Analytic inversion formula for confocal scanning microscopy

Abstract

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,

Superresolving scanning optical microscopy using holographic optical processing

“…Thus the use of an imaging-lens pupil-plane mask of suitable form gives the same resultant transfer function as given by Eq. (10). In this way singular-system theory may be regarded as a means of designing an optimum imaginglens pupil function.…”

“…We can easily see that this hologram has the same effect if we note that, in Eq. (10), h(f ) is multiplied by fi 5 (-f ); that j5O(f ) has a limit of N/A; and that ho(x) is identical to the cosine form of h(x) within the band of fi,(f). The ability to achieve the enhanced resolution with a phase-only mask has important practical implications, because accurate phase structures are normally much easier to fabricate than accurate amplitude structures.…”

On the Limitations of the Confocal Scanning Optical Microscope as a Profilometer

“…This is mainly due to the advantage that this instrument offers over more conventional optical microscopes . Among other things, confocal instruments have better resolution than their conventional counterparts [1,2], and are adequate for the implementation of super-resolving schemes [3,4] . They also reject out-of-focus information that can deteriorate the images of thick objects [5], such as some biological specimens [6,7] .…”

Super-resolution in confocal scanning microscopy: II. The incoherent case

“…This équivalence is used in I for investigating the problem with discrète data and for Computing its singular system. In a subséquent paper [11] it was shown that the inverse of the infinite-dimensional matrix also has a very simple analytic expression. As far as we know, similar results do not hold true in the incohérent case and therefore we must Super-resolution in confocal scanning micwscopy: Il 449 find a numerical approach for the détermination of the singular System of the intégral operator (1.5).…”