14 September 2007 Weighted least-square approach for simultaneous measurement of multiple reflective surfaces
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Phase shifting interferometry (PSI) is a highly accurate method for measuring the nanometer-scale relative surface height of a semi-reflective test surface. PSI is effectively used in conjunction with Fizeau interferometers for optical testing, hard disk inspection, and semiconductor wafer flatness. However, commonly-used PSI algorithms are unable to produce an accurate phase measurement if more than one reflective surface is present in the Fizeau interferometer test cavity. Examples of test parts that fall into this category include lithography mask blanks and their protective pellicles, and plane parallel optical beam splitters. The plane parallel surfaces of these parts generate multiple interferograms that are superimposed in the recording plane of the Fizeau interferometer. When using wavelength shifting in PSI the phase shifting speed of each interferogram is proportional to the optical path difference (OPD) between the two reflective surfaces. The proposed method is able to differentiate each underlying interferogram from each other in an optimal manner. In this paper, we present a method for simultaneously measuring the multiple test surfaces of all underlying interferograms from these superimposed interferograms through the use of a weighted least-square fitting technique. The theoretical analysis of weighted least-square technique and the measurement results will be described in this paper.
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Shouhong Tang, Richard E. Bills, Klaus Freischlad, "Weighted least-square approach for simultaneous measurement of multiple reflective surfaces", Proc. SPIE 6671, Optical Manufacturing and Testing VII, 66710T (14 September 2007); doi: 10.1117/12.735151; https://doi.org/10.1117/12.735151

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