Polarization-state analyzer

In this section we present a general theory for the measurement of polarization characteristics of light, Stokes vector, Mueller matrix, and optimization procedures for minimizing time and errors of measurement. Stokes vector for a beam of light is determined by carrying out a series of measurements for the intensity of light transmitted through a set of polarization elements. Fig. 1. shows the polarization state analyzer (PSA). 

Polarization modulation ellipsometers use a photo-elastic modulator to modulate the state of polarization of the incident beam. Polarizer and analyzer are fixed during the measurement. Eourier analysis of the time dependent signal gives the ellipse-... 

Fig. 3—Measurement of surface by HDI surface reflectance analyzer. In electromagnetic radiation (light), the polarization direction is defined as the direction of the electric field vector. The incident polarization of the light can be controlled. The instrument uses a variety of detectors to analyze the reflected polarization state of the light. (U.S. Patent 6,134,011). (a) Plane of the disk The SRA uses a fixed 60 degree (from the surface normal) angle of incidence. The plane of incidence is the same as the paper plane (b) Pit on a surface detected by reflected light channels of HDI instrument (c) Scratches on disk surface measured by HDI surface reflectance analyzer (d) Particles on the surface of disk detected by reflected light (black spot) and by scattered light (white spot) [8].

Measurement of reflectances for incident light of various polarization states and two oblique angles of incidence the results are analyzed with the Fresnel formulas. Large angles are required for high accuracy, and this requires large sample surfaces. 

We list in Table 13.1 all the possible measured irradiances (for unit incident irradiance) with a polarizer before the scattering medium and an analyzer before the detector. The light transmitted by an ideal polarizer Ps is polarized in state s R and L denote right-circular and left-circular polarization and L denote light polarized parallel and perpendicular to the scattering plane + and — denote light polarized obliquely to the scattering plane at +45° and — 45°. U denotes the absence of a polarizer or analyzer if U is indicated as... 

For the infrared circular polarization devices and techniques are not as readily available as e.g. in the visible range. Suitable retarders exist which exhibit virtually achromatic quarterwave behaviour from well above 4000 cm to about 700 cm (Korte et al., 1988), Sec. 3.2.3. Being based on internal total reflection they deviate the beam, nevertheless they render possible to take Fourier-transform spectra of a sample irradiated with circular polarized radiation as well as to analyze the polarization state of radiation... 

Elmer Photoelectric Polarimeter, Model 141. Optical rotatory dispersion measurements were made either with the Perkin-Elmer instrument equipped with a Bausch and Lomb High Intensity Grating Monochromator, or with a manual spectropolarimeter constructed by Kirschner and co-workers (1) at Wayne State University. This instrument has been modified by replacing the calcite polarizing and analyzing prisms with quartz prisms and changing light source to a 500-watt Hanovia Xenon Arc Lamp. 

To analyze this effect, we use HWP2 to rotate the polarization states by 45°. Under this operation,... 

In the volume case, the particle system is illuminated by a monochromatic plane wave whose propagation direction is along the Z-direction. In the surface case, the incident wave direction forms an angle Oi with respect to the surface normal and it is contained in the Z-Yplane. The scattered intensity is analyzed in the plane Z-Y (scattering plane) as shown in Fig. 1. We consider two linear polarization states of the incident field. The incident wave is 5-polarized when the electric field vibrates parallel to the X axis, and it is P-polarized when the electric field vibrates within the YZ plane. Similarly, we consider two polarization states for the scattered field The co-polarized case when both incident and scattered field have the same polarization states SS or PP) and the cross-polarized case when both fields are perpendicular to each other SP ox PS). 

As shown in Figure 8.12(a), under normal view the absorption axes of polarizer (point P) and analyzer (point A) are located at 90° and -90° on the equator of Poincare sphere, respectively. Point T, the polarization state of the hnearly polarized hght after the polarizer, overlaps exactly with point A, the absorption axis of the analyzer, resulting in complete light absorption and no light leakage from normal viewing direction. 

The detail compensation mechanism is explained using the Poincare sphere shown in Figure 8.23(b). When the unpolarized light from backlight source passes the polarizer (point P), it becomes linearly polarized and its polarization state is located at point T, which deviates from the absorption axis of the analyzer (point A). Then, such a linearly polarized light (point T)... 

The polarization contrast method (POL) is suitable for surfaces with structures that alter the polarization state of the light when it is reflected. When the analyzer and polarizer are crossed, optically anisotropic phases can be distinguished from optically isotropic phases. By eliminating troublesome lens reflections - which impair the clarity of the image - it is possible to increase the image contrast, even when examining polished sections of low reflectivity. 

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