The concept of a differential Shack–Hartmann (DSH) curvature sensor was recently proposed, which yields wavefront curvatures by measuring wavefront slope differentials. As an important feature of the DSH curvature sensor, the wavefront twist curvature terms can be efficiently obtained from slope differential measurements, thus providing a means to measure the Monge-equivalent patch. Specifically, the principal curvatures and principal directions, four key parameters in differential geometry, can be computed from the wavefront Laplacian and twist curvature terms. The principal curvatures and directions provide a “complete” definition of wavefront local shape. Given adequate sampling, these measurements can be useful in quantifying the mid-spatial-frequency wavefront errors, yielding a complete characterization of the surface being measured.
© 2008 Optical Society of America
Optical Design and Fabrication
Original Manuscript: January 14, 2008
Revised Manuscript: June 20, 2008
Manuscript Accepted: July 15, 2008
Published: August 21, 2008
Weiyao Zou, Kevin P. Thompson, and Jannick P. Rolland, "Differential Shack-Hartmann curvature sensor: local principal curvature measurements," J. Opt. Soc. Am. A 25, 2331-2337 (2008)