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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 2 — Jan. 16, 2012
  • pp: 1714–1726

Method of surface topography retrieval by direct solution of sparse weighted seminormal equations

Jeffrey Koskulics, Steven Englehardt, Steven Long, Yongxiang Hu, and Knut Stamnes  »View Author Affiliations

Optics Express, Vol. 20, Issue 2, pp. 1714-1726 (2012)

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A new method is presented to estimate the topography of a rough surface. A formulation is provided in which immediate measurements and a priori observations of surface elevation, slope and curvature, are considered simultaneously as a linear algebraic system of finite difference equations. Least squares solutions are computed directly by sparse orthogonal-triangular (QR) factorization of the weighted seminormal equations, an approach made practical for large systems with powerful computational hardware and algorithms that have become available recently. Retrievals are demonstrated from synthetic slope data and from measurements of slope on a rough water surface. The method provides a general approach to retrieving topography from measurements of elevation, slope and curvature.

© 2012 OSA

OCIS Codes
(010.7340) Atmospheric and oceanic optics : Water
(080.2720) Geometric optics : Mathematical methods (general)
(100.3190) Image processing : Inverse problems
(120.2830) Instrumentation, measurement, and metrology : Height measurements
(120.6660) Instrumentation, measurement, and metrology : Surface measurements, roughness
(240.6700) Optics at surfaces : Surfaces

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: November 9, 2011
Revised Manuscript: December 4, 2011
Manuscript Accepted: December 6, 2011
Published: January 11, 2012

Jeffrey Koskulics, Steven Englehardt, Steven Long, Yongxiang Hu, and Knut Stamnes, "Method of surface topography retrieval by direct solution of sparse weighted seminormal equations," Opt. Express 20, 1714-1726 (2012)

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