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 2 × 2 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 Wolf's 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.

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On the basis of the modal theory of coherence, we study partially coherent sources whose modes belong to the class of Laguerre-Gauss functions for which the Laguerre polynomial has zero order. These modes present a phase profile with a helicoidal structure, which is responsible for notable phenomena, such as the propagation of optical vortices, beam twisting, and the presence of dislocations in interference patterns. By suitably choosing the eigenvalues associated with such modes, different partially coherent sources are obtained: sources with a flattened Gaussian profile, twisted Gaussian Schell-model sources with a saturated twist, and a new class of sources having an annular profile. Owing to the shape-invariance property of the underlying modes, the fields radiated by these sources do not change their transverse profile through propagation, except for scale and phase factors. We also prove that, if any such source is covered by a circularly symmetric filter, the new modal structure can be found in a straightforward manner

We propose a high-precision digital automated quantitative determination of the modulus of the complex degree of coherence. The Thompson and Wolf experiment is repeated, using a CCD and a measurement method based on the fast Fourier transform. The experimental results agree very well with the predictions of the theory.

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