OrthogonalPolynomialsZernikeR Method

Computes the value of a Zernike polynomial.

Definition

Namespace: Meta.Numerics.Functions
Assembly: Meta.Numerics (in Meta.Numerics.dll) Version: 4.2.0+6d77d64445f7d5d91b12e331399c4362ecb25333
C#
public static double ZernikeR(
	int n,
	int m,
	double rho
)

Parameters

n  Int32
The order paramter, which must be non-negative.
m  Int32
The index parameter, which must lie between 0 and n inclusive.
rho  Double
The argument, which must lie between 0 and 1.

Return Value

Double
The value of Rnm(ρ).

Remarks

Zernike polynomials are orthononal on the interval [0,1] with the weight ρ.

They are often used in optics to characterize the imperfections in a lens. In this context, the amplitude of each is associated with a name given in the following table.

nmname
11tilt
20defocus
22astigmatism
31coma
33trefoil

Exceptions

ArgumentOutOfRangeExceptionn is negative, or m lies outside {0 .. n}, or rho lies outside [0, 1].

See Also