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

Jeffrey Koskulics, Steven Englehardt, Steven Long, Yongxiang Hu, Knut Stamnes

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

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 orthogonaltriangular (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.

Original languageEnglish
Pages (from-to)1714-1726
Number of pages13
JournalOptics Express
Volume20
Issue number2
DOIs
StatePublished - 16 Jan 2012

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