The research in super resolution following the main direction pointed out by Toraldo di Francia in 1952 and later experimentally continued by his collaborators, led us to investigate the formation of images by a small spherical lens in series with the conventional microscope. Following the principle of reverse interference postulated by Toraldo di Francia and using numerical procedures mostly based on Fourier analysis image, components have been separated in different regions of the frequency spectrum of the wavefronts imaged by the microscope: (i) In the background there is a speckle pattern that has been statistically analyzed. This pattern follows the classical statistics developed by Goodman and has a correlation radius that follows the classical Airy’s Fraunhofer diffraction pattern of a circular aperture. (ii) In the image is also present a systems of multiple interference fringes that are independent from the presence of the particle, since these fringes can be seen in regions that are away from the particle cross-section. These fringes are originated in the regions of the optical path before the light enters the sphere. From a very extensive literature existing in this subject it is possible to conclude that these fringes are a consequence of the birefringence induced by residual stresses present in the surface of the prism and generated during the fabrication process. The residual stresses produce an effect equivalent to a phase diffraction grating. (iii) The diffraction pattern produced by the spherical particle does not follow predictions of classical optics. The diffraction pattern can be described very well by a Bessel series expansion introduced by Toraldo di Francia in his multiple corona scheme to modify the pupil entrance of an optical system to improve resolution. Analyzing the diffraction pattern is possible to conclude that illumination of the particle results from the eigen-modes of a micro-resonator formed by the optical elements supporting the sphere and the sphere itself. An intriguing relationship seems to exist between the observed diffraction patterns and the theoretical interference patterns for 2 and 4 photon entanglements. (iv) The image contains light pulses that can be attributed to the presence of particles in the space between the supporting surface and the sphere. There are spherical particles but there is a large number of prismatic particles. Interestingly enough these particles have width to height ratios that seem to match those predicted for sodium chloride nanocrystals on the basis of experimental and theoretical results by scientists in the area of physical chemistry. The observed images again are diffraction images that do not correspond to classical diffraction patterns. In summary, the presence of a small polystyrene sphere on the optical field of a conventional optical microscope seems to have converted the microscope into a nanoscope. This means that the near field generated by evanescent illumination can be sensed by a microscope. We have been able to detect particles in the range of few tens of nanometers. Above all we can say that Toraldo di Francia was right when he predicted that the resolution of an optical system could be increased up to a limit basically dictated by the energy that one can muster to put inside a very small region.

Optical detection of information at the sub-wavelength level

LAMBERTI, Luciano
2006

Abstract

The research in super resolution following the main direction pointed out by Toraldo di Francia in 1952 and later experimentally continued by his collaborators, led us to investigate the formation of images by a small spherical lens in series with the conventional microscope. Following the principle of reverse interference postulated by Toraldo di Francia and using numerical procedures mostly based on Fourier analysis image, components have been separated in different regions of the frequency spectrum of the wavefronts imaged by the microscope: (i) In the background there is a speckle pattern that has been statistically analyzed. This pattern follows the classical statistics developed by Goodman and has a correlation radius that follows the classical Airy’s Fraunhofer diffraction pattern of a circular aperture. (ii) In the image is also present a systems of multiple interference fringes that are independent from the presence of the particle, since these fringes can be seen in regions that are away from the particle cross-section. These fringes are originated in the regions of the optical path before the light enters the sphere. From a very extensive literature existing in this subject it is possible to conclude that these fringes are a consequence of the birefringence induced by residual stresses present in the surface of the prism and generated during the fabrication process. The residual stresses produce an effect equivalent to a phase diffraction grating. (iii) The diffraction pattern produced by the spherical particle does not follow predictions of classical optics. The diffraction pattern can be described very well by a Bessel series expansion introduced by Toraldo di Francia in his multiple corona scheme to modify the pupil entrance of an optical system to improve resolution. Analyzing the diffraction pattern is possible to conclude that illumination of the particle results from the eigen-modes of a micro-resonator formed by the optical elements supporting the sphere and the sphere itself. An intriguing relationship seems to exist between the observed diffraction patterns and the theoretical interference patterns for 2 and 4 photon entanglements. (iv) The image contains light pulses that can be attributed to the presence of particles in the space between the supporting surface and the sphere. There are spherical particles but there is a large number of prismatic particles. Interestingly enough these particles have width to height ratios that seem to match those predicted for sodium chloride nanocrystals on the basis of experimental and theoretical results by scientists in the area of physical chemistry. The observed images again are diffraction images that do not correspond to classical diffraction patterns. In summary, the presence of a small polystyrene sphere on the optical field of a conventional optical microscope seems to have converted the microscope into a nanoscope. This means that the near field generated by evanescent illumination can be sensed by a microscope. We have been able to detect particles in the range of few tens of nanometers. Above all we can say that Toraldo di Francia was right when he predicted that the resolution of an optical system could be increased up to a limit basically dictated by the energy that one can muster to put inside a very small region.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11589/22188
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