Instrumentation, Measurement, and Metrology

Comparison of linear and nonlinear calibration methods for phase-measuring profilometry

[+] Author Affiliations
Peirong Jia

University of Ottawa, Department of Mechanical Engineering, Ottawa, Ontario, Canada, K1N 6N5

Jonathan Kofman

University of Waterloo, Department of Systems Design Engineering, Waterloo, Ontario, Canada, N2L 3G1

Chad English

Neptec Design Group Ltd., 302 Legget Drive, Kanata, Ontario, Canada, K2K 1Y5

Opt. Eng. 46(4), 043601 (April 05, 2007). doi:10.1117/1.2721025
History: Received July 08, 2006; Revised October 07, 2006; Accepted October 12, 2006; Published April 05, 2007
Text Size: A A A

In phase-shifting-based fringe-projection surface-geometry measurement, phase unwrapping techniques produce a continuous phase distribution that contains the height information of the 3-D object surface. Mapping of the phase distribution to the height of the object has often involved complex derivations of the nonlinear relationship. In this paper, the phase-to-height mapping is formulated using both linear and nonlinear equations, the latter through a simple geometrical derivation. Furthermore, the measurement accuracies of the linear and nonlinear calibrations are compared using measurement simulations where noise is included at the calibration stage only, and where noise is introduced at both the calibration and measurement stages. Measurement accuracies for the linear and nonlinear calibration methods are also compared, based on real-system measurements. From the real-system measurements, the accuracy of the linear calibration was similar to the nonlinear calibration method at the lower range of depth. At the higher range of depth, however, the nonlinear calibration method had considerably higher accuracy. It seems that as the object approaches the projector and camera for the higher range of depth, the assumption of linearity based on small divergence of light from the projector becomes less valid.

Figures in this Article
© 2007 Society of Photo-Optical Instrumentation Engineers

Citation

Peirong Jia ; Jonathan Kofman and Chad English
"Comparison of linear and nonlinear calibration methods for phase-measuring profilometry", Opt. Eng. 46(4), 043601 (April 05, 2007). ; http://dx.doi.org/10.1117/1.2721025


Access This Article
Sign in or Create a personal account to Buy this article ($20 for members, $25 for non-members).

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging & repositioning the boxes below.

Related Book Chapters

Topic Collections

PubMed Articles
Advertisement
  • Don't have an account?
  • Subscribe to the SPIE Digital Library
  • Create a FREE account to sign up for Digital Library content alerts and gain access to institutional subscriptions remotely.
Access This Article
Sign in or Create a personal account to Buy this article ($20 for members, $25 for non-members).
Access This Proceeding
Sign in or Create a personal account to Buy this article ($15 for members, $18 for non-members).
Access This Chapter

Access to SPIE eBooks is limited to subscribing institutions and is not available as part of a personal subscription. Print or electronic versions of individual SPIE books may be purchased via SPIE.org.