Absolute measurement of non-comatic aspheric surface errors

Freimann, R.; Dörband, Bernd; Höller, Frank

doi:10.1016/s0030-4018(99)00006-1

Cited by 19 publications

(11 citation statements)

References 17 publications

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“…3 shows a measurement example of an axially symmetric convex test part of diameter 32.4 mm and an aspherical deformation (P-V difference between best-fit sphere and asphere) of 169 μm. Shown is only the non-rotationally deviation, since this can be compared to results obtained with the absolute N-position test [14]. …”

Section: Absolute Testing Of Rotationally Symmetric Aspheres With Cghmentioning

confidence: 99%

Advances in 3D asphere testing and reconstruction

Pruß

Garbusi

2009

SPIE Proceedings

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One of the most challenging 3D metrology tasks in terms of required accuracy is the metrology of aspheric surfaces. Due to the required accuracies in the nanometer range, interferometry is one of the preferred methods. The reconstruction of the actual asphere shape from the measured phase data is presented for computer generated hologram approaches as well as for a new, flexible approach that was developed to avoid the use of null test configurations.

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Section: Absolute Testing Of Rotationally Symmetric Aspheres With Cghmentioning

confidence: 99%

Advances in 3D asphere testing and reconstruction

Pruß

Garbusi

2009

SPIE Proceedings

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“…of all zones results in long-range rotationally symmetric wavefront aberrations. Concerning the axis of rotation of the spindle, an insu cient adjustment of the origin of the polar coordinate system leads to a centre-zero error, see ®gure 10 [10]:…”

Section: Constant Positioning Errormentioning

confidence: 99%

Wavefront aberrations of rotationally symmetric CGHs fabricated by a polar coordinate laser plotter

Reichelt

Daffner

Tiziani

et al. 2002

Journal of Modern Optics

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Computer-generated holograms (CGHs) were fabricated by a polar coordinate laser plotter. The wavefront aberrations of these CGHs caused by fabrication inaccuracies were measured interferometrically. We tested Fresnel zone plates as typical examples of CGHs with focal ratios of f =10 and f=5 with a Fizeau interferometer. The tests comprised both binary phase holograms and binary amplitude holograms. The wavefront aberrations of the CGHs had an rms variation of about ¶=50. Two types of aberrations were identi®ed and could be referred to certain writing errors. Their size was deduced from the interferograms. IntroductionIn interferometric measurement technology, computer-generated holograms (CGHs) are used in an increased manner for wavefront shaping [1±3]. One reason for this is the relatively simple generation of wavefronts speci®cally adapted to the surface under test by means of the CGH. It is possible to design the CGH to be more¯exible than spherical lenses or mirrors, because the place of de¯ection and the angle of de¯ection of a beam are independent of each other. Furthermore, the dispersion inherent to any CGH does not pose any di culty, because laser interferometry uses quasi-monochromatic light. However, the wavefront aberrations introduced due to errors in the CGH pattern in¯uence the result of the measurement and, therefore, the CGH must be calibrated ®rst. At our institute we have the technology to produce both binary amplitude holograms and binary phase holograms.The purpose of this work was to control and to improve the quality of the CGHs produced with a polar coordinate plotter.

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“…Since then, much research has been conducted to improve the applications of CGHs for optical testing. The majority of the work has been about the different design schemes and fabrication techniques of the CGH, but there is not much literature about a systematic simulation-based error analysis of aspheric optical surfaces or systems [7,8]. The CGH is often designed using ray-trace software, but it is desirable to have more detailed knowledge about the correspondence of numerically simulated and experimentally found error sensitivity with regard to slight misadjustments that typically can hardly be avoided entirely in interferometric testing.…”

Section: Introductionmentioning

confidence: 99%

Error compensation in computer generated hologram-based form testing of aspheres

Stuerwald

2014

Appl. Opt.

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Computer-generated holograms (CGHs) are used relatively often to test aspheric surfaces in the case of medium and high lot sizes. Until now differently modified measurement setups for optical form testing interferometry have been presented, like subaperture stitching interferometry and scanning interferometry. In contrast, for testing low to medium lot sizes in research and development, a variety of other tactile and nontactile measurement methods have been developed. In the case of CGH-based interferometric form testing, measurement deviations in the region of several tens of nanometers typically occur. Deviations arise especially due to a nonperfect alignment of the asphere relative to the testing wavefront. Therefore, the null test is user- and adjustment-dependent, which results in insufficient repeatability and reproducibility of the form errors. When adjusting a CGH, an operator usually performs a minimization of the spatial frequency of the fringe pattern. An adjustment to the ideal position, however, often cannot be performed with sufficient precision by the operator as the position of minimum spatial fringe density is often not unique, which also depends on the asphere. Thus, the scientific and technical objectives of this paper comprise the development of a simulation-based approach to explain and quantify typical experimental errors due to misalignment of the specimen toward a CGH in an optical form testing measurement system. A further step is the programming of an iterative method to realize a virtual optimized realignment of the system on the basis of Zernike polynomial decomposition, which should allow for the calculation of the measured form for an ideal alignment and thus a careful subtraction of a typical alignment-based form error. To validate the simulation-based findings, a series of systematic experiments is performed with a recently developed hexapod positioning system in order to allow an exact and reproducible positioning of the optical CGH-based setup. Additionally a CGH phase function using an exact geometric model is compared to the other approaches. The phase function is utilized to enhance the overall reliability of the sensitivity functions with regard to alignment errors in interferometric testing.

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Absolute measurement of non-comatic aspheric surface errors

Cited by 19 publications

References 17 publications

Advances in 3D asphere testing and reconstruction

Advances in 3D asphere testing and reconstruction

Wavefront aberrations of rotationally symmetric CGHs fabricated by a polar coordinate laser plotter

Error compensation in computer generated hologram-based form testing of aspheres

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