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.

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

For pt.I see ibid. vol.3, p.195 (1987). The authors have shown that the resolution of a confocal scanning microscope can be improved by recording the full image at each scanning point and then inverting the data. These analyses were restricted to the case of coherent illumination. They investigate, along similar lines, the incoherent case, which applies to fluorescence microscopy. They investigate the one-dimensional and two-dimensional square-pupil problems and they prove, by means of numerical computations of the singular value spectrum and of the impulse response function, that for a signal-to-noise ratio of, say 10%, it is possible to obtain an improvement of approximately 60% in resolution with respect to the conventional incoherent light confocal microscope. This represents a working bandwidth of 3.5 times the Rayleigh limit.

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.

The musculature and associated innervation of adult and intramolluscan stages of Echinostoma caproni (Trematoda) visualised by confocal microscopy

Gross anatomy of muscle and sensory/motor innervation of adult and intramolluscan developmental stages of Echinostoma caproni have been investigated to ascertain the organisation and the functional correlates of any stage-specific patterns of staining. Using indirect immunocytochemistry to demonstrate neuroactive substances and the phalloidin-fluorescence technique for staining myofibril F-actin, the muscle systems and aminergic and peptidergic innervation of daughter rediae, cercariae, metacercariae, and pre- and post-ovigerous adults were examined and compared using confocal scanning laser microscopy. A complex arrangement of specific muscle fibre systems occurs within the body wall (composed of circular, longitudinal and diagonal fibres), suckers (radial, equatorial, meridional), pharynx (radial, circular), gut caeca (mainly circular), cercarial tail (circular, pseudo-striated longitudinal), and ducts of the reproductive system (circular, longitudinal), presumed to serve locomotor, adhesive, alimentary and reproductive functions. Immunostaining for serotonin (5-HT) and FMRFamide-related peptides (FaRPs) was evident throughout the central (CNS) and peripheral (PNS) nervous systems of all stages, and use of dual-labelling techniques demonstrated separate neuronal pathways for 5-HT and FaRP in both CNS and PNS. FaRP expression in the innervation of the ootype wall was demonstrated only in post-ovigerous worms and not in pre-ovigerous worms, suggesting an involvement of FaRP neuropeptides in the process of egg assembly. Comparison of the present findings with those recorded for other digeneans suggests that muscle organisation and innervation patterns in trematodes are highly conserved.