Pupil aberrations and effects

Lens design OPTI 517

Prof. Jose Sasian 1 OPTI 518 Prof. Jose Sasian 2 OPTI 518 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 Sasian 3 OPTI 518 Pupil aberration function

 WH,  W000 W 200 HH  W 111 H  W 020  

 2    2 WWHWH040    131 222       2 W220 HH W 311 HH H W 400 HH   WH,  W000 W 200 W 111 H W 020  HH 22    WHHWHHH040 131 WH 222 

   2 WHH220  W 311 H W 400  

Prof. Jose Sasian 4 OPTI 518 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 Sasian 5 OPTI 518 Prof. Jose Sasian 6 OPTI 518 The displacement vector at the entrance pupil

 1  5 HWHO,   Ж 



         11 42WHHHWHH040  131   H H HWH,   ЖЖ  22WH222  W 220 HW 311    

Prof. Jose Sasian 7 OPTI 518 

Beam deformation at pupil          11 42WHHHWHH040  131   H H  HWH,   ЖЖ  22WH222  W 220 HW 311    

Prof. Jose Sasian 8 OPTI 518 Distortion at entrance pupil represents a cross-section deformation

  

 1   WH, Ж H     42WHHHWHH  H H 1  040 131        Ж 22WH W HW  222 220 311 

   

Prof. Jose Sasian 9 OPTI 518 Pupil aberration interpretation (axially symmetric systems)

W 040 W 131 W 222 W 220 W 311

Prof. Jose Sasian 10 OPTI 518 Prof. Jose Sasian 11 OPTI 518 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 Sasian 12 OPTI 518 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 Sasian 13 OPTI 518 f/# change

P P

1 y  W u 311

f f y f /# dd 2 y

(fourth-order contribution)

Prof. Jose Sasian 14 OPTI 518 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 Sasian 15 OPTI 518 Kidney bean effect From pupil spherical aberration

Chief rays

Off-axis clipping aperture

Prof. Jose Sasian (eye iris) 16 OPTI 518 Entrance pupil ‘walking’

Prof. Jose Sasian 17 OPTI 518 Bow-Sutton conditions

See Kingslake’s lens design fundamentals New edition with Barry Johnson Prof. Jose Sasian 18 OPTI 518 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 y 1 2 WW*  W WW131 311 Ж u  131 131 040 2 y Prof. Jose Sasian 19 OPTI 518 Loss of telecentricity

Entrance Chief rays Spherical pupil aberration of the exit pupil

Prof. Jose Sasian 20 OPTI 518 Change in relative illumination

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

Prof. Jose Sasian 21 OPTI 518 Slyusarev effect

Prof. Jose Sasian 22 OPTI 518 Effects from pupil coma

Prof. Jose Sasian 23 OPTI 518 Petzval type lens example

Note nearly telecentricity Issues with MTF calculation

Prof. Jose Sasian 24 OPTI 518 Beam foot print at exit pupil

Prof. Jose Sasian 25 OPTI 518 Relative illumination

Prof. Jose Sasian 26 OPTI 518 Summary

• Pupil aberrations • Effects from pupil aberrations

Prof. Jose Sasian 27 OPTI 518