Upload
others
View
3
Download
0
Embed Size (px)
Citation preview
www.iap.uni-jena.de
Advanced Lens Design
Lecture 8: Field flattening
2013-12-03
Herbert Gross
Winter term 2013
1. Refraction
2. Fresnel formulas
3. Optical systems
4. Raytrace
5. Calculation approaches
2
Contents
ideal
image
plane
tangential
shell
sagittal
shell
image surfacesy'
Field Curvature and Image Shells
Imaging with astigmatism:
Tangential and sagittal image shell sharp depending on the azimuth
Difference between the image shells: astigmatism
Astigmatism corrected:
It remains one curved image shell,
Bended field: also called Petzval curvature
System with astigmatism:
Petzval sphere is not an optimal
surface with good imaging resolution
No effect of lens bending on curvature,
important: distribution of lens
powers and indices
3
Petzval Theorem for Field Curvature
Petzval theorem for field curvature:
1. formulation for surfaces
2. formulation for thin lenses (in air)
Important: no dependence on
bending
Natural behavior: image curved
towards system
Problem: collecting systems
with f > 0:
If only positive lenses:
Rptz always negative
k kkk
kkm
ptz rnn
nnn
R '
''
1
j jjptz fnR
11
optical system
object
plane
ideal
image
plane
real
image
shell
R
4
Correction of Astigmatism and Field Curvature
Different possibilities for the correction of astigmatism and field curvature
Two independend aberrations allow 4 scenarious
ST
-2.5 0 2.5
ST S T S T
-2.5 0 2.5 -2.5 0 2.5 -2.5 0 2.5
a) bended
image plane
residual
astigmatism
b) bended
image plane
corrected
astigmatism
c) flattened
image plane
residual
astigmatism
d) flattened
image plane
corrected
astigmatism
DzDz DzDz
y yy
Petzval Shell
The Petzval shell is not a desirable image surface
It lies outside the S- and T-shell:
The Petzval curvature is a result of the Seidel aberration theory
6
sagtan
petsag
ast
ss
ss
s
DD
DD
D 0(a)
pettan
petsag
ast
ss
ss
s
DD
DD
D 0(b)
T PSTP S
sagtan
petsag
petast
ss
ss
ss
DD
DD
DD
)21(
TP S
(d)
TP S
0
)32(
)32(
D
DD
DD
tan
petsag
petast
s
ss
ss(c)
pettan
sag
petast
ss
s
ss
DD
D
DD
2
0
2
TP S
(e)
2
''3'
tansss
sag
pet
DDD
Focussing into different planes of a system with field curvature
Sharp imaged zone changes from centre to margin of the image field
focused in center
(paraxial image plane)focused in field zone
(mean image plane)
focused at field boundary
z
y'
receiving
planes
image
sphere
Field Curvature
7
Field Curvature of a Mirror
Mirror: opposite sign of curvature than lens
Correction principle: field flattening by mirror
Gaussian
image
planeGaussian
image
plane
lens
mirror
Petzval
surface Petzval
surface
f' > 0 / R > 0f' > 0 / R < 0
New Achromate
An achromate is typically corrected for axial chromatical aberration
The achromatization condition for two thin
lenses close together reads
The Petzval sum usually is negative
and the field is curved
A flat field is obtained, if the following condition is fulfilled
This gives the special condition of simultaneous correction of achromatization
and flatness of field
perfect
image
plane
Petzval
shell
y'
f
RP
mean
image shell02
2
1
1
FF
j jjP fnR
11
02
2
1
1 n
F
n
F
2
1
2
1
n
n
New Achromate
This condition correponds to the
requirement to find two glasses on one
straight line in the glass map
The solution is well known as simple
photographic lens
(landscape lens) K5 F2stop
Flattening Meniscus Lenses
Possible lenses / lens groups for correcting field curvature
Interesting candidates: thick mensiscus shaped lenses
1. Hoeghs mensicus: identical radii
- Petzval sum zero
- remaining positive refractive power
2. Concentric meniscus,
- Petzval sum negative
- weak negative focal length
- refractive power for thickness d:
3. Thick meniscus without refractive power
Relation between radii
Fn d
nr r d'
( )
( )
1
1 1
r r dn
n2 1
1
21
211
'
'1
rr
d
n
n
fnrnn
nn
R k kkk
kk
ptz
r2
d
r1
2
2)1('
rn
dnF
drr 12
drrn
dn
Rptz
11
)1(1
0
)1(
)1(1
11
2
ndnrrn
dn
Rptz
11
Group of meniscus lenses
Effect of distance and
refractive indices
Correcting Petzval Curvature
r 2r 1
collimated
n n
d
3020 5010
-3
10-1
10-2
1/Rpet [1/mm]
40r
1
[mm]10
K5 / d=15 mm
SF66 / d=15 mm
K5 / d=25 mm
From : H. Zügge
12
Triplet group with + - +
Effect of distance and
refractive indices
Correcting Petzval Curvature
r 2r 1
collimated
n1
n2
r 3
d/2
7050 10010
-3
10-1
10-2
1/Rpet [1/mm]
r1
[mm]
BK7
SF66 / FK3 / SF66
From : H. Zügge
13
imageshell
flatimage
fieldlens
Effect of a field lens for flattening the image surface
1. Without field lens 2. With field lens
curved image surface image plane
Flattening Field Lens
14
Microscope Objective Lens
Possible setups for flattening the field
Goal:
- reduction of Petzval sum
- keeping astigmatism corrected
Three different classes:
1. No effort
2. Semi-flat
3. Completely flat
d)
achromatized
meniscus lens
a)
single
meniscus
lense
e)
two
meniscus
lenses
achromatized
b)
two
meniscus
lenses
c)
symmetrical
triplet
f)
modIfied
achromatized
triplet solution
DS
rel.
field0 0.5 0.707 1
1
0.8
0.6
0.4
0.2
0
diffraction
limit
plane
semi
plane
not
plane
Field Curvature
Correction of Petzval field curvature in lithographic lens
for flat wafer
Positive lenses: Green hj large
Negative lenses : Blue hj small
Correction principle: certain number of bulges
j j
j
n
F
R
1
j
j
jF
h
hF
1
16