Characterization of the interpolation bias in the analysis of deflectometry measurement data

Ali Pouya Fard; Angela Davies

doi:10.1117/12.2323420

18 August 2018 Characterization of the interpolation bias in the analysis of deflectometry measurement data

Ali Pouya Fard, Angela Davies

Author Affiliations +

Proceedings Volume 10749, Interferometry XIX; 107490G (2018) https://doi.org/10.1117/12.2323420
Event: SPIE Optical Engineering + Applications, 2018, San Diego, California, United States

Abstract

Zonal integration techniques are commonly used for surface shape reconstruction from slope measurements for phase measuring deflectometry (PMD) systems. The stability of zonal surface reconstruction algorithms relies on the symmetry of numerical differential equations for uniformly sampled grids. Modified zonal integration methods for non-uniformly sampled slope data can yield accurate results for the measurement of a single camera yet fail to produce accurate results for stereo deflectometry. In this publication, we identify and quantify a large systematic bias in the deflectometry measurement that is introduced during resampling or interpolation of phase data onto a uniform sample grid. This interpolation is commonly done in all forms of deflectometry and cannot be avoided in stereo phase measuring deflectometry. This surface reconstruction bias is largely independent of the integration method and the accuracy of the integration algorithm under different grid assumptions. This bias is a significant contributor to the well-known micronlevel low spatial-frequency errors in deflectometry that are commonly attributed to calibration errors. We show the dependence of the bias on different system parameters including surface shape, curvature, and the geometry of the system components, providing guidance on setup geometry for stereo PMD.

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Ali Pouya Fard and Angela Davies "Characterization of the interpolation bias in the analysis of deflectometry measurement data", Proc. SPIE 10749, Interferometry XIX, 107490G (18 August 2018); https://doi.org/10.1117/12.2323420

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