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.

Experimental investigation of thermal structures in regular three-dimensional falling films

Interfacial waves on the surface of a falling liquid film are known to modify heat and mass transfer. Under non-isothermal conditions, the wave topology is strongly influenced by the presence of thermocapillary (Marangoni) forces at the interface which leads to a destabilization of the film flow and potentially to critical film thinning. In this context, the present study investigates the evolution of the surface topology and the evolution of the surface temperature for the case of regularly excited solitary-type waves on a falling liquid film under the influence of a wall-side heat flux. Combining film thickness (chromatic confocal imaging) and surface temperature information (infrared thermography), interactions between hydrodynamics and thermocapillary forces are revealed. These include the formation of rivulets, film thinning and wave number doubling in spanwise direction. Distinct thermal structures on the films’ surface can be associated to characteristics of the surface topology.