Surface - Zernike Surface

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Zernike Surface

Page Contents

Description

•Surface deformations

Related Topics

Description

Creates the surface by specifying a combination of a base conic surface, an even order radial aspheric surface and Zernike surface (which can be optionally decentered). Therefore, although this surface is called the Zernike surface, it is capable of representing many surface forms, including that of a pure Zernike surface. The following describes the mathematical form of the surface for an non-tilted (Angle, ω=0) base conic surface:

In the case where the Angle, ω, parameter is used to tilt the base conic, the vertex of the base conic surface rotates around the conic axis like so:

And the form of the tilted base conic surface is replaced by:

Navigation

This feature can be accessed by selecting the Zernike Surface (Surface defined by Zernike polynomials) as the surface type in the Surface tab of a surface dialog box.

Controls

Control	Inputs / Description	Defaults
Logical Parent	Name of Parent entity.	Custom Element Name
Name	Name of surface supplied by user.	Surf n
Description	Description of the surface.
Traceable	Surface can be raytraced.	Checked
Use for trimming only	Never raytrace. Surface used for trimming only.	Unchecked
Type	Surface type.	Zernike Surface
Conic Base Surface
Rad	Radius of curvature for base surface.	0
Conic	Base surface conic constant.	0
Angle	Angle (in degrees) that the surface normal at the off axis point makes with the conic axis.	0
Aspheric Coefficients
Asph n	Even order aspheric coefficients.	0
Interpretation of Zernike Coefficients
Coeffs in Wavelens	Interpret the Zernike coefficients in waves. If unchecked, use system units.	Unchecked
Wavlen	Wavelength for coefficient interpretation.	0.5875618
Zernike Normalization Aperture
Semi-Ape X/Y	Normalization Aperture (Standard Zernike coefficients are normalized to a unit semi-aperture).	1,1
Zernike Offsets
Offset X/Y	Zernike offset (decenter) in X/Y direction	0,0
Zernike Coefficients
Zern i	Coefficient values (A_i) in waves or system units.	0

OK	Accept settings and close dialog box.
Cancel	Discard settings and close dialog box.
Apply	Accept settings and keep dialog box open.
Help	Access this Help page.

Application Notes

Zernike ordering

FRED uses a common, but not universal, Zernike term ordering as listed in the table below and considered to be the "Standard" set. This set is consistent with CodeV's standard Zernike polynomial ordering but not exactly the same as the Zemax standard Zernike ordering (or normalization). The variables x and y are the surface intersection coordinates and X and Y are the normalized coordinates in the aperture.

X = x/semiapeX, Y = y/semiapeY ; ρ ² = X² + Y² ; tan(φ) = Y/X

Term (Z_i)	Form	Name
0	1	Piston
1	ρ cos(φ)	Tilt along X
2	ρ sin(φ)	Tilt along Y
3	ρ² cos(2φ)	0/90 deg. primary astigmatism
4	2ρ²-1	Defocus
5	ρ² sin(2φ)	+-45 deg. primary astigmatism
6	ρ³ cos(3φ)	Trefoil along X axis
7	(3ρ²-2) ρ cos(φ)	3^rd order coma along X axis
8	(3ρ²-2) ρ sin(φ)	3^rd order coma along Y axis
9	ρ³ sin(3φ)	Trefoil along Y axis
10	ρ⁴ cos(4φ)	Tetrafoil along X axis
11	(4ρ²-3) ρ² cos(2φ)	0/90 deg. secondary astigmatism
12	6ρ⁴-6ρ²+1	3^rd order spherical
13	(4ρ²-3) ρ² sin(2φ)	+-45 deg. secondary astigmatism
14	ρ⁴ sin(4φ)	Tetrafoil along Y axis
15	ρ⁵ cos(5φ)	Pentafoil along X axis
16	(5ρ²-4) ρ³ cos(3φ)	Secondary trefoil along X axis
17	(10ρ⁴-12ρ²+3) ρ cos(φ)	Secondary coma along X axis
18	(10ρ⁴-12ρ²+3) ρ sin(φ)	Secondary coma along Y axis
19	(5ρ²-4) ρ³ sin(3φ)	Secondary trefoil along Y axis
20	ρ⁵ sin(5φ)	Pentafoil along Y axis
21	ρ⁶ cos(6φ)	Hexafoil along X axis
22	(6ρ²-5) ρ4 cos(4φ)	Secondary tetrafoil along X axis
23	(15ρ⁴-20ρ²+6) ρ² cos(2φ)	Tertiary astigmatism 0/90 deg.
24	20ρ⁶-30ρ⁴+12ρ²-1	5^th order spherical
25	(15ρ⁴-20ρ²+6) ρ² sin(2φ)	Tertiary astigmatism +/- 45 deg.
26	(6ρ²-5) ρ⁴ sin(4φ)	Secondary tetrafoil along Y axis
27	ρ⁶ sin(6φ)	Hexafoil along Y axis
28	ρ⁷ cos(7φ)	Heptafoil along X axis
29	(7ρ²-6) ρ⁵ cos(5φ)	Pentafoil along X axis
30	(21ρ⁴-30ρ²+10) ρ³ cos(3φ)	Tertiary trefoil along X axis
31	(35ρ⁶-60ρ⁴+30ρ²-4) ρ cos(φ)	Tertiary coma along X axis
32	(35ρ⁶-60ρ⁴+30ρ²-4) ρ sin(φ)	Tertiary coma along Y axis
33	(21ρ⁴-30ρ²+10) ρ³ sin(3φ)	Tertiary trefoil along Y axis
34	(7ρ²-6) ρ⁵ sin(5φ)	Pentafoil along Y axis
35	ρ⁷ sin(7φ)	Heptafoil along Y axis
36	ρ⁸ cos(8φ)	Octafoil along X axis
37	(8ρ²-7) ρ⁶ cos(6φ)	Secondary hexafoil along X axis
38	(28ρ⁴-42ρ²+15) ρ⁴ cos(4φ)	Tertiary trefoil along X axis
39	(56ρ⁶-105ρ⁴+60ρ²-10) ρ² cos(2φ)	Quaternary astigmatism 0/90 deg.
40	70ρ⁸-140ρ⁶+90ρ⁴-20ρ²+1	7^th order spherical
41	(56ρ⁶-105ρ⁴+60ρ²-10) ρ² sin(2φ)	Quaternary astigmatism +- 45 deg.
42	(28ρ⁴-42ρ²+15) ρ⁴ sin(4φ)	Tertiary trefoil along Y axis
43	(8ρ²-7) ρ⁶ sin(6φ)	Secondary hexafoil along Y axis
44	ρ⁸ sin(8φ)	Octafoil along Y axis
45	ρ⁹ cos(9φ)	Nonafoil along X axis
46	(9ρ²-8) ρ⁷ cos(7φ)	Secondary heptafoil along X axis
47	(36ρ⁴-56ρ²+21) ρ⁵ cos(5φ)	Tertiary pentafoil along X axis
48	(84ρ⁶-168ρ⁴+105ρ²-20) ρ³ cos(3φ)	Quaternary trefoil along X axis
49	(126ρ⁸-280ρ⁶+210ρ⁴-60ρ²+5) ρ cos(φ)	Quaternary coma along X axis
50	(126ρ⁸-280ρ⁶+210ρ⁴-60ρ²+5) ρ sin(φ)	Quaternary coma along Y axis
51	(84ρ⁶-168ρ⁴+105ρ²-20) ρ³ sin(3φ)	Quaternary trefoil along Y axis
52	(36ρ⁴-56ρ²+21) ρ⁵ sin(5φ)	Tertiary pentafoil along Y axis
53	(9ρ²-8) ρ⁷ sin(7φ)	Secondary heptafoil along Y axis
54	ρ⁹ sin(9φ)	Nonafoil along Y axis
55	ρ¹⁰ cos(10φ)	Decafoil along X axis
56	(10ρ²-9) ρ⁸ cos(8φ)	Secondary octafoil along X axis
57	(45ρ⁴-72ρ²+28) ρ⁶ cos(6φ)	Tertiary hexafoil along X axis
58	(120ρ⁶-252ρ⁴+168ρ²-35) ρ⁴ cos(4φ)	Tertiary tetrafoil along X axis
59	(210ρ⁸-504ρ⁶+420ρ⁴-140ρ²+15) ρ² cos(2φ)	Quinternary astigmatism 0/90 deg.
60	252ρ¹⁰-630ρ⁸+560ρ⁶-210ρ⁴+30ρ²-1	9^th order spherical
61	(210ρ⁸-504ρ⁶+420ρ⁴-140ρ²+15) ρ² sin(2φ)	Quinternary astigmatism +- 45 deg.
62	(120ρ⁶-252ρ⁴+168ρ²-35) ρ⁴ sin(4φ)	Quaternary tetrafoil along Y axis
63	(45ρ⁴-72ρ²+28) ρ⁶ sin(6φ)	Tertiary hexafoil along Y axis
64	(10ρ²-9) ρ⁸ sin(8φ)	Secondary octafoil along Y axis
65	ρ¹⁰ sin(10φ)	Decafoil along Y axis

Surface deformation

The Zernike Surface is a sagable surface.