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.

Infrared spectra of C2H2 under jet-cooled and para-H2 matrix conditions

In spectra of jet-cooled C2H2 recorded with an FTIR spectrometer, the ν5, ν4 + ν5, ν3 and ν2 + ν4 + ν5 bands all exhibit an intensity distribution corresponding to ∼6 K for rotation, with no evidence of nuclear spin conversion. Spectra of C2H2 isolated in solid p-H2 show no evidence of rotation of C2H2. The strong interaction between ν3 and ν2 + ν4 + ν5 in the gas phase is diminished in solid p-H2. Lines associated with dimer, trimer and tetramer of C2H2 are identified. Spectral features characteristic of solid state acetylene are observed under jet-cooled conditions. © 2007 Elsevier B.V. All rights reserved.

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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Properties of the protein matrix revealed by the free energy of cavity formation.

The classical picture of the hydrophobic stabilization of proteins invokes a resemblance between the protein interior and nonpolar solvents, but the extent to which this is the case has often been questioned. The protein interior is believed to be at least as tightly packed as organic crystals, and was shown to have very low compressibility. There is also evidence that these properties are not uniform throughout the protein, and conflicting views exist on the nature of sidechain packing and on its influence on the properties of the protein.

Optical spectroscopyof matrix-isolated halogenated fullerenes

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