56
www.iap.uni-jena.de Optical Design with Zemax for PhD - Advanced Lecture 13: Illumination I 2019-02-13 Herbert Gross Speaker: Uwe Lippmann Winter term 2014
www.iap.uni-jena.de
Optical Design with Zemax
for PhD - Advanced
Lecture 13: Illumination I
2019-02-13
Herbert Gross
Speaker: Uwe Lippmann
Winter term 2014
2
Preliminary Schedule
No Date Subject Detailed content
1 17.10. 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 24.10.Basic Zemax
handling
Raytrace, ray fans, paraxial optics, surface types, quick focus, catalogs, vignetting,
footprints, system insertion, scaling, component reversal
3 07.11.Properties of optical
systems
aspheres, gradient media, gratings and diffractive surfaces, special types of surfaces,
telecentricity, ray aiming, afocal systems
4 14.11. Aberrations I representations, spot, Seidel, transverse aberration curves, Zernike wave aberrations
5 21.11. Aberrations II Point spread function and transfer function
6 28.11. Optimization I algorithms, merit function, variables, pick up’s
7 05.12. Optimization II methodology, correction process, special requirements, examples
8 12.12. Advanced handling slider, universal plot, I/O of data, material index fit, multi configuration, macro language
9 09.01. Imaging Fourier imaging, geometrical images
10 16.01. Correction I Symmetry, field flattening, color correction
11 23.01. Correction II Higher orders, aspheres, freeforms, miscellaneous
12 30.01. Tolerancing I Practical tolerancing, sensitivity
13 06.02. Tolerancing II Adjustment, thermal loading, ghosts
14 13.02. Illumination I Photometry, light sources, non-sequential raytrace, homogenization, simple examples
15 20.02. Illumination II Examples, special components
16 27.02. Physical modeling I Gaussian beams, Gauss-Schell beams, general propagation, POP
17 06.03. Physical modeling II Polarization, Jones matrix, Stokes, propagation, birefringence, components
18 13.03. Physical modeling III Coatings, Fresnel formulas, matrix algorithm, types of coatings
19 20.03. Physical modeling IVScattering and straylight, PSD, calculation schemes, volume scattering, biomedical
applications
20 27.03. Additional topicsAdaptive optics, stock lens matching, index fit, Macro language, coupling Zemax-Matlab /
Python
Basic notations of photometry
Lambertian emitter
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: W/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
9
𝑑2Φ =𝐿
𝑟2𝑑𝐴𝑆⊥ 𝑑𝐴𝑅⊥
=𝐿
𝑟2cos 𝜃𝑆 cos 𝜃𝑅 𝑑𝐴𝑆 𝑑𝐴𝑅
Radiance independent of space coordinate
and angle
The radiant intensity varies with the cosine
of the emission angle
Integration over hemisphere
Integration of cone
Real sources with Lambertian
behavior:
black body, sun, LED
Lambertian Source
E()
x
z
L
x
z
10
𝐼 𝜃 = 𝐿 𝐴 cos 𝜃 = 𝐼0 cos 𝜃
Φ𝐿𝑎𝑚 = ∫ 𝐼 𝜃 𝑑Ω = 𝜋 𝐴 𝐿
Φ𝐿𝑎𝑚 𝜑 = 𝜋 𝐴 𝐿 sin2 𝜑
𝐿 Ԧ𝑟, Ԧ𝑠 = 𝐿 = 𝑐𝑜𝑛𝑠𝑡
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
13
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
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
15
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
16
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
17
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'100m
a) axis b) field
yp
480 nm
546 nm
644 nm
y'100m
yp
x'100m
xp
tangential sagittal
y'100m
a) axis b) field
yp
480 nm
546 nm
644 nm
y'100m
yp
x'100m
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
Ringradius 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 point source 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
Contrast 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
Fly‘s Eye 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
Fly‘s Eye Array Homogenizer
condenserarray
spherical surface with
secondary source
points
illumination
field
Simple model:Secondary source of a pattern of point sources
Fly‘s Eye Condensor with Field Array
d1
illumination
fieldfcond
condenser
lens
field
lens
D
L
array 1
u'
Dsub
'
array 2
farr1
farr2
d3
d2
z
Fly‘s Eye 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
Fly‘s 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 option: Sequential Mode
• relative illumination / vignetting
• relative irradiance distribution for simple sources (uniform or Lambertian)
Advanced possibility: Mixed Mode
• non-sequential component
• embedded into sequential optical systems
• examples: lightguide, arrays together with focussing optics, beam guiding, roof
prisms
General illumination calculation: Pure Non-Sequential Mode
• non-sequential raytrace with a completely 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 artificial 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 Component‘
Surface defines entrance port into the non-sequential group
Specification of Exit Port defines position of following sequential surface
Non-sequential component editor with many control parameters is used to describe the
element:
type of component
reference object
material
geometrical parameters
Sources and Detectors can be placed inside the non-sequential group, but:
Non-sequential rays generated by sources inside the group will not leave the non-
sequential group.
Detectors do not record sequential rays entering the non-sequential group.
51
Illumination in Zemax
Example:
Lens focusses into a rectangular lightpipe
52
Illumination in Zemax
Complete non-sequential raytrace
Switch into a different mode in Setup Mode Non-Sequential
Defining the system in the non-sequential editor, includes
1. sources
2. light guiding components
3. detectors
Various help function are available to
constitute the system
It is a object (component) oriented philosophy in
contrast to the surface-oriented sequential approach
Raytrace is slow compared to sequential algorithm has to determine which
object has the next intersection with the ray
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 over multiple ray trace runs
55
Illumination in Zemax
Typical output of a run:
56
Illumination in Zemax
