New data inversion formulae in confocal scanning microscopy

Whereas the resolving power of an ordinary optical microscope is determined by the classical Rayleigh distance, significant super-resolution, i.e. resolution improvement beyond that Rayleigh limit, has been achieved by confocal scanning light microscopy. Furthermore is has been shown that the resolution of a confocal scanning microscope can still be significantly enhanced by measuring, for each scanning position, the full diffraction image by means of an array of detectors and by inverting these data to recover the value of the object at the focus. We discuss the associated inverse problem and show how to generalize the data inversion procedure by allowing, for reconstructing the object at a given point, to make use also of the diffraction images recorded at other scanning positions. This leads us to a whole family of generalized inversion formulae, which contains as special cases some previously known formulae. We also show how these exact inversion formulae can be implemented in practice.

Super-resolution in confocal scanning microscopy: generalized inversion formulae

It was shown in previous papers that the resolution of a confocal scanning microscope can be significantly improved by measuring, for each scanning position, the full diffraction image and by inverting these data to recover the value of the object at the confocal point. In the present work, the authors generalize the data inversion procedure by allowing, for reconstructing the object at a given point, to make use of the data samples recorded at other scanning positions. This leads them to a family of generalized inversion formulae, either exact or approximate. Some previously known formulae are re-derived here as special cases in a particularly simple way.

Inversion from redundant data

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Resolution enhancement by data inversion techniques

Chapter 15

Iterative inversion of experimental data in weighted spaces

We present iterative algorithms for solving linear inverse problems with discrete data and compare their performances with the method of singular function expansion, in view of applications in optical imaging and particle sizing.

Inversion of light scattering data by singular system analysis

We consider the problem of inverting experimental data obtained in light scattering experiments described by linear theories. We discuss applications to particle sizing and we describe fast and easy-to-implement algorithms which permit the extraction, from noisy measurements, of reliable information about the particle size distribution. © 1987, SPIE.

The Use of Singular Systems and other Inversion Methods in Weighted L2- spaces

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Particle sizing by inversion of extinction data

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A new inversion procedure for confocal scanning microscopy and other bandlimited signal processing problems

We find a simple analytic expression for the inverse of an infinite matrix related to the problem of data reduction in confocal scanning microscopy and other band-limited signal processing problems. Potential applications of this result to practical problems are outlined. The matrix arises from a sampling expansion approach to the integral equation.

Clinical Spectrum, risk factors and outcome of immune reconstitution inflammatory syndrome in patients with tuberculosis-HIV coinfection.

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Infrared light on molecule-molecule and molecule-surface collisions

By analyzing measured infrared absorption of pure CH4 gas under both "free" (large sample cell) and "confined" (inside the pores of a silica xerogel sample) conditions we give a demonstration that molecule-molecule and molecule-surface collisions lead to very different propensity rules for rotational-state changes. Whereas the efficiency of collisions to change the rotational state (observed through the broadening of the absorption lines) decreases with increasing rotational quantum number J for CH4-CH4 interactions, CH4-surface collisions lead to J-independent linewidths. In the former case, some (weak) collisions are inefficient whereas, in the latter case, a single collision is sufficient to remove the molecule from its initial rotational level. Furthermore, although some gas-phase collisions leave J unchanged and only modify the angular momentum orientation and/or symmetry of the level (as observed through the spectral effects of line mixing), this is not the case for the molecule-surface collisions since they always change J (in the studied J=0-14 range).

First High-Resolution Analysis of the Absorption Spectrum of Propane in the 6.7-7.5 μm Spectral Region

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Experimental and density functional theory study of the vibrational properties of 2-mercaptobenzimidazole in interaction with gold

The vibrational properties of the 2-mercaptobenzimidazole (MBI) molecule in interaction with gold were examined by a combined approach of FTIR measurements and density functional theory (DFT). A complete assignment of the 42 normal modes of MBI has been performed on the basis of DFT calculations at the B3PW91 level in complement to the Raman and FTIR spectra. Calculations demonstrated that, on the deprotonated MBI molecule, the negative charge is localized on the sulfur atom, favoring the formation of a gold-sulfur bond upon reaction of MBI with gold. This was confirmed by the very good agreement between the calculated spectrum and the experimental spectra of different gold-MBI compounds, indicating that the vibrational properties of adsorbed MBI are chiefly determined by the coordination through the sulfur atom. © 2006 American Chemical Society.

Reply to the comment on 'The dispersed laser induced fluorescence spectrum of gas phase C60 at 308 nm'

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