Higher-order aberrations

Lens Design OPTI 517

Prof. Jose Sasian Higher order Aberrations

• Aberration function • Six-order terms (fifth-order transverse) • Wavefront shapes and field dependence • Coefficients • Pupil matching • References.

Prof. Jose Sasian References

• 1) J. Sasian, “Theory of sixth-order wave aberrations,” Applied Optics, June 2010. • 2) O. N. Stavroudis, “Modular Optical Design” • 3) Buchdahl, “Optical Aberration Coefficients” • 4) M. Herzberger, “Modern Geometrical Optics”

Prof. Jose Sasian “Back of the envelope”

Prof. Jose Sasian Coordinate system and reference sphere

 y'   E  ' yI  H

Exit pupil plane

Image plane

Prof. Jose Sasian Aberration function

Prof. Jose Sasian Prof. Jose Sasian Aberration orders

Roland Shack’s aberration diagram

Prof. Jose Sasian Terminology

•W240 Oblique spherical aberration

•W331 Cubic coma

•W422 Quartic astigmatism

•W420 Six order field curvature

•W511 Six order distortion

•W600 Six order piston

•W060 Six order spherical aberration

•W151

•W242

•W333

Prof. Jose Sasian Some earlier terminology

• Oblique spherical aberration • Elliptical coma • Line coma • Secondary spherical aberration • Secondary coma • Lateral coma • Lateral image curvature/astigmatism •Trefoil

Prof. Jose Sasian Wavefront deformation shapes

Prof. Jose Sasian Spherical aberration: W060

Prof. Jose Sasian W151 & W333

Prof. Jose Sasian W242

Prof. Jose Sasian Higher-order aberration coefficients

• Harder to derive/calculate than fourth- order • Intrinsic coefficients • Extrinsic coefficients • Depend highly on coordinate system

Prof. Jose Sasian Intrinsic spherical aberration

1 2  u  W040   A y  8  n 

2  1 y 1  u' u  y  8 y W060I  W040  2  A    2 u  W040 W040 2 r 2  n' n  r   y

2  1 y 1  u' u  y  8 y W060I  W040  2  A    2 u'  W040 W040 2 r 2  n' n  r   y

3 5 7  y  Y  y  c3 y  c5 y  c7 y ...  y  y  y1   y 

3 5 7  y  Y  y  c3 y  c5 y  c7 y ...  y  y  y1   y 

Controlling delta y gives control over higher-order Prof. JoseSpherical Sasian aberration Pupil aberrations

 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 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 Prof. Jose Sasian Prof. Jose Sasian Concept of pupil matching

• Not traditionally discussed. • Pupil matching concept is important. • Optical system connect: exit pupil of one connects with the entrance pupil of the next. • Any pupil mismatch produces an effect. • In general we have pupil mismatch

Prof. Jose Sasian Example: f/#

P P

1 y  W u 311

f f y f /# dd 2 y

(fourth-order contribution)

Prof. Jose Sasian Exit pupil becomes entrance pupil for next surface

3 5 7 Y  y  c3 y  c5 y  c7 y ...  y   y  y  y1   y 

Exit pupil for surface J Exit pupil for surface J+1

Prof. Jose Sasian Entrance pupil for surface J+1 Extrinsic aberrations    46 WHAAA,,,  WH  WH     46 WHBBB,,,  WH  WH 

 4444    WHABABAA ,,,,   WH   WH   WH   44  WHABA,,    WH 

1 WH,,,   WH  WH EAHBЖ 

Prof. Jose Sasian Prof. Jose Sasian Buchdahl-Rimmer fifth-order aberrations

32 23 y BFcos  2 cos 2  HCHEH 3 cos   54   232 B512123cosFF cos 2 H M M M cos cos H      223 4 5 NN12cos H  5 C 55  cos H  EH 5

32 2 x BFHCHsin    sin  2    sin    54 232 B52sinFHMMH sin 2    23 cos sin       23   4 NHCH355sin 2 sin    12 fifth-order terms

Prof. Jose Sasian Aberration correction concepts

• Destroy an aberration (early days) • Aberration correction (compensation): Add the opposite amount to have a net zero residual • Aberration balancing: Add a different aberration and minimize or trade-off performance; fourth vs. higher order. • Minimize an aberration. • Do not generate an aberration • Main mechanism for aberration correction is compensation and balancing

Prof. Jose Sasian Aberration balancing: 4th order vs. higher order

Prof. Jose Sasian Summary

• Higher-order aberrations • Pupil aberrations • Aberration correction and balancing

Prof. Jose Sasian