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Doppler asymmetric spatial heterodyne (DASH) interferometry is a novel concept for observing atmospheric winds. This paper discusses a numerical model for the simulation of fringe patterns and a methodology to correct fringe images for extracting Doppler information from ground-based DASH measurements. Based on the propagation of optical waves, the fringe pattern was modeled considering different angular deviations and optical aberrations. A dislocation between two gratings can introduce an additional spatial modulation associated with the diffraction order, which was seen in laboratory measurements. A phase correction is proposed to remove phase differences between different row interferograms, which is the premise for calculating the average interferogram to improve the signal-to-noise ratio. Laboratory tests, simulation results, and Doppler velocity measurements indicate that a matrix determined in the laboratory can be applied to correct interferograms obtained from ground-based DASH measurements.

A grazing incidence interferometric measurement procedure is applied to test rough convex steep rotationally symmetric aspherics. The measurement of rough surfaces is possible; i.e., without the need to polish the surfaces, due to the large effective wavelength ( λ eff =10µm) of the test. One measurement step using diffractive beam splitters and phase-shifting techniques delivers the surface information along one meridian. The full surface description can be stitched together from several phase results combined with appropriate object rotations. This publication includes, besides the short recapitulation of the measurement principle and experimental setup, a presentation of the simulated and measured data of an aspherical object under test. The data analysis of each meridian is focused on the elimination of the misalignment aberrations caused by specimen displacements. Finally, the stitching of multiple meridian regions to a 3D surface map of the specimen is shown.

Reducing the number of phase singularities in speckle interferometry by physical means increases the quality of the phase deconvolution and enhances the separability of fringe systems, especially for highly dynamic fringe systems. The reduction is achieved by tailoring the spatial coherence of the light source at the entrance of the interferometer. The reduction mechanism is non-intuitive and rests on a change of size and of position of the speckle patterns as a result of the spatially shaped coherence. After demonstrating the amount of reduction that may be achieved, the reduction mechanism is explained theoretically and via simulations, and it is vindicated in an experiment using a Michelson-Mach-Zehnder interferometer hybrid.

Grazing incidence interferometry has been applied to plane, cylindrical, acylindrical, and general rod-like surfaces using diffractive beam splitters. Here, in a first step towards measuring aspherics, we demonstrate that also rough convex steep rotationally symmetric spherics can be measured along one meridian in a single step using diffractive beam splitters and phase shifting techniques. The measurement of rough surfaces is possible, i.e., without the need to polish the surfaces, due to the large effective wavelength ( λ eff ≈10µm) of the test. We include, besides the short recapitulation of the measurement principle and experimental setup, a presentation of the measured data of one small meridian region for the special case of spherical objects under test. The subsequent data analysis combined with suitable simulations focuses on elimination of the misalignment aberrations from the results caused by specimen displacements in the setup.

In this paper a method for correcting the radial distortion of interferograms generated by a spatial heterodyne spectrometer system is presented. Instead of utilizing calibration patterns, the distortion model parameters are estimated based on the distorted fringe features generated by projecting the straight interference stripes onto the detector. Comparisons between polynomial models and division models indicate that division models can deliver competitive performance on the reconstructed image with fewer parameters. Simulated interferograms based on ray-tracing are used to demonstrate the correction of errors in the spatial, phase, and spectral domain caused by optical distortion.

This paper presents a method for wind velocity and Doppler temperature retrieval from interferograms of a Doppler asymmetric spatial heterodyne spectrometer. This method is based on the analytic representation of the signal and the subsequent algorithms. It turns out to be more robust than the conventional Fourier transform method at low SNR. The influence of optical dispersion on the accuracy of the retrieved parameters is also characterized. The effective optical path difference is suggested for use in wind and temperature retrieval routines. Computer simulations are used to characterize the accuracy of the proposed method, in particular regarding the influence of optical dispersion.

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. The theoretical description of the investigated methods and their experimental implementation are presented.

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. Here, we will present first results of an interferometric approach for a simultaneous and spatially resolved measurement of both phase and polarization, as long as the local polarization at any point is linear (e.g., for radially or azimuthally polarized light).

The homogeneity test of glass plates in a Fizeau interferometer requires the measurement of the glass sample in reflected as well as in transmitted light. For the measurement in transmitted light, the sample has to be inserted into the ray path of a Fizeau or Twyman-Green interferometer, which leads to a nested cavity setup. To separate the interference signals from the different cavities, we illuminate a Fizeau interferometer with an adaptive frequency comb. In this way, rigid glass plates can be measured, and linear variations in the homogeneity can also be detected. The adaptive frequency comb is provided by a variable Fabry-Perot filter under broadband illumination from a superluminescence diode. Compared to approaches using a two-beam interferometer as a filter for the broadband light source, the visibility of the fringe system is considerably higher.

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. A series arrangement of the gratings offers an on-axis geometry, which minimizes the systematic errors of the test. For illumination, an extended incoherent monochromatic light source is used. High-contrast fringes can be obtained by tailoring the degree of coherence via a periodic intensity distribution.

Absolute testing of spherical surfaces is a technological necessity because of increased accuracy requirements. In a Fizeau setup, the main part of the interferometer deviations thereby comes from the reference surface. We demonstrate the validity of an absolute testing procedure for the reference surface that has been proposed earlier. The procedure relies on the decomposition of the surface deviations into odd and even parts and could be used in partially coherent illumination. The odd deviations are obtained from a basic and a 180 degree-rotated position of an auxiliary sphere, and the even deviations can be measured with the help of a cat's eye position in double pass using an opaque half screen in the interferometer aperture.

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. Aberrations caused by misalignments are removed via fitting of suitable functionals provided by means of ray tracing simulations. It turns out that the usual misalignment approximations fail under these extreme conditions.

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). Here we investigate the effects of the DOE substrate errors on the proposed calibration procedure and present a set of criteria for designing an optimized combo-DOE. It is demonstrated that this optimized design enhances the overall consistency of the procedure. Furthermore, the rotationally varying part of the surface deviations is compared with the rotationally varying deviations obtained by an N-position averaging procedure and is found to be in good agreement.

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. Measurements with two different designs of combo-DOEs have been conducted, and their relative advantages and disadvantages are discussed.

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. After numerical integration, the results can be compared with those obtained previously by rotational averaging. The measurement principle is described, and calibration results are presented.

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. This test is combined with another method of optical metrology: the rotational averaging procedure. The implementation for grazing incidence is described and measurement results for hollow cylinders are presented. The gain in accuracy is demonstrated.

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. Measurement results for planar concave lenses are presented.

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. Accuracy, image sharpness, and residual distortion for both cases are discussed.