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Home , Chromatic aberration, Doublet (lens), Lens

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 location with λ (axial or longitudinal ) • Change of with λ (transverse or lateral chromatic aberration

Prof. Jose Sasian Chromatic Aberrations

• Variation of aberrations as a function of

• Chromatic change of : 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 • • Optical 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 correction as an • Third-order behavior odd aberration • Spherochromatism • Color correction in the • Secondary presence of axial color • Tertiary spectrum • Field lens to control lateral color: field 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   i1 i1  i

j 1 j 1  2  WAnny / Wy020   020  j jj 2   2 i1 i1   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 Ayy 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 i1   i V is the glass V-number Φ is the y is the marginal ray height j   y-bar is the chief ray height Wyy111    i1   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 : • Soda-lime, silica, lead (older glasses) • Crowns, flints, flints, dense flints • Barium glasses (~1938) • or rare-earth glasses •Titanium • 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 • • 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 nd -nC Partial dispersion

v=(nd-1)/(nF-nC) v-value, reciprocal dispersive power, 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 variation

Rate of slope change in the blue makes it Prof. Jose Sasian more difficult to correct for color Index interpolation Sellmeier

22 2 bd na 22... ce Schott

2 22468 nAAAAAA112  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 

 nd 1 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  1vv 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 α (Treated as two wedges)

Z

Z’

YY2 Zsag;' Z  2rr

'' 11 Y  ZZ12 Y    1 rr12 nd 1   120 vv12 YY 120 vv12

Prof. Jose Sasian Achromatic doublet YY  120 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 )

Zonal Critical airspace

Prof. Jose Sasian Achromatic doublet

•Must have opposite power (Glass) •Strong positive and weaker 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 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 . 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