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 y1 y 3 5 7 y Y y c3 y c5 y c7 y ... y y y1 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 42WHHHWHH H H 1 040 131 Ж 22WH 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 y1 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 B512123cosFF 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 B52sinFHMMH 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.