Lens Design II Lecture 2: Structural modifications 26--26 Herbert Gross Winter term 26 www.iap.uni-jena.de
2 Preliminary Schedule 9.. Aberrations and optimization Repetition 2 26.. Structural modifications Zero operands, lens splitting, lens addition, lens removal, material selection 3 2.. Aspheres Correction with aspheres, Forbes approach, optimal location of aspheres, several aspheres 4 9.. Freeforms Freeform surfaces 5 6.. Field flattening Astigmatism and field curvature, thick meniscus, plus-minus pairs, field lenses 6 23.. Chromatical correction I Achromatization, axial versus transversal, glass selection rules, burried surfaces 7 3.. Chromatical correction II secondary spectrum, apochromatic correction, spherochromatism 8 7.2. Special correction topics I Symmetry, wide field systems,stop position 9 4.2. Special correction topics II Anamorphotic lenses, telecentricity 2.2. Higher order aberrations high NA systems, broken achromates, induced aberrations 4.. Further topics Sensitivity, scan systems, eyepieces 2.. Mirror systems special aspects, double passes, catadioptric systems 3 8.. Zoom systems mechanical compensation, optical compensation 4 25.. Diffractive elements color correction, ray equivalent model, straylight, third order aberrations, manufacturing 5.2. Realization aspects Tolerancing, adjustment
3 Contents. Correction strategy 2. Structural changes 3. Zero operations 4. Material optimization
Struc Special Surfaces Action Material Lens Parameters Spherical Aberration Coma Astigmatism Petzval Curvature Distortion 5th Order Spherical Axial Color Lateral Color Secondary Spectrum Spherochromatism 4 Correction Effectiveness Effectiveness of correction features on aberration types Aberration Primary Aberration 5th Chromatic Lens Bending (a) (c) e (f) Makes a good impact. Makes a smaller impact. Makes a negligible impact. Zero influence. Power Splitting Power Combination a c f i j (k) Distances (e) k Stop Position Refractive Index (b) (d) (g) (h) Dispersion (i) (j) (l) Relative Partial Disp. GRIN Cemented Surface b d g h i j l Aplanatic Surface Aspherical Surface Mirror Diffractive Surface Symmetry Principle Field Lens Ref : H. Zügge
5 Strategy of Correction and Optimization If the potential of the setup seems to by not improvable, enlarge the number of degrees of freedom by structural changes of the system Possible options are: add a lens split a lens by distribution of nearly equal ray bending split a lens by decomposing it by a positive and negative part split a lens by decomposing it with two different materials add especially a field lens break a cemented component insert a burried surface make a surface aspherical make a surface free shaped insert a mirror replace a lens by a mirror implement a diffractive surface remove a lens cement two lenses make an asphere spherical
6 Strategy of Correction and Optimization Usefull options for accelerating a stagnated optimization: split a lens increase refractive index of positive lenses lower refractive index of negative lenses make surface with large spherical surface contribution aspherical break cemented components use glasses with anomalous partial dispersion kick, if the optimization is captured in a local minimum In general: it is preferred to preserve the achieved (good) result and perform small changes to let the optimization run again, change the weightings if the potential of the setup seems to by not improvable, enlarge the number of degrees of freedom
Number of Lenses Approximate number of spots over the field as a function of the number of lenses Linear for small number of lenses. Depends on mono-/polychromatic design and aspherics. Number of spots 2 8 6 monochromatic aspherical monochromatic polychromatic 4 2 Diffraction limited systems with different field size and aperture 8 6 2 4 6 8 diameter of field [mm] 2 6 2 4 8 lenses 4 Number of elements 4 2.2.4.6.8 numerical aperture
8 Spherical Aberration Correction Correction of spherical aberration by splitting the ray bending Optimal bending of lenses Splitting of lenses Smooth reducing of spherical aberration or marginal correction single plano convex lens two plano convex lenses dublet of two optimal bended lenses dublet with marginal corrected ray and residual zone W rms = 5.2 W rms =.9 W rms =.9 W rms =.22 achromat W rms =.68 splitted achromate W rms =.26 achromate with additional meniscus W rms =.59 four lenses W rms =.
9 Principle of Symmetry Perfect symmetrical system: magnification m = - Stop in centre of symmetry Symmetrical contributions of wave aberrations are doubled (spherical) Asymmetrical contributions of wave aberration vanishes W(-x) = -W(x) Easy correction of: coma, distortion, chromatical change of magnification front part rear part 2 3
Symmetrical Systems Ideal symmetrical systems: Vanishing coma, distortion, lateral color aberration Remaining residual aberrations:. spherical aberration 2. astigmatism 3. field curvature 4. axial chromatical aberration 5. skew spherical aberration skew spherical aberration
Symmetry Principle Application of symmetry principle: photographic lenses Especially field dominant aberrations can be corrected Also approximate fulfillment of symmetry condition helps Triplet significantly: quasi symmetry Realization of quasisymmetric setups in nearly all photographic systems Double Gauss (6 elements) Biogon Double Gauss (7 elements) Ref : H. Zügge
2 System Structure w j Distribution of refractive power good: small W W N N j.7.6 2 w j.5 w j n' j n m j n N y j ' u' N power : W =.273 j Symmetry content good: large S S N N j 2 s j.4.3.2 s j m n i n stop j i n j N ' u' N u' n' j j u n j j General trend : Cost of small W and large S : - long systems - many lenses. s j.9.8 5 5 2 25 3 35 symmetry : S =.9 j Advantage of w j, s j -diagram : Identification of strange surfaces.7.6.5.4.3.2. 5 5 2 25 3 35 j
3 System Structure w j s j 2.5 W =.92 Example:.6 optimizing W and S with.4 one additional lens.5 Starting system:.2.8 S =.47 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 7 8 9 6 w j s j 2.8.5 W =.586 S =.82 w j s j 2.5 W =.92.8.6.4 S =.47.6.4.5.2.5 Final design 2 3 4 5 6 7 8 9 2 3 2 3 4 5 6 7 9 8.2 2 3 4 5 6 7 8 9 2 3 2 3 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 w j 2 s j 3 4 2 5 8 9 W =.586 7 S =.82 6.8.5.6.4.5.2 2 3 4 5 6 7 8 9 2 3 2 3 4 2 3 4 5 6 7 8 9 2 3 2 3
Field-Aperture-Diagram Classification of systems with field and aperture size Scheme is related to size, correction goals and etendue of the systems w 4 36 32 Biogon Triplet photographic lithography Braat 987 28 Distagon Aperture dominated: Disk lenses, microscopy, Collimator 24 2 Sonnar Field dominated: Projection lenses, camera lenses, Photographic lenses Spectral widthz as a correction requirement is missed in this chart 6 2 8 4 split triplet projection Gauss projection double Gauss achromat Petzval projection micro x.4 diode collimator micro 4x.6 disc.2.4.6.8 lithography 23 micro x.9 constant etendue microscopy collimator focussing NA
5 Symmetrical Dublet Variable focal length f = 5...2 mm Invariant: object size y = mm numerical aperture NA =. Type of system changes: - dominant spherical for large f - dominant field for small f Data: f = 2 mm f = mm f = 5 mm f = 2 mm No focal length [mm] Length [mm] spherical c 9 field curvature c 4 astigmatism c 5 2 88 3.37-2. -2.27 2 48.65.9-4.5 3 5 26.74 3.45-7.34 4 2 75.98 3.93 2.3 5 5 59.2 6.7-5.33 f = 5 mm
6 Wide Angle Lenses - Symmetrical Radii of curvature of wide angle camera lenses - symmetrical setups Mostly radii 'concentric' towards the stop losition Locations z j of surfaces normalized for comparison Nearly linear trend, some exceptions near to the pupil Stop position centered 25 2 5 R j 5 Pleogon -5 - -5-2 -25 Double Gauss Biogon -.5 -.4 -.3 -.2 -...2.3.4.5 stop z j z j
7 Wide Angle Lenses - Asymmetrical Radii of curvature of wide angle camera lenses - asymmetrical setups No clear trend Locations z j of surfaces normalized for comparison Stop position in the rear part R j 3 Flektogon 2 - Fisheye -2-3 Distagon - -.8 -.6 -.4 -.2.2 stop z j
8 Relaxed System Example: achromate with cemented/splitted setup Equivalent performance Inner surfaces of splitted version more sensitive a ) Cemented achromate f = mm, NA =. 5-5 - -5 2 3 surface index Seidel coefficient spherical aberration spot enlargement for.2 surface tilt b ) Splitted achromate f = mm, NA =. 5-5 2 3 4 surface index - -5 Ref: H. Zügge
9 Best Location for Correction Changes The aberration contribution strongly depends on the heights of the marginal / chief ray at a surface Spherical aberration can be best corrected with a surface near to the pupil Astigmatism and distortion can be best corrected with a surface near to the image Field curvature does not depend on the surface location (see Petzval) Coma correction depends on marginal and chief ray and thus is more complicated. Usually a location near to the pupil is more helpful
2 Microscope Objective Lens Seidel surface contributions for x/.9 No field flattening group Lateral color in tube lens corrected spherical coma astigmatism.5 -.5.2 -.2 4 2-2 -4 curvature 5-5 distortion 2-2.2 axial chromatic lateral chromatic -.2-5 sum 3 5 8
2 Structural and Smooth Changes for Correction Smooth changes Lens bending Distances Structural changes: Lens splitting (a) (b) Power combinations Ref : H. Zügge (a) (b) (c) (d) (e)
22 Zero-Operations Operationen with zero changes in first approximation:. Bending a lens. 2. Flipping a lens into reverse orientation. 3. Flipping a lens group into reverse order. 4. Adding a field lens near the image plane. 5. Inserting a powerless thin or thick meniscus lens. 6. Introducing a thin aspheric plate. 7. Making a surface aspheric with negligible expansion constants. 8. Moving the stop position. 9. Inserting a buried surface for color correction, which does not affect the main wavelength.. Removing a lens without refractive power.. Splitting an element into two lenses which are very close together but with the same total refractive power. 2. Replacing a thick lens by two thin lenses, which have the same power as the two refracting surfaces. 3. Cementing two lenses a very small distance apart and with nearly equal radii.
23 Optimization Adding a meniscus lens with thickness zero: Two additional degrees of freedom Generates two adjacent local minima Different opportunities to generate a meniscus Ref : F. Bociort
24 Lens Removal Removal of a lens by vanishinh of the optical effect For single lens and cemented component Problem of vanishinh index: Generation of higher orders of aberrations a) Geometrical changes: radius and thickness ) adapt second radius of curvature 2) shrink thickness to zero b) Physical changes: index
25 Optimization: Discrete Materials Special problem in glass optimization: finite area of definition with discrete parameters n, n n Restricted permitted area as one possible contraint Model glass with continuous values of n, n in a pre-phase of glass selection, freezing to the next adjacend glass 2.9.8.7.6 area of permitted glasses in optimization area of available glasses.5.4 9 8 7 6 5 4 3 2 n
26 Basic Principles of Glass Selection Positive lenses with anomalous partial dispersion and high n: PK5, FK5, FK52, FK54 For monochromatic correction disadvantageous Negative lenses with anomalous partial dispersion andf low n: KzFS-glasses High indices for monochromatic correction: LaK, LaSF, LaF expensive, hard to manufacture, disadvantageous for color correction Low refracting glasses for field flattening in negative lenses: TiF, TiSAF expensive, hard to manufacture, disadvantageous for color correction
27 Principles of Glass Selection in Optimization Design rules for glass selection Different design goals:. Color correction: index n large dispersion difference desired positive lens field flattening Petzval curvature 2. Field flattening: large index difference + + desired negative lens color correction + - availability of glasses - - dispersion n Ref : H. Zügge
28 Relative Partial Dispersion Preferred glass selection for apochromates N-SF N-SF6 N-SF57 N-SF66 P-SF68 P-SF67 N-FK5A N-PK52A N-PK5 N-KZFS2 N-KZFS4 N-LAF33 N-LASF4 N-LAF37 N-LAF2 N-LAF35 N-LAK N-KZFS2
Buried Surface 29 Cemented surface with perfect refrcative index match No impact on monochromatic aberrations Only influence on chromatical aberrations Especially 3-fold cemented components are advantages Can serve as a starting setup for chromatical correction with fulfilled monochromatic correction Special glass combinations with nearly perfect parameters Nr Glas n d n d n d n d SK6.623. 6.28 22.32 F9.623 37.96 2 SK5.5895.3 6.23 2.26 LF2.5898 4.97 3 SSK2.6228.4 53.3 7.6 F3.62222 36.7 4 SK7.672.2 59.47.23 BaF5.678 49.24 d d 2 d 3