation statements)

References 3 publications

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“…The concept of "super-resolution" in microscopy was introduced in a 1955 paper by Toraldo di Francia [5], in which he defined super-resolution as the discrimination of details finer than the Abbe resolution limit. In the following, we shall use the term in this traditional, more general meaning to describe far field microscopy approaches allowing the analysis of structural details smaller than 200 nm [6,7].…”

Section: Introductionmentioning

confidence: 99%

Perspectives in Super-Resolved Fluorescence Microscopy: What Comes Next?

Cremer

Birk

2016

Front. Phys.

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Section: Introductionmentioning

confidence: 99%

Perspectives in Super-Resolved Fluorescence Microscopy: What Comes Next?

Cremer

Birk

2016

Front. Phys.

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“…The conventional space-bandwidth product has been of fundamental importance because of its interpretation as the number of degrees of freedom [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In most works, the space-bandwidth product, as its name implies, is the product of a spatial extent and a spatial-frequency extent.…”

Section: Introductionmentioning

confidence: 99%

Phase-space window and degrees of freedom of optical systems with multiple apertures

Özaktaş

Oktem

2013

J. Opt. Soc. Am. A

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We show how to explicitly determine the space-frequency window (phase-space window) for optical systems consisting of an arbitrary sequence of lenses and apertures separated by arbitrary lengths of free space. If the space-frequency support of a signal lies completely within this window, the signal passes without information loss. When it does not, the parts that lie within the window pass and the parts that lie outside of the window are blocked, a result that is valid to a good degree of approximation for many systems of practical interest. Also, the maximum number of degrees of freedom that can pass through the system is given by the area of its spacefrequency window. These intuitive results provide insight and guidance into the behavior and design of systems involving multiple apertures and can help minimize information loss.

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“…The conventional space-bandwidth product is of fundamental importance in signal processing and information optics because of its interpretation as the number of degrees of freedom of signals [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In this paper, we discuss the bicanonical width product, which generalizes the space-bandwidth product and which can often provide a tighter measure of the actual number of degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space–bandwidth product

Oktem

Özaktaş

2010

J. Opt. Soc. Am. A

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Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space-frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space-bandwidth product. The bicanonical width product, which is a generalization of the space-bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples.

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Resolving Power and Information

Cited by 287 publications

References 3 publications

Perspectives in Super-Resolved Fluorescence Microscopy: What Comes Next?

Perspectives in Super-Resolved Fluorescence Microscopy: What Comes Next?

Phase-space window and degrees of freedom of optical systems with multiple apertures

Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space–bandwidth product

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