www.iap.uni-jena.de

Optical Design with Zemax

for PhD - Basics

Seminar 2 : Illumination I

2014-11-19

Herbert Gross

Winter term 2014

2

Preliminary Schedule

No Date Subject Detailed content

1 12.11. Repetition Correction, handling, multi-configuration

2 19.11. Illumination I Simple illumination problems

3 26.11. Illumination II Non-sequential raytrace

4 03.12. Physical modeling I Gaussian beams, physical propagation

5 10.12. Physical modeling II Polarization

6 07.01. Physical modeling III Coatings

7 14.01. Tolerancing I Sensitivity, practical procedure

8 21.01. Tolerancing II Adjustment, thermal loading, ghosts

9 28.01. Additional topics I Adaptive optics, stock lens matching, index fit

10 04.02. Additional topics II Macro language, coupling Zemax-Matlab

Basic notations of photometry

Lambertian radiator

Flux calculation

Non-sequential raytrace

Light sources

Classical illumination systems

Beam homogeneization by integrator rods

Beam homogeneization by fly eye condensors

Miscellaneous

Illumination in Zemax

Contents

3

Radiometric vs Photometric Units

Quantity Formula Radiometric Photometric

Term Unit Term Unit

Energy Energy Ws Luminous Energy Lm s

Power

Radiation flux

W

Luminous Flux Lumen Lm

Power per area and solid angle

Ld

d dA

2

cos

Radiance W / sr /

m2

Luminance cd / m

2

Stilb

Power per solid angle

dAL

d

dI

Radiant Intensity W / sr

Luminous Intensity Lm / sr,

cd

Emitted power per area

dLdA

dE cos

Radiant Excitance W / m2

Luminous Excitance Lm / m2

Incident power per area

dLdA

dE cos

Irradiance W / m2

Illuminance Lux = Lm / m

2

Time integral of the power per area

H E dt

Radiant Exposure Ws / m2

Light Exposure Lux s

4

Solid Angle

ddA

r

dA

r

cos

2 2

2D extension of the definition of an angle:

area perpendicular to the direction over square of distance

Area element dA in the distance r with inclination

Units: steradiant sr

Full space: = 4p

half space: = 2p

Definition can be considered as

cartesian product of conventional angles

source point

d

rdA

n

yxr

dy

r

dx

r

dAd

2

5

Solid Angle: Special Cases

Cone with half angle j

Thin circular ring on spherical surface

j jp cos12

jjpjjp

dr

drrd

sin2

sin22

j

dj

r

ring

surfacep1cosj

r

z

x

y

j

d

dj

6

Irradiance

Irradiance: power density on a surface

Conventional notation: intensity

Unit: watt/m2

Integration over all incident directions

Only the projection of a collimated beam

perpendicular to the surface is effective

dLdA

dE cos

cos)( 0 EE

A

A

E()

Eo

7

d

s

dAS

S

n

Differential Flux

Differential flux of power from a

small area element dAs with

normal direction n in a small

solid angle dΩ along the direction

s of detection

Integration of the radiance over

the area and the solid angle

gives a power

S

SS

S

AdsdL

dAdL

dAdLd

cos

2

PdA

A

8

Fundamental Law of Radiometry

Differential flux of power from a

small area element dAS on a

small receiver area dAR in the

distance r,

the inclination angles of the

two area elements are S and

R respectively

Fundamental law of radiometric

energy transfer

The integration over the geometry gives the

total flux

ESES

ES

dAdAr

L

dAdAr

Ld

coscos2

2

2

z

s

s

xs

ys

source

receiver

xR

yR

zR

AS

r

ns

AR

nR

S

R

9

Radiance independent of space coordinate

and angle

The irradiance varies with the cosine

of the incidence angle

Integration over half space

Integration of cone

Real sources with Lambertian

behavior:

black body, sun, LED

constLsrL

,

Lambertian Source

jpj 2sin)( ALLam

coscos oEALE

LAdEHR

Lam p )(

E()

x

z

L

x

z

10

Radiation Transfer

Basic task of radiation transfer problems:

integration of the differential flux transfer law

Two classes of problems:

1. Constant radiance, the integration is a purely geometrical task

2. Arbitrary radiance, a density function has to be integrated over the geometrical light tube

Special cases:

Simple geometries, mostly high symmetric , analytical formulas

General cases: numerical solutions

- Integration of the geometry by raytracing

- Considering physical-optical effects in the raytracing:

1. absorption

2. reflection

3. scattering

ESESES dAdAr

LdAdA

r

Ld coscos

22

2

11

Raytube-Modell

Decomposition of the light cone into small infinitesimal ray tubes

The irradiance scales with the

area change

L,M,N

x

y

y'

x'

Ry

Rx

A

A'

R'y

R'x

r

AR

r

R

rA

yx

11'

12

Raytube-Modell

Optical power flux

General transfer:

Jacobian matrix of differential

area transform

dx

dy

dy

dx

dy

dy

dx

dx

dy

dy

dx

dy

dy

dx

dx

dx

J''''

''

''

AJA '

112

1,

2 coscos

jjjj

jj

jAA

r

L

surface No j

xj

yj

zj

rj,j+1

Ajnj

j

zj+1

xj+1

yj+1surface No j+1

Aj+1

nj+1j+1

13

Non-Sequential Raytrace

Conventional raytrace:

- the sequence of surface hits of a ray is pre-given and is defined by the index vector

- simple and fast programming of the surface-loop of the raytrace

Non-sequential raytrace:

- the sequence of surface hits is not fixed

- every ray gets ist individual path

- the logic of the raytrace algorithm determines the next surface hit at run-time

- surface with several new directions of the ray are allowed:

1. partial reflection, especially Fresnel-formulas

2. statistical scattering surfaces

3. diffraction with several grating orders or ranges of deviation angles

Many generalizations possible:

several light sources, segmented surfaces, absorption, …

Applications:

1. illumination modelling

2. statistical components (scatter plates)

3. straylight calculation

14

Nonsequential Raytrace: Examples

Signal

1 2 3 4

Reflex 1 - 2

Reflex 3 - 2

1

2

3

1. Prism with total internal

reflection

2. Ghost images in optical systems

with imperfect coatings

15

Non-Sequential Raytrace: Examples

3. Illumination systems, here:

- cylindrical pump-tube of a solid state laser

- two flash lamps (A, B) with cooling flow tubes (C, D)

- laser rod (E) with flow tube (F, G)

- double-elliptical mirror

for refocussing (H)

Different ray paths

possible

A: flash lamp gas

H

4

B: glass tube of

lamp

C: water cooling

D: glass tube of cooling

5

6

3

2

1

7

E: laser rod

F: water cooling

G: glass tube of cooling

16

Simple raytrace:

S/N depends on the number of rays N

Improved SNR: raytube propagation transport of energy density

Illumination Simulation

N = 2.000 N = 20.000 N = 200.000 N = 2.000.000

N = 100.000

0

1

-0.5 -0.3 -0.1 0.1 0.3 0.50

1

-0.5 -0.3 -0.1 0.1 0.3 0.50

1

-0.5 -0.3 -0.1 0.1 0.3 0.5

N = 10.000 N = 63

NTR

= 63 NTR

= 63 NTR

= 63

Special problems in the layout of illumination systems:

1. complex components: segmented, multi-path

2. special criteria for optimization:

- homogeneity

- efficiency

3. incoherent illumination: non-unique solution

Illumination Systems

Lighthouse optics

Fresnel lenses with height 3 m

Separated segments

Complex Geometries

CAD model of light sources:

1. Real geometry and materials

2. Real radiance distributions

Bulb lamp

XBO-

lamp

Realistic Light Source Models

Angle Indicatrix Hg-Lamp high Pressure

cathode

0

800

1200

1600

0 1020

30

40

50

60

70

80

90

100

110

120

130

140

150

160170

180190200

210

220

230

240

250

260

270

280

290

300

310

320

330

340350

400

azimuth angles :

30°50°

70°

90°

110°

130°

150°

Polar diagram of angle-dependent

intensity

Vertical line:

Axis Anode - Cathode

XBO-

lamp

Arrays - Illumination Systems

Illumination LED lighting

Ref: R. Völkel / FBH Berlin

source

collector condenser objective

lens

object

plane

image

plane

field stop aperture stopback focal plane -

pupil

Köhler Illumination Principle

Principle of Köhler

illumination:

Alternating beam paths

of field and pupil

No source structure in

image

Light source conjugated

to system pupil

Differences between

ideal and real ray paths

condenser

object

plane

aperture

stopfield

stop filter

collector

source

Illumination Optics: Collector

Requirements and aspects:

1. Large collecting solid angle

2. Correction not critical

3. Thermal loading

large

4. Mostly shell-structure

for high NA

W(yp)

200

a) axis b) field

200

W(yp)

yp

480 nm

546 nm

644 nm

yp

W(yp)

200

a) axis b) field

200

W(yp)

yp

yp

480 nm

546 nm

644 nm

Illumination Optics: Condenser

2. Abbe type, achromatic, NA = 0.9 , aplanatic, residual spherical

3. Aplanatic achromatic, NA = 0.85

y'100 m

a) axis b) field

yp

480 nm

546 nm

644 nm

y'100 m

yp

x'100 m

xp

tangential sagittal

y'100 m

a) axis b) field

yp

480 nm

546 nm

644 nm

y'100 m

yp

x'100 m

xp

tangential sagittal

Illumination Optics: Condenser

2. Epi-illumination

Complicated ring-shaped components

around objective lens

object

ring lens

illuminationobservation

object

ring lens

illuminationobservationcircle 1

circle 2

Basic problem:

Generation of a desired intensity distribution in space/angle domain

Coherent beams:

- appropriate phase element

- free space propagation delivers re-distribution of intensity

- optional phase correcting element

- components: 1. smooth aspheres

2. diffractive elements

3. holograms

Incoherent beams:

- superposition of folded beams with subapertures

- basic principle of energy conservation

- components: 1. segmented mirrors

2. lenslet arrays

3. light pipes

4. fibers

5. axicons

Partial coherent beams:

problems with residual speckle

Principles of Beam Profiling

Generation of a ring profile

Axicon:

cone surface with peak on axis

Ringradisu in the focal plane

of the lens

Ring width due to diffraction

fnR )1(

a

fR

22.1

Axicon Lens Combination

R

o

ff

a

R

o

f

Beam Profiling / Overview

beam profiling

incoherent coherent

single

aperture

multiple

perture

single

aperture

multiple

aperture

super-

position

aperture

fillingnear field far field

aspherical

lens

geometrical

transform

bi-prism,

axicon

spectrum

shaping

holographic

transform

phase

filtering

phase

grating

spatial

phase

filtering

microlenses

partial coherent

geometrical

transform

tailoring

edge ray

principle

LSQ

numerical

source

integration

Rev: H.-P. Herzig

Superposition of subapertures with different

profiles

Flip of orientation due to reflection

Simple example:

Towards tophat from gaussian profile

by only one reflection

Beam Profile Folding for one Reflection

intensity

x

input

profile

1 2 3

single

contributions

overlay

flip due to

reflection

Ideal homogenization:

incoherent light without interference

Parameter:

Length L, diameter d, numerical aperture angle , reflectivity R

Partial or full coherence:

speckle and fine structure disturbs uniformity

Simulation with pint ssource and lambert indicatrix or supergaussian profile

Rectangular Slab Integrator

x

I()

x'

I(x')

d

L

Principle of a light pipe / slab integrator:

Mixing of flipped profiles by overlapping of sub-apertures

Spatial multiplexing, angles are preserved

Number of internal reflexions determine the quality of homogeneity

Rectangular Integrator Slab

length L

width

asquare

rod

virtual

intersection

point

point of

incidence

exit

surface

Number of reflection depends on

length and incident angle

Kontrast V as a function of

length

Rectangular Mixing Integrator Rod

a

uLm

'tan2

a u'L )

V

1

1

0.1

1.5 2

0.01

0.5

diameter

a

length

L

x

u

x'

u'

reflections

3

3 a

2

2

1

1

0

3

2

1

Rectangular Slab Integrator

Full slab integrator:

- total internal reflection, small loss

- small limiting aperture

- problems high quality of end faces

- also usable in the UV

Hollow mirror slab:

- cheaper

- loss of 1-2% per reflection

- large angles possible

- no problems with high energy densities

- not useful in the UV

slab integrator

hollow integrator

Conical Light Taper

Waveguide with conical boundary

Lagrange invariant: decrease in diameter causes increase in angle:

Aperture transformed

Number of reflections:

- depends on diameter/length ratio

- defines change of aperture angle

'sinsin uDuD outin

u'

u

L

Din

/

2

n

Dout

/

2

Reflexion

No j

j

r i

n

Array of lenslets divides the pupil in supabertures

Every subaperture is imaged into the field plane

Overlay of all contributions gives uniformity

Problems with coherence: speckle

Different geometries: square, hexagonal, triangles

Simple setup with one array

Improved solution with double array and additional

imaging of the pupil

Flyeye Array Homogenizer

farrD

arr

xcent

u

xray

Dsub

subaperture

No. j

change of

direction

condenser

1 2 3 5

array

4

focal plane of the

array

receiver

plane

starting

plane

farr

fcon

Dill

Dsub

Flyeye Array Homogenizer

condenserarray

spherical surface with

secondary source

points

illumination

field

Simple model: Secondary source of a pattern of point sources

Fly Eyes Condensor with Field Array

d1

illumination

fieldfcond

condenser

lens

field

lens

D

L

array 1

u'

Dsub

'

array 2

farr1

farr2

d3

d2

z

Flyeye Array Homogenizer

a b

Example illumination fields of a homogenized gaussian profile

a) single array

b) double array

- sharper imaging of field edges

- no remaining diffraction structures

Partial Coherent Illumination

Flys Eye Condenser

Partial coherent radiation out of a fiber

Single step flys eye condenser

Residual speckle (green, mean) depends on

focal length of collimator and divergence of the beam

Modern mode decomposition: localized shifted modes

- Non-orthogonal basis mode decomposition

- Optimized basis to fulfill sampling theorem

- Mode support localized corresponding

to coherence cells

axialer Punkt

off-axis Punkt

maximal

Phase mit Kipp

d2

Kollimator Array Kondensor

-

30

-

20

-

100

1

0

2

0

3

0

0

0.

2

0.

4

0.

6

0.

8

1

-

30

-

20

-

100

1

0

2

0

3

0

0

0.

2

0.

4

0.

6

0.

8

1

= 1.35 mrad

C = 2.67 %

= 0.68 mrad

C = 8.39 %

I(x)

-5 -4 -3 -2 -1 0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x

single

gaussian

beamlets

given

intensity

profile

approximated

intensity

profile

Fly Eyes Condensor in the Phase Space

-1 0 1

-4 -2 0 2 4 -4 -2 0 2 4 -5 0 5 -5 0 5 -5 0 5

-2 -1 0 1 2-2 -1 0 1 2-2 -1 0 1 2-2 -1 0 1 2

I(u)

I(x)

before array after array after condenser in array focal plane in receiver plane

x

u

x

u

Lenses of constant focal length

Size of refractive lenses large: diffraction neglectable

Improved mixing effect due to statistical variation of location and size of lenses

Geometry : Voronoi distribution

Statistical Array of Micro Lenses

Statistical Array of Micro Lenses

Phase of

mask

Far field

coherent

Micro speckle

Statistical Scatter Plate: Coherence

Speckle in farfiel due to

residual coherence

1. coherent

2. partial coherent

divergence 0.5 mrad

3. partial coherent

divergence 1.0 mrad

Reflection based array:

Facetted mirror

Segmented Mirror

Thick asphere:

- point and slope coupled by

equation

Fresnel lens:

- wrapped height h

- error due to wrong ray bending

location

- smallest size of period at point

of largest slope (mostly edge)

Diffractive element:

- smallest lateral period in range

of wavelength g(r)

- grating equation/diffraction

dominates direction of light

propagation

46

Fresnel Lens

F

a) smooth asphere

F

b) Fresnel lens

h wrapping height

gmin

smallest

period

Principle:

Change of lateral intensity profile

during propagation for non-flat

phase

Setup:

1. first asphere introduces

phase for desired redistribution

2. propagation over z

3. second asphere corrects

the phase

Usually the profile exists only

over o short distance

z

x

profile

I(x)

x

profile

I(x)

x

behind

before

phase

x

before

behind

phase

asphere 1 asphere 2

transfer over

distance

d

Geometrical Refractive Beam Profiling

Analytical solution for circular symmetry

Conservation of energy:

Change of energy density

distribution

Scheme:

Gaussian

profile

2nd asphere1st asphere

tophat profile

change of intensity distribution

due to perturbed phase

'

0'0

''2)'(2)(

r

r

out

r

r

in drrrIdrrrI pp

22

002

iiwIwIp

p

Geometrical Refractive Beam Profiling

Transform of Gauss into Tophat

Simple options:

Relative illumination / vignetting for systems with rotational symmetry

Advanced possibility:

- non-sequential component

- embedded into sequential optical systems

- examples: lightguide, arrays together with focussing optics, beam guiding,...

General illumination calculation:

- non-sequential raytrace with complete different philosophy of handling

- object oriented handling: definition of source, components and detectors

49

Illumination in Zemax

Relative illumination or vignetting plot

Transmission as a function of the field size

Natural and arteficial vignetting are seen

50

Relative Illumination

0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25

y field in °

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

relative

illumination

natural vignetting

cos4 w

onset of

truncation

total

illumination

vignetting

Partly non-sequential raytrace:

Choice of surface type ‚non-sequential‘

Non-sequential component editor with many control parameters is used to describe the

element:

- type of component

- reference position

- material

- geometrical parameters

Some parameters are used from the lens data editor too:

entrance/exit ports as interface planes to the sequential system parts

51

Illumination in Zemax

Example:

Lens focusses into a rectangular lightpipe

52

Illumination in Zemax

Complete non-sequential raytrace

Switch into a different control mode in File-menue

Defining the system in the non-sequential editor, separated into

1. sources

2. light guiding components

3. detectors

Various help function are available to

constitue the system

It is a object (component) oriented philosophy

Due to the variety of permutations, the raytrace

is slow !

53

Illumination in Zemax

Many types of components and options are available

For every component, several

parameters can be fixed:

- drawing options

- coating, scatter surface

- diffraction

- ray splitting

- ...

54

Illumination in Zemax

Starting a run requires several control

parameters

Rays can be accumulated

55

Illumination in Zemax

Typical output of a run:

56

Illumination in Zemax