Far field calculation of distorted Gaussian beams.

Far field calculations of beams, such as laser beams, are often applied in optical engineering. Current beam propagation methods fail in certain range parameters due to high storage requirements of the algorithms. This paper presents a new beam propagation method for far field calculations of distorted Gaussian beams in a homogeneous medium including optical elements, such as lenses.

Simultaneous measurement of phase transmission and linear or circular dichroism of an object under test.

This publication presents a novel interferometric method for the simultaneous spatially resolved analysis of an object under test regarding the phase transmission function and the magnitude and orientation of dichroism. Analogous to the classical phase-shifting interferometry, the measurement strategy is based on the variation of phase and polarization in an interferometer. This procedure allows one to analyze simultaneously and spatially resolved the dichroic properties of the object and its impact on the phase of the incoming light in one measurement cycle.

Simultaneous measurement of phase transmission and birefringence of an object under test.

This paper presents a novel interferometric method for the simultaneous spatially resolved analysis of an object under test regarding the phase transmission function and the magnitude and orientation of the (uniaxial) birefringence. The measurement strategy is based on variations of the phase and polarization and processing the interference patterns so obtained. With this method, which is very similar to the classical phase-shifting interferometry, a complete analysis of birefringent properties of the object and its impact on the phase of the incoming light can be done in one measurement cycle.

Approach for the production chain of printed polymer optical waveguides-an overview.

Research for new production chains in the field of waveguide fabrication is a challenging task. Realizing a cost efficient manufacturing process allows integrating optical data communication in arbitrary structures, for example, the wing of an airplane or the body of a car. The production chain described in this paper contains the design, simulation, and fabrication process of printed polymer optical waveguides (POWs).

Adjustable diffractive spiral phase plates.

We report on the fabrication and the experimental demonstration of Moiré diffractive spiral phase plates with adjustable helical charge. The proposed optical unit consists of two axially stacked diffractive elements of conjugate structure. The joint transmission function of the compound system corresponds to that of a spiral phase plate where the angle of mutual rotation about the central axis enables continuous adjustment of the helical charge.

Incoherent averaging of phase singularities in speckle-shearing interferometry.

Interferometric speckle techniques are plagued by the omnipresence of phase singularities, impairing the phase unwrapping process. To reduce the number of phase singularities by physical means, an incoherent averaging of multiple speckle fields may be applied. It turns out, however, that the results may strongly deviate from the expected √N behavior.

Simultaneous measurement of phase and local orientation of linearly polarized light: implementation and measurement results.

Optical components manipulating both polarization and phase of wave fields find many applications in today's optical systems. With modern lithography methods it is possible to fabricate optical elements with nanostructured surfaces from different materials capable of generating spatially varying, locally linearly polarized-light distributions, tailored to the application in question. Since such elements in general also affect the phase of the light field, the characterization of the function of such elements consists in measuring the phase and the polarization of the generated light, preferably at the same time.

Observation of the geometric spin Hall effect of light.

The spin Hall effect of light (SHEL) is the photonic analogue of the spin Hall effect occurring for charge carriers in solid-state systems. This intriguing phenomenon manifests itself when a light beam refracts at an air-glass interface (conventional SHEL) or when it is projected onto an oblique plane, the latter effect being known as the geometric SHEL. It amounts to a polarization-dependent displacement perpendicular to the plane of incidence.

Phase-shifting Zernike phase contrast microscopy for quantitative phase measurement.

Zernike phase contrast microscopy is extended and combined with a phase-shifting mechanism to perform quantitative phase measurements of microscopic objects. Dozens of discrete point light sources on a ring are constructed for illumination. For each point light source, three different levels of point-like phase steps are designed, which are alternatively located along a ring on a silica plate to perform phase retardation on the undiffracted (dc) component of the object waves.

Diffractive simultaneous bidirectional shearing interferometry using tailored spatially coherent light.

Measurements of wavefront deformations can be carried out with the help of lateral shearing interferometers. Here the focus is on a setup providing two shears along orthogonal directions simultaneously to generate the data needed for a reconstruction. We describe a diffractive solution using Ronchi phase gratings with a suppressed zeroth order for both the doubling of the wavefront under test and the bidirectional shearing unit.

Flexible beam shaping system using fly's eye condenser.

Normally, fly's eye condensers are used to homogenize light. However, in the case of fully coherent light, a fly's eye condenser, in connection with some simple optical elements, such as a diffractive axicon, a grating, and a telescope, can be used as a quite flexible beam shaping system, forming arrays of rings, parts of rings, or other structures with varying diameters. We present the principle, some simulation results, and some first experimental results.

Effect of fabrication errors on the diffraction pattern produced by sawtooth gratings.

In this work we investigate, analytically and numerically, the effect on the diffracted field produced by typical fabrication errors in sawtooth gratings. The analysis is carried out for the near and far field, showing the effects on the intensity and on the diffraction orders efficiency. When the grating profile is not perfect but presents a curved profile or overdevelopment error, some different diffraction orders appear, changing the intensity and the efficiency of each order.

Phase-shift extraction for generalized phase-shifting interferometry.

A simple algorithm for blind extraction of phase shifts is proposed for generalized phase-shifting interferometry from only three interferograms. Based on the statistical property of the object wave, the algorithm calculates approximately the involved phase shifts as initial values. The extraction is further improved by an iterative method, considering the fact that the closer the phase shifts approach their real values, the more uniform the reconstructed reference wave will become.

Interferometric quasi-absolute tests for aspherics using a radial shear position.

Increasing accuracy requirements in aspheric metrology make the development of absolute testing procedures for aspheric surfaces important. One strategy is transferring the standard practice three-position test for spheres to aspherics. The three-position test, however, involves a cat's eye position and therefore has certain drawbacks.

Transverse angular momentum and geometric spin Hall effect of light.

We present a novel fundamental phenomenon occurring when a polarized beam of light is observed from a reference frame tilted with respect to the direction of propagation of the beam. This effect has a purely geometric nature and amounts to a polarization-dependent shift or split of the beam intensity distribution evaluated as the time-averaged flux of the Poynting vector across the plane of observation. We demonstrate that such a shift is unavoidable whenever the beam possesses a nonzero transverse angular momentum.

Interferometric null test of a deep parabolic reflector generating a Hertzian dipole field.

We report on interferometric characterization of a deep parabolic mirror with a depth of more than five times its focal length. The interferometer is of Fizeau type; its core consists of the mirror itself, a spherical null element, and a reference flat. Because of the extreme solid angle produced by the paraboloid, the alignment of the setup appears to be very critical and needs auxiliary systems for control.

Design considerations for the absolute testing approach of aspherics using combined diffractive optical elements.

Aspheric optical surfaces are often tested using diffractive optics as null elements. For precise measurements, the errors caused by the diffractive optical element must be calibrated. Recently, we reported first experimental results of a three position quasi-absolute test for rotationally invariant aspherics by using combined-diffractive optical elements (combo-DOEs).

Achieving Gaussian outputs from large-mode-area higher-order-mode fibers.

We describe an alternative to fiber-gratings for converting higher-order LP(0m) (m>1) fiber modes into a nearly fundamental Gaussian shape at the output of a fiber. This schematic enables the use of light propagation in higher-order modes of a fiber, a fiber-platform that has recently shown great promise for achieving very large mode areas needed for future high-power lasers and amplifiers. The conversion will be done by using a binary phase plate in the near field of the fiber, which emits the LP(0m) mode.

Quasi-absolute measurement of aspheres with a combined diffractive optical element as reference.

We have already reported a method for the quasi-absolute test of rotationally symmetric aspheres by means of combined diffractive optical elements (combo-DOEs). The combo-DOEs carry the information for the ideal shape of an aspheric surface under test as well as a spherical wave for the measurement at the cat's eye position. An experimental demonstration of the procedure is given.

Calibration for cylindrical specimens in grazing-incidence interferometry via integration of difference measurements.

Cylindrical specimens may be tested advantageously by using grazing-incidence interferometry. A multiple positions test in combination with rotational averaging has recently been used to separate the surface deviations of the specimen from the interferometric aberrations. To reduce the measuring time and to check whether the results are reliable, a second procedure is now investigated, which uses the principle of the multiple positions test to determine quantities proportional to the difference quotients of the surface deviations.

Absolute calibration in grazing incidence interferometry via rotational averaging.

Interferometry in grazing incidence can be used to test cylindrical mantle surfaces. The absolute accuracy of the resulting surface profiles is limited by systematic wavefront aberrations caused in the interferometer, in particular due to an inversion of the test wavefront in an interferometer using diffractive beam splitters. For cylindrical specimens, a calibration method using four positions has therefore been investigated.

Simultaneous characterization of the quality and orientation of cylindrical lens surfaces.

A diffractive grazing-incidence interferometer for the test of cylindrical lenses is described. Besides surface aberrations from the ideal shape, the interferometer allows for the simultaneous determination of the relative position and orientation of surfaces to another. The measurement principle as well as a classification of deviation types is given.

Compensation for anamorphotic distortion in grazing-incidence interferometry testing planar specimens.

One important feature of grazing-incidence interferometry is the anamorphotic distortion or the fore-shortened view of the interference pattern along the optical axis caused by the geometry of theinterferometer. To compensate for the consequential lower resolution along the optical axis, a setup was built in which the object plane is imaged onto a rectifying grating, ensuring sharp mapping of the whole specimen onto the detector. A volume hologram and a diffraction grating serve as rectifying elements and are applied to measure various types of planar objects such as mirrors and structured plastic samples.

Dual-wave-front computer-generated holograms for quasi-absolute testing of aspherics.

Testing of aspherics by means of computer-generated holograms (CGHs) is well known. To perform a quasi-absolute test of rotationally symmetric aspheric surfaces, two wave fronts must be encoded in the CGH. Both the null lens and a spherical lens have to be stored.

Form assessment of hollow cylindrical specimens.

Grazing-incidence interferometry that makes use of diffractive axicons for the measurement of cylindrical mantle surfaces has already been reported. However, measurement of concave rod structures poses a severe problem because these structures are subject to spurious fringes caused by parasitic diffraction orders of the diffractive axicons. By breaking the symmetry of the interferometric setup it is possible to obtain unique interferograms of the inner mantle surfaces of hollow cylinders as cages for roller bearings or other workpieces produced on lathe machines that have a suitable surface finish.