| Zugriffsnummer | 13692 |
| Dokumenttyp | Konferenzartikel |
| Sprache | Englisch |
| Titel | Method for evaluation of interferometric data: surface type and surface error type matched fitting of interferograms |
| Autor(in); Institution |
Weingärtner, Ingolf; 4.21, Bildoptik und Spektrometrie, PTB-Braunschweig
Schulz, Michael; 4.21, Bildoptik und Spektrometrie, PTB-Braunschweig
Elster, Clemens; 8.31, Messdatenverarbeitung, PTB-Berlin
|
| Quelle/Jahr | Fringe 2001 : the 4th International Workshop on Automatic Processing of Fringe Patterns:(2001), 187 - 192 |
| Herausgeber(in) |
Osten, Wolfgang
|
| ISBN | 2-84299-318-7 |
| Verlag | Paris [u.a.]: Elsevier |
| Konferenzangaben | 4th International Workshop on Automatic Processing of Fringe Patterns, Bremen, 17-19, September, 2001, Germany |
| Freie Schlagworte | Interferometry ; shape measurement ; fault detection ; 3D optical metrology ; evaluation of inter-ferometric data |
| Zusammenfassung | Interferometry is applied to determine the shape of a wavefront or specific parameters of the wavefront like defocus, tilt, or, generally speaking, polynomial contributions, e.g. Zernike coefficients. The methods for evaluating interferograms depend on the type of interferometry and on the final goal of the evaluation. In case of phase shifting interferometry the data from several interferograms are combined and the shape of a wavefront can directly be determined from these interferograms. In case of processing interferogram fringes, however, various methods, e.g. following fringes or using Fourier transform methods, yield information about the shape of a wavefront from only one interferogram by relatively complicated mathematical procedures. Both methods have advantages and shortcomings. Alternatively, if the intention is to get a very high reproducibility and a small measurement time and if the wavefront can be described by a small set of parameters it can be favourable to avoid the usage of phase shifting interferometry but to record only one interferogram and retrieve the desired information by an advanced method of processing the interferometric data. For this purpose, a model of the interferometer is designed and a set of parameters defined which describes the properties of the shape of the wavefront appropriately. Mathematical algorithms are used to calculate an interferogram with certain assumptions about the parameters and finally to compare this theoretical interferogram with the experimentally recorded interferogram. Special global and local optimisation strategies, including the determination of the inhomogeneity in the interferometer, are applied to find the values for the parameters which describe the actual wavefront. The methods described can be used with all interferometers, presumed the image data ate accessible. Surfaces used in optics are mostly macroscopically smooth. A portion of the surface can then be fitted very accurately with a small set of polynomials of low order, this represents the surface type fit. Furthermore, modern polishing methods frequently introduce more or less periodic disturbances on the surface with small lateral dimensions, the so-called waviness, and sometimes local faults. These surface errors can be fitted by a small set of periodic functions and local functions, this represents the surface error type fit. The method described is applied in the context of a measurement principle which determines topography of extended test samples by first making scanning measurements of curvature and second calculating topography from curvature. This method focuses on the avoidance of error influences, is directly traced back to the base unit of length, does not rely on external form references, and has the advantage that the errors of the stages and wholebody movement of the artefact have no direct influence on the uncertainty of measurement. This measurement tech-nique uses a scanning curvature sensor which mainly consists of a device for determining topography with a high lateral resolution over an area which is small in comparison to the size of the whole specimen under test. The curvature sensor is realised with help of small interferometer, and the task is to determine the curvature of the wavefront at certain points of the interferogram. The mathematical algorithms and experimental results are described. |
Zitierung
Weingärtner, I., Schulz, M., & Elster, C. (2001). Method for evaluation of interferometric data: surface type and surface error type matched fitting of interferograms. 4th International Workshop on Automatic Processing of Fringe Patterns, Bremen, 17-19, September, 2001, Germany.