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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 24 — Aug. 20, 2013
  • pp: 5925–5931

Application of the random ball test for calibrating slope-dependent errors in profilometry measurements

Yue Zhou, Young-Sik Ghim, Ali Fard, and Angela Davies  »View Author Affiliations

Applied Optics, Vol. 52, Issue 24, pp. 5925-5931 (2013)

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Optical profilometers such as scanning white light interferometers and confocal microscopes provide high-resolution measurements and are widely utilized in many fields for measuring surface topography. Slope-dependent systematic errors can be present in the measurement and can be the same order of magnitude as features on the surface to be measured. We propose a self-calibration technique, the random ball test (RBT), for calibrating slope-dependent errors of such instruments. The calibration result can be used to compensate future measurements of similar spherical geometries such as profiles of refractive microlenses. A simulation study validates the approach and shows that the RBT is effective in practical limits. We demonstrate the calibration on a 50× confocal microscope and find a surface slope-dependent bias that increases monotonically with the magnitude of the surface slope and is as large as 800nm at a surface slope of 12°. The uncertainty of the calibration is smaller than the observed measurement bias and is dominated by residual random noise. Effects such as drift and ball radius uncertainty were investigated to understand their contribution to the calibration uncertainty.

© 2013 Optical Society of America

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.2830) Instrumentation, measurement, and metrology : Height measurements
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.4630) Instrumentation, measurement, and metrology : Optical inspection
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: May 22, 2013
Revised Manuscript: July 19, 2013
Manuscript Accepted: July 26, 2013
Published: August 14, 2013

Yue Zhou, Young-Sik Ghim, Ali Fard, and Angela Davies, "Application of the random ball test for calibrating slope-dependent errors in profilometry measurements," Appl. Opt. 52, 5925-5931 (2013)

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