www.iap.uni-jena.de

Optical Design with Zemax

for PhD - Basics

Lecture 3: Properties of optical systems

2019-11-06

Herbert Gross

Speaker: Yi Zhong

Summer term 2019

2

Preliminary Schedule

No Date Subject Detailed content

1 23.10. Introduction

Zemax interface, menus, file handling, system description, editors, preferences, updates,

system reports, coordinate systems, aperture, field, wavelength, layouts, diameters, stop

and pupil, solves

2 30.10.Basic Zemax

handling

Raytrace, ray fans, paraxial optics, surface types, quick focus, catalogs, vignetting,

footprints, system insertion, scaling, component reversal

3 06.11.Properties of optical

systems

aspheres, gradient media, gratings and diffractive surfaces, special types of surfaces,

telecentricity, ray aiming, afocal systems

4 13.11. Aberrations I representations, spot, Seidel, transverse aberration curves, Zernike wave aberrations

5 20.11. Aberrations II Point spread function and transfer function

6 27.11. Optimization I algorithms, merit function, variables, pick up’s

7 04.12. Optimization II methodology, correction process, special requirements, examples

8 11.12. Advanced handling slider, universal plot, I/O of data, material index fit, multi configuration, macro language

9 08.01. Imaging Fourier imaging, geometrical images

10 15.01. Correction I Symmetry, field flattening, color correction

11 22.01. Correction II Higher orders, aspheres, freeforms, miscellaneous

12 29.01. Tolerancing I Practical tolerancing, sensitivity

13 05.02. Tolerancing II Adjustment, thermal loading, ghosts

14 12.02. Illumination I Photometry, light sources, non-sequential raytrace, homogenization, simple examples

15 19.02. Illumination II Examples, special components

16 26.02. Physical modeling I Gaussian beams, Gauss-Schell beams, general propagation, POP

17 04.03. Physical modeling II Polarization, Jones matrix, Stokes, propagation, birefringence, components

18 11.03. Physical modeling III Coatings, Fresnel formulas, matrix algorithm, types of coatings

19 18.03. Physical modeling IVScattering and straylight, PSD, calculation schemes, volume scattering, biomedical

applications

20 25.03. Additional topicsAdaptive optics, stock lens matching, index fit, Macro language, coupling Zemax-Matlab /

Python

1. Aspheres

2. Gratings

3. Diffractive elements

4. Special surfaces

5. Telecentricity

6. Afocal systems

7. Aperture data and diameters

8. Ray aiming

3

Contents

22 yxz

222

22

111 yxc

yxcz

22

22 yxRRRRz xxyy

Conic section

Special case spherical

Cone

Toroidal surface with

radii Rx and Ry in the two

section planes

Generalized onic section without

circular symmetry

Roof surface

2222

22

1111 ycxc

ycxcz

yyxx

yx

z y tan

4

Aspherical Surface Types

222

22

111 yxc

yxcz

1

2

b

a

2a

bc

1

1

cb

1

1

ca

Explicite surface equation, resolved to z

Parameters: curvature c = 1 / R

conic parameter

Influence of on the surface shape

Relations with axis lengths a,b of conic sections

Parameter Surface shape

= - 1 paraboloid

< - 1 hyperboloid

= 0 sphere

> 0 oblate ellipsoid (disc)

0 > > - 1 prolate ellipsoid (cigar )

5

Conic Sections

Conic aspherical surface

Variation of the conical parameter

Aspherical Shape of Conic Sections

z

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

y

22

2

111 yc

cyz

6

Equation

c : curvature 1/Rs

: eccentricity ( = -1 )

radii of curvature :

22

2

)1(11 cy

ycz

2

tan 1

s

sR

yRR

2

32

tan 1

s

sR

yRR

vertex circle

parabolic

mirror

F

f

z

y

R s

C

Rsvertex circle

parabolic

mirror

F

y

z

y

ray

Rtan

x

Rsag

tangential circle

of curvature

sagittal circle of

curvature

Parabolic Mirror

7

Simple Asphere – Parabolic Mirror

sR

yz

2

2

axis w = 0° field w = 2° field w = 4°

Equation

Radius of curvature in vertex: Rs

Perfect imaging on axis for object at infinity

Strong coma aberration for finite field angles

Applications:

1. Astronomical telescopes

2. Collector in illumination systems

8

Simple Asphere – Elliptical Mirror

22

2

)1(11 cy

ycz

F

s

s'

F'

Equation

Radius of curvature r in vertex, curvature c

eccentricity

Two different shapes: oblate / prolate

Perfect imaging on axis for finite object and image loaction

Different magnifications depending on

used part of the mirror

Applications:

Illumination systems

9

Equation

c: curvature 1/R

: Eccentricity

22

2

)1(11 cy

ycz

ellipsoid

F'

F

e

a

b

oblate

vertex

radius Rso

prolate

vertex

radius Rsp

Ellipsoid Mirror

10

Aspheres - Geometry

z

y

aspherical

contour

spherical

surface

z(y)

height

y

deviation

z

sphere

z

y

perpendicular

deviation rs

deviation z

along axis

height

y

tangente

z(y)

aspherical

shape

Reference: deviation from sphere

Deviation z along axis

Better conditions: normal deviation rs

11

Perfect stigmatic imaging on axis:

Hyperoloid rear surface

Strong decrease of performance

for finite field size :

dominant coma

Alternative:

ellipsoidal surface on front surface

Asphere: Perfect Imaging on Axis

1

1

1

1

1

2

2

2

2

n

ns

r

n

s

n

sz

ns

z

r

F

0

100

50

Dspot

w in °0 1 2

m]

12

Improvement by higher orders

Generation of high gradients

Aspherical Expansion Order

r

y(r)

0 0.2 0.4 0.6 0.8 1-100

-50

0

50

100

12. order

6. order

10. order8. order

14. order

2 4 6 8 10 12 1410

-1

100

101

102

103

order

kmax

Drms

[m]

13

Aspheres: Correction of Higher Order

Correction at discrete sampling

Large deviations between

sampling points

Larger oscillations for

higher orders

Better description:

slope,

defines ray bending

y y

residual spherical

transverse aberrations

Corrected

points

with

�y' = 0

paraxial

range

�y' = c dzA/dy

zA

perfect

correcting

surface

corrected points

residual angle

deviation

real asphere with

oscillations

points with

maximal angle

error

14

Deviation of Light

reflection

mirror

scattering

scatter plate

refraction

lens

diffraction

grating

Mechanisms of light deviation and ray bending

Refraction

Reflection

Diffraction according to the grating equation

Scattering ( non-deterministic)

'sin'sin nn

'

g mo sin sin

15

Grating Diffraction

Maximum intensity:

constructive interference of the contributions

of all periods

Grating equation

g mo sin sin

grating

g

incident

light

+ 1.

diffraction

order

s =

in-phase

grating

constant

16

Grating Equation

Intensity of grating diffraction pattern

(scalar approximation g >> )

Product of slit-diffraction and

interference function

Maxima of pattern:

coincidence of peaks of both

functions: grating equation

Angle spread of an order decreases

with growing number od periods N

Oblique phase gradient:

- relative shift of both functions

- selection of peaks/order

- basic principle of blazing

2

22

sin

sinsin

ugN

ugN

ug

ug

gNI

mg osinsin

-3 -2 -1 0 1 2 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

u = sin

17

Ideal diffraction grating:

monochromatic incident collimated

beam is decomposed into

discrete sharp diffraction orders

Constructive interference of the

contributions of all periodic cells

Only two orders for sinusoidal

Ideal Diffraction Grating

grating

g = 1 / s

incidentcollimated

light

grating constant

-1.

-2.

-3.

0.

-4.

+1.

+2.

+3.

+4.

diffraction orders

18

Real Diffraction Grating

Real diffraction grating:

1. Finite number of periods

2. Finite width of diffraction orders

grating

incident

light

- 1.

0.

diffraction

orders :

finite width

+ 1. : spectral width

finite divergenceN : finite

number of

periods

19

Diffractive Elements

z

h2

hred(x) : wrapped

reduced profile

h(x) :

continuous

profile

3 h2

2 h2

1 h2

hq(x) : quantized

profile

Original lens height profile h(x)

Wrapping of the lens profile: hred(x) Reduction on

maximal height h2

Digitalization of the reduced profile: hq(x)

20

egdn

gms

n

ns

ˆ''

'

grooves

s

s

e

d

gp

p

Surface with grating structure:

new ray direction follows the grating equation

Local approximation in the case of space-varying

grating width

Raytrace only into one desired diffraction order

Notations:

g : unit vector perpendicular to grooves

d : local grating width

m : diffraction order

e : unit normal vector of surface

Applications:

- diffractive elements

- line gratings

- holographic components

21

Diffracting Surfaces

Diffractive Optics:

Local micro-structured surface

Location of ray bending :

macroscopic carrier surface

Direction of ray bending :

local grating micro-structure

macroscopic

surface

curvature

local

grating

g(x,y)

lens

bending

angle

m-th

order

thin

layer

22

s

y

x

Strahl

Brechzahl :

n(x,y,z)

b

c s

b

c

y'

x'

z

nn

y

nn

x

nn

Dnndt

rd

2

2

Ray: in general curved line

Numerical solution of Eikonal equation

Step-based Runge-Kutta algorithm

4th order expansion, adaptive step width

Large computational times necessary for high accuracy

23

Raytracing in GRIN media

3

15

2

1413

3

12

2

1110

4

9

3

8

2

76

8

5

6

4

4

3

2

21,

ycycycxcxcxc

zczczczchchchchchcnn o

Analytical description of grin media by Taylor expansions of the function n(x,y,z)

Separation of coordinates

Circular symmetry, nested expansion with mixed terms

Circular symmetry only radial

Only axial gradients

Circular symmetry, separated, wavelength dependent

8

19

6

18

4

17

2

1615

38

14

6

13

4

12

2

1110

2

8

9

6

8

4

7

2

65

8

4

6

3

4

2

2

1,

hchchchcczhchchchccz

hchchchcczhchchchcnn o

n n c c h c c h c c h c c h c c ho , ( ) ( ) ( ) ( ) ( ) 1 2 1

2

3 1

4

4 1

6

5 1

8

6 1

10

n n c c z c c z c c z c c zo , ( ) ( ) ( ) ( ) 1 2 1

2

3 1

4

4 1

6

5 1

8

n n c h c h c h c h c z c z c zo , , , , , , , , 1

2

2

4

3

6

4

8

5 6

2

7

3

24

Description of GRIN media

Curved ray path in inhomogeneous media

Different types of profiles

Gradient Lens Types

n(x,y,z)

non

i

nentrance

(y)

y

z

nexit

(y)

radial gradient

rod lens

axial gradient

rod lens

radial and axial

gradient

rod lens

radial gradient

lens

axial gradient

lens

radial and axial

gradient lens

25

Collecting Radial Selfoc Lens

L

P P'

F

F'

L

P P'

F'

Thick Wood lens with parabolic index

profile

Principal planes at 1/3 and 2/3 of

thickness

n2 > 0 : collecting lens

n2 < 0 : negative lens

2

20)( rnnrn

26

Gradient Lenses

Refocusing in parabolic profile

Helical ray path in 3 dimensions

axis ray bundle

off axis ray bundle

waist

points

view

along z

perspectivic viewy

x

y

x

y'

x'

z

27

Gradient Lenses

Types of lenses with parabolic profile

Pitch length

ymarginal

ycoma

2

0

2

0

2

20

2

11

1

)(

rAn

rnn

rnnrn

r

rnn

np

2

2

22

2

0

0.25 Pitch

Object at infinity

0.50 Pitch

Object at front surface

0.75 Pitch

Object at infinity

1.0 Pitch

Object at front surface

Pitch 0.25 0.50 0.75 1.0

28

Special stop positions:

1. stop in back focal plane: object sided telecentricity

2. stop in front focal plane: image sided telecentricity

3. stop in intermediate focal plane: both-sided telecentricity

Telecentricity:

1. pupil in infinity

2. chief ray parallel to the optical axis

Telecentricity

telecentric

stopobject imageobject sides chief rays

parallel to the optical axis

29

Double telecentric system: stop in intermediate focus

Realization in lithographic projection systems

Telecentricity

telecentric

stopobject imagelens f1 lens f2

f1

f1

f2

f2

30

The Special Infinity Cases

Simple case:

- object, image and pupils are lying in a finite

distance

- non-telecentric relay systems

Special case 1:

- object at infinity

- object sided afocal

- example: camera lens for distant objects

Special case 2:

- image at infinity

- image sided afocal

- example: eyepiece

Special case 3:

- entrance pupil at infinity

- object sides telecentric

- example: camera lens for metrology

Special case 4:

- exit pupil at infinity

- image sided telecentric

- example: old fashion lithographic lens

31

The Special Infinity Cases

Very special: combination of above cases

Examples:

- both sided telecentric: 4f-system, lithographic lens

- both sided afocal: afocal zoom

- object sided telecentric, image sided afocal:

microscopic lens

Notice: telecentricity and afocality can not be combined on the same side of a system

32

Image in infinity:

- collimated exit ray bundle

- realized in binoculars

Object in infinity

- input ray bundle collimated

- realized in telescopes

- aperture defined by diameter

not by angle

object at

infinity

image in

focal

plane

lens acts as

aperture stop

collimated

entrance bundle

image at

infinity

stop

image

eye lens

field lens

Object or field at infinity

33

1.Telecentric object space

Set in menue General / Aperture

Means entrance pupil in infinity

Chief ray is forced to by parallel to axis

Fixation of stop position is obsolete

Object distance must be finite

Field cannot be given as angle

2.Infinity distant object

Aperture cannot be NA

Object size cannot be height

Cannot be combined with telecentricity

3.Afocal image location

Set in menue General / Aperture

Aberrations are considered in the angle domain

Allows for a plane wave reference

Spot automatically scaled in mrad

34

Telecentricity, Infinity Object and Afocal Image

35

Infinity cases

sample layoutexit pupilentrance

pupilimageobjectcase

finitefinitefinitefinite1

infinity

image

telecentric

finitefinitefinite2

infinity

image

telecentric

infinity

object

telecentric

finitefinite3

finitefiniteinfinityinfinity4

finiteinfinityfinitefinite5

finitefinitefiniteinfinity6

finitefiniteinfinityfinite7

finite

infinity

object

telecentric

infinityfinite8

infinity

image

telecentric

finitefiniteinfinity9

example

relay

metrology lens

lithographic

projection lens

4f-system

afocal zoom

telescopes

beam expander

metrology lens

camera lens

focussing lens

eyepiece

collimator

microscopic lens

infinity metrology

lens

finiteinfinityfiniteinfinity10

infinityfiniteinfinityfinite11

impossible

impossible

finiteinfinityinfinityinfinity12

infinityinfinityfiniteinfinity13

impossible

impossible

infinityfiniteinfinityinfinity14

infinityinfinityinfinityfinite15

impossible

impossible

infinityinfinityinfinityinfinity16 impossible

Systematic of all

infinity cases

Physically impossible:

1. object and entrance

pupil in infinity

2. image and exit

pupil in infinity

Different possible options for specification of the aperture in Zemax:

1. Entrance pupil diameter

2. Image space F#

3. Object space NA

4. Paraxial working F#

5. Object cone angle

6. Floating by stop size

Stop location:

1. Fixes the chief ray intersection point

2. input not necessary for telecentric object space

3. is used for aperture determination in case of aiming

Special cases:

1. Object in infinity (NA, cone angle input impossible)

2. Image in infinity (afocal)

3. Object space telecentric

Aperture data in Zemax

36

There are several different types of

diameters in Zemax:

1. Surface stop

- defines the axis intersection of the chief

ray

- usually no influence on aperture size

- only one stop in the system

- is indicated in the Lens Data Editor

by STO

- if the initial aperture is defined, the size

of the stop semi-diameter is determined

by marginal raytrace

37

Diameters in Zemax

2. Userdefined diameter at a surface in

the Lens Data Editor (U)

- serves also as drawing size in the

layout (for nice layouts)

- if the diameter in the stop plane is

fixed, the initial aperture can be

computed automatically by

General / Aperture Type /

Float by Stop Size

This corresponds to a ray aiming

3. Individual diameter of perhaps

complicated shape at every surface

(‚apertures‘)

- no impact on the drawing

- is indicated in the Lens Data Editor

by a star

- the drawing of vignetted rays can

by switched on/off

38

Diameters in Zemax

4. Individual aperture sizes for every field point can be set by

the vignetting factors of the Field menu

- real diameters at surfaces must be set

- reduces light cones are drawn in the layout

VDX, VDY: relative decenter of light cone in x, y

VCX, VCY: compressian factors in x, y

VAN: azimuthal rotation angle of light cone

- If limiting diameters are set in the system, the corresponding

factors can be calculated by the Set Vig command

Diameters and stop sizes

39

40

Diameters in Zemax

In the Lens data editor menue, the diameters

and apertures can be converted

automatically

Userdefined diameter at a surface in

the Lens Data Editor (U)

- serves also as drawing size in the

layout (for nice layouts)

- if the diameter of the system stop

is fixed, the initial aperture can be

computed automatically by

General / Aperture Type /

Float by Stop Size

This corresponds to a ray aiming on the rim of the stop surface.

The aperture values in the PRESCRIPTION DATA list then changes with the diameter

A more general aiming and determination of the opening for all predefined diameters is not

possible in Zemax

41

Ray Aiming