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Chromatic Aberrations Chromatic Aberrations Lens Design OPTI 517 Prof. Jose Sasian Second-order chromatic aberrations 22 WH,cos W000 W 200 H WH 111 W 020 • Change of image location with λ (axial or longitudinal chromatic aberration) • Change of magnification with λ (transverse or lateral chromatic aberration Prof. Jose Sasian Chromatic Aberrations • Variation of lens aberrations as a function of wavelength • Chromatic change of focus: W020 • Chromatic change of magnification W111 • Fourth-order:W040 and other • Spherochromatism Prof. Jose Sasian Chromatic Aberrations 2 WH cos W020 111 Prof. Jose Sasian Topics • Chromatic coefficients •Apochromats • Optical glass and selection • Index interpolation • Super-apochromats • Achromats: crown and flint: • Buried surface different solutions • Monochromatic design: one • Achromats: dialyte; single task at a time glass • Mangin lens • Lateral color correction as an • Third-order behavior odd aberration • Spherochromatism • Color correction in the • Secondary spectrum presence of axial color • Tertiary spectrum • Field lens to control lateral color: field lenses in general • Conrady’s D-d sum Prof. Jose Sasian Chromatic aberration coefficients For a system of j surfaces For a system of thin lenses j j Wyy WAnny111 j jj/ 111 i1 i1 i j 1 j 1 2 WAnny / Wy020 020 j jj 2 2 i1 i1 i Prof. Jose Sasian With stop shift W020 0 y WW 2 111y 020 Prof. Jose Sasian Review of paraxial quantities y r u’ s’ n 1 nn/ Prof. Jose Sasian n Chromatic coefficients y2 11 11 Wnn020 ' 2'sr sr y 2 1 1 1 1 W020 n'n' n n 2 s' r s r y 2 1 1 1 1 y n W020 n' n A 2 s' r s r 2 n Prof. Jose Sasian Stop shifting Prof. Jose Sasian Prof. Jose Sasian Stop shifting New chief ray New stop Old stop plane at CC New chief ray height yE shift yE yE H at old pupil yE yE A Marginal ray height shift H H at old pupil yE yE A Prof. Jose Sasian Chromatic coefficients yn WA020 2 n yE A shift H H yE A 2 AA shift shift 2 HHH AA n WA111 y n Prof. Jose Sasian Can show equality using the Lagrange invariant Prof. Jose Sasian y yA The ratio E yyAE Prof. Jose Sasian The ratio AA/ Marginal ray Old chief ray New chief ray Parameters are stop at the surface When the stop is shifted at the cc Ж Ay11 Ay Ж Ay Ay 22 A1 0 Ayy yAA yy y A 21 21 21 cc yyA yy AA cc 21 21 yA Prof. Jose Sasian yy y The ratio 21 cc yycc Marginal ray yy yy 21qq 21 pp qp stop yy qp p qp Old and new q chief rays Does not depend on plane where it is calculated given similar triangles Prof. Jose Sasian For a system of thin lenses j 1 2 Wy020 2 i1 i V is the glass V-number Φ is the optical power y is the marginal ray height j y-bar is the chief ray height Wyy111 i1 i Prof. Jose Sasian Glass • Schott, Hoya, Ohara glass catalogues (A wealth of information; must peruse glass catalogue) • Crowns and flints are divided at V=50 • Normal glasses: • Soda-lime, silica, lead (older glasses) • Crowns, light flints, flints, dense flints • Barium glasses (~1938) • Lanthanum or rare-earth glasses •Titanium • Fluorites and phosphate • Environmental and health issues in the production of glass. Lead replaced with Titanium and Zirconium. Prof. Jose Sasian Other materials • For the UV • For the IR • Plastics • Advances come usually with new materials that extend or have new properties. • The design is limited by the material Prof. Jose Sasian Prof. Jose Sasian Glass properties n nF-nC nd-1 1 λ 486.1 587.6 656.3 589.8 F (H) d (He) C (H) D (Na) nd -1 Refractivity nF-nC Mean dispersion nd -nC Partial dispersion v=(nd-1)/(nF-nC) v-value, reciprocal dispersive power, Abbe number P=(nd-nC)/(nF-nC) Partial dispersion ratio Prof. Jose Sasian Glass properties • Homogeneity • Transmission •Stria • Bubbles • Ease of fabrication; soft glasses • Coefficient of thermal expansion • Opto-thermal coefficient • Birefringence Prof. Jose Sasian Index of refraction variation Rate of slope change in the blue makes it Prof. Jose Sasian more difficult to correct for color Index interpolation Sellmeier bd22 na2 ... ce22 Schott 2 22468 nAAAAAA112 4 6 8 ... Hartmann Conrady Kettler-Drude Must verify index of refraction Prof. Jose Sasian The optical wedge α 1 θ δ ' 11n ' 21 ' n 22 n 1 ' 12 The deviation is independent of the angle of incidence for small θ (First order approximation) Prof. Jose Sasian Wedge nd 1 nnnnFC 11 FC nndC11 nn dC n 1 d v nnFC δ Deviation nn dC P ∆ Dispersion nn FC ε Secondary dispersion v P v Prof. Jose Sasian Achromatic wedge pair 12 0 12vv 12 Deviation without dispersion v2 21 v1 v212 12 1 1vv 12 vv 12 vvv112 1 v 11 vv12 nd 1 1 1 v 22 vv12 nd 2 1 1 PP12 vv12 Prof. Jose Sasian Achromatic wedge •There is deviation •There is no dispersion •Red and blue rays are parallel •Independent of theta to first order Schematic drawing Prof. Jose Sasian Achromatic doublet α (Treated as two wedges) Z Z’ YY2 Zsag;' Z 2rr '' 11 Y ZZ12 Y 1 rr12 nd 1 120 vv12 YY 120 vv12 Prof. Jose Sasian Achromatic doublet YY 120 vv 12 Independent of conjugate Requires finite difference 12 v vv 11 12 vv 12 Can lead to strong v optical powers 22 vv12 Prof. Jose Sasian Relative sag (for 100 mm focal length) Zonal spherical aberration Critical airspace Prof. Jose Sasian Achromatic doublet •Must have opposite power (Glass) •Strong positive and weaker negative lens •Cemented doublet •Crown in front •Flint in front •Corrected for spherical aberration •Degrees of freedom •Large achromats and cementing •Conrady D-d sum •Zonal spherical aberration Prof. Jose Sasian Conrady’s D-d sum • In the presence of sphero-chromatism the best state of correction is achieved when: Dd n0 D d Is the difference of optical path between the marginal F and C rays. Prof. Jose Sasian Conrady’s D-d sum D d Optical__ path difference Dnff dn Dn cc dn D d n Minimizes the rms OPD difference by joining the opd curves at the edge of The aperture. Valid for fourth order sphero-chromatism. Prof. Jose Sasian Cemented doublet solutions • Correction for chromatic change of focus • Correction for spherical aberration • Degrees of freedom: relative powers for a set of glasses; shapes • Crown in front: two solutions • Flint in front: two solutions • Note multiple solutions Prof. Jose Sasian Crown in front and flint in front doublet solutions (BK7 and F2) Prof. Jose Sasian Contact options for doublets Full contact (cemented) Air spaced Edge contacted Center contacted Prof. Jose Sasian Limitations Secondary spectrum, spherochromatism and zonal spherical aberration set limits F=100 mm, f/4, 0.5 wave scale Prof. Jose Sasian Achromatic doublet 20 inch diameter F/12 BK7 F4 Prof. Jose Sasian In this lecture • Chromatic coefficients • Basic glass properties • Achromatic wedge-pair and lens doublets • Examples • D-d method • Achromatic doublet • Diversity of solutions Prof. Jose Sasian.
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