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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 40, Iss. 34 — Dec. 1, 2001
  • pp: 6203–6209

Estimating the Root Mean Square of a Wave Front and its Uncertainty

Angela Davies and Mark S. Levenson  »View Author Affiliations


Applied Optics, Vol. 40, Issue 34, pp. 6203-6209 (2001)
http://dx.doi.org/10.1364/AO.40.006203


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Abstract

The root mean square (rms) of the surface departure or wave-front deformation is an important value to extract from an optical test. The rms may be a tolerance that an optical fabricator is trying to meet, or it may be a parameter used by an optical designer to evaluate optical performance. Because the calculation of a rms involves a squaring operation, the rms of the measured data map is higher on average than the rms of the true surface or wave-front 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 wave-front deformation, as can be the case in the testing of ultraprecision optics. We describe and demonstrate a simple data analysis method to arrive at an unbiased estimate of the rms and a means to determine the measurement uncertainty.

© 2001 Optical Society of America

OCIS Codes
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.4800) Instrumentation, measurement, and metrology : Optical standards and testing
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure

Citation
Angela Davies and Mark S. Levenson, "Estimating the Root Mean Square of a Wave Front and its Uncertainty," Appl. Opt. 40, 6203-6209 (2001)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-40-34-6203

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