Advanced Lens Design - uni-jena.de...Diffractive elements color correction, ray equivalent model,...
Transcript of Advanced Lens Design - uni-jena.de...Diffractive elements color correction, ray equivalent model,...
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Advanced Lens Design
Lecture 15: Diffractive elements
2015-02-10
Herbert Gross
Winter term 2014
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Preliminary Schedule
1 21.10. Basics Paraxial optics, imaging, Zemax handling
2 28.10. Optical systems Optical systems, raytrace, advanced handling
3 04.11. Aberrations I Geometrical aberrations, wave aberrations
4 11.11. Aberrations II PSF, OTF, sine condition, aplanatism, isoplanatism
5 18.11. Optimization I Basic principles, merit function setup, optimization in Zemax
6 25.11. Optimization II Initial systems, solves, bending, AC meniscus lenses, constraints, effectiveness of variables
7 02.12. Structural modifications Zero operands, lens splitting, lens addition, lens removal, material selection
8 09.12. Aspheres and freeforms Correction with aspheres, Forbes approach, freeform surfaces, optimal location of aspheres, several aspheres
9 16.12. Field flattening Astigmatism and field curvature, thick meniscus, plus-minus pairs, field lenses
10 06.01. Chromatical correction Achromatization, apochromatic correction, axial versus transversal, glass selection rules, burried surfaces
11 13.01. Special correction topics Symmetry, sensitivity, anamorphotic lenses, field lens, telecentricity, stop position
12 20.01. Higher order aberrations high NA systems, broken achromates, induced aberrations
13 27.01. Advanced optimization strategies
Local vs global optimization, control of iteration, growing requirements
14 03.02. Mirror systems special aspects, double passes, catadioptric systems
15 10.02. Diffractive elements color correction, ray equivalent model, straylight, third order aberrations, manufacturing
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1. Basic principle
2. Diffraction orders and efficiency
3. Calculation models
4. Miscellaneous
5. Correction
6. Broadband solutions
7. Manufacturing
3
Contents
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Deviation of Light
reflection
mirror
scattering
scatter plate
refraction
lens
diffraction
grating
Mechanisms of light deviation and ray bending
Refraction
Reflection
Diffraction according to the grating equation
Scattering ( non-deterministic)
'sin'sin nn
'
g mo sin sin
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Diffractive Optics:
Local micro-structured surface
Location of ray bending :
macroscopic carrier surface
Direction of ray bending :
local grating micro-structure
Local aspherical phase effect local grating constant, q ist the wrapping factor
macroscopic
surface
curvature
local
grating
g(x,y)
lens
bending
angle
m-th
order
thin
layer
mj
mj
jm yxckyx,
),(
),(
2),(
yx
qyxg
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Diffractive Elements
z
h2
hred(x) : wrapped
reduced profile
h(x) : continuous
profile
3 h2
2 h2
1 h2
hq(x) : quantized
profile
ray refracted at
smooth asphereray refracted at
Fresnel lens
wrapping
Original lens height profile h(x)
Wrapping of the lens profile: hred(x) Reduction on
maximal height h2
Digitalization of the reduced profile: hq(x)
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Diffraction Orders
diffractive
structure
diffraction orders
mm-1
m-2m-3
m+2m+1
m+3
desired
order
Usually all diffraction orders are obtained simultaneously
Blazed structure: suppression of perturbing orders
Unwanted orders: false light, contrast and efficiency reduced
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Efficiency of Diffractive Elements
diff
0
0.2
0.4
0.6
0.8
1
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
m = 2
m = 1
m = 0
m = 3
design
Efficiency optimized for one desired central wavelength
Strong dispersion for other wavelengths
Reduction of efficiency for deviating wavelengths
(figure: scalar approximation)
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95.0
Nc
1sin 2
0 2 4 6 8 10 12 14 160.4
0.5
0.6
0.7
0.8
0.9
1
N
0.4053
0.8106
0.9496
0.9872
real
Efficiency of Binary DOE's
Binarized diffractive elements have a reduced efficiency
The efficiency grows theoretically with the number of quantization levels
For 8 levels the efficiency is
In reality for a larger number of levels the efficiency shrinks due to tolerances
Estimation of N levels
in scalar approximation
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Fresnel Zone Plate
Circular rings at radii
Classical Fresnel zone lens:
only rings with same sign of phase have tranmission 1
Modern zone plate (Wood):
phase steps of at the rings,
improved power transmission
fr r r r r12345 F
f+f+2
f+3
f+4
f+5
fmrm 2
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Diffractive Lens
Diffractive Fresnel lens
Zone rings with radii
Blaze in every zone (surface slope)
k
rk
Zone No k
f
hk
k
fkmrk 2
kkkk
k rrn
mh
tan
cos1
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egdn
gms
n
ns
ˆ''
'
grooves
s
s
e
d
gp
p
Surface with grating structure:
new ray direction follows the grating equation
Local approximation in the case of space-varying
grating width
Raytrace only into one desired diffraction order
Notations:
g : unit vector perpendicular to grooves
d : local grating width
m : diffraction order
e : unit normal vector of surface
Applications:
- diffractive elements
- line gratings
- holographic components
12
Diffracting Surfaces
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Discrete topography on the surface
Phase unwrapped to get a smooth surface
Only one desired order can be
calculated with raytrace
Model approximation
according to Sweatt:
same refraction by small height
and high index
numerical optimized DOE
phase unwrapped
ERL-model( equivalent refractive lens )
black box modelSweatt-model( thin lens with high index )
Modellierung Diffractive Elements
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Phase function redistributed:
large index / small height
typical : n = 10000
Calculation in conventional software with raytrace possible
Diffractive Optics: Sweatt Model
),(**2),(2),( yxznyxznyx
equivalent refractive
aspherical lens
real index n synthetic
large index n*
Sweatt lens
zz*
the same ray
bending
ray bending
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Fresnel zone plate: works as lens
p-phase jumps at Fresnel zones, - only odd zones are considered - no destructive interference
Fresnel Zone Plate
phase of lens intensity I(x,z)intensity I(x,y)
I(x) I(z)
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Transition Refractive - Diffractive
refractive :
one direction
n
diffractive blazed :
one direction
g
g
+1. order
+2. order
-2. order
-1. order
0. order
diffractive binary :
all directions
Refractive: no surface structure
Blazed diffractive: only one diffraction order,
for one wavelength and one angle of incidence
Binary diffractive: several orders simultaneously
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qh
L
g
q = 1 q = 2 q = 4 q = 8)()/( )()( diffperiodic
dr
prism TxTxT
m
ni
mgxL
xrecte
g
xrectxT
1
2
)(
Transition Refractive - Diffractive
Phase of refracting blaze grating: convolution of prism transmission with periodic
interference function
Notation:
L total width
g length of period
blaze angle
m index of periods
q order of phase jump with
height h
Complete transmission:
1. one period with linear phase
2. total width
3. periodicity of cell
-
L / d = 8
prism / interference total
L / d = 4
L / d = 1
-20 0 20 40 60 80 100
0
0.5
1
-20 0 20 40 60 80 100
0
0.5
1
-20 0 20 40 60 80 100
0
0.5
1
-20 0 20 40 60 80 100
0
0.5
1
-20 0 20 40 60 80 100
0
0.5
1
-20 0 20 40 60 80 100
0
0.5
1
Transition Refractive - Diffractive
Higher number of
periods
Increasing order q
Widths of orders
decrease
Limiting case:
one prism,
slit diffraction
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Lens with diffractive structured
surface: hybrid lens
Refractive lens: dispersion with
Abbe number n = 25...90
Diffractive lens: equivalent Abbe
number
Combination of refractive and
diffractive surfaces:
achromatic correction for compensated
dispersion
Usually remains a residual high
secondary spectrum
Broadband color correction is possible
but complicated
refractive
lens
red
blue
green
blue
red
green
red
bluegreen
diffractive
lens
hybrid
lens
R D
453.3
CF
dd
n
Achromatic Hybrid Lens
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Dispersion by grating diffraction:
Abbe number
Relative partial dispersion
Consequence :
Large secondary spectrum
n-P-diagram
Diffractive Optics: Dispersion
330.3''
CF
ee
n
2695.0''
'
',
CF
Fg
FgP
normal
line
ne
0.8
0.6
0.4
0.2-20 0 4020 60 80
DOE
SF59SF10
F4KzFS1
BK7
PgF'
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Combination of DOE
and aspherical carrier
Diffractive Optics: Singlet Solutions
50 m
0s'
y'
yp
yp
-0.5 mm50 m
0s'
y'
yp
yp
-0.5 mm50 m
0s'
y'
yp
yp
-0.5 mm50 m
0s'
y'
yp
yp
-0.5 mm
diffractive
surface,
carrier
aspherical
refractive
surface,
aspherical
diffractive
surface, phase
aspherical
all 2. order
d
d
d
d,a
a
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Upper part:
conventional lens
Lower part : lens with
diffractive surface
Diffractive Optics: Example Lens
0
Wrms
0 5 10w
486
588
656
poly
0.5
0.25
0
Wrms
0 5 10w
486
588
656
poly
0.5
0.25
y' y'
yp
yp
x'
xp
axis fieldfield
y' y'
yp
yp
x'
xp
axis fieldfield
all refractive lens
lens with one
diffractive surface
diffractive
-
Data :
- = 193 nm
- NA = 0.65
- b = 50
- sfree = 7.8 mm
Properties:
- short total track
- extreme large free working distance
- few lenses
Hybrid - Microscope Objective Lens
diffractive
element
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Straylight suppression
Diffractive Optics: Hybrid Lens
0. order
1. order
2. order
transmitted
light
blocked light
DOE
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Nearly index matched materials
Height of second layer
Efficiency
Broad Band DOE: Nearly Index Matching
x
z
ho
h(x)
n1
n2
)()(1)(1)(
21
2
2
1
1
''
eeee
CF
e nnnn
n
n
)()( 21 ee
e
nnh
m
nn
nn
oo
onim
)()(
)()(sinc
21
212
dif
0
0.2
0.4
0.6
0.8
1
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
air
nim
[m]
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Principle of achromatic correction
Ratio of Abbe numbers defines refractive power distribution
Diffractive element: Abbe number n = -3.45
Diffractive element gets only
approx. 5% of the refractive
power
diffglas
glas
refr FFnn
n
diffglas
diffs
refr FFnn
n
Color Correction of a Hybrid System
first refractive
power
short 1
long 2
image plane
corrected
second powerrefractive /diffractive
refractivesolution
diffractivesolution
1
2'1
'2
bending angles
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Dispersion by grating diffraction:
Abbe number: small and negative !
Relative partial dispersion
Consequence :
Large secondary spectrum
n-P-diagram
Diffractive Optics: Dispersion
330.3''
CF
ee
n
2695.0''
'
',
CF
Fg
FgP
normal
line
ne
0.8
0.6
0.4
0.2-20 0 4020 60 80
DOE
SF59SF10
F4KzFS1
BK7
PgF'
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Achromatic doublet
Ratio of Abbe numbers and refractive powers
Visible : 5% refractive power of DOE
Infrared : strong variations depending on substrat material
Diffractive Optics: Dispersion
nrefr/ndiff
m
BK7
SF6
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
5
10
15
20
25
30
35
40
silica
CaF2
poly-carbonat
LAF2
0 2 4 6 8 10 12
20
40
60
80
100
120
m
nrefr/ndiff
ZnS
ZnSe
sapphireCaF2
germanium
a) VIS b) IR
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Spherical Hybrid Achromate
Classical achromate:
- two lenses, different glasses
- strong curved cemented surface
Hybride achromate:
- one lens
- one surface spherical with
diffractive structure
- tolerances relaxed
1 2 3
refractive
solution
1 2
diffractive
solution
1
2
3
tilt
sensitivity
1 2
tilt
sensitivity
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Types of achromates
a) Spherical surfaces
uncemented
b) Hybrid with aspherical and
diffractive surface
Relaxed tolerances for
hybrid solution
classical
solution
1
2
3 4
aspherical
diffractive
solution
coma for
surface tilt
a) classical
solution
1 2 3 4
b) aspherical
diffractive
solution
1 2
all surfaces
spherical
apherical diffractive
Aspherical Hybrid Achromate
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Expansion of the optical pathlength for one field point:
Primary Seidel aberrations:
No field curvature
No distortion (stop at lens)
Ray bending in a plane corresponds to linear collineation
Equivalent bending of lens
Primary Aberrations of a Diffractive Lens
f
r
w
DOE
chief
rayimage
plane
f
rw
f
wr
f
r
f
rrW
4
3
282
2)(
22
2
3
3
42
2
2am
ccfX
diff
diff
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Seidel spherical aberration of a hybrid lens (A4: aspherical equivalent asphericity)
Optimal bending: choice of A4
Large spherochromatism
Optimization of refractive power of the DOE (10% instead of 5%)
Optimization of a Hybrid Lens
4
4
2
2
34
823
)1(
)1(4
1)1(
2
4yAm
n
n
nn
n
n
n
nn
nFySSS
ref
difrefsph
n
n
nn
n
n
n
nn
n
m
FA
ref 23
)1(
)1(4
1)1(
2
32
2
2
3
4
dif
sphref
gauss
ss
n
,
f
sFF
sphref
refdif
ref
refdif
dif
dif
,
nn
n
nn
n
f
sFF
sphref
refdif
ref
refdif
ref
ref
,
nn
n
nn
n
-
Realizations of Diffractive Elements
grating of index
example: HOEsurface contour multi phase level
binary grating
phase grating amplitude grating
DOE's
blazed
DOE's
quantized
DOE's
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Phase reduced by 2m m: wrapping height perhaps rather small feature sizes at the boundary (large slope)
Changed wrapping number m from center to boundary to prevent from small sizes
Discrete binarization, constant lateral feature size
Discretisation and Wrapping
phase
x
x
reduced
phase
phase 2m
near boundarym
phase
x
x
reduced
phase
phase 2m
phase
x
x
discrete
phase
spatial constant transverse
feature size
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Scaling error in mask
Typical Tolerances
x
Maske
1. Schritt
x
Maske
2. Schritt
Tolerances of Diffractive Elements
surface
gradient
wrongideal profile
edge
profile
rounded
profile
discrete
approximated
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Round edges in a Fresnel lens:
enlarged diffraction fringes
Encircled energy broadened
Diffractive Optics: Rounding of Edges
a
b
c
d
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
Log Ipsf
(x) E(r)
x r0 0.1 0.2 0.3 0.4 0.5
0.8
0.85
0.9
0.95
1
-0.5 0 0.5
10-4
10-3
10-2
10-1
100
ab
c
d
-
Different profile shapes of linear gratings
General diffractive elements
Grating and Diffractive Structures
37 Ref: R. Steiner
7200 lines/mm (139 nm period)
profile depth 70 nm
multi level DOE 5 mRef: Brenner/Jahns, Kley
Ref: Axetris Corp.