G. Guattari

Bessel-Gauss beams

Abstract A new type of solution of the paraxial wave equation is presented. It encompasses as limiting cases both the diffraction-free beam and the gaussian beam. The propagation features of this solution are discussed.

An example of a Collett-Wolf source

Abstract It is shown that a Collett-Wolf source can be produced starting from a spatially incoherent source and using a collimating lens and an amplitude filter. The results of an experiment testing this prediction are reported.

Beam coherence-polarization matrix

We present an approach for describing the properties of a quasi-monochromatic, beam-like field that is both partially polarized and partially coherent from the spatial standpoint. It is based on the use of a single matrix, called the beam coherence-polarization matrix, whose elements have the form of mutual intensities. This approach, which can be viewed as an approximate form of Wolfs general tensorial theory of coherence, appears to be very simple, yet it is able to cover significant aspects of the beam behaviour that would not be accounted for by a scalar theory or by a local polarization matrix approach. A peculiar interference law applying to mutual intensities is derived. We show through simple examples how this approach leads to distinguish fields that would appear identical in a scalar treatment or in a local polarization matrix description. Hints for extensions are given.

Modal expansion for J0-correlated Schell-model sources

Abstract We evaluate the modes for a Schell-model planar source whose degree of spectral coherence is a Bessel function of zero order and whose optical intensity distribution is an arbitrary circularly symmetric function. These modes are shown to be connected with certain fields recently described as diffraction-free beams.

Coherent-mode decomposition of partially polarized, partially coherent sources

It is shown that any partially polarized, partially coherent source can be expressed in terms of a suitable superposition of transverse coherent modes with orthogonal polarization states. Such modes are determined through the solution of a system of two coupled integral equations. An example, for which the modal decomposition is obtained in closed form in terms of fully linearly polarized Hermite Gaussian modes, is given.

Observation of optical redshifts and blueshifts produced by source correlations

Abstract Frequency shifts of the optical spectra emitted by a pair of suitably correlated small sources have been recently predicted by Wolf and demonstrated experimentally in the acoustic domain by Bocko, Douglass and Knox. We show that a small modification in the form of the correlation functions used by Wolf leads to a model of the correlated pair that can be easily synthesized in the optical domain. The results of experimental tests exhibiting redshifts and blueshifts are presented.

Shannon number and degrees of freedom of an image

Abstract The problem of the determination of the number of significant degrees of freedom of an image is considered. The equivalence with the Shannon number is shown to hold with a great generality.

Holographic Methods for Painting Diagnostics

A holographic method for detecting detached regions between the priming layers and the underlying wood support in panel paintings is described. Experimental results obtained by the application of the method both on laboratory models and on an ancient Italian panel painting are presented. The great advantages that this technique can offer to the conservation and restoration of works of art are emphasized.

Intensity-based modal analysis of partially coherent beams with Hermite–Gaussian modes

Many partially coherent beams are made up of a superposition of mutually uncorrelated Hermite-Gaussian modes. We prove that knowledge of the transverse intensity profile of such a beam is sufficient for evaluating the weights of the modes in an exact way. Simulations indicate that the proposed method resists noise well.

Coherence and the spatial distribution of intensity

We address the following problem: Can two wave fields with different coherence properties produce the same optical intensity everywhere in the space? Limiting ourselves to paraxial propagation, we prove that in the one-dimensional case the answer is negative. On the other hand, in the two-dimensional case we show through examples that the answer is affirmative. Some consequences are discussed.