www.iap.uni-jena.de

Optical Design with Zemax

for PhD - Basics

Lecture 1: Introduction

2013-05-02

Herbert Gross

Summer term 2013

Time: Thursday, 8.30 – 12.00

Location: Computerpool, Helmholtzweg 4

Web page on IAP homepage under ‚learning/materials‘ provides slides and exercises

Zemax files

Contents (type of the lecture):

Not: pure Zemax handling

But: - optical design with Zemax as tool

- understanding of simulation opportunities and limits

- learning by doing

- mix of theory/principles, presented examples and own exercises

- questions and dialog welcome

The content is adapted and is changed depending on progress

Seminar: Exercises and solution of given problems integrated in the lecture

2

Overview

3

Preliminary Schedule

No Date Subject Detailed content

1 02.05. Introduction

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

preferences, updates, system reports, coordinate systems, aperture, field,

wavelength, glass catalogs, layouts, raytrace, system insertion, scaling,

component reversal

2 16.05. Fundamentals Diameters, stop and pupil,pick ups, solves, variables, ray fans, quick focus,

3D geometry, ideal lenses, vignetting, footprints, afocal systems,

3 23.05. Properties of optical systems I Aspheres, gratings and diffractive surfaces, special types of surfaces,

telecentricity

4 30.05. Properties of optical systems II Ray aiming, Delano diagram, lens catalogs

5 06.06. Aberrations I Representations, geometrical aberrations, spot, Seidel, transverse aberration

curves, Zernike wave aberrations

6 13.06. Aberrations II PSF, MTF, ESF

7 20.06. Imaging Fourier imaging, geometrical images

8 27.06. Advanced handling I Slider, universal plot, I/O of data, multi configurations

9 04.07. Optimization Algorithms, merit function, methodology, correction process, examples

10 11.07. Correction I Principles, simple systems

1. Kingslake Lens design fundamentals, SPIE Press, 2010

2. Mouroulis / McDonald Geometrical Optics and Optical Design, Oxford, 1997

3. Fischer / Tadic-Galeb Optical System Design, McGraw Hill, 2000

4. Malacara / Malacara Handbook of Lens Design, Dekker, 1994

5. Laikin Lens Design, Dekker, 2007

6. W. Smith Modern Optical Engineering, Graw Hill, 2000

7. W. Smith Modern lens design, McGraw Hill, 2005

8. Geary Lens Design with practical Examples, Willmann-Bell, 2002

9. Gross (Ed.) Handbook of optical systems, Vol 1-5, Wiley, 2005

10. Shannon The art and science of optical design,

Cambridge Univ. Press, 1997

11. G. Smith Practical computer-aided lens design, Willman Bell, 1998

12. J. Bentley / G. Olson Lens design, SPIE Press, 2012

4

Literature on optical design

1. Introduction

2. Zemax interface, menues, file handling, preferences

3. Editors, updates, windows, preferences

4. Coordinate systems and notations

5. System description, reports

6. Component reversal, system insertion, scaling

7. Solves and pickups, variables

8. 3D geometry

9. Aperture, field, wavelength

10. Glass catalogs

11. Raytrace

12. Layouts

5

Contents 1st Lecture

Modelling of Optical Systems

Principal purpose of calculations:

System, data of the structure(radii, distances, indices,...)

Function, data of properties,

quality performance(spot diameter, MTF, Strehl ratio,...)

Analysisimaging

aberration

theorie

Synthesislens design

Ref: W. Richter

Imaging model with levels of refinement

Analytical approximation and classification

(aberrations,..)

Paraxial model

(focal length, magnification, aperture,..)

Geometrical optics

(transverse aberrations, wave aberration,

distortion,...)

Wave optics

(point spread function, OTF,...)

with

diffractionapproximation

--> 0

Taylor

expansion

linear

approximation

Five levels of modelling:

1. Geometrical raytrace with analysis

2. Equivalent geometrical quantities,

classification

3. Physical model:

complex pupil function

4. Primary physical quantities

5. Secondary physical quantities

Blue arrows: conversion of quantities

Modelling of Optical Systems

ray

tracing

optical path

length

wave

aberration W

transverse

aberrationlongitudinal aberrations

Zernike

coefficients

pupil

function

point spread

function (PSF)

Strehlnumber

optical

transfer function

geometricalspot diagramm

rms

value

intersectionpoints

final analysis reference ray in

the image space

referencesphere

orthogonalexpansion

analysis

sum of

coefficientsMarechal

approxima-

tion

exponentialfunction

of the

phase

Fourier

transformLuneburg integral

( far field )

Kirchhoffintegral

maximum

of the squared

amplitude

Fouriertransformsquared amplitude

sum of

squaresMarechalapproxima-

tion

integration ofspatial

frequencies

Rayleigh unit

equivalencetypes of

aberrationsdifferen

tiationinte-

gration

full

aperture

single types of aberrations

definition

geometricaloptical

transfer function

Fouriertransform

approximation

auto-correlationDuffieux

integral

resolution

threshold value spatial frequency

threshold value spatial

frequency approximationspot diameter

approximation diameter of the

spot

Marechalapproximation

final analysis reference ray in the image planeGeometrical

raytrace

with Snells law

Geometrical

equivalents

classification

Physical

model

Primary

physical

quantities

Secondary

physical

quantities

There are 4 types of windows in Zemax:

1. Editors for data input:

lens data, extra data, multiconfiguration, tolerances

2. Output windows for graphical representation of results

Here mostly setting-windowss are supported to optimize the layout

3. Text windows for output in ASCII numerical numbers (can be exported)

4. Dialog boxes for data input, error reports and more

There are several files associates with Zemax

1. Data files (.ZMX)

2. Session files (.SES) for system settings (can be de-activated)

3. Glass catalogs, lens catalogs, coating catalogs, BRDF catalogs, macros,

images, POP data, refractive index files,...

There are in general two working modes of Zemax

1. Sequential raytrace (or partial non-sequencial)

2. Non-sequential

Zemax Interface

Helpful shortcuts:

1. F3 undo

2. F2 edit a cell in the editor

3. cntr A multiconfiguration toggle

4. cntr V variable toggle

5. F6 merit function editor

6. cntr U update

7. shift cntr Q quick focus

Window options:

1. several export options

2. fixed aspect ratios

3. clone

4. adding comments or graphics

Zemax Interface

Coordinate systems

2D sections: y-z shown

Sign of lengths, radii, angles:

z / optical axis

y / meridional section

tangential plane

x / sagittal plane

+ s- s

negative:

to the left

positive:

to the right+ R

+ j

reference

angle positive:

counterclockwise

+ R1

negative:

C to the leftpositive:

C to the right

- R2

C1C2

Coordinate Systems and Sign of Quantities

Interface surfaces

- mathematical modelled surfaces

- planes, spheres, aspheres, conics, free shaped surfaces,…

Size of components

- thickness and distances along the axis

- transversal size,circular diameter, complicated contours

Geometry of the setup

- special case: rotational symmetry

- general case: 3D, tilt angles, offsets and decentrations, needs vectorial approach

Materials

- refractive indices for all used wavelengths

- other properties: absorption, birefringence, nonlinear coefficients, index gradients,…

Special surfaces

- gratings, diffractive elements

- arrays, scattering surfaces

11

Description of Optical Systems

Single step:

- surface and transition

- parameters: radius, diameter, thickness,

refractive index, aspherical constants,

conic parameter, decenter, tilt,...

Complete system:

- sequence of surfaces

- object has index 0

- image has index N

- tN does not exist

Ray path has fixed

sequence

0-1-2-...-(N-1)-N surface

index

object

plane

1

0 2

image

plane

N-23 j N-1.... .... N

0

1

2 3 j N-2 N-1 (N)

thickness

index

surfaces

surface j

medium j

tj / nj

radius rj

diameter Dj

System Model

Menu: Reports / Prescription

data

Menu:

reports / prescription data

System Data Tables

System Data Tables

Necessary data for system calculation:

1. system surfaces with parameters (radius)

2. distances with parameters (length, material)

3. stop surface

4. wavelength(s)

5. aperture

6. field point(s)

Optional inputs:

1. finite diameters

2. vignetting factors

3. decenter and tilt

4. coordinate reference

5. weighting factors

6. multi configurations

7. ...

System data

Useful commands for system changes:

1. Scaling (e.g. patents)

2. Insert system

with other system file

File - Insert Lens

2. Reverse system

16

System Changes

Setting of surface properties

local tilt

and

decenterdiameter

surface type

additional drawing

switches

coatingoperator and

sampling for POP

scattering

options

Surface Properties and Settings

Value of the parameter dependents on other requirement

Pickup of radius/thickness: linear dependence on other system parameter

Determined to have fixed: - marginal ray height

- chief ray angle

- marginal ray normal

- chief ray normal

- aplanatic surface

- element power

- concentric surface

- concentric radius

- F number

- marginal ray height

- chief ray height

- edge thickness

- optical path difference

- position

- compensator

- center of curvature

- pupil position

Solves

Examples for solves:

1. last radius forces given image aperture

2. get symmetry of system parts

3. multiple used system parts

4. moving lenses with constant system length

5. bending of a lens with constant focal length

6. non-negative edge thickness of a lens

7. bending angle of a mirror (i'=i)

8. decenter/tilt of a component with return

Solves

Open different menus with a right-mouse-click in the corresponding editor cell

Solves can be chosen individually

Individual data for every surface in this menu

Solves

General input of tilt and decenter:

Coordinate break surface

Change of coordinate system with lateral translation and 3 rotations angles

Direct listing in lens editor

Not shown in layout drawing

21

3D Geometry

Auxiliary menus:

1. Tilt/Decenter element

2. Folding mirror

22

3D Geometry

Local tilt and decenter of a surface

1. no direct visibility in lens editor

only + near surface index

2. input in surface properties

3. with effect on following system surfaces

23

3D Geometry

Imaging on axis: circular / rotational symmetry

Only spherical aberration and chromatical aberrations

Finite field size, object point off-axis:

- chief ray as reference

- skew ray bundels:

coma and distortion

- Vignetting, cone of ray bundle

not circular symmetric

- to distinguish:

tangential and sagittal

plane

O

entrance

pupil

y yp

chief ray

exit

pupil

y' y'p

O'

w'

w

R'AP

u

chief ray

object

planeimage

plane

marginal/rim

ray

u'

Definition of Aperture and Field

Quantitative measures of relative opening / size of accepted light cone

Numerical aperture

F-number

Approximation for small

apertures:

'sin unNA

EXD

fF

'#

NAF

2

1#

image

plane

marginal ray

exit

pupil

chief ray

U'W'

DEX

f'

Aperture Definition

Important types of optical materials:

1. Glasses

2. Crystals

3. Liquids

4. Plastics, cement

5. Gases

6. Metals

Optical parameters for characterization of materials

1. Refractive index, spectral resolved n()

2. Spectral transmission T()

3. Reflectivity R

4. Absorption

5. Anisotropy, index gradient, eigenfluorescence,…

Important non-optical parameters

1. Thermal expansion coefficient

2. Hardness

3. Chemical properties (resistence,…)

Optical materials

in [nm] Name Color Element

248.3 UV Hg

280.4 UV Hg

296.7278 UV Hg

312.5663 UV Hg

334.1478 UV Hg

365.0146 i UV Hg

404.6561 h violett Hg

435.8343 g blau Hg

479.9914 F' blau Cd

486.1327 F blau H

546.0740 e grün Hg

587.5618 d gelb He

589.2938 D gelb Na

632.8 HeNe-Laser

643.8469 C' rot Cd

656.2725 C rot H

706.5188 r rot He

852.11 s IR Cä

1013.98 t IR Hg

1060.0 Nd:YAG-Laser

Test wavelengths

refractive

index n

1.65

1.6

1.5

1.8

1.55

1.75

1.7

BK7

SF1

0.5 0.75 1.0 1.25 1.751.5 2.0

1.45

Flint

Kron

Description of dispersion:

Abbe number

Visual range of wavelengths:

Typical range of glasses

ne = 20 ...120

Two fundamental types of glass:

Crone glasses:

n small, n large

Flint glasses

n large, n small

n

n

n nF C

1

' '

ne

e

F C

n

n n

1

' '

Dispersion and Abbe number

Material with different dispersion values:

- Different slope and curvature of the dispersion curve

- Stronger change of index over wavelength for large dispersion

- Inversion of index sequence at the boundaries of the spectrum possible

refractive index n

F6

SK18A

1.675

1.7

1.65

1.625

1.60.5 0.75 1.0 1.25 1.751.5 2.0

VIS

flint

n small

slope large

crown

n largeslope small

Dispersion

29

Schott formula

empirical

Sellmeier

Based on oscillator model

Bausch-Lomb

empirical

Herzberger

Based on oscillator model

Hartmann

Based on oscillator model

n a a a a a ao + + + + +

1

2

2

2

3

4

4

6

5

8

n A B C( )

+

+

2

212

2

222

n A B CD E

Fo

o

( )

( )

+ + + +

+

2 4

2

2

2 22

2 2

mmit

aaaan

o

oo

o

168.0

)(222

3

22

22

1

+

++

+

+

5

4

3

1)(a

a

a

aan o

Dispersion formulas

Relative partial dispersion :

Change of dispersion slope with

Definition of local slope for selected

wavelengths relative to secondary

colors

Special selections for characteristic

ranges of the visible spectrum

= 656 / 1014 nm far IR

= 656 / 852 nm near IR

= 486 / 546 nm blue edge of VIS

= 435 / 486 nm near UV

= 365 / 435 nm far UV

P

n n

n nF C

1 2

1 2

' '

n

400 600 800 1000700500 900 1100

e : 546 nm

main color

F' : 480 nm

1. secondary

color

g : 435 nmUV edge

C' : 644 nm

s : 852 nm

IR edge

t : 1014 nm

IR edge

C : 656 nmF : 486 nm

d : 588 nm

i : 365 nm

UV edge

i - g

F - C

C - s

C - t

F - e

g - F

2. secondary

color

1.48

1.49

1.5

1.51

1.52

1.53

1.54

n()

Relative partial dispersion

Usual representation of

glasses:

diagram of refractive index

vs dispersion n(n)

Left to right:

Increasing dispersion

decreasing Abbe number

Glass diagram

Selection of glass catalogs in

GENERAL / GLASS CATALOGS

Viewing of dispersion curves

ANALYSIS / GLASS AND GRADIENT

Viewing of glass map

33

Glasses in Zemax

Viewing of transmission curves

also for several glasses in comparison

ANALYSIS / GLASS AND GRADIENT

Definition of a glass as a variable point in the

map (model glass)

34

Glasses in Zemax

Establishing a special own

material

Select menue:

Tools / Catalogs / Glass catalogs

Options:

1. Fit index data

2. Fit melt data

Input of data for wavelengths

and indices

It is possible to establish own

material catalogs with additional

glasses as an individual library

35

Material Index Fit

Melt data:

- for small differences of real materials

- no advantage for new materials

Menue option:

‚Glass Fitting Tool‘

don‘t works (data input?)

36

Material Index Fit

Menue: Fit Index Data

Input of data: 2 options:

1. explicite entering wavelengths and indices

2. load file xxx.dat with two columns:

wavelength in m and index

Choice of 4 different dispersion formulas

After fit:

- pv and rms of approximation visible

- no individual errors seen

- new material can be added to catalog

- data input can be saved to file

37

Material Index Fit

zoptical

axis

y j

u'j-1

ij

dj-1

ds j-1

ds j

i'j

u'j

n j

nj-1

mediummedium

surface j-1

surface j

ray

dj

vertex distance

oblique thickness

rr

Ray: straight line between two intersection points

System: sequence of spherical surfaces

Data: - radii, curvature c=1/r

- vertex distances

- refractive indices

- transverse diameter

Surfaces of 2nd order:

Calculation of intersection points

analytically possible: fast

computation

38

Scheme of raytrace

yj

z

Pj+1

sj

xj

yj+1

xj+1

Pj

surface

No j

surface

No j+1

dj sj+1

intersection

point

ej

normal

vector

ej+1

ray

distance

intersection

point

normal

vector

General 3D geometry

Tilt and decenter of surfaces

General shaped free form surfaces

Full description with 3 components

Global and local coordinate systems

39

Vectorial raytrace

Vignetting/truncation of ray at finite sized diameter:

can or can not considered (optional)

No physical intersection point of ray with surface

Total internal reflection

Negative edge thickness of lenses

Negative thickness without mirror-reflection

Diffraction at boundaries

index

j

index

j+1

axis

negative

un-physical

regular

irregular

axis

no intersection

point

axis

intersection:

- mathematical possible

- physical not realized

axis

total

internal

reflection

Raytrace errors

Definition of a single ray by two points

First point in object plane:

relative normalized coordinates: Hx, Hy

Second point in entrance pupil plane:

relative normalized coordinates Px, Py

Single Ray Selection

axis

x p

pupil plane

object plane

x

y

first point

yp

second point

HyHx

Py

Px

Selection of 2 points on the ray on object and entrance pupil plane

Real and paraxial rays are tabulated

Coordinate reference can be selected to be local or global

42

Raytrace in Zemax

Graphical control of system

and ray path

Principal options in Zemax:

1. 2D section for circular symmetry

2. 3D general drawing

Several options in settings

Zooming with mouse

43

Layout options

Different options for 3D case

Multiconfiguration plot possible

Rayfan can be chosen

44

Layout options

Professional graphic

Many layout options

Rotation with mouse or arrow buttons

45

Layout options

Looking for the ray bundle cross sections

46

Footprints