Post on 25-Jul-2020
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Prof. Jose Sasian
AstigmatismField Curvature
Distortion
Lens Design OPTI 517
Prof. Jose Sasian
Earliest through focus images
1.T. Young, “On the mechanism of the eye,”2.Phil Trans Royal Soc Lond 1801; 91: 23–88 and plates.
Prof. Jose Sasian
Astigmatism through focus
Prof. Jose Sasian
AstigmatismW H W H W W HW W H W H W H W H W H( , ) cos( )
cos( ) cos ( ) cos( )
111 020
2200
2
0404
1313
2222 2 2
2202 2
3113
4004
Prof. Jose Sasian
Anastigmatic
• Aplanatic: free from spherical aberration and coma.
• Stigmatic ~ pointy• Astigmatism: No pointy• Anastigmatic: No-No pointy = pointy• Anastigmatic: free from spherical aberration,
coma, and astigmatism• Aplanatic: coined by John Herschel• Astigmatism: coined by George Airy
Prof. Jose Sasian
2222
12
uW A yn
Cases of zero astigmatism
Prof. Jose Sasian
Field behavior22
220222
222 )(cos),( HWHWHW
2222
12
uW A yn
2 2220
1 14 2
uW A y Ж Pn
Prof. Jose Sasian
Review of aberrations coefficients040
131
222
220
311
020
111
18121214
12
12
I
II
III
P IV
V
L
T
W S
W S
W S
W S
W S
W C
W C
Prof. Jose Sasian
Structural coefficients
Prof. Jose Sasian
Seidel sum for thin lens(stop at lens)
DCYBXYAXySI 2234
41
2 212IIS Жy EX FY
2IIIS Ж
2 1IVS Ж
n
0VS
2 1LC y
0TC
212
nnnA
22
1nnD
1
14
nnnB
11
nnnE
nnC 23
nnF 12
12
12
21
21
rrrr
cccc
X
uuuu
mmY
''
11
))(1( 1 xccncn
Prof. Jose Sasian
Thin lens astigmatism2
IIIS Ж When the stop is a the thin lens astigmatism is fixed.
Shifting the stop in the presence of spherical aberration or coma Allows changing astigmatism
* 22III III II IS S
Prof. Jose Sasian
Controlling astigmatism
Prof. Jose Sasian
1) Stop position: singlet lens
Coma and astigmatism are zero!
* 22III III II IS S SS S S 1
2
0
0
un
A
Prof. Jose Sasian
2) Canceling/balancing negative and positive astigmatism
Prof. Jose Sasian
• In this case one adds a lens which contributes the opposite amount of astigmatism.
• The spherical aberration and coma of the new lens are corrected by the system that has the degrees of freedom for such.
• New lens hopefully contributes little comaand spherical aberration.
3-a) Adding a degree of freedom
Prof. Jose Sasian
3-b) Adding a degree of freedomRitchey-Chretien I
At best surface (Sagittal field surface)
1.7 waves of astigmatism @ f.3.3
Prof. Jose Sasian
3-c) Adding a degree of freedomRitchey-Chretien II
0.0 waves of astigmatism @ f/1.9 after conic tweak
Prof. Jose Sasian
4) Shells near the image plane (or aspheric plate)
Prof. Jose Sasian
Offner unit magnification relay
•Offner relay system:•Three spherical mirrors•Negative unit magnification•No primary aberrations•Ring field concept•Improvement of field with shell
Prof. Jose Sasian
However; beware of ghosts
Prof. Jose Sasian
Field curvature2 2
22014
uW Ж P A yn
P Cn
1
1 1
1 1n nn nn nrk k' '''
1
'k n
Petzval sum:
For a system of thin lenses:
Prof. Jose Sasian
Field curvature interpretation• Assume same glass and consider sag
of Petzval surface at a height y:
• If the Petzval sum is zero then the lens has constant thickness across the aperture or across the field.
• Compare with the image displacement S caused by a plano parallel plate:
• The conclusion is that Petzval field curvature arises because the overall lens thickness variation across the aperture (in the general case the index of refraction enters as a weight).
2 2'2 ' 2k
y n n yn r
Snnt
1
Prof. Jose Sasian
Thickness variation in atelecentric lens
Prof. Jose Sasian
Four classical ways• 1) A thick meniscus lens can contribute optical power but no field
curvature if both surfaces have the same radius. Consider doubleGasuss lens. Note the correction for color.
• 2) Separated thin lenses: Bulges and constrictionsConsider the Cooke triplet and lenses for microlithography.
• 3) A field flattener: Fully contributes to Petzval but not to spherical, coma, or astigmatism. Also there is little contribution to optical power.Consider Petzval lens with a field flattener.
• 4) New achromat: use to advantage new glass types.
1
'k n
Prof. Jose Sasian
Four classical ways
Use of a thick meniscus lens Use of a field flattener lens
Prof. Jose Sasian
Four classical ways
Creating beam bulges and constrictions
Prof. Jose Sasian
Four classical ways: Use of glass
BK7-F2P=-139 mm
BK7P=-152 mm
V-number for flint increasesV-number for crown decreases
N for crown increasesN for flint decreases
babbaa Fff
SSKN5-LF5P=-219 mm
F=100 mm
1
'k n
Prof. Jose Sasian
DistortionW H W H W W HW W H W H W H W H W H( , ) cos( )
cos( ) cos ( ) cos( )
111 020
2200
2
0404
1313
2222 2 2
2202 2
3113
4004
W311 H3cos()W511 H5cos()
DistortionH hh
100
With respect to chief ray, geometrical or physical centroid
Prof. Jose Sasian
Distortion
Top row, (barrel) distortion:0%, 2.5%, 5% and 10%. Bottom row, (pincushion) distortion 0%, 2.5%, 5% and 10%.
Prof. Jose Sasian
1) By Symmetry about the stop or phantom stop
Distortion is an odd aberration: It can be cancelled by symmetryAbout the stop
Prof. Jose Sasian
2) Aspheric plate or bending a field flattener
Prof. Jose Sasian
Exercise: Galilean telescope
A plano-convex lens objective with a focal length of about 750-1000 mm.A plano-concave lens for the eyepiece (ocular) with a focal length of about 50 mm. The objective lens was stopped downto an aperture of 12.5 to 25 mm. The field of view is about 15 arc-minutes. The instrument's magnifying power is 15-20.