Table 2. Fringe Zernike Polynomials {Z_n, n = 1,…, 9, 16, 25, 36, 37}.

n	Fringe Zernike Polynomial	Aberration Type
1	1	Piston
2	ρcosθ	Distortion - Tilt (x-axis)
3	ρsinθ	Distortion - Tilt (y-axis)
4	2ρ 2 − 1	Defocus - Field Curvature
5	ρ 2cos2θ	Astigmatism, Primary (0° or 90°)
6	ρ 2sin2θ	Astigmatism, Primary ( ± 45°)
7	(3ρ 3 − 2ρ)cos2θ	Coma, Primary (x-axis)
8	(3ρ 3 − 2ρ)sin2θ	Coma, Primary (y-axis)
9	6ρ 4 − 6ρ 2 + 1	Spherical Aberration, Primary
16	20ρ 6 − 30ρ 4 + 12ρ 2 − 1	Spherical Aberration, Secondary
25	70ρ 8 − 140ρ 6 + 90ρ 4 − 20ρ 2 + 1	Spherical Aberration, Tertiary
36	252ρ 10 − 630ρ 8 + 560ρ 6 − 210ρ 4 + 30ρ 2 − 1	Spherical Aberration, Quaternary
37	924ρ 12 − 2772ρ 10 + 3150ρ 8 − 1680ρ 6 + 420ρ 4 − 42ρ 2 + 1	Spherical Aberration, 12th order