WOLFRAM|DEMONSTRATIONS PROJECT

Zernike Polynomials and Optical Aberration

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aberration
piston
tip
tilt
defocus
astigmatism 1
astigmatism 2
coma 1
coma 2
trefoil 1
trefoil 2
spherical
5th-order astigmatism 1
5th-order astigmatism 2
quadrafoil 1
quadrafoil 2
5th-order coma 1
5th-order coma 2
5th-order trefoil 1
5th-order trefoil 2
pentafoil 1
pentafoil 2
5th-order spherical
annulus radius
intensity map visualization options
surface
density
contours
3D surface
colors
LakeColors
The Zernike polynomials are commonly used in the analysis of adaptive optics systems. Annular Zernikes are particularly useful for analyzing the aberrations of telescopes with annular pupils (e.g., Cassegrain telescopes). Choose a type of aberration and a radius of the annulus to see the resulting polynomial.