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OrthogonalPolynomialsZernikeR Method

Computes the value of a Zernike polynomial.

Namespace:  Meta.Numerics.Functions
Assembly:  Meta.Numerics (in Meta.Numerics.dll) Version: 4.0.5.0 (4.0.5.0)
Syntax
public static double ZernikeR(
	int n,
	int m,
	double rho
)

Parameters

n
Type: SystemInt32
The order paramter, which must be non-negative.
m
Type: SystemInt32
The index parameter, which must lie between 0 and n.
rho
Type: SystemDouble
The argument, which must lie between 0 and 1.

Return Value

Type: 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
See Also