Pupil aberrations and effects Lens design OPTI 517...Pupil aberrations and effects Lens design OPTI 517. Prof. Jose Sasian OPTI 518 2. Prof. Jose Sasian OPTI 518 3 Some references

Prof. Jose SasianOPTI 518

1

Pupil aberrations and effects

Lens design OPTI 517

Prof. Jose SasianOPTI 518

2

Prof. Jose SasianOPTI 518

3

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

4

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

5

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

6

Prof. Jose SasianOPTI 518

7

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

8

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

9

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

10

Pupil aberration interpretation(axially symmetric systems)

222W040W 131W 220W 311W

Prof. Jose SasianOPTI 518

11

Prof. Jose SasianOPTI 518

12

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

13

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

14

f/# change

y

3111Wu

y

/ #2

f ffd d y

P P

(fourth-order contribution)

Prof. Jose SasianOPTI 518

15

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

16

Kidney bean effect

Chief rays

Off-axis clipping aperture(eye iris)

From pupil spherical aberration

Prof. Jose SasianOPTI 518

17

Entrance pupil ‘walking’

Prof. Jose SasianOPTI 518

18

Bow-Sutton conditions

See Kingslake’s lens design fundamentalsNew edition with Barry Johnson

Prof. Jose SasianOPTI 518

19

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

20

Loss of telecentricity

Chief rays Spherical aberrationof the exit

pupil

Entrancepupil

Prof. Jose SasianOPTI 518

21

Change in relative illumination

• Vignetting• Image distortion• Cosine to the fourth law• Pupil distortion

Prof. Jose SasianOPTI 518

22

Slyusarev effect

Prof. Jose SasianOPTI 518

23

Effects from pupil coma

Prof. Jose SasianOPTI 518

24

Petzval type lens example

Note nearly telecentricityIssues with MTF calculation

Prof. Jose SasianOPTI 518

25

Beam foot print at exit pupil

Prof. Jose SasianOPTI 518

26

Relative illumination

Prof. Jose SasianOPTI 518

27

Summary

• Pupil aberrations• Effects from pupil aberrations