VLE 2 Optical Instruments I
.pdf
6. Achromats
41
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Principle (1)
Chromatic aberration
Dependency of the refractive index n (dispersion) and therefore, also the focal length of the wavelength.
Blue Red
source: Demtröder, Experimentalphysik 2
42
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Principle (2)
Minimization of chromatic aberration by a combined system of a focussing lens and a defocussing lens with different refractive indices: achromate
Glue
source: Demtröder, Experimentalphysik 2
43
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Principle (3)
source: http://www.letusdirect.com/what-does-achromat-mean.html
44
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Achromatism condition and Abbe number
Postulate:
Lens system shall have the same optical refraction power:
F-line ( = 486.1 nm, blue) C-line ( = 656.3 nm, red)
Glue
Wavelength in nm |
source: www.ursusmajor.ch |
|
Fraunhofer lines: characteristic absorption lines in the sun spectrum (self absorption at ionized Atoms inside the sun)
45
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Achromatism condition and Abbe number
Two lenses with small distance (compare lecture part1):
Ds D1 |
D2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
Lens system shall have for the C-line and the |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||||||||||||
|
|
|
Glue |
|
|
|
|
|
|
|
|
|
|
|
||||||||||||||||||||
F-line the same optical refractive power: |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||||||||||||||
DFs DCs DF1 DF 2 DC1 DC 2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||||||||
n |
|
|
1 |
|
1 |
|
n |
|
|
1 |
|
|
1 |
|
n |
|
|
1 |
|
1 |
|
n |
|
|
1 |
|
1 |
|
||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||||||||||||
|
1 |
R |
R |
|
|
1 |
R |
|
R |
|
|
|
1 |
R |
R |
|
|
1 |
R |
|
R |
|
|
|||||||||||
|
F1 |
|
|
|
F 2 |
|
21 |
|
22 |
|
C1 |
|
|
|
C 2 |
|
21 |
|
22 |
|||||||||||||||
|
|
|
11 |
|
12 |
|
|
|
|
|
|
|
|
|
|
|
|
11 |
|
12 |
|
|
|
|
|
|
|
|
||||||
Rearrange: |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
n |
|
|
|
|
1 |
|
1 |
|
n |
|
|
|
|
1 |
|
1 |
|
|
||
|
n |
|
|
|
|
|
n |
|
|
|
|
0 |
||||||||
|
|
|
|
|
|
|
|
|
|
|||||||||||
|
|
|
R |
R |
|
|
|
|
R |
|
R |
|
|
|||||||
|
F1 |
|
C1 |
|
|
|
F 2 |
|
C 2 |
|
21 |
|
22 |
|
||||||
|
|
|
|
|
11 |
|
12 |
|
|
|
|
|
|
|
|
|
|
|
||
46
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Achromatism condition and Abbe number
Introduction of the refractive index nd for the Frauenhofer Line D3 ( = 589,3 nm, Index is d instead D3 for simplicity reason)
|
nF1 nC1 |
n |
|
|
1 |
|
|
1 |
|
|
|
nF 2 nC 2 |
n |
|
|
1 |
|
1 |
|
|
||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0 |
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||||||
|
n |
|
1 |
|
1 |
R |
|
R |
|
n |
|
1 |
|
1 |
R |
|
R |
|
|
|||||||||||
|
d1 |
|
d1 |
|
|
|
|
d 2 |
|
d 2 |
|
21 |
|
22 |
|
|||||||||||||||
|
|
|
|
|
|
|
11 |
|
12 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||
Abbe number: |
|
d |
|
|
|
nd 1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||
|
|
nF nC |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
n |
|
|
1 |
|
1 |
|
|
|
n |
|
|
1 |
|
1 |
|
||||
Refractive power at D -line: D |
|
|
|
|
|
|
|
D |
|
|
|
|
|
|||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|||||||||||||||
|
|
|
|
1 |
R |
R |
|
|
|
1 |
R |
|
R |
|
|
|||||||||||
3 |
|
|
|
d |
1 |
|
|
|
d1 |
|
|
|
d 2 |
|
d 2 |
|
21 |
|
22 |
|||||||
|
|
|
|
|
|
|
|
|
|
|
|
11 |
|
12 |
|
|
|
|
|
|
|
|
|
|
||
Achromatism condition: |
Dd1 |
|
|
|
Dd 2 |
0 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||||
|
d1 |
|
|
|
|
d 2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
47
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Achromatism condition and Abbe number
If the achromatism condition is fullfilled the F-line and the C-line haf the same refractive power.
Choice of the right kind of glass is mainly done by a nd-d diagram. 
Today method of choice:
Optimization algorithm for aimed refractive power depending on specific cost and low final chromatic aberration.
48
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
7. Optical light guides
49
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Optical light guide
source: http://en.wikipedia.org/wiki/Optical_fiber
source: http://en.wikipedia.org/wiki/Optical_fiber
50
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany