Polarization-shifting method for step interferometry

Phaseless Antenna Characterization by Effective Aperture Field and Data Representations

Abstract: The problem of antenna characterization from phaseless near-field data is addressed by appropriate use of the available information on the Antenna Under Test (AUT) and on the scanning geometry to provide efficient representations for both the unknowns and the data. Such a strategy allows improving the reliability and the accuracy of the proposed characterization algorithm and, at the same time, shortens the overall measurement process. An extensive numerical and experimental analysis, together with a comparison with existing approaches, endorses the algorithm reliability and accuracy and confirms its usefulness for antennas having a general radiating (vector) behavior, i.e., either focusing or non-focusing.

Visualization of two-dimensional phase gradients by subtraction of a reference periodic pattern.

Abstract: We describe a simple method for visualization of phase objects The phase object is placed between a printed two-dimensional periodic pattern and a CCD camera The ray deflection that is due to the phase object distorts the image of the pattern This image is subtracted from a reference image and then, by squaring and low-pass filtering, a measurement of the two-dimensional refractive-index changes is obtained Because the optical system does not require special alignment or illumination, the method presented has potential application for detection of gas leaks in industrial environments

Composition law for polarizers

Abstract: The polarization process when polarizers act on an optical field is studied. We give examples for two kinds of polarizers. The first kind presents an anisotropic absorption—as in a Polaroid film—and the second one is based on total reflection at the interface with a birefringent medium. Using the Stokes vector representation, we determine explicitly the trajectories of the wave light polarization during the polarization process. We find that such trajectories are not always geodesics of the Poincare sphere as is usually thought. Using the analogy between light polarization and special relativity, we find that the action of successive polarizers on the light wave polarization is equivalent to the action of a single resulting polarizer followed by a rotation achieved, for example, by a device with optical activity. We find a composition law for polarizers similar to the composition law for noncollinear velocities in special relativity. We define an angle equivalent to the relativistic Wigner angle which can be used to quantify the quality of two composed polarizers.

Robust one-beam interferometer with phase-delay control.

Abstract: A robust one-beam interferometer with external phase-delay control is described. The device resembles a Mach-Zehnder interferometer in which the two arms are together in one collimated beam. However, the proposed device is not an amplitude-division interferometer but a wave-front division one. The phase-delay control occurs at the interferometer output with the help of two polarizing beam splitters, a quarter-wave plate, a Faraday rotator, and a polarizer. An additional phase delay is introduced by application of an electrical current to the Faraday rotator or by rotation of the polarizer (the latter is of topological origin), which permits the use of techniques of phase-stepping interferometry.

Achromatic wavefront forming with space-variant polarizers: Application to phase singularities and light focusing

Abstract: We investigate the polarization-to-phase conversion of space-variant polarized light waves. Our analysis can be considered as an extension of Pancharatnam's phase to the case of space-variant polarization. In two particular cases - azimuthally and radially variant polarization - we found striking consequences. Using an azimuthally variant polarizer combined with a circular analyzer, it is possible to induce spin-to-orbital angular momentum exchange and to generate optical vortices of arbitrary charge. Radially variant polarizers with linear or quadratic radial dependence of the transmission direction generate nondiffracting beams or focus light, respectively. Our results are potentially relevant for the design of achromatic wavefront forming (and correcting) elements based strictly on space-variant polarization optics.

Quantal phase factors accompanying adiabatic changes

Abstract: A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiar dynamical phase factor. An explicit general formula for γ(C) is derived in terms of the spectrum and eigenstates of Ĥ(R) over a surface spanning C. If C lies near a degeneracy of Ĥ, γ(C) takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy. As an illustration γ(C) is calculated for spinning particles in slowly-changing magnetic fields; although the sign reversal of spinors on rotation is a special case, the effect is predicted to occur for bosons as well as fermions, and a method for observing it is proposed. It is shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor.

Optical Shop Testing

Abstract: Fringe scanning techniques, now renamed heterodyning or phase shift interferometry, are covered in a completely rewritten chapter. New chapters have been added to cover wavefront fitting and evaluation as well as holographic and Moire methods. The chapter on parameter measurements has been completely rewritten and an appendix added suggesting appropriate tests for typical optical surfaces.

V Phase-Measurement Interferometry Techniques

Abstract: Publisher Summary This chapter describes the phase-measurement interferometry techniques. For all techniques, a temporal phase modulation is introduced to perform the measurement. By measuring the interferogram intensity as the phase is shifted, the phase of the wavefront can be determined with the aid of electronics or a computer. Phase modulation in an interferometer can be induced by moving a mirror, tilting a glass plate, moving a grating, rotating a half-wave plate or analyzer, using an acousto-optic or electro-optic modulator, or using a Zeeman laser. Phase-measurement techniques using analytical means to determine phase all have some common denominators. There are different equations for calculating the phase of a wavefront from interference fringe intensity measurements. The precision of a phase-measuring interferometer system can be determined by taking two measurements, subtracting them, and looking at the root-meansquare of the difference wavefront. The chapter discusses the simulation results. The elimination of the errors that reduce the measurement accuracy depends on the type of measurement being performed. Phase-measurement interferometry (PMI) can be applied to any two-beam interferometer, including holographic interferometers. Applications can be divided into: surface figure, surface roughness, and metrology.

Digital wave-front measuring interferometry: some systematic error sources.

Abstract: Digital wave-front measuring interferometry is a well-established technique but only few investigations of systematic error sources have been carried out so far. In this work three especially serious error sources are discussed in some detail: inaccuracies of the reference phase values needed for this type of evaluation technique; disturbances due to extraneous fringes; and spatially high frequency noise on the wave fronts caused by dust particles, inhomogeneities, etc. For the first two error sources formulas of the resulting phase deviation are derived and compensation possibilities discussed and experimentally verified. To study the occurrence of wave-front irregularities caused by dust particles a model has been developed and countermeasures derived which assure sufficient regularity of contour line plots. The repeatability of the present experimental setup was better than λ/200 within the 3σ limits.

The Adiabatic Phase and Pancharatnam's Phase for Polarized Light

Abstract: In 1955 Pancharatnam showed that a cyclic change in the state of polarization of light is accompanied by a phase shift determined by the geometry of the cycle as represented on the Poincare sphere. The phase owes its existence to the non-transitivity of Pancharatnam's connection between different states of polarization. Using the algebra of spinors and 2 × 2 Hermitian matrices, the precise relation is established between Pancharatnam's phase and the recently discovered phase change for slowly cycled quantum systems. The polarization phase is an optical analogue of the Aharonov-Bohm effect. For slow changes of polarization, the connection leading to the phase is derived from Maxwell's equations for a twisted dielectric. Pancharatnam's phase is contrasted with the phase change of circularly polarized light whose direction is cycled (e.g. when guided in a coiled optical fibre).