An interferometric method for measuring the two-dimensional distribution of the state of polarization (SOP) of light is presented. A pair of Savart plates, a half-wave plate, and an analyzer are inserted between the lenses of a double-diffraction imaging system, so that multiple interference fringes are generated over the video camera. The Fourier analysis of the image obtained from the video camera allows us to determine the two-dimensional distributions of the four Stokes parameters over the object plane. No mechanical or active components for polarization control are required and two dimensional distributions of any parameters related to SOP can be determined from the single image. Principle of this method is experimentally demonstrated by measuring the SOP distribution of the light transmitted by a liquid crystal cell.

Snapshot complete imaging polarimeter using Savart plates

A novel interferometric polarimeter capable of mapping a spatiotemporal change in the state of polarization (SOP) of light is described. The polarimeter has a reference beam of light with two orthogonal linearly polarized components that interfere with the counterpart components of an elliptically polarized signal beam. The resultant interference pattern is recorded by a computer by the use of a wideband metal-oxide semiconductor video camera. The interference pattern reduces to the ellipticity and azimuth of the ellipse at an instant of time, by which the spatiotemporal change in the SOP is mapped. No optical elements are used for the control of polarization in the polarimeter, and this allows for the mapping of a rapid change in the SOP. Successful experiments are demonstrated by generating an elliptically polarized beam whose SOP varies in space and time.

Contour mapping of the spatiotemporal state of polarization of light.

A development of two-dimensional birefringence distribution measurement system with a sampling rate of 1.3 MHz

In this paper, we reviewed our recent work on the statistical properties of polarization speckle, described by stochastic
Stokes parameters fluctuating in space. Based on the Gaussian assumption for the random electric field components and
polar-interferometer, we investigated theoretically and experimentally the statistics of Stokes parameters of polarization
speckle, including probability density function of Stokes parameters with the spatial degree of polarization, autocorrelation
of Stokes vector and statistics of spatial derivatives for Stokes parameters.

Statistics of polarization speckle: Theory versus experiment

We review some of the statistical properties of polarization-related speckle phenomena, with an introduction of a less known concept of polarization speckles and their spatial degree of polarization. As a useful means to characterize twopoint vector field correlations, we review the generalized Stokes parameters proposed by Korotkova and Wolf, and introduce its time-domain representation to describe the space-time evolution of the correlation between random electric vector fields at two different space-time points. This time-domain generalized Stokes vector, with components similar to those of the beam coherence polarization matrix proposed by Gori, is shown to obey the wave equation in exact analogy to a coherence function of scalar fields. Because of this wave nature, the time-domain generalized Stokes vector is referred to as generalized Stokes vector wave in this paper.

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Polarization speckles and generalized Stokes vector wave: A review

This paper describes a new photoelastic technique for the spatiotemporal stress analysis. In a polarimeter developed, an elliptically polarized signal beam of light, modulated in state of polarization by two-dimensional principal-stress distributions interferes with a reference beam of light consisting of orthogonal linearly polarized two components. A time-sequential series of two-dimensional interference patterns are received one after another by a MOS video camera, followed by a computer. Of the elliptically polarized signal beam, the orthogonal field components along the directions of the principal stresses in a two-dimensional photoelastic sample can be computed from a recorded interference pattern, which offer the data needer for mapping the spatiotemporal principal-stress distribution over the sample. Not only each of the two orthogonal principal stresses but also the principal-stress difference are mapped in a time-sequential diagram. No use of any movable polarization element such as a rotating analyzer allows us to follow a rapid change in stress distribution within the maximum frame rate 2066 s−1 of the MOS video camera.

K. Oka

Papers

Polarimetry for spatiotemporal photoelastic analysis