Classification of systems with field and aperture size
photographic Biogon
40° lithography Braat 1987
Scheme is related to size, correction goals and etendue of the systems
36° 32° Triplet Distagon
28°
Aperture dominated: Disk lenses, microscopy, Collimator Field dominated: Projection lenses, camera lenses, Photographic lenses
24° Sonnar
20° projection
16° 12°
double Gauss
split triplet
projection
projection Gauss
8°
lithography 2003
diode collimator
achromat
0°
0
0.2
0.4
micro 100x0.9
micro 40x0.6
micro 10x0.4
4°
Spectral widthz as a correction requirement is missed in this chart
constant etendue
Petzval
disc
0.6
0.8
microscopy collimator focussing
NA
Typical Example Systems 1
1. Photo objective lens
2. Microscope objective lens
3. Binocular
4. Infrared afocal system
Typical Example Systems 2
5. Relay optics
6. Scan-objective lens
7. Collimator objective lens possible surfaces under test
Typical Example Systems 3
8. Projector lens
9. Telescope
M1
M2
10. Lithography projection lens
M3
Typical Example Systems 4
11. Illumination collector system
12. Illumination condenser system
image free formed surface
13. Head mounted display total internal reflection eye pupil
free formed surface field angle 14°
Typical Example Systems 5
eye
14. Stereo microscope
eyepiece tube system
zoom system
common objective lens
object plane stereo angle
common axis
15. Zoom system f = 61
f = 113
f = 166
Achromate
Achromate: - Axial colour correction by cementing two different glasses - Bending: correction of spherical aberration at the full aperture - Aplanatic coma correction possible be clever choice of materials
Crown in front
Four possible solutions: - Crown in front, two different bendings - Flint in front, two different bendings Typical: - Correction for object in infinity - spherical correction at center wavelength with zone - diffraction limited for NA < 0.1 - only very small field corrected
Flint in front
solution 1
solution 2
Achromate: Realization Versions
Advantage of cementing: solid state setup is stable at sensitive middle surface with large curvature Disadvantage: loss of one degree of freedom Different possible realization forms in practice
Achromate : Basic Formulas
Idea: 1. Two thin lenses close together with different materials 2. Total power
F = F1 + F2
3. Achromatic correction condition Individual power values
F1
ν1
+
F1 =
F2
ν2
=0
1
ν 1− 2 ν1
⋅F
F2 =
1
ν 1− 1 ν2
⋅F
Properties: 1. One positive and one negative lens necessary 2. Two different sequences of plus (crown) / minus (flint) 3. Large ν-difference relaxes the bendings 4. Achromatic correction indipendent from bending 5. Bending corrects spherical aberration at the margin 6. Aplanatic coma correction for special glass choices 7. Further optimization of materials reduces the spherical zonal aberration
Achromate: Correction
Cemented achromate: 6 degrees of freedom: 3 radii, 2 indices, ratio ν1/ν2 Correction of spherical aberration: diverging cemented surface with positive spherical contribution for nneg > npos ∆ s' rim
Choice of glass: possible goals 1. aplanatic coma correction 2. minimization of spherochromatism 3. minimization of secondary spectrum
case with 2 solutions
R
Bending has no impact on chromatical correction: is used to correct spherical aberration at the edge Three solution regions for bending 1. no spherical correction 2. two equivalent solutions 3. one aplanatic solution, very stable