Lens Design II Lecture : Further topics 28--8 Herbert Gross Winter term 27 www.iap.uni-ena.de
2 Preliminary Schedule Lens Design II 27 6.. Aberrations and optimization Repetition 2 23.. Structural modifications Zero operands, lens splitting, lens addition, lens removal, material selection 3 3.. Aspheres Correction with aspheres, Forbes approach, optimal location of aspheres, several aspheres 4 6.. Freeforms Freeform surfaces, general aspects, surface description, quality assessment, initial systems 5 3.. Field flattening Astigmatism and field curvature, thick meniscus, plus-minus pairs, field lenses 6 2.. Chromatical correction I Achromatization, axial versus transversal, glass selection rules, burried surfaces 7 27.. Chromatical correction II Secondary spectrum, apochromatic correction, aplanatic achromates, spherochromatism 8 4.2. Special correction topics I Symmetry, wide field systems, stop position, vignetting 9.2. Special correction topics II Telecentricity, monocentric systems, anamorphotic lenses, Scheimpflug systems 8.2. Higher order aberrations High NA systems, broken achromates, induced aberrations 8.. Further topics Sensitivity, scan systems, eyepieces 2 5.. Mirror systems special aspects, double passes, catadioptric systems 3 22.. Zoom systems Mechanical compensation, optical compensation 4 3.. Diffractive elements Color correction, ray equivalent model, straylight, third order aberrations, manufacturing 5 5.2. Realization aspects Tolerancing, adustment
3 Contents. Sensitivity 2. Scan systems 3. Eyepieces
4 Sensitivity by large Incidence Small incidence angle of a ray: small impact of centering error Large incidence angle of a ray: - strong non-linearity range of sin(i) - large impact of decenter on ray angle b) large incidence: large impact of decenter i surface normal ideal ray a) small incidence: small impact of decenter real surface location: decentered ideal surface location real ray i surface normal ideal ray real ray Ref: H. Sun
System Structure w Distribution of refractive power good: small W W N N.7.6 2 w.5 w n' n m n N y ' u' N power : W =.273 Symmetry content good: large S S N N 2 s.4.3.2 s m n i n stop i n N ' u' N u' n' u n General trend : Cost of small W and large S : - long systems - many lenses. s.9.8 5 5 2 25 3 35 symmetry : S =.9 Advantage of w, s -diagram : Identification of strange surfaces.7.6.5.4.3.2. 5 5 2 25 3 35
System Structure w s 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 s 2.8.5 W =.586 S =.82 w s 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 2 s 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
7 Sensitivity of a System Representation of wave Seidel coefficients [l] Double Gauss.4/5 Ref: H.Zügge surfaces
8 Sensitivity of a System Quantitative measure for relaxation with normalization A k A F F h h F F Non-relaxed surfaces:. Large incidence angles 2. Large ray bending 3. Large surface contributions of aberrations 4. Significant occurence of higher aberration orders 5. Large sensitivity for centering Internal relaxation can not be easily recognized in the total performance Large sensitivities can be avoided by incorporating surface contribution of aberrations into merit function during optimization
9 Further Parameter of Sensitivity Possible further criteria for modefied merit function to obtain relaxed systems. cos-g-factor of ray bending G n ' s ' e n s e 2. Squared sum of incidence angles N i i' 2N 2 2 Target: minimum value for i, i' performance as built performance nominal performance = 2 = 2 limit 3. Optimization of performance and performance change simultaneously D m M p m p m 2
Relaxed Design Photographic lens comaprison Data: F# = 2. f = 5 mm Field 2 Same size and quality Considerably tigher tolerances in the first solution Ref: D. Shafer
As Built Performance Influence of tolerances on the performance of a Tessar camera lens a) nominal design b) as built performance quality with tolerances Ref: C. Menke
Scan Systems: Introduction Basic setup lens lens 2 chief ray due to scan angle point source virtual source point for scan angle scan angle s scan mirror t D s' marginal ray L field size Scan-magnification m =...2 d m d Virtual source point on curved line: special flattening formula Requirements: - Duty cycle - Point resolution - Speed - Accuracy - Linearity - Cost
Scan Systems: Introduction Deflecting components allows a field scan Mostly rotating mirrors Pre-obective scanning rotating scan mirror scan angle scan obective lens image plane y y Post-obective scanning image surface scan lens scan mirror
Deflecting Components Different types of deflecting elements non-mechanical electro-optic acousto-optic rotation polygon rotating wedge mechanical oscillation galvanometric holographic translation microlens-array
5 Scanning Unit x-y Scanning Units Historic polygon scanner: constant angular velocity Galvo, resonant galvo linear adusted or sinusodial Bidirectional MEMS, DMDs Assembly Two mirror, two axis Pupil relay Each after another Constant angular velocity Exposure of field varies Correction by velocity adustment lens with h = f θ 2. rotating mirror e distane d. rotating mirror θ angle image plane y proection of scan-angles Asymmetric pincushion distortion y' d tan y d x' cos y e tan X Ref: B. Böhme
Scan Systems: Introduction Scan resolution: Number of resolvable points in the field of view corresponds to angle resolution N L D Airy 2 DExP l max Information capacity:. Resolvable points 2. Speed of scanning log angle resolution holographic scanner polygon mirror growing scan capacity resonant galvo scanner galvo scanner acoustic optical modulator electro optical modulator scan speed log v
7 Scanner Lenses Ideal scanner lens h = f Landscape lens = Simplest scanner lens Distortion correction concentric surfaces to pupil USP 4436382: F - tan F - Scan angle 2x3 Monochromatic diffraction limited F--corrected 5 5 2 24 28 3.4 Ref: B. Böhme
Scan Systems: F--Scan Lenses Paraxial image height Desired in scan systems: linearity of image position to angle size Solution : special distortion y' y' f L tan 2 f D tan Definition of deviation as aberration 6 5 4 3 distortion corrected D y' f 2 linear % D 2 3 4 5 6 7 8 - %
Scan Systems: Optical Design General aspect : remote pupil. 2. 3. Diameter size for telecentric scan lenses 4. 5. 6. D 2 L D ExP Separation of beam path for mirror systems source image plane mirror
Scan Systems: Example Simple system Not f--corrected Non-telecentric Polychromatic Field of view 2x6.7 D spot [m] 25 2 5 5 axis. 6.7 5.6 diffraction limit l m.48.56.64
Scan Systems: Example Monochromatic Scan field 2x2 Numerical apertur.25 Telecentric F--correction With field lens w [ ].5 -.5 -. -.5 -.2 a) telecentricity error b) f--distortion y/y max 2 -.5%.5%.5 c) wave aberration W rms [l]..8.6.4.2 diffraction limit 2 spherical coma - 5-5.2 astigmatism -.2 curvature distortion (standard). -..4.2 -.2 -.4 2 3 4 5 6 7 8 9 sum scan mirror
Laser Scan Microscope Complete setup: obective / tube lens / scan lens / pinhole lens Scanning of illumination / descanning of signal Scan mirror conugate to system pupil plane Digital image processing necessary obect plane obective lens pupil plane tube lens intermediate image scan lens scan mirror pinhole lens field point axis point pupil imaging beam forming laser source
2 arcmin Kellner Eyepiece Corresponds to Ramsden type Field lens moved Eye lens achromatized LONGITUDINAL SPHERICAl ABER. ASTIGMATIC FIELD CURVES DISTORTION..5.5 24.75 7.875 7.875 2.5 5.25 5.25.25 2.625 2.625 -... DIOPTER -3.. 3. DIOPTER -2.. 2. Distortion (%) tan sag
Eyepiece: Notations Field lens reduces chief ray height Eye lens adapts pupil diameter instrument pupil stop intermediate image eye lens f eye pupil Matching of. Field of view 2. Pupil diameter 3. Pupil location field lens f 2 F' Eye relief : s' - distance between last lens surface and eye cornea x' z' e x - required : 5 mm - with eyeglasses : 2 mm Pupil size: 2-8 mm
Evolution of Eyepiece Designs Huygens Loupe Monocentric Ramsden Von-Hofe Plössl Kellner Kerber Erfle Bertele König Erfle type Erfle diffractive Bertele Nagler Erfle type (Zeiss) Aspheric Nagler 2 Scidmore Bertele Wild Dilworth