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Estimating the RMS of a Wavefront and Its Uncertainty



Angela Davies, M. Levenson


The root mean square (RMS) of the surface departure or wavefront deformation is a common value to extract from an optical test. The RMS may be a tolerance an optical fabricatior is trying to meet or it may be a parameter used by an optical designer to evaluate optical performance. Because the calculation of RMS involves a squaring operation, the RMS of the measured data map is higher on average than the RMS of the true surface or wavefront deformation, even if the noise is zero on average. The bias becomes significant as the scale of the noise becomes comparable to the true surface or wavefront deformation, as can be the case in testing ultraprecision optics. We describe and demonstrate a simple data analysis method to arrive at an unbiased estimate of the RMS and a means of determining the measurement uncertainty.
Applied Optics


figure metrology, measurement uncertainty, RMS, root mean square, surface metrology


Davies, A. and Levenson, M. (2001), Estimating the RMS of a Wavefront and Its Uncertainty, Applied Optics (Accessed July 15, 2024)


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Created December 1, 2001, Updated February 19, 2017