pupil aberrations and effects lens design opti 517...pupil aberrations and effects lens design opti...
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Pupil aberrations and effects
Lens design OPTI 517
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Some references• T. Smith, “The changes in aberrations when the object
and stop are moved,” Trans. Opt. Soc. 23, 139-153, 1921/1922
• C. C. Wynne, “Primary aberrations and conjugate change,” Proc. Phys. Soc. Lond. 65 b, 429-437 (1952)
• J. Sasian, Interpretation of pupil aberrations in imaging systems, SPIE V. 6342-634206 (2006)
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Pupil aberration function
000 200 111 020
22040 131 222
2
220 311 400
,W H W W H H W H W
W W H W H
W H H W H H H W H H
000 200 111 020
2 2
040 131 222
2220 311 400
,W H W W W H W H H
W H H W H H H W H
W H H W H W
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Pupil aberrations• Object-image interchange role with entrance-and exit pupils• The chief ray becomes the marginal ray, and the marginal ray
becomes the chief ray. Lagrange invariant changes sign• Image and pupil aberrations are connected
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The displacement vector at the entrance pupil
040 131
222 220 311
4 21 1,2 2
H
W H H H W H H H HW H
Ж Ж W H W H W
51 ,H W H OЖ
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Beam deformation at pupil
040 131
222 220 311
4 21 1,2 2
H
W H H H W H H H HW H
Ж Ж W H W H W
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Distortion at entrance pupilrepresents a cross-section deformation
040 131
222 220 311
1 ,
4 21
2 2
HW HЖ
W H H H W H H H H
Ж W H W H W
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Pupil aberration interpretation(axially symmetric systems)
222W040W 131W 220W 311W
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Pupil aberrations consequences
• Can now determine aberration change upon object shift
• Spherical aberration of the pupil• Coma of the pupil• Astigmatism and field curvature of the
pupil• Extrinsic sixth-order aberrations• Bow-Sutton conditions
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Effects from pupil aberrations• F/# change• Kidney bean effect. This is a partial obscuration in the
form of a kidney bean caused by pupil spherical aberration
• Loss of telecentricity in relay systems. The chief slope varies as a function of the field of view.
• Vignetting. Spherical aberration of the pupil can lead to light vignetting.
• Pupil walking. Notably in fish eye lenses.• Slyusarev effects. Due to pupil coma, the exit pupil
changes size impacting the relative illumination• Pupil Apodization
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f/# change
y
3111Wu
y
/ #2
f ffd d y
P P
(fourth-order contribution)
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System corrected for all fourth-order aberrations over entire object and image spaces
(Described by D. Shafer)
• Two mirrors• Six reflections• Afocal m=+/- 1• Spacing R/2 or
0.707 R• R1=R2
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Kidney bean effect
Chief rays
Off-axis clipping aperture(eye iris)
From pupil spherical aberration
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Entrance pupil ‘walking’
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Bow-Sutton conditions
See Kingslake’s lens design fundamentalsNew edition with Barry Johnson
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Bow-Sutton Conditions• Since the lens is symmetrical ubar’=ubar• Thus Coma pupil = image distortion• A unit magnification the system is fully symmetrical for the stop and
for the image systems and so, Coma pupil = image distortion=0• When the object moves at other conjugate coma of the pupil
according to stop shift equations is,• New pupil coma=old pupil coma + pupil spherical aberration *
y/ybar.• The old coma is zero, thus,• New pupil coma=pupil spherical aberration * y/ybar.• Therefore if pupil spherical aberration is zero then the new pupil
coma is zero.• And therefore image distortion is zero.• ubar’=ubar, still holds for the second conjugate
2
131 31112
W W Ж u 131 131
*040
yW W Wy
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Loss of telecentricity
Chief rays Spherical aberrationof the exit
pupil
Entrancepupil
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Change in relative illumination
• Vignetting• Image distortion• Cosine to the fourth law• Pupil distortion
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Slyusarev effect
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Effects from pupil coma
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Petzval type lens example
Note nearly telecentricityIssues with MTF calculation
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Beam foot print at exit pupil
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Relative illumination
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Summary
• Pupil aberrations• Effects from pupil aberrations