astigmatism field curvature distortion · gasuss lens. note the correction for color. • 2)...
TRANSCRIPT
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.