www.iap.uni-jena.de

Medical Photonics Lecture 1.2

Optical Engineering

Lecture 12: Photometry and Illumination

2018-01-25

Herbert Gross

Winter term 2017

2

Schedule Optical Engineering 2017

No Subject Ref Date Detailed Content

1 Introduction Gross 19.10. Materials, dispersion, ray picture, geometrical approach, paraxial approximation

2 Geometrical optics Gross 02.11. Ray tracing, matrix approach, aberrations, imaging, Lagrange invariant

3 Diffraction Gross 09.11. Basic phenomena, wave optics, interference, diffraction calculation, point spread function, transfer function

4 Components Kempe 16.11. Lenses, micro-optics, mirrors, prisms, gratings

5 Optical systems Gross 23.11. Field, aperture, pupil, magnification, infinity cases, lens makers formula, etendue, vignetting

6 Aberrations Gross 30.11. Introduction, primary aberrations, miscellaneous 7 Image quality Gross 07.12. Spot, ray aberration curves, PSF and MTF, criteria

8 Instruments I Kempe 14.12. Human eye, loupe, eyepieces, photographic lenses, zoom lenses, telescopes

9 Instruments II Kempe 21.12. Microscopic systems, micro objectives, illumination, scanning microscopes, contrasts

10 Instruments III Kempe 11.01. Medical optical systems, endoscopes, ophthalmic devices, surgical microscopes

11 Optic design Gross 18.01. Aberration correction, system layouts, optimization, realization aspects

12 Photometry Gross 25.01. Notations, fundamental laws, Lambert source, radiative transfer, photometry of optical systems, color theory

13 Illumination systems Gross 01.02. Light sources, basic systems, quality criteria, nonsequential raytrace

14 Metrology Gross 08.02. Measurement of basic parameters, quality measurements

Photometric units

Photometric calculations

Photometry in optical systems

Color theory

Types of light sources

LEDs

Laser sources

Components

Illumination systems

Beam profiling

Content

4

Photometric Properties

Relations of the 4 main definitions

Cassarly's diamond

Ref.: J. Muschaweck

illuminance

intensity

flux luminance

per solid angle

per area

per projected

area times n2

per etendue

per projected

solid angle

times n2

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

5

Photometric Quantities

Radiometric quantities:

Physical MKSA units, independent of receiver

Photometric quantities:

Referenced on the human eye as receiver

Conversion by a factor Km

Sensitivity of the human eye V(l)

for photopic vision (daylight)

ll l )(VKmV

W

LmKm 673

V(l )

l400 450 500 550 600 650 700 750

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Illuminance description

1 Lux just visible

50 - 100 Lux coarse work

100 Lux projection onto

screen

100 - 300 Lux fine work

1000 Lux finest work

100000 Lux sunlight on paper

6

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

7

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

8

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

L radiance of the source

Integration of the radiance over

the area and the solid angle

gives a power

S

SS

S

AdsdL

dAdL

dAdLd

cos

2

PdA

A

9

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

10

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

p 2sin)( ALLam

coscos oEALE

LAdEHR

Lam p )(

E()

x

z

L

x

z

11

Transfer of Energy in Optical Systems

Conservation of energy

Differential flux

No absorption

Sine condition fulfilled

d d2 2 '

ddudAuuLd cossin2

T 1

y

dA dA's's

EnP ExP

n n'

F'F

y'

u u'

'sin''sin uynuyn

12

Illumination Fall-off

Irradiance decreases in the image field

Two reasons:

1. projection due to oblique ray bundles

2. enlarged distances along oblique chief rays

Natural vignetting: smooth function

depends on: 1. stop location

2. distortion correction

entrance

pupil

y yp

chief ray

chief ray

exit

pupil

y' y'p

w'

w

R'Ex

U

axis bundle

off axis

bundle

marginal

ray

E(y) E(y')U'

13

Natural Vignetting

Consideration with the help of entrance and exit pupil:

1. transfer from source to entrance pupil

2. transfer between pupils

3. transfer from exit pupil into image plane

'cos

cos

'' 4

422

w

w

s

s

dA

dA

n

n

dA

dA

AP

EP

EP

AP

object entrance

pupil

exit

pupilimage

sp

dA

dAEN

dAEX

dA'

U w

U'

w' '

system

marginal

ray

chief ray

s'p

14

Real Systems: Vignetting

Artificial vignetting by

truncation of rays

Change of usable pupil area

due to lens diameters, stops,...

Approximation for uniform

illuminated pupils:

irradiance decreases proportional

to effective pupil area E(w)

w

pupil area

field angle

clear

obstructed

clearclear

obstructed

E(0)

15

Change of color perception:

bleaching of chemical receptors

Effect of Bezold:

the color perception depends

in addition on the environmental

color

Subjective Color Perception with the Eye

Mixing of colors:

1. additive: RGB = red gree blue

2. subtractive: CMY = cyan magenta yellow

Mixing of Colors: Additive - Subtractive

Additive mixing of color: RGB Subtractive mixing of color: CMY

Color perception values of the eye:

spectral integration over the three receptors with sensitivity and stimulus (l)

Spectral signal over all receptors

(color valence)

Color Perception with the Human Eye

LLMMSSF

nm

nm

dlL

780

380

)()( lll

nm

nm

dmM

780

380

)()( lll

nm

nm

dsS

780

380

)()( lll

relativesensitivity

l400 500 550 600 650 700 750

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

450

450

545 558

)(ll

)(lm

)(ls

Color is a subjective physiological perception

Color is characterized by:

1. hue, basic type of pure color

2. saturation, relative mixing of white, pureness of colors

3. brightness

The color perception is only created by the human cones near to the fovea

White, gray and black are not colors

For self luminous light sources:

spectral power density S(l)

Color Metric

source

S( l )

receiver

( l )direct transfer

Color of bodies:

superposition of several spectral functionalities:

1. light source S(l)

2. transmission of transfer media T(l)

3. reflection of the body R(l)

4. eventually re-emissivity of the body E(l)

Color Metric

llllll dRETS )()()()()(

source

S( l )

receiver

( l )

reflection

R( l )

transmission

T( l )

re-emission

E( l )

Mixing of colors by superposition in the

eye pupil

1. spatial mixing beyond the resolution

limit

application: digital projection

2. temporal mixing beyond the typical

integration time

resolution approximatly 25 Hz

application: TV

Color Perception

normal color wheelcolor wheel with

brightness sector

Summation of colors:

vectorial addition of components

Color vectors:

color valence

1. direction: type of color

2. length: brightness

Additivity

Inner summation: only positive components

Outer summation: also negative components possible

From two colors not every mixing color can be created

B

B

R

R

F

BBRRF

Vectorial Addition of Colors

Three primary color components allow for the

creation of every color

The primary component vector must be

independent

Classical selection of basic colors: RGB

In principle the selection of the fundamental

components is arbitrary

( 2nd law of Graßmann)

The decompositioin of a color into the three

basic components is unique

( 1st law of Graßmann)

The transition between the colory values is smooth

(3rd law of Graßmann)

B

B

R

R

F

G

G

GGBBRRF

Theory of Three Basic Colors

Projection of the 3 color vectors in one plane:

2-dimensional representation of color

An additional normalization simplifies the system

R,G,B ---> r,g,b

Two values describes the color completly

The 2D components can be calculated by

barycentric values from the 3D datat

G

R

B

F

GBR

Rr

GBR

Bb

GBR

Gg

1 gbr

GGBBRRF

Plane Color Coordinates

R

G

B

1

1

1

r+g+b = 1

direction of

the hue

B

G

R

F

r

b

g

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.0

0.2

0.1

1.00.90.80.70.60.50.40.30.0 0.20.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.0

0.2

0.1

According to Maxwell, the color can be described by an equal sided triangle

The 3 corners represent the basic color types

A point inside the triangle defines an arbitrary color

by the barycentric values

(foot point projections)

In general the triangle is a cross section area of a

plane in the cartesian coordinate system of the

three colors

The distance from the origin describes the hue

Maxwells Color Triangle

There are different possibilities for spectral sensitivity curves

The systems are convertable by matrix algorithms

The most important

systems are:

1. LMS eye cons

2. RGB

3. XYZ standard

The observed color

perception is given

by

The power density is given by

(law of Abney)

Spectral Sensitivity Curves

)()()()( llll zZyYxXF

ZYXF LZLYLXL )(l

l400 500 550 600 650 700 750

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

m

l

s

450

450

545 558

l in

nm400 500 600 700-0.1

0

0.1

0.2

0.3

0.4

b( l )

g( l )

r( l )

l in

nm400 450 500 550 600 650 700 750

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

y( l )

z( l )

x( l )

XYZ

RGB

LMS

linear

conversion

The following representations must by distinguished:

1. pectral matching functions for every basic color

2. normalized functions

3. spectral color values

X, Y , Z

Standard Spectral Function

l in

nm400 450 500 550 600 650 700 750

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

y( l )

z( l )

x( l )

)(,)(,)( lll zyx

)(,)(,)( lll zyx

3x3 matrices allow for a conversion between the color systems

Color values

Spectral matching functions

Example:

XYZ to RGB

Mapping Between the Color Systems

B

G

R

ZZZ

YYY

XXX

Z

Y

X

BGR

BGR

BGR

)(

)(

)(

)(ˆ

)(

)(

l

l

l

l

l

l

b

g

r

ZZZ

YYY

XXX

z

y

x

BGR

BGR

BGR

Z

Y

X

B

G

R

17859.000255.000092.0

01571.025242.009116.0

08283.009116.041845.0

CIE standard valence system

Special selection of the primary colors

Color coordinates x,y,z

Outer boundary:

pure spectral colors

every collor corresponds to a

wavelength

Point 1/3,1/3:

white point, colorless

Connection of red and blue end

of spectral line:

purple line

Color Triangle

y

x

line of spectral

colors

0.80.70.60.50.40.30.20.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

410 -

380450

460470

480

485

490

495

500

505

510

515

520

540

550

560

570

580

590

600

610620

650

700 - 780

0.9 1.0

1.0

530

purple line

white

non-

colored

Correspondences of colors areas in the

classical color triangle to conventional

names

Wavelength ranges of spectral colors

Conventional Colors

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0

0.9

y

green

yellow

orange

purple

blue

whitered

Color l in nm

red 750 ... 640

orange 640 ... 600

yellow 600 ...555

green 555 ... 485

blue 485 ... 430

violet 430 ... 375

31

Types of Light Sources

Ref: I. Babushkin

source type coherence spectrum directionality brightness

lamp incoherentbroad band

whiteall

laser coherent

single

wavelength

monochrom

atic

directed

beam

super

continuum

source

coherentbroad band

white

directed

beam

low

very high

high

32

Comparison Imaging vs Illumination

Imaging optics

- point to point transfer

- transfer of information

Illumination

- mapping extended source on

extended target

- imaging to be avoided

- transfer of flux

Comparison

- different tasks

- different tools

- different methods

Ref.: J. Muschaweck

imaging

illumination

Types of Light Sources

Source type Examples

Thermal radiator Black body

Globar sources

Incandescent bulbs

Electrical arc lamps

Luminescent radiator Discharge lamps

Fluorescent tube

Semiconductor diodes, LED

Laser

34

Lamps

Different types of lamps

CAD model of light sources:

1. Real geometry and materials

2. Real radiance distributions

Bulb lamp

XBO-

lamp

Realistic Light Source Models

Geometry

Luminance distribution

XBO - Xenon Source

typical geometry

of a lamp

anode

XBO 3000 HP

cathode

22 mm

40°

40°5.3 mm

4.5 mm

12.5 mm

7 mm luminance distribution of the lamp

XBO 5000 W HP

L

x

y

x

y

cathode anode

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

Xenon lamp Line spectrum

HG-Xe-lamp

Spectral Distributions

l

I

1

0.5

0380 580 780 980

l

I

1

0.5

0380 580 780 980

Log I(l)

10000

1000

100

10

1300 400 500 600 800700

l in nm

Halogen

NV 30 W

Halogen

100 W

XBO 150

HBO 100

XBO 75

HBO 200

Spectral Distributions of Lamps

40

Spectrum of HBO Mercury Lamp

Typical line spectrum

Several lines in UV

Ref.: M. Kempe / www.zeiss-campus.magnet.fsu.edu

Comparison of Light Source Properties

Lamp type Lamp type Efficiency in lm/W Lifetime in h

Incandescent lamp 16 – 34 < 1500

Fluorescent lamp 80 7000 – 18000

Halogen bulb 25 2000 – 4000

Fluorescent tube

Na /Hg low pressure 100 – 200 14000 – 18000

Hg high pressure 50 – 120 24000

Hg very high pressure 60

Xenon 15 – 50

Hg and Xenon 22 – 53

Semiconductor

diode, LED

LED , red ( 615 nm ) 50 – 100 20000 – 50000

LED , blue ( 460 nm ) 10 20000 – 50000

LED , green ( 525 nm ) 20 – 30 20000 – 50000

LED , white 20 – 30 appr. 10000

Organic light

emitting diode,

OLED

yellow 35 30000 at 100 Cd/m2

blue 10 3000 – 10000 at 150 Cd/m2

white 20 5000 – 20000 at 150 Cd/m2

Laser

Semiconductor laser 200

YAG solid state laser 10

Argon gas laser 1

Efficiency

Ratio of light power to electrical/excitation power

Black body radiation as

reference

light

in

P

P

%14ˆ94max W

lmPlanck

in lm/W

L in cd/m2

1010108104 1061020

200

160

120

80

40

fluorescence

lamp

halogen

incandescent

lamp

Xe arc lamp

Hg lamp with

short arc

halogen metal

vapor lamp

Na lamp with

high pressure

Na lamp

with low

pressure

Xe lamp with

short arc

0

43

LED

View of a light emitting diode

View along axis in distance 5 mm:

circular symmetry is a nightmare

View from the side

- raytrace model

- measured component

Ref.: J. Muschaweck

44

LEDs

Family of commercial visible LEDs

Different sizes, brightness,...

Ref.: J. Muschaweck

LEDs

Material Color Wavelength

in nm

FWHM

in nm

Luminance

in cd/m2

InGaAsP NIR 1300 50 – 150

GaAs:Si NIR 940

GaAs:Zn NIR 900 40

GaAlAs NIR 880 30 – 60

GaP:Zn,N dark red 700

GaP red 690 90

GaAlAs red 660

GaAs6P4 red 660 40 2570

GaAs0.35P0.65:

N

orange 630

InGaAlP red 618 20 2 107

GaAsP0.4 amber 610

SiC yellow 590 120 137

GaP green 560 40 1030

InGaAlN green 520 35 107

GaN blue 490

InGaN blue 450 – 460 25 3 106

InGaN blue 400 – 430 20 3 104

SiC dark blue 470

GaN UV 365 – 380 15 3 104

LED without lens: Lambert source

LED with lens: stronger forward directed beam

Light Cone of LEDs

planar

Lambert

directed

beam

isotropic

hemisphere

parabolicspherical

semiconductor

plastic

semiconductorsemi-

conductor

plastic

Spectral broadening of LEDs to generate quasi white radiation

Layer with phospheresence

Original emission in the blue

Broad spectrum in VIS, structured

White Light LEDs

l

P

luminescence

blue

phosphorescence

total LED

400 500 700600

OLEDs

The color locations are outside the sRGB / PAL / HDTV standard

sRGB/PAL/HDTV MicroOLED

Ref: K. Lindig

Laser Source Properties

Criterion Types Examples

Behavior in time pulsed systems solid state laser, excimer laser

continuous wave laser HeNe-laser

Spectral width,

coherence

single mode HeNe-laser

multiple mode YAG-solid state laser with high power,

fiber laser, Ti:Sa-laser

Spectral position

UV excimer laser

VIS Argon-ion-laser, HeNe-laser

IR CO2-laser

Beam quality

Fundamental mode HeNe-laser

multiple modes YAG-solid state laser with high power,

excimer laser

Beam shape

high NA semiconductor laser

low NA HeNe-laser, CO2-laser

small diameter HeNe-laser

large diameter CO2-laser

ring structures CO2 -laser with unstable resonator

elliptical excimer laser, semiconductor laser

astigmatic semiconductor laser

asymmetric CO2 - waveguide laser

Power range signal laser HeNe-laser

power laser CO2-laser

Laser Source Data

Laser type l

Typical

power /

energy

Operation

mode

Pulse

length

Beam

diameter

in mm

Divergence

2

in mrad

efficiency

in %

Excimer, ArF 193 nm 30 W / 1 J pulse 20 ns 6x20 –

20x30 2 – 6 0.2

Nitrogen-gas

laser 337 nm

0.5 W / 10

mJ pulse 10 ns

2x3 –-

6x30 1–3x7 0.1

Argon-ion laser 455 –

529 nm 0.5 – 20 W cw 0.7 –- 2 0.4–1.5 0.1

HeNe-gas laser 632.8 nm 0.1 – 50

mW cw 0.5 – 2 0.5 – 1.7 0.1

HF-chemical

Laser

2.6 – 3.3

m 5 kW / 4 kJ

cw or

pulse 20 ns 2 – 40 1 – 15 10

CO2 – gas laser 10.6 m 1 kW / 1kJ cw or

pulse

50 – 150

ns 3 – 4 1 – 2 15 – 30

Ruby – solid

state laser 694 nm 10 J puls 0.5 ms 1.5 – 25 0.2 – 10 0.5

Semiconductor

laser

0.4 – 30

m 100 mW

cw or

pulse

0.1 – 1

s 0.001– 0.5 200 x 600 30

Nd:YAG-solid

state laser, flash

bulb

1.064 m 1 kW pulse 0.1 – 20

ns 0.75 – 6 2 – 18 0.5

Nd:YAG-solid

state laser,

diode-pumped

1.064 m 2 W cw 0.75 - 6 2 – 18 5

Dye laser 400 –

950 nm 10 W / 0.1 J

cw or

pulse 5 – 20 ns 0.4 - 0.6 1 – 2 0.1

Typical setup of a semiconductor

laser

Astigmatic beam radiation:

1. fast axis perpendicular to junction

2. slow axis parallel to junction

Semiconductor Laser

metal contact

metal contact

insulatorp-region

heterojunction

n-region

substrate

light

x

y

x

y

x

y

z

Q

perpendicular

parallel

2

2

)(

w

r

oeIrI

Gaussian Beams, Transverse Beam Profile

I(r) / I0

r / w

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-2 -1 0 1 2

0.135

0.0111.5

0.589

1.0

Transverse beam profile is gaussian

Beam radius w at 13.5% intensity

Expansion of the intensity distribution around the waist I(r,z)

Gaussian Beams

z

asymptotic

lines

x

hyperbolic

caustic curve

wo

w(z)

R(z)

o

zo

-4 -3 -2 -1 1 2 3 4

-4

-3

-2

-1

1

2

3

4

z / z

r / w

o

o

asymptotic

far field

waist

w(z)

o

intensity

13.5 %

Geometry of Gaussian Beams

Illumination systems:

Different requirements: energy transfer efficiency, uniformity

Performnace requirements usually relaxed

Very often complicated structures components

Problem with raytracing: a ray corresponds to a plane wave with infinity extend

Usual method: Monte-Carlo raytrace

Problems: statistics and noise

Illumination systems and strange components needs often a strong link to CAD data

There are several special software tools, which are optimized for (incoherent) illumination:

- LightTools

- ASAP

- FRED

55

Illumination

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

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

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

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

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

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