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.

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.

Infrared light on molecule-molecule and molecule-surface collisions

By analyzing measured infrared absorption of pure CH4 gas under both "free" (large sample cell) and "confined" (inside the pores of a silica xerogel sample) conditions we give a demonstration that molecule-molecule and molecule-surface collisions lead to very different propensity rules for rotational-state changes. Whereas the efficiency of collisions to change the rotational state (observed through the broadening of the absorption lines) decreases with increasing rotational quantum number J for CH4-CH4 interactions, CH4-surface collisions lead to J-independent linewidths. In the former case, some (weak) collisions are inefficient whereas, in the latter case, a single collision is sufficient to remove the molecule from its initial rotational level. Furthermore, although some gas-phase collisions leave J unchanged and only modify the angular momentum orientation and/or symmetry of the level (as observed through the spectral effects of line mixing), this is not the case for the molecule-surface collisions since they always change J (in the studied J=0-14 range).