3D shape measurement using curvature data

Kim, ByoungChang; Kwon, MinChel; Choo, ByoungUck; Yoon, InJeong

doi:10.1117/12.827242

SPIE Proceedings

2009

DOI: 10.1117/12.827242

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3D shape measurement using curvature data

ByoungChang Kim

MinChel Kwon

ByoungUck Choo³

et al.

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Orthonormal curvature polynomials over a unit circle: basis set derived from curvatures of Zernike polynomials

Zhao

Burge

2013

Opt. Express

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Zernike polynomials are an orthonormal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. In optical testing, slope or curvature of a surface or wavefront is sometimes measured instead, from which the surface or wavefront map is obtained. Previously we derived an orthonormal set of vector polynomials that fit to slope measurement data and yield the surface or wavefront map represented by Zernike polynomials. Here we define a 3-element curvature vector used to represent the second derivatives of a continuous surface, and derive a set of orthonormal curvature basis functions that are written in terms of Zernike polynomials. We call the new curvature functions the C polynomials. Closed form relations for the complete basis set are provided, and we show how to determine Zernike surface coefficients from the curvature data as represented by the C polynomials.

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Orthonormal curvature polynomials over a unit circle: basis set derived from curvatures of Zernike polynomials

Zhao

Burge

2013

Opt. Express

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Free-Form Surface Reconstruction Method from Second-Derivative Data

Kim¹,

Kim²,

Kim³

2014

Korean Journal of Optics and Photonics

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We present an algorithm for surface reconstruction from the second-derivative data for free-form aspherics, which uses a subaperture scanning system that measures the local surface profile and determines the three second-derivative values at those local sampling points across the free-form surface. The three second-derivative data were integrated to get a map of x-and y-slopes, which went through a second Southwell integration step to reconstruct the surface profile. A synthetic free-form surface 200 mm in diameter was simulated. The simulation results show that the reconstruction error is 19 nm RMS residual difference. Finally, the sensitivity to noise is diagnosed for second-derivative Gaussian random noise with a signal to noise ratio (SNR) of 16, the simulation results proving that the suggested method is robust to noise.

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3D shape measurement using curvature data

Cited by 2 publications

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Orthonormal curvature polynomials over a unit circle: basis set derived from curvatures of Zernike polynomials

Orthonormal curvature polynomials over a unit circle: basis set derived from curvatures of Zernike polynomials

Free-Form Surface Reconstruction Method from Second-Derivative Data

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