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

[Optical Society of America ]

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

Related Journal Articles

• Absolute Measurement of Planarity with Fritz’s Method: Uncertainty Evaluation (AO)
• Simple Method for Improving the Sampling in Profile Measurements by use of the Ronchi Test (AO)
• Calibration of a 300-mm-Aperture Phase-Shifting Fizeau Interferometer (AO)
• Colorimetric method for phase evaluation (JOSAA)
• Iterative algorithm for three flat test (OE)

Related Conference Papers

• A Light Source for the 1S0-3P0 Optical Clock Transition in Ytterbium
• Ultrahigh Dynamic-Range Portable Distance Meter Using an Optical Frequency Comb
• Displacement Metrology Setup with Sub-pm Stability in Air Utilizing a Fs-Comb Based Wavelength Synthesizer
• The Optical Equivalent to a Microwave Frequency Synthesizer
• High-Accuracy Form Measurement with Multiple Sensor Systems