Chromatic Aberrations

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Erica Rodgers
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1 Chromatic Aberrations Lens Design OPTI 517

2 Second-order chromatic aberrations W H W W H W H W, cos Change of image location with λ (axial or longitudinal chromatic aberration) Change of magnification with λ (transverse or lateral chromatic aberration

3 Chromatic Aberrations Variation of lens aberrations as a function of wavelength Chromatic change of focus: W 020 Chromatic change of magnification W 111 Fourth-order:W 040 and other Spherochromatism

4 Chromatic Aberrations W 111H cos W 2 020

5 Topics Chromatic coefficients Optical glass and selection Index interpolation Achromats: crown and flint: different solutions Achromats: dialyte; single glass Mangin lens Third-order behavior Spherochromatism Secondary spectrum Tertiary spectrum Apochromats Super-apochromats Buried surface Monochromatic design: one task at a time Lateral color correction as an odd aberration Color correction in the presence of axial color Field lens to control lateral color: field lenses in general Conrady s D-d sum

6 Chromatic aberration coefficients For a system of j surfaces For a system of thin lenses j W 111 A j j n / n y j i1 j 1 W 020 j j j 2 A n n y i1 / j W 111 yy i1 j W y i1 i 2 i

7 With stop shift W W 2 y y W

8 Review of paraxial quantities y r u s n/ n n 1 n

9 Chromatic coefficients 2 y W020 n n 2 s' r s r W 020 ' y s' 1 r n' n' n n 1 1 s r W 020 y n' n s' r s r y n A 2 n

10 Stop shifting

12 Stop shifting New chief ray New stop New chief ray height at old pupil Marginal ray height at old pupil Old stop plane at CC y E y E y E shift shift y y y E E E H y E H A A H

13 Chromatic coefficients y n W 2 n A 020 shift y y E E H A A H 2 A A shift shift 2 H H H A A n W A y 111 n

14 Can show equality using the Lagrange invariant

15 The ratio ye y A y y A E

16 The ratio A/ A Marginal ray Old chief ray New chief ray Parameters are at the surface stop Ж AyAy 1 1 Ж AyAy 2 2 A y y y A A y y A A y A When the stop is shifted at the cc A 1 0 y2 y1 ycc A y y A cc

17 The ratio y y y y y 2 1 cc cc Marginal ray Old and new chief rays q stop p y y y y q p 2q 1q 2p 1p y q q y p Does not depend on plane where it is calculated given similar triangles p

18 For a system of thin lenses 1 j 2 W y i1 j W 111 yy i1 i i V is the glass V-number Φ is the optical power y is the marginal ray height y-bar is the chief ray height

19 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.

20 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

22 Glass properties n 1 n F -n C n d -1 n d -1 Refractivity n F -n C Mean dispersion n d -n C Partial dispersion F (H) d (He) C (H) D (Na) λ v=(n d -1)/(n F -n C ) v-value, reciprocal dispersive power, Abbe number P=(n d -n C )/(n F -n C ) Partial dispersion ratio

23 Glass properties Homogeneity Transmission Stria Bubbles Ease of fabrication; soft glasses Coefficient of thermal expansion Opto-thermal coefficient Birefringence

24 Index of refraction variation Rate of slope change in the blue makes it more difficult to correct for color

25 Index interpolation Sellmeier b d n a c e Schott n 1 A A A A A A Hartmann Conrady Kettler-Drude Must verify index of refraction

26 The optical wedge ' n ' 2 1 n ' 2 2 ' 1 2 α θ n δ 1 The deviation is independent of the angle of incidence for small θ (First order approximation)

27 v P v Wedge nd 1 nf 1 nc 1 nf nc nd 1 nc 1 nd nc nd 1 v nf nc δ Deviation nd nc P Dispersion nf nc ε Secondary dispersion

28 Achromatic wedge pair v1 v2 v v1 v 1 2 v v v v v1 v1 v2 1 1 v 1 v v n d1 2 1 v 2 v v n 1 v 1 2 d 2 1 v P P Deviation without dispersion

29 Achromatic wedge There is deviation There is no dispersion Red and blue rays are parallel Independent of theta to first order Schematic drawing

30 α Achromatic doublet (Treated as two wedges) Z Z 2 Y Y Z sag ; Z' 2r r 1 1 Y Z Z Y r r n v v 1 2 Y1 Y2 v v ' ' d

31 Achromatic doublet Y v Y v v v v v v v Independent of conjugate Requires finite difference v v 1 2 Can lead to strong optical powers

32 Relative sag (for 100 mm focal length) Zonal spherical aberration Critical airspace

33 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

34 Conrady s D-d sum In the presence of sphero-chromatism the best state of correction is achieved when: D dn0 D d Is the difference of optical path between the marginal F and C rays.

35 Conrady s D-d sum D d Optical _ path _ difference Dn f dn f Dnc dncd d n Minimizes the rms OPD difference by joining the opd curves at the edge of The aperture. Valid for fourth order sphero-chromatism.

36 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

37 Crown in front and flint in front doublet solutions (BK7 and F2)

38 Contact options for doublets Full contact (cemented) Air spaced Edge contacted Center contacted

39 Limitations Secondary spectrum, spherochromatism and zonal spherical aberration set limits F=100 mm, f/4, 0.5 wave scale

40 Achromatic doublet 20 inch diameter F/12 BK7 F4

41 In this lecture Chromatic coefficients Basic glass properties Achromatic wedge-pair and lens doublets Examples D-d method Achromatic doublet Diversity of solutions

Optical Materials. Optimizing refractive index and dispersion

$Optical Materials. Optimizing refractive index and dispersion$ Optical Materials General comments Specifying optical materials Dispersion Thermal coefficients Athermalization Thermal expansion Thermal variation of refractive index Other glass data Optimizing refractive