Abstract
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. A virtual 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.
Highlights
To receive traceable and comparable measurement results, it is mandatory to provide a statement of uncertainty achieved with the instruments and algorithms employed in the measurement process
The model does currently not include electrical and thermal noise, wavelength instabilities, and mechanical vibrations, which contribute to the statistical error. It does not model possible systematic errors, which occur when the probe is moved to the subaperture employing an erroneous tilt angle for the calculation of the radial interval or topography measurement deviations caused by aberrations in the imaging optics. This contribution considers the modeling of statistical lateral displacement errors er;k in annular subaperture stitching interferometry (ASSI)
A series of calibration measurements indicate that the statistical lateral displacement errors occurring during repositioning of the interferometric sensor between subaperture measurements are feasibly modeled as a normal distribution
Summary
To receive traceable and comparable measurement results, it is mandatory to provide a statement of uncertainty achieved with the instruments and algorithms employed in the measurement process. National metrology institutes are working on primary instruments and calibration artifacts to provide the basis of traceable uncertainty statements in industrial applications.[1,2] A universal calibration artifact comprising six different material measures with varying scales for the holistic calibration of an optical instrument employing a single specimen is proposed in Ref. 1. The national metrology institute of Germany, Physikalisch-Technische Bundesanstalt (PTB), recently proposed a multispherical artifact for traceable calibration of form measurements of freeform surfaces,[3] which may foster the standardization of uncertainty statements for the measurand of the associated form measuring instruments. In addition to the availability of traceable calibration artifacts to characterize the measurement uncertainties related to the instruments, a meaningful statement of uncertainty requires profound knowledge about uncertainties introduced by the calculations and algorithms involved in the translation of the recorded images to the surface topography. The resulting uncertainty in the surface topography is determined by virtual experiments
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