Transcript Lecture Series

IV
Practical Aspects of Lens Design
October 2008
Rudi Rottenfusser – Carl Zeiss MicroImaging
The Most Important Microscope Component
The Objective
Lenses
Glass Parameters (excerpt)
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Refractive Index
Dispersion
Thermal Expansion Coeff.
Spectral Transmission
No Autofluorescence
No Schlieren, bubbles, inclusions
Reflectivity
Film Adhesion (AR coatings)
Chemical Resistance
Resistance to Humidity
Availability
Topics
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Airy Disk / Point Spread Function
Resolution Criteria – Rayleigh, Sparrow, etc.
Definition: Depth of field / focus
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Aberrations
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The Objective
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What do the markings mean
What to consider when selecting an objective
Website - References
What happens to the image of the object
when it travels through the various
microscope components?
1) No Lens Aberrations
(“perfect lens”)
On Axis image
Wave fronts
In phase
½λ Out of phase
Relative sizes of Airy disk (D) as a function of Numerical Aperture
D
NA:
0.4
D
D
0.8
1.3
Airy Disk
D
D  1.22

NAObjective
D = Diameter of Airy disk in image plane
Airy Disk
D
D  1.22

NAObjective
Rayleigh Limit of Lateral Resolution
d=½D
0.61
d
NAObjective
Resolution in z as defined
by the “Airy Body” is
n
z
NA2
Airy Disks of 2 clearly imaged separate points:
Rayleigh Criterion for resolution
• Minimum distance dmin
is reached, when the
principal maximum of
object 1 (center of Airy
Disk) coincides with first
minimum of object 2
Intensity
• Intensity of maxima = 20%
higher than intensity of
“dip” between maxima
X
dmin
Two points at minimum
distance to be “resolved”
Rayleigh Limit of
lateral resolution
d
0.61
NAObjective
d = ½ D (radius)
Objectives - Definitions: Depth of Field / Focus
Different formulas (e.g. Berek 1927, Shillaber 1944, Françon 1961,
Martin 1966, Michel 1981, Piller 1977)
 n
n
T

e
2
NA
M  NA
From Shinya Inoué / Kenneth R. Spring book:
“Video Microscopy Fundamentals - 2nd edition”
Chapter 2.4.6
T = Depth of field (µm)
λ = Wavelength (µm)
n = Refractive Index
M = Magnification (Image Ratio)
e = diffraction-limited resolution
d in image plane (µm)
Example: C-Apochromat 40x/1,2W
1 Rayleigh unit = 0,42 µm in object plane
= 0,668 mm in image plane
In general: At high NA the depth of field is small and the depth of
focus at the image side is large. This reverses at low magnifications!
What happens to the image of the object
when it travels through the various
microscope components?
2) Considering Aberrations
Aberrations
• Spherical Aberration
• Chromatic Aberration (axial)
• Chromatic Aberration (lateral or radial)
• Curvature of Field
• Astigmatism
• Distortion
• Internal Reflexes
Spherical Aberration
Plan-Apochromat 40x/0.95 corr.
Correction Collar set at 0.21mm
Spherical Aberration
Plan-Apochromat 40x/0.95 corr.
Correction Collar set at 0.17mm
Spherical Aberration
Infinite number of prisms
with different angles
and, therefore, different
refractive powers
Spherical Aberration
Due to the spherical character of the lens, rays
do not cross over at the same Focal Point
Spherical Aberration is reduced by smaller aperture
Less confused “Zone
of Confusion”
Fixing Spherical Aberration
Reducing Spherical Aberration
Multiple Elements
Aspheric Lens
Exaggerated
How to generate Spherical Aberration:
Maximum Intensity in an
image of a point object
Incorrect Cover Glass
How to generate Spherical Aberration:
(Full Width, Half Max)
Resolution [µm]
Incorrect Cover Glass
Choose the right
cover glass!
Types and Thickness Ranges
No.0 ......... 0.08 - 0.12 mm
No.1 ......... 0.13 - 0.17 mm
No.1.5....... 0.16 - 0.19 mm
No.2 ......... 0.19 - 0.23 mm
No.3 ......... 0.28 - 0.32 mm
No.4 ......... 0.38 - 0.42 mm
No.5 ......... 0.50 - 0.60 mm
Use 0.170 mm thick cover slips !
How to generate Spherical Aberration:
Focusing deeper into the sample
40x/1.3 Oil immersion objective – Energy at different depths of penetration z in water
Benefit of Water Immersion Objectives
(with cover slip correction)
Water Immersion
n~1.3
Cover Slip n=1.52
Aquaeus Medium
n~1.3
Chromatic Aberration (Axial)
Remember “Dispersion” of Light!
Fixing Chromatic Aberration
n ≈ 1.55
n ≈ 1.65
The classic “Achromat” (Doublet)
Objectives -
Definitions: 
Corrected Wavelength (nm):
UV
Plan Neofluar
VIS
IR
-
-
(435)
480
546
-
644
-
-
Plan Apochromat -
-
435
480
546
-
644
-
-
C-Apochromat
405
435
480
546
608
644
-
-
-
435
480
546
608
644
800
1064
365
IR C-Apochromat -
Objectives Best Focus
1 RU
480 nm
RU = Rayleigh Unit
546
nm
644
nm
Lateral Chromatic Aberration (LCA)
(Chromatic Magnification Difference)
Image
Lateral Chromatic Aberration (LCA)
Lateral Chromatic Aberration (LCA)
Different manufacturers correct for LCA in different ways:
Leica:
The tube lens corrects for a fixed amount of LCA
Nikon:
The objectives themselves are fully corrected
Olympus:
The objectives themselves are fully corrected
Zeiss:
The tube lens corrects for objectives with different LCA’s
Astigmatism
Tangential
Sagittal
Spherical
Aberration
Intensity
Distribution
Astigmatism
in Airy Disk
Coma
Curvature of field: Flat object does not
project a flat image
(Problem: Camera Sensors are flat)
f1
f2
image
object
Objectives -
Definitions: Flatness
Flatness at 435nm:
SF 18
SF 25
Plan Neofluar
1R
Plan Apochromat
< 0,5 R
C-Apochromat
0,6 - 1 R
1 - 2R
Distortion
Pincushion
Barrel
Internal Straylight
Reflexes (unwanted reflections)
%R
4
uncoated
Anti Reflection (AR) Coating
2
Single layer
~ 1%
Multi layer
400
700
 [nm]
~ 0.1%
Internal Straylight
Anti-Reflex (AR) Coating
How does it work?
/4
Questions?
Objective Markings
Thread Diameter
0.8”x1/36” (RMS) 27mm, 25mm
Mounting Distance (Specimen to Flange):
22, 45, 60, 75mm, others?
Magnification
“Standard” Sequence
10

R10 10  1.2589254...
1.251
=
1.25x
1.252
=
1.6x
1.253
=
2x
1.254
=
2.5x
1.255
=
3.2x
1.256
=
4x
1.257
=
5x
1.258
=
6.3x
1.259
=
8x
1.2510
=
10x
1.2511
=
12.5x…
Why these
strange
numbers?
1. Magnification
2. Working Distance
3. Numerical Aperture (NA) – Resolution / Depth of Field
4. Image Quality – minimized Aberrations (spherical, chromatic, flatness of field,
astigmatism, coma, distortion)
5. Adaptation to specific Applications (Contrasting Techniques, Cover Slips,
Chambers, Shape of front lens for Access)
6. Spectral Transmission (Visible,IR,UV?)
7. No Autofluorescence
8. No Strain (Pol)
9. Temperature Tolerance
10. Temperature Isolation (heating!)
11. Chemical Resistance
12. Electrical Shielding
13. Minimal Path Gradient (2-photon)
14. Perfect Parfocality and Parcentricity
15. Compact yet durable
16. Inexpensive
What to consider when
selecting an objective:
For a comprehensive lookup of objectives, consult Websites!
(Example for Zeiss: www.zeiss.com/campus)
Description of Classes of Objectives
Example
(Screenprint)
Please refer to
appropriate
web sites from
Leica
Nikon
Olympus
Thank you, and do enjoy
your microscopes !
Rudi Rottenfusser
Office:
Cell:
Email:
Microscopy Support:
Imaging Support:
Website:
Educational Site:
508/289-7541
508/878-4784
[email protected]
800/233-2343
800/509-3905
www.zeiss.com/micro
www.zeiss.com/campus