ALD13 Advanced Lens Design 9
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Advanced Lens Design Lecture 9: Chromatical correction 2013-12-10 Herbert Gross Winter term 2013 www.iap.uni-jena.de 2 Contents 1. Dispersion 2. Glass diagram 3. Relative partial dispersion 4. Achromate 5. Apochromate 6. Schupman principle 7. Dialyte system 8. Burried surfaces 9. Transverse color aberratios 3 Overview on Chromatical Aberrations 1. Third order chromatical aberrations: - axial chromatical aberration error of the marginal ray by dispersion - transverse chromatical aberration error of the chief ray by dispersion 2. Higher order chromatical aberrations: - secondary spectrum residual axial error, if only selected wavelength are coinciding - spherochromatism chromatical variation of the spherical aberration, observed in an achromate - chromatical variation of all monochromatic aberrations e.g. astigmatism, coma, pupil location,... 4 Dispersion and Abbe number . Description of dispersion: Abbe number n 1 n n n F ' C' refractive index n . Visual range of wavelengths: 1.8 typically d,F,C or e,F’,C’ used 1.75 ne 1 ne nF ' nC' 1.7 SF1 flint . Typical range of glasses 1.65 ne = 20 ...100 1.6 . Two fundamental types of glass: Crown glasses: 1.55 n small, n large, dispersion low BK7 Flint glasses: 1.5 n large, n small, dispersion high crown 1.45 0.5 0.75 1.0 1.25 1.5 1.75 2.0 5 Dispersion Material with different dispersion values: - Different slope and curvature of the dispersion curve - Stronger change of index over wavelength for large dispersion - Inversion of index sequence at the boundaries of the spectrum possible refractive index n 1.7 flint F6 n small slope large 1.675 1.65 crown n large slope small 1.625 SK18A VIS 1.6 0.5 0.75 1.0 1.25 1.5 1.75 2.0 6 Glass Diagram . Usual representation of glasses: diagram of refractive index vs dispersion n(n) . Left to right: Increasing dispersion decreasing Abbe number 7 Relative Partial Dispersion . Long crown and short flint as special realizations of large P Long crown Short flint Crown Flint Ref.:H. Zuegge 8 Anomalous Partial Dispersion N-SF57 P . There are some special glasses with g,F SF1 a large deviation from the normal line . Of special interest: long crowns and short flints line of normal dispersion KZFSN4 PSK53A LASFN30 FK51 FK5 LAK8 ZKN7 n Pg,F n heavy flints with character of long crowns flint long crowns long crown short flint short flints crown normal line n 9 Anomalous Partial Dispersion . Arrows in the glass map: indication of the deviation from the PhF' normal line . Vertical component: at the red horizontal: at the blue end of the spectrum P a n b P normal line 12 12 d 12 12 Glass nd P hF' n arrow of deviation nd PtC' red side glass location PhF' blue side nd 10 Axial Colour: Achromate (a) (b) (c) . Compensation of axial colour by appropriate glass choice . Chromatical variation of the spherical aberrations: spherochromatism (Gaussian aberration) . Therefore perfect axial color correction BK7 BK7 F2 BK7 N-SSK8F2 (on axis) are often not feasable n = 1.5168 n = 1.5168 1.6200 n = 1.5168 1.6177 n = 64.17 n = 64.17 36.37 n = 64.17 49.83 F= 1 F = 2.31 -1.31 F = 4.47 -3.47 r p r p r p 1 1 1 486 nm 588 nm 656 nm z z z -2.5 0 -0.20 0 0.20 -100 0 100 Ref : H. Zügge Achromate . Achromate . Longitudinal aberration . Transverse aberration . Spot diagram 486 nm 587 nm 656 nm y' = 486 nm axis rp 1 = 656 nm sinu' = 587 nm 1.4° 486 nm 587 nm 656 nm 2° s' [mm] 0 0.1 0.2 Achromate . Achromate: - Axial colour correction by cementing two Crown in different glasses front - Bending: correction of spherical aberration at the full aperture - Aplanatic coma correction possible be clever choice of materials . Four possible solutions: - Crown in front, two different bendings - Flint in front, two different bendings Flint in front . Typical: - Correction for object in infinity - spherical correction at center wavelength with zone - diffraction limited for NA < 0.1 - only very small field corrected solution 1 solution 2 Achromate: Realization Versions . Advantage of cementing: solid state setup is stable at sensitive middle surface with large curvature . Disadvantage: a) flint in front loss of one degree of freedom . Different possible realization forms in practice edge contact cemented b) crown in front edge contact cemented contact on axis broken, Gaussian setup Achromate : Basic Formulas . Idea: 1. Two thin lenses close together with different materials 2. Total power F F1 F2 F F 3. Achromatic correction condition 1 2 0 n1 n 2 . Individual power values 1 1 F1 F F F n 2 1 2 n1 1 n1 n . Properties: 2 1. One positive and one negative lens necessary 2. Two different sequences of plus (crown) / minus (flint) 3. Large n-difference relaxes the bendings 4. Achromatic correction indipendent from bending 5. Bending corrects spherical aberration at the margin 6. Aplanatic coma correction for special glass choices 7. Further optimization of materials reduces the spherical zonal aberration Achromate: Correction . Cemented achromate: 6 degrees of freedom: 3 radii, 2 indices, ratio n1/n2 . Correction of spherical aberration: diverging cemented surface with positive spherical contribution for nneg > npos s'rim . Choice of glass: possible goals 1. aplanatic coma correction case with 2 solutions 2. minimization of spherochromatism 3. minimization of secondary spectrum R . Bending has no impact on chromatical 1 correction: is used to correct spherical aberration case with one solution at the edge and coma case without solution, correction . Three solution regions for bending only sperical minimum 1. no spherical correction 2. two equivalent solutions 3. one aplanatic solution, very stable 16 Optimization of Achromatic Glasses . For one given flint a line indicates the usefull crown glasses and vice versa . Perfect aplanatic line of corresponding glasses (corrected for coma) Condition: 2 . 1 1 n1 1 n1 n2 1 n 2 n1 n1 n2 n2 n1 1 r s' n n n n n n n n 1 2 2 1 2 2 1 2 2 2 2 n n fixed flint glass line of minimal spherical aberration line of minimal spherical aberration fixed crown glass n n 17 Achromate Spherical Correction Seidel surface contributions, same scale n2 n1 =70 / n2=30 / n1/n2 = 2.33 . The correction of the spherical aberration in an achromate for the marginal ray is performed by the undercorrecting effect of n 1 the cemented surface n2 n1 =65 / n2=40 / n1/n2 = 1.63 . A necessary condition for this is n1 < n2 . For large values of e n1 /n 2 n must be considerably larger then n since 2 1 n1 n2 the cemented surface is rather weak bended n1 =55 / n2=45 / n1/n2 = 1.43 . For values of e close to 1, the radii are strongly bended, the undercorrection of the cemented surface can only compensate the dominating n1 n2 first surface for a small difference in the n n1 =55 / n2=45 / n1/n2 = 1.22 . The figure shows the corresponding layouts and Seidel contributions for the case n1 = 1.5 and n2 =1.8 n1 n2 n1 =55 / n2=47 / n1/n2 = 1.17 n1 18 Achromate Spherical Correction . Spherical aberration for n1 = 1.5 Log n2 = 1.5 Sph n /n = 2.33 1 1 2 10 n1/n2 = 1.86 n1/n2 = 1.63 n1/n2 = 1.43 n1/n2 = 1.22 n1/n2 = 1.20 n1/n2 = 1.17 0 10 -1 10 -2 n2 10 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 19 Achromate . Crown glass locations for M flint aplanatic achromates glass crown glass n location n n flint 1.8 aplanatic crown lines 1.7 1.6 available glasses 1.5 n 80 70 60 50 40 30 20 Achromatic Solutions in the Glass Diagram large n-differences give relaxed bendings flint crown negative lens positive lens Achromat Coma Correction: Achromate Image height: y’ = 0 mm y’ = 2 mm Achromat . Bending of an achromate Pupil section: meridional meridional sagittal bending Transverse y' y' y' - optimal choice: small residual spherical Aberration: 0.05 mm 0.05 mm 0.05 mm aberration (a) - remaining coma for finite field size . Splitting achromate: additional degree of freedom: - better total correction possible (b) - high sensitivity of thin air space . Aplanatic glass choice: vanishing coma (c) . Cases: a) simple achromate, Achromat, splitting sph corrected, with coma (d) b) simple achromate, coma corrected by bending, with sph Achromat, aplanatic glass choice c) other glass choice: sph better, coma reversed (e) d) splitted achromate: all corrected e) aplanatic glass choice: all corrected Wave length: Ref : H. Zügge Achromate . Residual aberrations of an achromate . Clearly seen: 1. Distortion 2. Chromatical magnification 3. Astigmatism 23 Spherochromatism: Achromate . Residual spherochromatism of an achromate . Representation as function of apeture or wavelength longitudinal aberration defocus variation rp 1 656 pupil height : rp = 1 r = 0.707 587 p rp = 0.4 rp = 0 486 nm 587 nm 656 nm 486 z z 0 0.04 0.08 0.12 -0.04 0 0.04 0.08 24 Axial Colour: Achromate and Apochromate . Effect of different materials . Axial chromatical aberration changes with wavelength . Different levels of correction: apochromate achromate 1.No correction: lens, one zero crossing point 644 2.Achromatic correction: C' - coincidence of outer colors - remaining error for center residual error apochromate wavelength - two zero crossing points lens 3. Apochromatic correction: - coincidence of at least three e 546 colors residual error achromate - small residual aberrations singlet - at least 3 zero crossing points - special choice of glass types F' s' with anomalous partial 480 dispertion necessery -100 0 100 25 Axial Colour : Apochromate P gF .