Grazing Incidence Interferometry Research Articles

Investigation into the Co-Phase Detection Methodology for Segmented Plane Mirrors Utilizing Grazing Incidence Interferometry

Segmented plane mirrors constitute a crucial component in the self-aligned detection process for large-aperture space optical imaging systems. Surface shape errors inherent in segmented plane mirrors primarily manifest as tilt errors and piston errors between sub-mirrors. While the detection and adjustment techniques for tilt errors are well-established, addressing piston errors poses a more formidable challenge. This study introduces a novel approach to achieve long-range, high-precision, and efficient co-phase detection of segmented plane mirrors by proposing a segmented plane mirror shape detection method based on grazing incidence interferometry. This method serves to broaden the detection range of piston errors, mitigate the issue of the 2π ambiguity resulting from piston errors in co-phase detection, and extend the detection capabilities of the interferometer. By manipulating the incident angle of the interferometer, both rough and precise adjustments of the segmented plane mirrors can be effectively executed.

Interferometric grazing incidence test of rough steep convex spherics: experimental data analysis.

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 (λeff≈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.

Interferometric grazing incidence test of rough steep convex spherical and aspherical surfaces: first simulations and experimental proof of principle.

In the past, grazing incidence interferometry has been applied for rough plane, cylindrical, acylindrical, and general rod-like surfaces using diffractive beam splitters. Here, we demonstrate that also rough convex steep rotational symmetric spherical or aspherical surfaces can be measured along one meridian in a single step using diffractive beam splitters and phase-shifting techniques. The extension to the whole surface can be attained by successive meridional measurements of the surface under test by azimuthal adjustments. The principle of the method is given and for a spherical ball lens as an extremely curved surface simulated, and experimental data are presented. The features of the interferogram are discussed, and the experimental evaluation of a single meridian including the unwrapped phase data is shown.

Correction method for segmenting valid measuring region of interference fringe patterns

Segmenting the valid measuring region from an interferogram is an important step in the grazing incidence interferometry, which is related to the accuracy of the measurement result. For the spurious fringes which are generated by the diffuse reflection of the chamfering in the edge of the object surface, we propose a method-spin segment to correct the result of the image segment. First, a phase schematic diagram whose stripe feature is clearer than the original interference fringe patterns is generated. Next, the difference of the gray gradient between the fringe's local normal direction and local tangent direction is calculated to judge the valid measurement region. The principles of selecting some parameters are summarized and the calculation steps are shown. To examine the correction method, the results of an experimental application of spin segment are given to verify the feasibility and accuracy.

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. 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.

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. 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.

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

Interferometric shape measurement of rough surfaces at grazing incidence

Interferometric shape measurements of technical objects are hampered by stochastic phase variations in the micro region caused by the surface roughness of the test object. Without special precautions, low-contrast interference patterns or even totally stochastic fringe patterns may be observed. However, illuminating the surface under test at grazing incidence reduces the phase variations because it increases the effective wavelength by a factor of 1/cos β, where β is the angle of incidence. Here, an interferometer for testing plane objects is described where the test wavefront is provided by means of diffractive optical elements (DOEs). A pair of identical DOEs is used to do the necessary beam splitting and beam shaping. The resulting fringes, showing the surface deviations of the test object from the ideal plane, are evaluated by means of phase-shifting interferometry. Serial measurements on different rough surfaces were made to find out the limits of grazing-incidence interferometry when technical objects are measured. To do this, different incidence angles have been realized by choosing a suitable set of diffractive elements. The contrast of the interference fringes has been taken as the evaluation criterion for the measurability of the shape of the rough surfaces within the grazing incidence interferometer.

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. Special design issues for the computer-generated holograms and the interferometric setup are discussed, and test examples are given.

Grazing Incidence Interferometry for High Precision Measurements of Cylindrical Form Deviations

Grazing incidence interferometers equipped with diffracting elements (computer generated holograms) are now being used to measure the cylindricity, roundness and straightness of cylindrical parts. The method is non-contact, with automatic work piece alignment and is capable of recording thousand of points on the surface in a few seconds. It incorporates parallel data acquisition of the cylindrical surfaces, so that an excellent radial resolution can be obtained. There are some questions regarding the basic theory and the accuracy when measuring workpieces with short wavelength errors. Experimental results using a CylinderMaster CM 25, and a modification for measuring blind holes are presented.

Diffractive grazing-incidence interferometer

I propose a symmetric geometry for grazing-incidence interferometry of flat surfaces using diffraction gratings for beam splitting and recombination. The geometry employs a reference mirror to correct for relative inversion of the measurement and reference wave fronts. Preliminary testing with a 4-microm equivalent-wavelength system shows a 3 sigma repeatability of 20 nm for both smooth and rough surfaces, including a variety of precision-engineered metal, ceramic, and glass objects. The system has a comfortable working distance and large field of view, suitable for production testing.

Holographically recorded axicon for grazing incidence interferometry

Holographically recorded axicon for grazing incidence interferometry

Holographically recorded axicon for grazing incidence interferometry

A diffractive axicon for grazing incidence interferometry of cylindrical objects is presented. For industrial measurement, an element with a diameter of 8 cm was manufactured. The axicon was recorded in dichromated gelatine (DCG) with a high-precision rotating stage. The diffraction theory for the design of the element is presented. The axicon was tested interferometrically. Some possible errors are discussed.

Testing of rod objects by grazing-incidence interferometry: experiment

A grazing-incidence interferometer for the testing of technical surfaces for macroscopic surface deviations is described. Computer-generated holograms serve as beam splitters and references for the workpieces tested. The sensitivity of the interferometer depends on the period of the computer-generated holograms. The method is demonstrated at a rod object of convex profile. Using phase-stepping techniques, the grazing-incidence interferometer provides fast measurements of the entire mantle surface of the test sample with submicrometer precision.

Testing of rod objects by grazing incidence interferometry: theory

Interferometry at grazing incidence allows one to perform macroscopic shape tests of rough surfaces with submicrometer precision. The highest measurement accuracy is achieved with a null test: the object wave front is adapted to the ideal surface under test through the use of diffractive optical elements. Deviations between the ideal and the real surface shape result in characteristic phase distributions at the interferometer output. Rod objects with rather arbitrary cross-section profiles are especially suitable for this type of measurement. The design of appropriate test wave fronts can be carried out by means of geometrical considerations. Expressions describing aberrations that are due to misalignments of the work piece can easily be derived. Misalignment aberrations and genuine surface deviations are separated by least-squares fitting.

Grazing incidence interferometry applied to the measurement of cylindrical surfaces

Usually, rough surfaces cannot be measured by interferometric methods because the wavefronts are disturbed by speckle noise. This problem can be overcome by an increase of the test wavelength. One way to increase the effective wavelength is to use grazing incidence interferometry. We suggest an interferometer specifically adapted for the measurement of cylinders or tubes. Reference and object wavefront are generated using problem-specific computer-generated holograms as beamsplitters. The method can be extended to other geometries. We introduce the principle and show first experimental results.

Flatness Analysis Of Hard Disks

The special flatness requirements of hard disks are discussed. Color schlieren and grazing incidence interferometry, the two methods currently dominating the market, are compared with the more recently developed moire deflectometry method. We show that since the color schlieren does not detect vital disk flatness information and since interferometry is too vibration sensitive and relatively expensive, moire deflectometry is a superior method for flatness analysis of hard disks.