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Form deviations caused by lateral displacement errors in annular subaperture stitching interferometry


Annular subaperture stitching interferometry (ASSI) is a common approach for the measurement of aspherical surfaces. A common obstacle of ASSI is the occurrence of lateral displacement errors when the sensor or specimen is repositioned between the subaperture measurements. Our contribution focuses on modeling of the statistical displacement errors. Avirtual experiment is presented simulating the propagation of the displacement errors through a cumulative and a global stitching algorithm to the retrieved surface form. For the considered experimental setup, the uncertainty in lateral position depends on the positioning uncertainties of the employed motion system and the uncertainty in the absolute distance measurement between the sensor and specimen. The lateral displacement uncertainty is determined experimentally employing a calibratable lateral grating. Thus, it is traceable to the SI unit of the length (meter). The experimental results show that the lateral displacement errors may be modeled by a normal distribution, and the results of the virtual experiment indicate that the statistical lateral displacement errors transfer linear through the stitching procedure and also cause a normal distributed topography error. This enables the assignment of an expanded uncertainty to each individual sample point employing the Zernike polynomial expression of the topography measurement.


Markus Schake: 4.2 Imaging and Wave Optics, PTB-Braunschweig
Jörg Riebeling: Universität Kassel, FB 16 Elektrotechnik/Informatik Messtechnik, Kassel
Gerd Ehret: 4.2 Imaging and Wave Optics, PTB-Braunschweig

For further information:

Optical Engineering 59(12), 124105 (2020), https://doi.org/10.1117/1.OE.59.12.124105


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