Zernike polynomial fitting of lateral shearing interferometry

Shen, Wei; Chang, Ming‐Wen; Wan, Der-Shen

doi:10.1117/1.601600

Cited by 37 publications

(10 citation statements)

References 6 publications

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“…For the R-W method [13][14][15], the basis functions of the difference fronts are also Zernike polynomials fZ j x; yg; that is, fG x;j g fZ j g, which gives ΔW x x; y; s Wx s; y − Wx − s; y X J j1 A R x;j Z j x; y;…”

Section: R-w Methodsmentioning

confidence: 99%

“…The RimmerWyant (R-W) method, elliptical orthogonal transformation (EOT), and numerical orthogonal transformation (NOT) can be classified under this category. In the R-W method, as in the original wavefront, the basis functions for the expansion of the difference fronts are also Zernike polynomials [13][14][15]. In EOT and NOT, the basis functions are elliptical Zernike polynomials, which are orthogonal over elliptical regions [16][17][18], and numerical orthonormal polynomials, which are orthogonal over the discrete points at which the difference fronts are measured [19], respectively.…”

Section: Introductionmentioning

confidence: 99%

“…In zonal reconstruction [4][5][6][7][8][9][10], the wavefront at specific grid points is estimated directly from a set of discrete difference fronts. On the other hand, in modal reconstruction [11][12][13][14][15][16][17][18][19][20][21][22][23][24], the wavefront is decomposed into a set of complete basis functions, the coefficients of which are evaluated from the discrete difference fronts. As pointed out by Southwell [24], if the wavefront under test can be expanded into a set of basis functions, then modal reconstruction is superior to zonal reconstruction because of its better noise propagation properties and efficient calculations.…”

Section: Introductionmentioning

confidence: 99%

“…For modal reconstruction, Zernike polynomials are commonly used as basis functions for wavefront expansion [13][14][15][16][17][18][19][20][21][22][23]. The wavefront Wx; y is hypothesized to be expanded by the first J Zernike polynomials in the following form:…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Modal wavefront reconstruction based on Zernike polynomials for lateral shearing interferometry: comparisons of existing algorithms

et al. 2012

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Four modal methods of reconstructing a wavefront from its difference fronts based on Zernike polynomials in lateral shearing interferometry are currently available, namely the Rimmer-Wyant method, elliptical orthogonal transformation, numerical orthogonal transformation, and difference Zernike polynomial fitting. The present study compared these four methods by theoretical analysis and numerical experiments. The results show that the difference Zernike polynomial fitting method is superior to the three other methods due to its high accuracy, easy implementation, easy extension to any high order, and applicability to the reconstruction of a wavefront on an aperture of arbitrary shape. Thus, this method is recommended for use in lateral shearing interferometry for wavefront reconstruction.

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Section: R-w Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modal wavefront reconstruction based on Zernike polynomials for lateral shearing interferometry: comparisons of existing algorithms

et al. 2012

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“…Higher order distortions could be detected with a shearing interferogram as well, but the evaluation is somehow more difficult than with other methods (see for example Rimmer(1974) 7 or Shen(1994) 8 ). For testing the higher order aberrations and possible fast changes in the wavefront we installed a Shack-Hartmann sensor.…”

Section: Wavefront Deformationmentioning

confidence: 99%

<title>Beam quality and polarization analysis of the ALFA laser at Calar Alto and the influence on brightness and size of the laser guide star</title>

et al. 1999

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The ALFA-Laser of the MPE/MPIA adaptive optic system utilizes a 4W cw-laser for the creation of a sodium layer guide star. The artificial star serves as a reference source for the adaptive optics system installed at the Calar Alto observatory in southern Spain. Several distortion sources are affecting the laser beam and result in a laser guide star spot size too large on which to lock the adaptive optics loop properly. Therefore a number of analysis tools have been installed just before the last beam expander and measurements of the beam quality have been performed. In this contribution we present parts of the experimental setup and results of these measurements. In addition we report on experimental studies of the guide star brightness when exciting the sodium layer with different polarization states of the laser radiation. A surprisingly large gain in response flux, when using circular polarization, has been measured. The complicated behavior of the polarization state with telescope position, due to phase changes at the beam relay mirrors, makes a control loop necessary to keep the projected beam optimal.

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Review of self-referenced measurement algorithms: Bridging lateral shearing interferometry and multi-probe error separation

et al. 2017

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Zernike polynomial fitting of lateral shearing interferometry

Cited by 37 publications

References 6 publications

Modal wavefront reconstruction based on Zernike polynomials for lateral shearing interferometry: comparisons of existing algorithms

Modal wavefront reconstruction based on Zernike polynomials for lateral shearing interferometry: comparisons of existing algorithms

<title>Beam quality and polarization analysis of the ALFA laser at Calar Alto and the influence on brightness and size of the laser guide star</title>

Review of self-referenced measurement algorithms: Bridging lateral shearing interferometry and multi-probe error separation

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