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

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.

[1]  David L. Fried,et al.  Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements , 1977 .

[2]  Shih Tang,et al.  Two-dimensional scanning laser slope gauge: measurements of ocean-ripple structures. , 1993, Applied optics.

[3]  Clemens Elster,et al.  Reconstructing surface profiles from curvature measurements , 2002 .

[4]  J. Hedley,et al.  Light transfer at the ocean surface modeled using high resolution sea surface realizations. , 2011, Optics express.

[5]  Timothy A. Davis,et al.  Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization , 2011, TOMS.

[6]  B. Gotwols,et al.  Two-dimensional optical measurement of wave slope. , 1983, Applied optics.

[7]  Richard H. Hudgin,et al.  Optimal wave-front estimation , 1977 .

[8]  F. Bréon,et al.  Spaceborne observations of ocean glint reflectance and modeling of wave slope distributions , 2006 .

[9]  Svenja Ettl,et al.  Shape reconstruction from gradient data. , 2007, Applied optics.

[10]  Howard Schultz,et al.  Retrieval of short ocean wave slope using polarimetric imaging , 2008 .

[11]  Michael W. Spencer,et al.  The Aquarius Scatterometer: An Active System for Measuring Surface Roughness for Sea-Surface Brightness Temperature Correction , 2006, 2006 IEEE International Symposium on Geoscience and Remote Sensing.

[12]  Seung-Whan Bahk.  Highly accurate wavefront reconstruction algorithms over broad spatial-frequency bandwidth. , 2011, Optics express.

[13]  Reinhard Klette,et al.  Height data from gradient fields , 1996 .

[14]  Matthew Harker,et al.  Least squares surface reconstruction from measured gradient fields , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[15]  J. Herrmann,et al.  Least-squares wave front errors of minimum norm , 1980 .

[16]  Bobby R. Hunt,et al.  Matrix formulation of the reconstruction of phase values from phase differences , 1979 .

[17]  Bernd Jähne,et al.  Combined optical slope/height measurements of short wind waves: principle and calibration , 2005 .

[18]  C. Cox,et al.  Contours of slopes of a rippled water surface. , 2011, Optics Express.

[19]  M. Grédiac.  Method for surface reconstruction from slope or curvature measurements of rectangular areas. , 1997, Applied optics.

[20]  Walter Munk,et al.  An inconvenient sea truth: spread, steepness, and skewness of surface slopes. , 2009, Annual review of marine science.

[21]  W. Southwell.  Wave-front estimation from wave-front slope measurements , 1980 .

[22]  Gary G. Gibson,et al.  Sea surface wind speed estimation from space-based lidar measurements , 2008 .

[23]  G. Quispel,et al.  Geometric integration using discrete gradients , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[24]  Xin Zhang.  An algorithm for calculating water surface elevations from surface gradient image data , 1996 .

[25]  Reinhard Klette,et al.  Local and global integration of discrete vector fields , 1996, TFCV.

[26]  R. Hudgin.  Wave-front reconstruction for compensated imaging , 1977 .

[27]  C. Cox,et al.  Measuring the two-dimensional structure of a wavy water surface optically: A surface gradient detector , 1994 .

[28]  B. Jähne,et al.  Imaging of short ocean wind waves: a critical theoretical review , 1994 .

[29]  Reinhard Klette,et al.  Height data from gradient maps , 1996, Other Conferences.