課程第一本印刷day5os

Optical

System

Design

Using

ZemaxK?hler

IlluminationK?hler

Illumination5

-

2u

In

this

example,

we

will

tie

together

everything

wehave

done

in

theclass

so

faru

First

order

optical

principlesu

Sequential

optimization

and

analysisu

Non-sequential

analysisu

The

example

is

aK?hlerillumination

system,

which

is

a

widely

usedmethod

of

providing

uniform

illumination

in

projectors,

microscopes,u

The

K?hler

illumination

system

consists

ofastandard

projector

lenswitha

condenser

optic

that

illuminates

the

slide/film/light

modulatwhich

is

the

image

being

projectedK?hler

Illuminationu

With

K?hler

illumination,

a

bright,

non-uniform

source

is

imaged

ontothe

aperture

of

the

condenser

systemu

The

object

to

be

projected

is

positioned

at

the

stop

of

the

condenseru

The

object

is

uniformly

illuminated,

since

all

points

in

the

field

ofoverlap

at

the

aperture5

-

3K?hler

Illumination5

-

4u

We

will

design

the

projection

lens

first,

and

use

an

“off

the

shelf”design

rather

than

designing

one

from

scratchu

We

will

then

design

the

illumination

systemu

We

will

then

combine

the

two

systems

intoa

single

systemu

Finally

we

will

switch

to

non-sequential

mode

and

do

a

complete

endto

end

system

analysisOptical

System

Design

Using

ZemaxThe

Projection

LensProjection

Optics5

-

6u

We

want

to

concentrate

on

the

illumination

optics.

Use

the

Zemaxdouble

Gauss

lens

file

for

the

projection

optics.u

However,

this

file

is

pointing

the

wrong

way.

It

is

imagingadistantscene

to

a

close

detector.u

We

want

to

project

a

close

scene

onto

a

distant

screenu

Zemax

has

a

handy

tool

for

doing

this,

but

as

the

application

ischangingfrom

imaging

to

projection

it

requiresa

little

set

up

firstu

Load

Samples\Sequential\Objectives\Double

Gauss

28

degreefield.zmxLock

Down

the

Design5

-

7u

As

this

is

intended

to

be

an

“off

the

shelf”

optic,

we

will

not

do

anyoptimization.

We

want

to

make

sure

the

design

does

not

change.

So:u

Optimize…Remove

All

Variablesu

Remove

any

solves

(there

are

none,

but

just

listed

for

completeness)u

Use

Convert

Semi-Diameters

to

Circular

Apertures

button

on

the

LensData

Editoru

Set

the

system

aperture

to

“Float

By

Stop”u

System

Explorer…Ray

Aiming

(Paraxial)Reverse

the

Lensu

To

spin

the

lens

around,

use

ReverseElementson

the

Lens

DataEditor5

-

8Swap

the

Back

Focusu

Copy

the

image

thickness

(57.315

mm)

to

the

object

surfaceu

Set

the

field

definition

to

object

height,

y-fields:

(0,

15.1,21)u

(24x36

mm

film)u

Change

the

image

thickness

to

5000,

as

the

screen

will

be

5

metersaway5

-

9Refocus

the

Lensu

The

screen

is

only

5

meters

away,

which

is

long

but

not

infiniteu

This

is

an

off-the

shelf

optic,

so

we

cannot

re-optimize

itu

But

we

can

adjust

the

object

conjugate

(thickness

of

surface

0)

forbest

focus

on

the

image

surfaceu

Optimize…Quick

Adjust:5

-

10Refocus

the

Lensu

The

object

thicknesschanges

from

57.315

to59.276u

Spotis

about

0.5

mm,

5

meters

away!

Notbad!u

Save

this

lens

as

“Double

Gauss

Projector.ZMX”5

-

11Relative

Illuminationu

Analyze….Extended

Scene

Analysis…Relative

Illumination

showshow

the

image

brightness

varies

assuming

a

uniform

plane

object5

-

12Image

Simulationu

Image

is

nice

and

crisp,

but

note

darkening

around

edges

and

incorners5

-

13Optical

System

Design

Using

ZemaxCondenser

DesignCondenser

Designs5

-

15u

Condenser

optics

take

energy

from

a

source

and

couple

it

into

aprojector

opticu

In

an

Abbe

condenser,

we

form

an

image

of

the

source

at

the

filmplane,

so

the

projected

image

suffers

from

having

an

image

of

thesource

imposed

upon

itu

Typically

rectified

by

using

a

ground-glass

platebehind

the

filmu

Can

be

inefficientu

In

aK?hler

illumination

system,

the

film

plane

is

placed

at

the

exitpupil,

not

the

image

plane,

of

the

condenser

opticsu

Since

all

field

points

from

the

source

overlap

(integrate)

at

the

pupithis

is

naturally

averyuniformlocationu

And

by

considering

the

optical

invariant,

the

rest

of

the

designrequirements

for

the

condenser

follows

naturallyThe

Optical

Invariant?u

Remember

Day

1,

in

the

discussion

on

conservation

of

energy:u

In

a

2D

system,

the

Lagrange

invariant

equates

marginal

and

chief

rayheight-angle

products

togetherThe

same

is

true

atthe

pupils

for

theproduct

of

marginalray

height

and

chiefray

angles5

-

16Optical

Invariant5

-

17u

We

know

the

exit

pupil

of

the

illumination

system

should

be

the

samesize

as

the

object

of

the

projection

system,

since

we

want

to

place

thefilm

gate

at

the

exit

pupilu

And

to

match

the

light

grasp

(Etendue)

of

the

two

optical

systems,

wewant

the

image

of

the

source

produced

by

the

illumination

system

tofill

the

entrance

pupil

of

the

projectoru

So,

if

we

know

the

source

size,

and

the

size

of

the

entrance

pupil

ofthe

projector,

we

know

the

magnificationu

We

also

know

that

the

distance

from

the

illumination

system’s

exitpupil

to

the

entrance

pupil

of

the

projector,

since

the

illumination

epupil

is

at

the

same

location

as

the

projector

objectEntrance

Pupil

Propertiesu

Click

Analyze…Reports…Prescription

Data

and

look

at

the

section“General

Lens

Data”u

This

shows

mainly

paraxial

data

about

the

lens.

We

want

the

entrancepupil

location

and

diameter.u

Note

that

entrance

pupil

location

is

always

measured

relative

tosurface

1,

not

the

object

surface5

-

18K?hler

Illumination5

-

19u

So

here’s

the

numbers:u

Assume

the

source

is

a

filament

of

8

mm

lengthu

Magnification:

entrance

pupil

diameter/source

diameteru

37/8

=

4.625u

Image

location

is

at

aperture

of

the

projectoru

59.273

(OBJof

DBG)

+

50.745

(EPP)

=

110.018u

So

we

want

to

image

an

8

mm

object

to

a

37

mm

image,

located

110mm

away

from

the

exit

pupilu

That’s

all

the

information

we

need

to

design

the

illumination

opticsDesign

Rules

for

Illuminators5

-

20u

Since

the

exit

pupil

is

at

the

film

plane,

imaging

quality

is

not

soimportantu

It’s

generally

better

to

weight

boundary

conditions

so

that

all

yourmechanical

and

system

constraints

are

met,

rather

than

attempting

togeta

diffraction-limited

systemu

They

are

usually

designed

at

just

one

wavelength,

as

chromaticaberrations

are

not

importantK?hler

Illumination5

-

21uu

We

will

design

the

condenser,

then

combine

the

2

lens

filesu

File…New.

Use

sequential

mode.u

Object

thickness: 4

mmu

System

aperture:u

Type:

object

space

NA,

aperture

value:

0.7750

degree

angle

of

acceptanceu

Field

data:

object

height,

y-field

values:

0.0,

2.8,

4.0u

Wavelength

data:

0.587micronsu

Insert

surfaces

until

Image

is

surface

7u

Make

surface

5

the

“Stop”

surfaceK?hler

Illuminationu

The

condenser

has

2

lenses.

Enter

the

radius,

thickness

and

glassvalues

as

below:u

B270

is

a

high-transmission

crown

glass,

with

good

thermal

propertiesand

without

the

coloration

found

in

“float”

glassu

For

low

temperature

sources,

acrylic

lenses

may

be

used5

-

22K?hler

Illumination5

-

23u

Now

build

the

merit

function:u

Use

default

RMS

-

Spot

Radius

-

Centroidu

Gaussian

quadrature,

4

Rings,

6

Armsu

Will

use

conic

aspheresu

Glass: 5

-

20

-

5u

Air:

1

-

1000

-1u

Need

toconstrainreal

(not

paraxial)

magnificationu

Constrain

ratio

of

ray

angles

at

object

and

image

(heights

and

anglesareequivalent

due

to

optical

invariant)u

REAB

operandu

Need

to

match

source

distribution

at

film

gate

to

object

sizeu

REAY

operand

totargetheight

of

marginal

rayu

Thicknessof

surface

0

must

be

>

4Merit

Function5

-

24K?hler

Illuminationu

Now

optimize!5

-

25K?hler

Illuminationu

Object

thickness

is

out

of

specification

(0.4

instead

of

>4)u

Magnification

is

out

of

specification

(-10

instead

of

-4.6)u

Try

hammering,

but

it

won’t

help

muchu

The

design

needs

a

bit

more

freedom:u

Make

the

conic

terms

of

surfaces

2

and

4

variablesu

We’re

not

looking

for

outstanding

image

quality,

but

it

should

bereasonable5

-

26Design

Review5

-

27u

Much

better!u

Object

thickness

is

3.687u

Since

this

is

the

source-to-lens

distance,

we

must

achieve

itu

Simply

remove

variable

and

operand,

set

to

4,

reoptimizeu

Could

have

done

that

in

the

first

place,

but

you

usually

don’t

know

unyou

try!Design

Review5

-

28u

Magnification

is

also

out

of

spec

at

-4.1

instead

of

-4.6,

but

let’s

sthat

this

is

“close

enough”

for

nowu

One

lens

is

20.1

mm

thick,

the

spec

was

20

mm,

but

we

can

tidy

thatup

later

if

neededu

For

now,

let’s

saythis

design

is

finishedu

Click

Lens

DataEditor…Aperture…Convert

Semi-Diameters

toCircular

Apertures

to

lock

the

lens

sizesu

Save

as

“condenser_Optimized.zmx”Add

the

Two

Filesu

We

are

now

going

to

add

the

double

Gauss

projector

lens

to

this

file,to

make

the

complete

systemu

Remember

that

surface

5

of

the

condenser

is

the

same

surface

assurface

0

of

the

projectoru

Delete

surface

6

(thickness

maintained

by

surface

1

of

projection

lenu

File…Insert

Lens

(Double

Gauss

Projector.zmx)5

-

29Note

the

imageof

the

source

being

formed

at

the

stop

of

the

projectorK?hler

Illuminationu

The

LDE

now

contains

information

about

the

condenser

and

theprojectoru

Save

as

“Kohler

Illumination.zmx”5

-

30K?hler

Illuminationu

Now

that

the

systemhas

been

designed

sequentially,

we

will

use

non-sequential

ray

tracing

to

evaluate

the

systemusing

the

filament

sourand

the

slide

objectu

File…Convert

to

NSC

Group5

-

31Non-Sequential

Designu

Take

a

moment

to

review

the

contents

of

the

NSC

group5

-

32Add

a

Source

Object5

-

34u

The

source

should

be

4

mm

in

front

of

the

first

lensu

As

this

is

NS

ray

tracing,

the

object

ordering

does

not

matteru

But

it’s

convenient

to

add

sources

before

geometry

objectsu

Personal

choiceu

Insert

new

object

1:

Source

Filamentu

Y

Position:

4u

Z

Position:

-4u

Tilt

About

X:

90u

#

Layout

Rays:

25u

#

Analysis

Rays:

5,000,000u

Length:

8u

Radius:

1u

Turns:

12u

Look

at

an

NSC

3D

LayoutK?hler

Illuminationu

Some

of

the

rays

are

“l(fā)ost”

(we

may

consider

that

later),

but

manytravel

towards

the

screen

location5

-

35Source

Coloru

The

system

is

currently

tracing

rays

at

thewavelength

defined

in

thewavelengths

dialogu

But

this

is

an

incandescent

source,

withacolor

temperature

of

4000°u

Set

the

source

properties

like

so:Sobolsamplingis

avery

efficient

way

ofgenerating

pseudo-random

numbersequences5

-

36System

Units5

-

37u

Set

the

source

units

to

lumens,

andanalysis

units

to

lumens/m2u

The

source

is

now

1

lumen:

could

entermeasured

value,

but

its

easier

to

dorelative

numbers

if

the

source

is

1,

soleave

it

at

1

for

nowLayout

Plotsu

Set

layout

plots

to

color

rays

by

“Wavelength”5

-

38K?hler

Illumination5

-

39u

What

we

expect:u

Uniform

intensity

from

the

source

at

the

location

of

the

transparencyu

Sourceis

imaged

at

the

pupil

of

the

projectoru

An

enlarged

image

of

the

transparency

should

be

seen

at

the

screenlocationu

How

to

check:u

Put

detectors

at

the

aperture

of

the

condenser,

the

projector

and

atthe

screen

locationu

Position

a

slide

object

at

the

aperture

of

the

condenseru

Trace

lots

of

rays!u

Add

4

rows

to

the

NSCE

after

the

last

lens

objectu

Ctrl+Insert

does

“insert

after”Detectors5

-

40u

We

have

two

annulus

objects,

the

film

plane

and

the

stop

of

thedoubleGauss

lensu

Place

a

detector

color

ateachobjectu

First

detector

objectu

Position

relative

to

film

plane

annulus

+0.001u

X,Y

half-width

22;

100

pixels

in

x

and

yu

Set

color

=

4

so

that

true

color

data

is

shown

in

the

layoutDetectorsu

Second

detector

objectu

Position

relative

to

double-gauss

stop

annulus

+0.001u

x,

y

half-width10,

250

pixels

in

x

and

yu

Third

detector

objectu

Position

relative

to

last

lensu

Z

=

thickness

of

last

lens

,

100

pixels

x

&

y,

half-width

1100

in

x

&y,

set

to

“do

not

draw”

so

layout

plots

are

OK5

-

41Trace

Rays!u

We

are

tracing

5

million

rays

through

this

system!u

Multi-CPU

machines

are

great!5

-

42CondenserStopu

Here’s

the

distribution

at

the

stop.

Only

about

18%

of

the

sourcepower

arrives.u

Increased

brightness

at

the

edge

is

a

good

thing,becausetheprojector

brightness

rolls

off

at

the

edge5

-

43Projector

Stopu

Nice

image

of

the

source!5

-

44Screenu

The

projector

relative

illumination

results

in

amore

uniformilluminance

at

the

screen5

-

45Source

Color

Temperature5

-

46u

Note

how

orange

the

source

isu

4000°

K

is

quite

a

low

temperature

for

a

white-light

sourceu

Increase

it

to

7000°

K:

much

whiter!K?hler

Illumination5

-

47u

The

behavior

of

the

source

is

as

desired.

However,

the

efficiency

isonly

about

18%.u

We

designed

the

condenser

optics

for

a

cone

angle

of

50°,

but

thereal

source

radiates

into

360°!u

Now

check

the

projector

operationu

Insert

a

new

object

in

the

NSCE

before

the

first

detector

object:u

Object

12:

slideu

Data

file:

Barchart.bmpu

Z

position:

-0.001

relative

to

film

gate

object

4u

X

full

width:

24u

Aspect

ratio:

1K?hler

Illumination5

-

48u

Change

the

detector

parameters:u

Object

13

(film

gate

detector)

u

X,

Y

half

width:

20u

Object

15

(screen

detector)u

X,

Y

pixels:

500u

Repeatthe

ray

traceK?hler

Illuminationu

Good

imagery,

although

more

detailed

work

is

necessary5

-

49Recycle

Light5

-

50u

Lots

of

light

escapes,

as

we

only

allowed

for

a

50°

cone

in

theoriginal

sequential

designu

To

increase

the

efficiency,

try

adding

a

reflector

behind

the

source:u

Insert

new

object

entry

below

the

source

(now

object

2):

standardsurfaceu

Z

position:

-24

u

Material:

mirroru

Radius:

20u

Max

aperture:

20u

Min

aperture

2

(amountinghole)u

This

will

catch

many

of

the

raysRecycling

mirroru

Captures

many

rays5

-

51Recycling

Mirroru

Note

a

slight

darkening

at

the

center

of

the

film

plane,

because

of

thehole

in

the

recycling

mirroru

Also

note

a

slightly

brighter

ring,

due

to

light

that

TIRs

being

re-circulatedu

Total

powerhas

doubled

at

the

film

plane:5

-

52Screenu

Not

all

that

power

gets

to

the

screen

though,

because

it

is

at

thewrong

angle

to

get

through

the

projection

lens5

-

53Luminous

Intensityu

Look

at

the

detector

data

in

angle

space,

log

scaling,

with

and

withouthe

recycling

mirror5

-

54You

Can’t

Beat

Etendue!5

-

55u

We

made

the

mirror

a

hemisphere,

and

it

does

capture

all

those

raysand

delivers

them

to

the

front

of

thecondenser

lensu

But

rays

outside

the

Etendue

of

the

projector

are

lost,

or

e

sourcesof

stray

lightu

The

recycling

optics

must

still

match

the

Etendue

of

the

systemThings

Not

Considered5

-

56u

This

is

just

an

overview

of

illumination

modelingu

There

are

lots

that

have

not

been

coveredu

The

effects

of

the

mechanicalmounts

on

stray

lightu

Scatteringu

Thin-film

coatings

and

optical

efficiencyu

Lots

moreu

These

are

all

in

thescopeof

Zemax,

but

not

of

this

course!Optical

System

Design

Using

ZemaxBlack

Box

SystemsProprietary

Optics5

-

58u

We

designed

the

K?hler

illumination

system

assuming

the

projectoroptics

were

off-the-shelf

(OTS)u

If

this

truly

was

an

OTS

system,

we

would

likely

not

have

the

completelens

prescriptionu

Often

manufacturers

will

sell

you

optical

systemswithout

divulging

tcomplete

optical

design

for

proprietary

reasonsu

Example:microscope

objectives,

SLR

camera

lenses,

etc.u

How

could

we

analyze

or

optimize

the

condenser

optics

withoutknowing

the

surface

details

of

the

projector

system?u

The

manufacturer

would

need

to

provideuswitha

black

box

lenssystemExport

Black

Box

Toolu

Zemax

has

a

tool

that

allows

you

to

export

a

range

of

sequential

surfacto

an

“encrypted”

ZBB

fileu

Found

under

File…Zemax

Black

Boxu

Once

created,

this

encrypted

file

can

be

reloaded

into

Zemax

using

the“Black

Box

Lens”

surface5

-

59Black

Box

Lensu

The

black

box

(BB)

lens

surface

reads

data

from

the

ZBB

file

todetermine

how

rays

trace

through

the

encrypted

surface

rangeu

Most

analyses

are

supported

and

user

cannot

obtain

any

informationabout

surfaces

inside

the

black

box5

-

60Additional

Considerations5

-

61u

Some

limits

on

surface

types

and

analysis

types

supported

with

BBu

See

description

of

tool

in

Chp.

8

of

manual

for

completelistu

Always

good

to

verify

that

the

analyses

of

interest

to

customer

givesame

results

when

converted

to

BB

as

original

system

didu

256-bit

encryption

algorithm

is

good,

but

not

unbreakableu

Surface

coatings

are

also

encrypted

in

process

of

exporting

to

BBumended

to

send

BBsystemto

customer

as

ZAR

to

ensure

allpanying

files

are

included

(ZBB,

ZMX,

etc.)u

ZAR

file

created

underFile…Create

Arch