Table 1.

Zernike Polynomial Indices, RMS Normalization Factors, and Common Names

	n	Zn(r,θ)	RMS	Name
2nd order	3	r2 sin(2θ)	$\sqrt{6}$	astigmatism
	4	2r2 – 1	$\sqrt{3}$	defocus
	5	r2 cos(2θ)	$\sqrt{6}$	astigmatism
3rd order	6	r3 sin(3θ)	$2\sqrt{2}$	trefoil
	7	(3r3 – 2r) sin(θ)	$2\sqrt{2}$	coma
	8	(3r3 – 2r) cos(θ)	$2\sqrt{2}$	coma
	9	r3 sin(3θ)	$2\sqrt{2}$	trefoil
4th order	10	r4 sin(4θ)	$\sqrt{10}$	quadrafoil
	11	(4r4 – 3r2) sin(2θ)	$\sqrt{10}$	secondary astigmatism
	12	6r4 – 6r2 + 1	$\sqrt{5}$	spherical
	13	(4r4 – 3r2) cos(2θ)	$\sqrt{10}$	secondary astigmatism
	14	r4 cos(4θ)	$\sqrt{10}$	quatrefoil