Lens Design II Lecture : Further topics 26--2 Herbert Gross Winter term 25 www.iap.uni-ena.de
Preliminary Schedule 2 2.. Aberrations and optimization Repetition 2 27.. 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.. Freeforms Freeform surfaces 5 7.. Field flattening Astigmatism and field curvature, thick meniscus, plus-minus pairs, field lenses 6 24.. Chromatical correction I Achromatization, axial versus transversal, glass selection rules, burried surfaces 7.2. Chromatical correction II secondary spectrum, apochromatic correction, spherochromatism 8 8.2. Special correction topics I Symmetry, wide field systems,stop position 9 5.2. Special correction topics II Anamorphotic lenses, telecentricity 5.. Higher order aberrations high A systems, broken achromates, induced aberrations 2.. Further topics Sensitivity, scan systems, eyepieces 2 9.. Mirror systems special aspects, double passes, catadioptric systems 3 26.. Zoom systems mechanical compensation, optical compensation 4 2.2. Diffractive elements color correction, ray equivalent model, straylight, third order aberrations, manufacturing 5 9.2. Realization aspects Tolerancing, adustment
3 Contents. Sensitivity 2. Scan systems 3. Eyepieces
System Structure w Distribution of refractive power good: small W W.7.6 2 w.5 w n' n m n y ' u' power : W =.273 Symmetry content good: large S S 2 s.4.3.2 s m n i n stop i n ' u' 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
6 Sensitivity of a System Representation of wave Seidel coefficients [l] Double Gauss.4/5 Ref: H.Zügge surfaces
7 Sensitivity of a System Quantitative measure for relaxation with normalization A k A F F h h F F on-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
8 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 i i' 2 2 2 Target: maximum 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
9 Misalignment Sensitivity Misalignment: special criteria Mostly coma and astigmatism on axis as drawback Seidel aberration surface contribution: c a Ay 2 'u ' 2 y m n stop Ay 'u ' u n u y n stop nistop m n Criterion for relaxation: sum of squares c c a a 2 2,
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
Deflecting Components Different types of deflecting elements non-mechanical electro-optic acousto-optic rotation polygon rotating wedge mechanical oscillation galvanometric holographic translation microlens-array
Scan Systems: Introduction Scan resolution: umber of resolvable points in the field of view corresponds to angle resolution 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
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
4 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
5 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 ot f--corrected on-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 umerical 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
Evolution of Eyepiece Designs Huygens Loupe Monocentric Ramsden Von-Hofe Plössl Kellner Kerber Erfle Bertele König Erfle type Erfle diffractive Bertele agler Erfle type (Zeiss) Aspheric agler 2 Scidmore Bertele Wild Dilworth
Eyepiece: otations 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
2 arcmin Kellner Eyepiece Corresponds to Ramsden type Field lens moved Eye lens achromatized LOGITUDIAL SPHERICAl ABER. ASTIGMATIC FIELD CURVES DISTORTIO..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