Zernike polynomials used in Sensoft – our wavefront sensor software: expressions for the first 7 terms |
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Zernike polynomials are generally expressed in terms of the normalized radius r of the pupil, and the azimuthal angle , by the following expression : φ r cos (m^{n} φ + φ This is the general expression in terms of the Seidel polynomials. The Annular Zernike polynomials, on the other hand, involve aberration balancing, in which aberrations of a lower order are combined with those of the higher order for reducing the wavefront error. For example, the expression for 3rd order spherical aberration also contains a defocus term. They also take into account the effect of the annulus _{0})e of the optical element. is the zero-offset : it gives the orientation of the particular aberration with respect to the x-axis. φ_{0} |

Aberration |
Annular Zernike polynomials |
Seidel polynomials |

Defocus(n=2,m=0) |
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Tilt(n=1,m=1) |
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Coma(n=3,m=1) |
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Spherical 3rd order(n=4,m=0) |
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Astigmatism(n=2,m=2) |
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Triangular Coma(n=3,m=3) |
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Quadratic Astigmatism(n=4,m=4) |