Optical design with Zemax PhD Advanced 2 Illumination I.pdf
Transcript of Optical design with Zemax PhD Advanced 2 Illumination I.pdf
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www.iap.uni-jena.de
Optical Design with Zemax
for PhD - Basics
Seminar 2 : Illumination I
2014-11-19
Herbert Gross
Winter term 2014
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Lighthouse optics
Fresnel lenses with height 3 m
Separated segments
Complex Geometries
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CAD model of light sources:
1. Real geometry and materials
2. Real radiance distributions
Bulb lamp
XBO-
lamp
Realistic Light Source Models
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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
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Arrays - Illumination Systems
Illumination LED lighting
Ref: R. Völkel / FBH Berlin
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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
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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
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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
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Illumination Optics: Condenser
2. Epi-illumination
Complicated ring-shaped components
around objective lens
object
ring lens
illuminationobservation
object
ring lens
illuminationobservationcircle 1
circle 2
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Flyeye Array Homogenizer
condenserarray
spherical surface with
secondary source
points
illumination
field
Simple model: Secondary source of a pattern of point sources
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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
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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
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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
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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
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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
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Statistical Array of Micro Lenses
Phase of
mask
Far field
coherent
Micro speckle
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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
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Reflection based array:
Facetted mirror
Segmented Mirror
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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
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Fresnel Lens
F
a) smooth asphere
F
b) Fresnel lens
h wrapping height
gmin
smallest
period
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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
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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
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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
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Illumination in Zemax
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Relative illumination or vignetting plot
Transmission as a function of the field size
Natural and arteficial vignetting are seen
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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
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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
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Illumination in Zemax
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Example:
Lens focusses into a rectangular lightpipe
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Illumination in Zemax
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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 !
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Illumination in Zemax
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Many types of components and options are available
For every component, several
parameters can be fixed:
- drawing options
- coating, scatter surface
- diffraction
- ray splitting
- ...
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Illumination in Zemax
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Starting a run requires several control
parameters
Rays can be accumulated
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Illumination in Zemax
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Typical output of a run:
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Illumination in Zemax