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Prof. Jose SasianOPTI 518
1
Pupil aberrations and effects
Lens design OPTI 517
Prof. Jose SasianOPTI 518
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Prof. Jose SasianOPTI 518
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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)
Prof. Jose SasianOPTI 518
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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
Prof. Jose SasianOPTI 518
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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
Prof. Jose SasianOPTI 518
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Prof. Jose SasianOPTI 518
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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
Prof. Jose SasianOPTI 518
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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
Prof. Jose SasianOPTI 518
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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
Prof. Jose SasianOPTI 518
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Pupil aberration interpretation(axially symmetric systems)
222W040W 131W 220W 311W
Prof. Jose SasianOPTI 518
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Prof. Jose SasianOPTI 518
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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
Prof. Jose SasianOPTI 518
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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
Prof. Jose SasianOPTI 518
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f/# change
y
3111Wu
y
/ #2
f ffd d y
P P
(fourth-order contribution)
Prof. Jose SasianOPTI 518
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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
Prof. Jose SasianOPTI 518
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Kidney bean effect
Chief rays
Off-axis clipping aperture(eye iris)
From pupil spherical aberration
Prof. Jose SasianOPTI 518
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Entrance pupil ‘walking’
Prof. Jose SasianOPTI 518
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Bow-Sutton conditions
See Kingslake’s lens design fundamentalsNew edition with Barry Johnson
Prof. Jose SasianOPTI 518
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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
Prof. Jose SasianOPTI 518
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Loss of telecentricity
Chief rays Spherical aberrationof the exit
pupil
Entrancepupil
Prof. Jose SasianOPTI 518
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Change in relative illumination
• Vignetting• Image distortion• Cosine to the fourth law• Pupil distortion
Prof. Jose SasianOPTI 518
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Slyusarev effect
Prof. Jose SasianOPTI 518
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Effects from pupil coma
Prof. Jose SasianOPTI 518
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Petzval type lens example
Note nearly telecentricityIssues with MTF calculation
Prof. Jose SasianOPTI 518
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Beam foot print at exit pupil
Prof. Jose SasianOPTI 518
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Relative illumination
Prof. Jose SasianOPTI 518
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Summary
• Pupil aberrations• Effects from pupil aberrations