E. R. Pike

On the recovery and resolution of exponential relaxational rates from experimental data: Laplace transform inversions in weighted spaces

In three previous papers the authors have considered the problem of Laplace transform inversion when the unknown function is of bounded, strictly positive support. The improvement in resolution due to a priori knowledge of the support was quantified and methods for the choice of an optimum sampling of data were given. The authors discuss some undesirable edge effects encountered in practice with these methods and indicate a way to refine such calculations by considering the problem of Laplace transform inversion in weighted L2 spaces. A smoothly varying weight takes into account a partial knowledge of the localisation of the solution which can be estimated a priori from the knowledge of its first and second moments which are easily derived from the data before inversion. In such a way the reconstructed solution is forced to be small where it is likely to be small and the troublesome edge effects found in the previous methods are suppressed. The results show somewhat surprising improvements in typical inversions. The extensions of the method required for the analysis of sampled and truncated experimental data are also discussed and applied.

Super-resolution in confocal scanning microscopy. V. Axial super-resolution in the incoherent case

For pt.IV see ibid., vol.8, p.1 (1992) One of the basic properties of confocal scanning laser microscopy (CSLM) is the possibility of high axial resolution in the case of fluorescent objects. As a consequence 3D images of 3D objects can be obtained. In the previous papers of this series it has been demonstrated that an improvement of lateral resolution in CSLM (lateral super-resolution) can be obtained if, at each step of the scanning procedure, the full image is detected in the image plane and these data are inverted to estimate the object at the confocal point. In this paper we prove that the same data contain sufficient information for improving also the axial resolution of CSLM (axial super-resolution). The analysis is performed in the case of a simplified model, i.e. two-dimensional objects (one lateral plus one axial dimension) and lenses with a small numerical aperture.

New optical processor for super-resolution in confocal scanning microscopy

An optical processor is proposed in order to improve resolution in confocal scanning microscopy. It consists of a complex mask placed in the image plane followed by a Fourier lens. The design of the complex mask is based on the solution of a suitable integral equation. 1.