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Coma Aberration Coma aberration Lens Design OPTI 517 Prof. Jose Sasian Coma 0.25 wave 1.0 wave 2.0 waves 4.0 waves Spot diagram 2 2 W H, , W200 H W020 W111H cos 4 3 2 2 2 W040 W131H cos W222 H cos 2 2 3 4 W220 H W311H cos W400 H ... Prof. Jose Sasian Coma though focus Prof. Jose Sasian Cases of zero coma 1 u WAAy131 2 n •At y=0, surface is at an image •A=0, On axis beam concentric with center of curvature •A-bar=0, Off-axis beam concentric, chief ray goes through the center of curvature •Aplanatic points Prof. Jose Sasian Cases of zero coma Prof. Jose Sasian Aplanatic-concentric Prof. Jose Sasian Coma as a variation of magnification with aperture I 1 u WH131 , AAyH 2 n Prof. Jose Sasian Coma as a variation of magnification with aperture II S S’ m=s’/s Prof. Jose Sasian Sine condition Coma aberration can be considered as a variation of magnification with respect to the aperture. If the paraxial magnification is equal to the real ray marginal magnification, then an optical system would be free of coma. Spherical aberration can be considered as a variation of the focal length with the aperture. u sinU U U’ u' sinU ' Prof. Jose Sasian Sine condition On-axis L Sine condition YY’ L' O’ h YY’ O’ UU’L' L O h’ PP’ PP’ Optical path length between y and y’ is Optical path length between O and O’ is Laxis and does not depend on Y or Y’ Loff-axis = Laxis + L’ - L L = L + h’ n’ sin(U’) - h n sin(U) Lhsin( U ) L ''sin(') hU off-axis axis u sinU hn' 'sin( U ') hn sin( U ) u' sinU ' That is: OPD has no linear phase errors as a function Prof.of field Jose of Sasian view! Imaging a grating m sin(U ) d d sin(U ) m d'sin(U ') Prof. Jose Sasian Contribution from an aspheric surface 1 y 4 W131 8Ay 4 n 2 y y-bar chief ray y marginal ray Prof. Jose Sasian Aberrations and symmetry 2 2 W H, , W200 H W020 W111H cos 4 3 2 2 2 W040 W131H cos W222 H cos 2 2 3 4 W220 H W311H cos W400 H ... •Coma is an odd aberration with respect to the stop •Natural stop position to cancel coma by symmetry Prof. Jose Sasian Structural coefficients: Thin lens (stop at lens) n 2 A 1 nn 1 2 S y 4 3 AX 2 BXY CY 2 D I 4 1 22 4n 1 SII Ж y EX FY B 2 nn 1 2 SIII Ж 3n 2 C 1 n 2 c1 c2 r2 r1 SIV Ж X n c1 c2 r2 r1 n 2 D 2 SV 0 1 m u'u n 1 Y 1 1 m u'u n 1 C y 2 E L nn 1 nc (n 1)(c1 cx ) CT 0 2n 1 F n Prof. Jose Sasian Coma vs Bending Coma II EX FY Shape factor X Prof. Jose Sasian Principal surface In an aplanat working at m=0 the equivalent refracting surface is a hemisphere Prof. Jose Sasian Cassegrain’s principal surface Since the equivalent refracting surface in a Cassegrain telescope is a paraboloid then the coma of that Cassegrain is the same of a paraboloid mirror with the same focal length. Prof. Jose Sasian Aplanat doublets Prof. Jose Sasian Kingslake’s cemented aplanat Chromatic correction Spherical aberration correction Coma correction Still cemented Prof. Jose Sasian Control of coma in the presence of an aspheric mirror near a pupil In the presence of a strong aspheric surface near the stop or pupil, coma aberration can be corrected by moving the surface 1 y 4 W131 8Ay 4 n 2 y Prof. Jose Sasian Coma correction by natural stop position Original Natural y stop position stop position S S II y I Optical system Object plane Image plane In the presence of spherical aberration there is a stop position for which coma is zero. At that stop position spherical aberration might be corrected. Then the system becomes aplanatic and the stop Prof. Jose Sasian can be shifted back to its original position. The aplanatic member(s) in a family of solutions Doublet Ritchey-Chretien Prof. Jose Sasian Camera Schmidt Aspheric plate at mirror center of curvature A-bar=0 Stop aperture at aspheric plate Note symmetry about mirror CC No spherical aberration No coma No astigmatism. Anastigmatic over a wide field of view! Prof. Jose Sasian Satisfies Conrady’s D-d sum Notes • Need to make aplanatic zero-field systems (that are fast). The alignment becomes easier. • Lenses for lasers diodes/optical fibers • Microscope objectives Prof. Jose Sasian Summary • Coma aberration • Coma as an odd aberration • Sine condition • Natural stop position • Aplanatic doublets • Zero-field systems Prof. Jose Sasian.
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