ZernikeR Method (n, m, rho)

Computes the value of a Zernike polynomial.

Declaration Syntax

Visual Basic

Visual C++

public static double ZernikeR(
	int n,
	int m,
	double rho
)

Public Shared Function ZernikeR ( _
	n As Integer, _
	m As Integer, _
	rho As Double _
) As Double

public:
static double ZernikeR(
	int n, 
	int m, 
	double rho
)

static member ZernikeR : 
        n:int * 
        m:int * 
        rho:float -> float

Parameters

n (Int32): The order paramter, which must be non-negative.

m (Int32): The index parameter, which must lie between 0 and n.

rho (Double): The argument, which must lie between 0 and 1.

Return Value

The value of R_n^m(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.

n	m	name
1	1	tilt
2	0	defocus
2	2	astigmatism
3	1	coma
3	3	trefoil