13 lecture 13 zoom and confocal systems
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Design and Correction of Optical
Systems
Lecture 13: Zoom and Confocal Systems
2013-07-10
Herbert Gross
Summer term 2013
2
Preliminary Schedule
1 10.04. Basics Law of refraction, Fresnel formulas, optical system model, raytrace, calculation
approaches
2 17.04. Materials and Components Dispersion, anormal dispersion, glass map, liquids and plastics, lenses, mirrors,
aspheres, diffractive elements
3 24.04. Paraxial Optics Paraxial approximation, basic notations, imaging equation, multi-component
systems, matrix calculation, Lagrange invariant, phase space visualization
4 08.05. Optical Systems Pupil, ray sets and sampling, aperture and vignetting, telecentricity, symmetry,
photometry
5 15.05. Geometrical Aberrations Longitudinal and transverse aberrations, spot diagram, polynomial expansion,
primary aberrations, chromatical aberrations, Seidels surface contributions
6 22.05. Wave Aberrations Fermat principle and Eikonal, wave aberrations, expansion and higher orders,
Zernike polynomials, measurement of system quality
7 29.05. PSF and Transfer function Diffraction, point spread function, PSF with aberrations, optical transfer function,
Fourier imaging model
8 05.06. Further Performance Criteria Rayleigh and Marechal criteria, Strehl definition, 2-point resolution, MTF-based
criteria, further options
9 12.06. Optimization and Correction Principles of optimization, initial setups, constraints, sensitivity, optimization of
optical systems, global approaches
10 19.06. Correction Principles I Symmetry, lens bending, lens splitting, special options for spherical aberration,
astigmatism, coma and distortion, aspheres
11 26.06. Correction Principles II Field flattening and Petzval theorem, chromatical correction, achromate,
apochromate, sensitivity analysis, diffractive elements
12 03.07. Optical System Classification Overview, photographic lenses, microscopic objectives, lithographic systems,
eyepieces, scan systems, telescopes, endoscopes
13 10.07. Special System Examples Zoom systems, confocal systems
1. Principle of zoom systems
2. Various setups for zoom systems
3. Simple calculation schemes
4. Example systems
5. Miscellaneous topics concerning zoom systems
6. Confocal principle
7. Confocal chromatical sensor
8. Confocal microscope
3
Contents
Zoom Lenses
Change of focal length
Magnification enlarged / scene reduced
a) focal length f = 30 mm c) focal length f = 250 mmb) focal length f = 100 mm
Ref: W. Osten
Basic Principle
Two thin lenses in a certain distance t:
Focal length
Refractive power
Kinds of zoom systems
tff
fff
21
21
2121 FFtFFF
221 FFF
1
22
h
h
c) Infinite-infinite (I-I)
b) Infinite-finite (I-F)
a) Finite-finite (F-F)
Change of Focal Length
Distance t increased
First lens fixed
moved
lenschanged
distance
t changed focal
length f
Change of Focal Length
Distance t increased
Image plane fixed
two lenses moved
t f
image
plane
Two Solutions
Paraxial matrix formulation:
Two states of the system,
Invariant image position s
Quadratic equation for s:
always two solutions with
m' = 1/m
zA
C D
B
x x'
object
planeimage
plane
u u'
s s'
zoom system
.''
''' const
DsC
BsA
DCs
BAss
DCs
BAs
Du
xC
Bu
xA
DuCx
BuAx
u
xs
'
''
Principle of Smallest Change of Total Track
Zoom factor : ratio of magnification change
Equivalent : ratio of focal lengths
Zoom system :
- change of magnification
- constant length
mmfL
12
min
max
m
mM
min
max
f
fM
min
max
M
-4 -3 -2 -1 0 1 2 3 4-10
-5
0
5
10
m
L/f
Principle of Smallest Change
Goal :
smallest change of length
Preferred points of operation:
m = 1 , m = -1
Setup :
1. Change of magnification :
variator group
2. Correcting the image
location: compensator group
)1/()/(4)/(2
2/2)/(
2
1
24
2
fsfsfs
fsfs
dL
dmf
-10 -8 -6 -4 -2 0 2-10
-8
-6
-4
-2
0
2
4
6
8
10
L / f
s / f
f dm/dL
m
Mechanical Compensated Zoom Systems
Simple explanation of variator and compensator
Movement of variator arbitrary
Compensator movement
depends on variator
Perfect invariance of
image plane possible
objective
lens
variator
linear
compensator
nonlinearrelay
lens
P
P
P
image
plane
Two-Component F-F System
Setup :
Given : L, m, f1, f2 :
Wüllner equations:
f1
f2
L
t1
t2
t3
object image
m
mffffL
LLt
2
2121
2
2
1
42
221
221211
tffm
tffmfft
213 ttLt
221
21
tff
fff
Two-Component F-F System
Solution space :
focal lengths:
1. f1 > L/4
2. f2 > L/4
3. 1/f1 + 1/f2 < 4/L
Calculation with Newton-
imaging equation and
tj > 0
Ranges with 0 - 1- 2 - 3 - 4
solutions for focal lengths
1
[1/L]
2 [1/L]
0 4 15-15 10-10 -5
no solution
1
2
3
4
3
2
2
15
-15
4
10
0
-10
-5
a)
b)
c)
d)
Two-Component F-F System
Examples:
1. Number of solutions
2. Zoom curves
3. m-ranges
d) f1= L/3
f2 = L/3
t1 = 25 , t
2 = 29.3 , m = -1.35
t1 = 16.5 , t
2 = 16.7 , m = -11.8
t1 = 11.3 , t
2 = 80.7 , m = -13.5
t1 = 5.9 , t
2 = 7.6 , m = -4.8
t1 = 16.4 , t
2 = 26.6 , m = +6.0
t1 = 3.1 , t
2 = 4.3 , m = -16
L
m
c) f1
= L/10
f2 = -L/10
t2
t1
t1
t2
t1
t2
t1
t2
b) f1
=-L/10
f2 = L/10
a) f1
= L/12
f2 = L/12
t2
t1
0 20 40 60 80 100
0 20 40 60 80 100L
0 20 40 60 80 100L
L
m
m
m
0 20 40 60 80 100-4
-3
-2
-1
0
-25
-20
-15
-10
-5
0
-8
-6
-4
-2
0
-20
-10
0
10
20
t1
t2
Three-Component Zoom System
Setup:
1. lens
fixed
Given :
M, L
Arbitrary but recommended :
Calculation : central position
third lensfirst lens fixed second lens image
planef1 f
2f3
t1
t2
s'
s'2
f1
s3
LM
MF
11
LM
MF
12
13
)1(13
M
MMFFF
)1(
1
1
1
MF
Mt
)1(
1
1
2
MMF
Mt
)1(
13'
MMF
Ms
Three-Component Zoom System
Arbitrary zoom positions:
given is t1
Example:
121
1122'
tff
tffs
c
bbt
42
2
2
Lstb 21 '
23231 ')'()( sfsftLc
3312121323211321 FFFttFFFtFFFtFFFF
F
[1/mm]
-20 0 20 40 60 80 100 120 140 1600
20
40
60
80
100
120
140
160
180
[mm]
t1
t2
fmin
=16.3 mm
fmax
=163 mm
middle:
fm
=100 mm
Symmetrical Afocal Setup
Telescope angle magnification :
Major positions
Symmetrical layout
f1
f1
f2
asymmetric 1
> 1
tmax
asymmetric 2
tmin
<
symmetric
tm
tm
= 1
last
first
h
h
w
w
'
Magnification First distance
Second distance
|| = |max| > 1 tmax 0
|| = 1 tm tm
|| = 1/|max| < 1 0 tmin
Matrix Solution: Optical Compensated Afocal Zoom
Shifting from middle position:
Matrix
Middle position:
Conditions:
a) symmetrical zoom position : = 1
b) asymmetrical zoom position : < 1
f1
f1f
2
tm
tm
f1
f1
f2
tm
+ztm
-z
21
2
2121 FFtFtFtA mmmm
2
2
1
2
21
2
121 222 FFtFFFtFFC mmm
1
01
10
1
1
01
10
1
1
01
121 F
zt
F
zt
FDC
BA mm
aa
aa
21
2
221
2
2121 FFzFzFFtFFtA mma
2
2
1
2
2
2
1
2
21121 22 FFzFFtFFtFFFC mma
AD
u
u 1'0
'
0
ux
uC 1)( min ma tA
0)0( mC
Symmetrical Afocal Setup
Calculation:
Example:
2
max
min
max
M
13 1max12
1
11
max
max
1
mt
max
max
1
minmax
11
tt
1
1
max
max
1
1
t
111
max
max
1
2
t
1
122
max
max
1
mtL
0 20 40 60 80 100 1200
0.5
1
1.5
2
2.5
3
3.5
4
max
= 4
min
= 1/4
2. lens
1. lens
= 1
Optical Compensated Zoom Systems
Combined movement of two rigid coupled lenses
Image plane location only approximately constant
Only one moving part
image with
defocusfixed group coupled
moved lensesrelay lens fixed
P
P
P
Optical Compensation
Rayleigh range changes with m:
Optimized zeros
2
2
2
4
in
uDNA
R
image plane
with defocuszoom system
fixed
relay lensobject
+ Ru
- Ru
z
m
General Three Component Optical Compensated System
Setup
Calculation:
Tube lengths:
Focal length:
Deviation:
z
coupled movement : z
F'1
F2 F'
2
F'3F
3
f1
f2
f3
t1 t
1
e1
e2
lens 1 lens 2 lens 3
image
plane
21101 ffte 32202 ffte
21
2
212
2
21
2
2
2
1
2
2
2
321
2
2
21
2
2
2
3112
23
eefzeezz
eef
effeefz
eef
feeezz
z
2
2121
2
2
321
zzeeeef
ffff
Three Component Optical Compensated System
Approximated solution:
- auxiliary parameters B,C
- practical starting values for B, C
12
2
2 eefB 12 ttC
BM
MC
M
MCz
22
max1
1
41
1
2
12
max
2
3 112 B
zBCf
22CB
BBf
21CB
CBe
12 eCe
max21321 22 zeefffL
f1 f2 f3 Focal length f
Image location
Parameter B/C
2
+ + + – + 0–1
+ + – + + 0.5–1
+ – + + + 0–0.5
+ – – no solution
– + + + – 0–1
– + – – – 0.5–1
– – + – – 0.5–1
– – – no solution
Three Component Optical Compensated System
Typical deviation behaviour
-1 -0.5 0 0.5
-0.05
0
0.05
M = 1.3
M = 1.5
M = 2.0
M = 2.5
M = 3.0
1
z/zmax
z [a.u.]
Performance Variation over z
System layout of a simple but real example
f = 200 mm
f = 100 mm
f = 50 mm
f = 67 mm
f = 133 mm
f1 f
2f3 f
4
t2
Performance Variation over z
Seidel
surface
contrib.
coma distortion axial chromatical lateral chromatical
lens 1
lens 2
lens 3
sum
spherical aberration
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
-0.1
0
0.1
-0.1
0
0.1
-0.1
0
0.1
-0.1
0
0.1
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
-0.2
-0.1
0
0.1
0.2
-0.2
-0.1
0
0.1
0.2
-0.2
-0.1
0
0.1
0.2
-0.2
-0.1
0
0.1
0.2
1 2 3 4 5
-5
0
5
1 2 3 4 5
-5
0
5
1 2 3 4 5
-5
0
5
1 2 3 4 5
-5
0
5
1 2 3 4 5
-5
0
5
1 2 3 4 5
-5
0
5
1 2 3 4 5
-5
0
5
1 2 3 4 5
-5
0
5
1 2 3 4 5
-0.5
0
0.5
1 2 3 4 5
-0.5
0
0.5
1 2 3 4 5
-0.5
0
0.5
1 2 3 4 5
-
0.5
0
0.5
Real photographic zoom lens
Three moving groups:
1. variator: focal length
2. compensator: focussing
3. object distance
Zoom Lens
e)
f' = 203 mm
w = 5.64°
F# = 16.6
d)
f' = 160 mm
w = 7.13°
F# = 13.7
c)
f' = 120 mm
w = 9.46°
F# = 10.9
b)
f' = 85 mm
w = 13.24°
F# = 8.5
a)
f' = 72 mm
w = 15.52°
F# = 7.7
group 1 group 2 group 3
Combined Zoom with Focussing
Photography:
Additional floating element for focussing
Problem : Breathing, change of field size during focussing
non-telecentric chief ray at focussing group
s = 2.5 m
f = 134 mmf = 100 mm f = 162 mm
infinity
focussing G1
G2
G3
G4 G
5
Combined Zoom with Focussing
System without breathing
Special movement of focus group
zoom
group 1
zoom
group 2
focusing group
infinity
common movement
separated movementfront part rear part
object
distance
0
2.5 m
0.25 m
0.4
0.6
vergence
in [dpt]
0100200300z
[mm]
Example
Professional factor 5 zoom lens with 5
moving groups
Very smooth and excellent correction
f = 29 mm
f = 35 mm
f = 50 mm
f = 70 mm
f = 105 mm
f = 146 mm
spherical coma astigma distortion ax chrom la chrom
1st
group
2nd
group
3rd
group
4th
group
sum
5th
group
curvature
Ref: Tokumaru, USP 4846562 (1988)
Fixed Pupil Position
Usual:
1. two moving groups
2. Pupil locations changes
Three moving groups : Pupil position can be held constant
Scheme and parameters:
object imagef1
f2 f
3EnPExP
s
p
p'
t1
t2
s'
P'P
Fixed Pupil Position
Calculation straightforward
Large solution space
Example 1 for illustration :
ln|m|
z
[mm]-200 -150 -100 -50 0 50 100
-1.5
-1
-0.5
0
0.5
1
1.5
Fixed Pupil Position
Example for illustration :
60 80 100 120 140 160 180 200-1.5
-1
-0.5
0
0.5
1
1.5
ln|m|
z
[mm]
m = -0.25
f3 = 40f
2 = -19f
1 = 40
m = -0.38
m = -0.5
m = -0.75
m = -1
m = -1.5
m = -2
m = -3
m = -4
object imageentrance
pupilexit
pupil
Stop Position
Example with the stop at three different locations
Comparison of Seidel contributions
Best correction for the stop at rear group
a) f = 18 mm
stop at
1st
lens
stop at
2nd
lens
stop at
3rd
lens
b) f = 50 mm c) f = 125 mmstop
Stop Position
Seidel
lens 1
lens 2
lens 3
sum
sph coma ast dist la chr
a) stop at 1st lens b) stop at 2nd lens
sph coma ast dist la chr
c) stop at 3rd lens
sph coma ast dist la chr
Correction of Zoom Systems
Typical compensator group
Typical variator group
Principle:
- No compensation for all movement positions possible
- Correcting every group
Color Correction of the Moving Groups
Axial and lateral
color:
Comparison of
singlet/doublet
solution
= 0.3
= 0.57
= 1.0
= 1.7
= 3.0
lateral colour [a.u.]
axial colour [a.u.]
a) Singlet solution b) Doublet solution
0 0.5 1 1.5 2 2.5 3 3.5
10-4
10-3
10-2
10-1
100
0 0.5 1 1.5 2 2.5 3 3.510
-3
10-2
10-1
100
101
102
Singlets
Doublets
Singlets
Doublets
Example Optical Compensated Zoom
Five components, optical
compensated
Deviation curve
f = 400 mm
f = 234 mm
f = 162 mm
f = 127 mm
f = 100 mm
t1
z [mm]
f [mm]
image
plane
scaled
z/Ru
100 150 200 250 300 350 400-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
z
1
2
-2
-1diffraction
limited range
Example Optical Compensated Zoom
Five components, optical
compensated
Wrms and single
Zernike coefficients Wrms
[] c40
[]
t1
[mm]
a) b)
60 80 100 120 140 160 180 200 2200
5
10
15
20
60 80 100 120 140 160 180 200 220-40
-30
-20
-10
0
10
t1
[mm]
60 80 100 120 140 160 180 200 220-1
0
1
2
3
4
5
6
60 80 100 120 140 160 180 200 220-1.5
-1
-0.5
0
0.5
1
c31
[] c)
t1
[mm]
t1
[mm]
c22
[] d)
Solid State Zoom Systems
Lenses with variable
focal length
Calculation:
Critical value:
First lens focuses onto the second lens
f1
f2
ts
s'
sst
s
s
)1(
1
'
1
1
12
)1(
1
'
1
1
1
tsts
t
11
'
sts
sm
stc
111
Solid State Zoom Systems
Solution
areas
Second solution:
Intermediate image
1
[1/mm]
< 0
2
[1/mm]
-0.05 0 0.05 0.1 0.15-0.2
-0.1
0
0.1
-0.05 0 0.05 0.1 0.15
-20
-15
-10
-5
0
5
10
15
20
25
1
[1/mm]
> 0
msolution a solution a solution bsolution b
f1
f2
ts
s'
Zoom System with 2 Stages
2-stage cascaded zoom system
Intermediate image plane
Zoom factor M = 300
970 mm
Zwischen-
bildBild1. Zoom
Gruppe2. Zoom
Gruppe
3. Zoom
Gruppe
4. Zoom
Gruppe
Hauptzoom Relay-Zoom
Ref: Caldwell, USP 7227682 (2007)
Confocal Distance Sensor
Principle of the confocal distance sensor
objective
lens
beam
splitter pinhole detector
in focus
out of focus
Illumination
pinhole
objective
-6 -4 -2 0 2 4 60
0.2
0.4
0.6
0.8
1
S [a.u.] dS/dz [a.u.]
DPH
= 0.3 Dairy
DPH
= 1.0 Dairy
DPH
= 1.8 Dairy
z
[Ru]
z [Ru]
linearity
-3 -2 -1 0 1 2 3-1
-0.5
0
0.5
1
a) b)
Chromatical Confocal Sensor
Spectral sensitive sensor
Objective lens with large axial
chromatical aberration
white light
source
pinhole
focussing
objectiveconfocale
pinhole
detector
grating
measuring
range
chromatical
objective
z
[mm]-4.0 -2.0 0 4.02.0
480 nm
546 nm
656 nm
-6 -4 -2 0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
z
[mm]
E
480 nm
546 nm
656 nm
Confocal Imaging with Hyper Chromate
Wide field 20x0.5
Confocal with chromate at
low aperture 20x0.5
Confocal with chromate at
high aperture 50x0.9
Ref: R. Semmler
Goal: 1. large chromatical spreading (large CHL) z 2. large numerical aperture 3. corrected spherochromatism
In the case of a large ratio z / f, the numerical aperture shows a considerable change in the measuring interval
Design approach:
1. Achromate with positive flint
and negative crown
2. Achromates cascaded
3. Improved spherochromatism
by asphere
4. monochromatic lens with
buried surface adapter
Principle
z
= 644 nm
= 546 nm
= 480 nm
47
NA=0.3 z=3 no doublet.ZMXConfiguration 1 of 3
Layout
Hyper chromate07.03.2013Total Axial Length: 60.45674 mm
Surface: IMA
0.0000 (deg)
Config 1
4.00
Config 2 Config 3
NA=0.3 z=3 no doublet.ZMXConfiguration: All 3
Configuration Matrix Spot Diagram
Hyper chromate07.03.2013 Units are µm. Airy Radius: 1.563 µm
Scale bar : 4 Reference : Chief Ray
-5 -4 -3 -2 -1 0 1 2 3 4 5
Pupil Radius: 9.7107 Millimeters
Millimeters
NA=0.3 z=3 no doublet.ZMXConfiguration 1 of 3
Longitudinal Aberration
Hyper chromate07.03.2013Wavelengths: 0.450 0.546 0.675
Spherical Coma Astigmatism Field Curvature Distortion Axial Color Lateral Color
SUM1 2 3 STO
NA=0.3 z=3 no doublet.zmxConfiguration 1 of 3
Seidel Diagram
Hyper chromate2013/3/7Wavelength: 0.4500 µm.Maximum aberration scale is 0.50000 Millimeters.Grid lines are spaced 0.05000 Millimeters.
1st surface: aspherical
Case 1-1
NAimage = 0.3, NAobject = 0.22
Δz = 3 mm, f = 13 mm
zfree = 16.3 mm
Optical Design
Fourier optical model:
- object/sample to be assumed as a plane mirror
- fiber source incoherent, diameter Dfib, uniformly radiating
- optical system with point spread function hpsf
- confocal detection by fiber (pinhole) size Dfib
Incoherent imaging model to get the
intensity of at the fiber
Calculation of the confocal signal by
integration over the pinhole
Confocal Depth Measuring System
focal plane
for
selected
sample
surface
fiber
recoupling into fiber
confocal selection
D
z
hyperchromatic
system
2
)()(),( zhaIzaI psffibima
ar
imaconf dydxzaIzaS ),(),(
Confocal Signal for Different Pinhole Sizes
Numerical result for different sizes a of the fiber radius
The width increases with the fiber diameter
The diffraction fine structure disappears with growing a
S()
0.58 0.585 0.59 0.595 0.6 0.605 0.61 0.615 0.620
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
a = 0
a = 10 mm
a = 5 mm
a = 20 mm
Confocal Laser Scan Microscope
Complete setup: objective / tube lens / scan lens / pinhole lens
Scanning of illumination / descanning of signal
Scan mirror conjugate to system pupil plane
Digital image processing necessary
object
plane
objective
lens
pupil
plane
tube
lens
intermediate
image
scan
lens
scan
mirror
laser
source
beam
forming
pinhole
lens
pupil imaging
axis point
field point
Fourier optical model:
- illumination with point spread function hill
- object function plane, tobj, scanned
- detection with point spread function hdet
- detector function by pinhole size Dph
General transform of amplitudes
illhUU 12
Confocal Laser Scan -Microscope
illumination
hill
sourceobject tobj
scan
pinhole
detector
Dph
detection
hdet
U1 U2 U’2 U3 U’3
objtUU 22'
det23 ' hUU
phDUU 33'
Ref: M.Wald
2
objdetillima thhI
objdetillima thhI 2
phillima DhhI 2
det
2
Image Formation Confocal LSM
Special cases:
Brightfield, perfectly small pinhole
D=d(x)d(y), imaging coherent
Fluorescence, coherence destroyed
perfectly small pinhole
Point like object tobj = d(x) d(y)
Point object and perfectly small
pinhole
Plane mirror object tobj = const.
perfectly small pinhole
22
detillima hhI
dydxzyxhI detima
2)2,,(
det ill
det ill dethhill
Normalized transverse coordinate v
Usual PSF: Airy
Confocal imaging:
Identical PSF for illumination and observation
assumed
Resolution improvement be factor 1.4 for
FWhM
sin'
2 xv
4
1 )(2)(
v
vJvI
2
1 )(2)(
v
vJvI
Confocal Microscopy: PSF and Lateral Resolution
-8 -6 -4 -2 0 2 4 6 80
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
I(v)
incoherent
coherent
Normalized axial coordinate
Conventional wide field imaging:
Intensity on axis
Axial resolution
Confocal imaging:
Intensity on axis
Axial resolution improved by factor 1.41
for FWhM
4
2/
)2/sin()(
u
uuI
2
2/
)2/sin()(
u
uuI
Confocal Microscopy: Axial Sectioning
cos1'
45.0)(
nz approx
wide
cos1'
319.0
nzconfo
)2/(sin8 2
zu
u
I(u)
-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,
incoherent
coherent
Large pinhole: geometrical optic
Small pinhole:
- Diffraction dominates
- Scaling by Airy diameter a = D/DAiry
- diffraction relevant for pinholes
D < Dairy
Confocal signal:
Integral over pinhole size
Size of Pinhole and Cnfocality
a
dvvvuUuS0
22),()(
x / DAiry
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
DPH / DAiry
NA = 0.30
NA = 0.60
NA = 0.75
NA = 0.90
geometrical
-25 -20 -15 -10 -5 0 5 10 15 20 250
2
4
6
8
10
12
S(u)
u
a = 3
a = 2
a = 1
a = 0.5
Confocal Signal with Spherical Aberration
S(u)
u-30 -20 -10 0 10 20 30
0
1
2
3
4
5
6
7
8
9
10
relative pinhole size:a = 3a = 2a = 1a = 0.5
spherical aberration 2
Spherical aberration:
- PSF broadened
- PSF no longer symmetrical around image plane during defocus
Confocal signal:
- loss in contrast
- decreased resolution
Depth resolved
images
Confocal Images
Ref.: M. Kempe