It is shown that, for an incoherent superposition of the orthogonally polarized laser beams, the vector singularities of a specific type arise at the transversal cross section of a paraxial combined beam instead of common singularities, such as amplitude zeros or optical vortices (inherent in scalar, i.e. homogeneously polarized, fields), and C points, where polarization is circular, and L lines, along which polarization is linear (inherent in completely coherent vector, i.e. inhomogeneously polarized fields). There are U lines (closed or closing at infinity) along which the degree of polarization equals zero and the state of polarization is undetermined, and isolated P points where the degree of polarization equals unity and the state of polarization is determined by the non-vanishing component of the combined beam. U surfaces and P lines correspond to such singularities in three dimensions, by analogy with L surfaces and C lines in three-dimensional completely coherent vector fields. P lines directly reflect the snake-like distortions of a wavefront of the singular component of the combined beam. Crossing of the U line (surface) is accompanied by a step-like change of the state of polarization onto the orthogonal one. U and P singularities are adequately described in terms of the complex degree of polarization with the representation at the Stokes space, namely at and inside of the Poincaré sphere. The conditions of topological stability of U and P singularities are discussed, as well as the peculiarities of the spatial distribution of the degree of polarization in the closest vicinity to such singularities. Experimental examples of reconstruction of the combined beam's vector skeleton formed by U and P singularities as the extrema of the complex degree of polarization are given. Comparison with the related investigations is provided.

Important part of this review is devoted to description of feasibilities for experimental measuring of coherence by measuring of spatial polarization distributions of www.intechopen.com Modern Metrology Concerns 264 inhomogeneously polarized fields. We represent the newest metrological tool connected with novel concept of optical currents (optical flows). Namely, we show that some intimate characteristics of complex optical fields with arbitrary degree of spatial coherence and arbitrary degree of polarization may be "deciphered" indirectly, by observation of the influence of such fields on embedded micto-and nanoparticles. This original metrological approach seems to be prospective for development of so-called optical traps and tweezers for manipulation of isolated particles of micro-and nanoscales. Separate section of the Chapter is devoted to application of local Stokes-polarimetry in diagnostics of biological tissues, in the context of early (pre-clinical) diagnostics of some widespread diseases. We represent both experimental and data processing techniques leading to high-sensitive and reliable diagnostics. All considered metrological approaches and techniques are original, generated by recently by the members of our team. Some prospects of further investigations in the direction represented in this Chapter, as well as necessity and possible ways for overcoming some present shortcomings of optical metrology in the field of coherence and polarization, are outlined in the last section.

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We report the feasibilities for revealing and diagnostics of unconventional phase singularities into optical fields, namely, the singularities of spatial coherence functions into partially coherent vortex beams. It is shown that the vortices of the spatial coherence function are comprehensively diagnosed through the strip version of the Thomas Young's interference experiment. Namely, the magnitude of a topological charge and its sign are determined, respectively, by the magnitude and the direction ofbending of the Young's interference fringes, which are produced by the edge diffraction waves from the rims of an opaque strip positioned in the vortex beam. Such experiment provides complete data on the azimuthal behavior of a phase of the spatial coherence function. On the other hand, non-localized ring singularities of the spatial coherence function and of the complex degree of coherence occurring in the radial distribution of a phase are detected through conventional Young's interference experiment with two pinholes at an opaque screen. It is remarkable that the last of the mentioned coherence phase singularities takes place, when amplitude zeroes of the field are absent. Instead of this, the modulus of the complex degree of coherence vanishes alone.