Super-resolution in confocal scanning microscopy

Bertero, M.; Brianzi, Paola; Pike, E. R.

doi:10.1088/0266-5611/3/2/006

Cited by 70 publications

(57 citation statements)

References 6 publications

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“…. , tN then, as in similar problems [7,8], one has to invert a linear operator transforming a function f into a finite-dimensional vector:…”

Section: Discrete Datamentioning

confidence: 99%

“…As in [7,8] it is easy to prove that, when N tends to infinity and the distance between adjacent points tends to zero (in the case (2.18) that means A-+ 1) in such a way that tN -+ CO, then the kernel (2.16) converges uniformly to the kernel (2.6) and therefore from some perturbatkve lemmas for compact operators [20] it follows that the singular values a N , k converge to a k and the singular functions u N , k converge (in the norm o f L 2 ) to u k .…”

Section: (220)mentioning

confidence: 99%

“…The case of a bounded support of the data and of discrete data can be treated as in [7,8]. In these papers we mainly considered the case where P ( y ) is a gamma distribution.…”

Section: Inversion In Weighted Spacesmentioning

confidence: 99%

“…As in our previous work on Laplace transform inversion [ 7 ] and Fraunhofer diffraction [SI we consider two data-point distributions: the first is a set of equidistant points:…”

mentioning

confidence: 99%

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Particle size distributions from spectral turbidity: a singular-system analysis

Bertero¹,

Mol²,

Pike³

1986

Inverse Problems

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Abstract. The problem of the inversion of spectral turbidity measurements to obtain distributions of droplet size in polydisperse aerosols is considered by introducing a recently developed generalised theory of information based on singular-system analysis. In this work we limit ourselves to the anomalous scattering approximation but give for this case an extensive treatment, with examples, of the reconstruction of the distribution as a continuous function in both weighted and unweighted L 2 spaces from finite sampled data sets. The methods are entirely parallel to those already used successfully in the related problems of particle size distribution by photon correlation spectroscopy and by Fraunhofer diffraction.

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“…. , tN then, as in similar problems [7,8], one has to invert a linear operator transforming a function f into a finite-dimensional vector:…”

Section: Discrete Datamentioning

confidence: 99%

Section: (220)mentioning

confidence: 99%

“…The case of a bounded support of the data and of discrete data can be treated as in [7,8]. In these papers we mainly considered the case where P ( y ) is a gamma distribution.…”

Section: Inversion In Weighted Spacesmentioning

confidence: 99%

“…As in our previous work on Laplace transform inversion [ 7 ] and Fraunhofer diffraction [SI we consider two data-point distributions: the first is a set of equidistant points:…”

mentioning

confidence: 99%

See 2 more Smart Citations

Particle size distributions from spectral turbidity: a singular-system analysis

Bertero¹,

Mol²,

Pike³

1986

Inverse Problems

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“…In two recent papers', 2 we proposed a method for enhancing resolution in confocal scanning microscopy. 3 First we summarize the main points of the procedure in the case of a onedimensional optical system with ideal lenses.…”

mentioning

confidence: 99%

Analytic inversion formula for confocal scanning microscopy

1987

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We find a simple analytic expression for the inverse of an operator related to the problem of data reduction in confocal scanning microscopy. Potential applications of this result to the practical scanning-microscope problem are outlined.In two recent papers', 2 we proposed a method for enhancing resolution in confocal scanning microscopy. 3 First we summarize the main points of the procedure in the case of a onedimensional optical system with ideal lenses. Letf(y) be the complex effective transparency (or reflectivity for a reflection microscope) in the object plane; by this we mean that, for a given scanning position, the image g(x) formed by an ideal microscope with a uniformly filled illumination lens is g(x) = J sinc(x -y)sinc(y)f(y)dy,

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Three‐dimensional DNA image cytometry by confocal scanning laser microscopy in thick tissue blocks

et al. 1991

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A method for the quantification of nuclear DNA in thick tissue blocks by confocal scanning laser microscopy is presented. Tissues were stained en bloc for DNA by chromomycin A3. Three-dimensional images, 60 Fm deep, were obtained by stacking up confocal fluorescent images obtained with an MRC-BOO (Bio-Rad, Richmond, CA). The effects due to bleaching and attenuation by depth of fluorescence emission were corrected mathematically. The DNA contents were estimated by summing up the detected emission intensities (discretized into pixel gray levels) from each segmented nucleus. Applications to an adult rat liver and to a human in situ carcinoma of theesophagus are shown to demonstrate, respectively, the precision of the method and its potential usefulness in histopathology. Comparisons are made with DNA histograms obtained on the same materials by image cytometry on smears and by flow cytometry. Ploidy peaks obtained with the confocal method, although wider than with other methods, are well separated. Confocal image cytometry offers the invaluable advantage of preserving the tissue architecture and therefore allowing, for instance, the selection of histological regions and the evaluation of the degree of heterogeneity of a tumor.Key terms: DNA cytometry, confocal laser microscopy, histology, 3-D There is a considerable interest in DNA cytometry, notably because of the importance of searching for correlations of nuclear DNA content with cancer prognosis in individual patients (e.g., 22, 40, 62).The two methods commonly used a t present for nuclear DNA content analysis, image cytometry (ICM) and flow cytometry (FCM), are not devoid of limitations. Observing the tissue architecture may be important in identifying regions for cytometry and, therefore, the main shortcoming of ICM on smears or imprints and of FCM is obviously that they do not allow the study of DNA contents in situ. Even ICM on histological sections does not allow this, as the tissue structure is observed in projection and the resulting nuclear profiles are usually either incomplete if the section is thin or overlapping if the section is thick enough to include a sufficient proportion of complete nuclei. Finally, preparation procedures for ICM and FCM may produce a selection bias of a given cell type (9) and/or nuclear debris (27).'This paper is an expanded version of a work presented at the

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Super-resolution in confocal scanning microscopy

Cited by 70 publications

References 6 publications

Particle size distributions from spectral turbidity: a singular-system analysis

Particle size distributions from spectral turbidity: a singular-system analysis

Analytic inversion formula for confocal scanning microscopy

Three‐dimensional DNA image cytometry by confocal scanning laser microscopy in thick tissue blocks

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