j Jacobi matrix 295 Index flattening mirror 258 flint glass 231 form tolerance 598, 605 ff free-form aspheres 456 Fresnel zone plate 499, 503 f

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1 749 a Abbe number 41, 222, 269, 490, 502 aberrations 2, 216 astigmatism 13, 28 axial chromatic aberration 13, 269 axial color 13, 269 chromatic aberrations 2, 13, 187, 268, 280 chromatic difference in magnification 13, 187, 280 coma 13, 24 compensating aberrations 216 distortion 13, 46, 182 ff, 562 fifth-order aberration 50 field curvature 13, 28 high-order aberration 50, 53 ff, 265 lateral chromatic aberration 13, 188, 280 lateral color 13, 188, 280 longitudinal aberration 20 monochromatic aberrations 2, 20, 226 ff preventing aberrations 216 primary aberration 13, 16 ff, 29 primary chromatic aberration 13 ff primary monochromatic aberration 13 ff pupil aberration 10, 45 secondary aberration 50 secondary spectrum 269, 272 f Seidel aberration 13 spherical aberration 13, 21, 64 spherochromatism 13, 283, 508, 515 statistical aberrations 199 thin lens aberration 41 third-order aberration 13 transverse aberration 2 vector theory 555 ff wave aberration 5, 14 ff, 80 ff zonal 216, 231 achromat 231, 248, 260, 269 ff, 339 acutance 168 adaptive method 368 adjustment 652 f bonding tolerances 639 clocking 654, 664 compensator 652, 663 image rotation 703 on-axis astigmatism 654 on-axis coma 656 Aldis theorem 61 anamorphism 549 ff, 562 anamorphotic factor 567 anamorphotic system 141, 544, 566 anastigmatic telescope 572 aplanatic 61, 67 f, 233 condition 61 imaging 59, 67 f, 440 lens 67 f, 234, 402 point 67 f surface 67 ff, 217, 223, 233, 249 aplanatism 61 apochromat 273 apodization 82, 101 area criterion 155 Argand diagram 146 aspherical surface 223 f, 238 ff, 433 ff best location 444 carrier surface for diffractive element 517 centering 636 conic sections 434, 238 constants 440 correction 217 free-form 456 polynomial expansion 436 Seidel coefficients 443, 447 tolerance 613 asphericity 608 assembling 641, 647 astigmatism 13, 28 adjustment 654 binodal astigmatism 560 Handbook of Optical Systems: Vol. 3. Aberration Theory and Correction of Optical Systems. Edited by Herbert Gross Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN:

2 750 clocking 654 Coddington equations 552 correction 250 on-axis astigmatism 654 prism tolerances 712 vectorial 559 athermalization 528 atmospheric perturbations 205 autocorrelation function 199, 620 axial chromatic aberration 13 axial color 13, 269 axial gradient 465, 472 axial run-out 645 axis ray 546 b bananicity 184 barrel distortion 184, 265, 562 barrier function 315 f basal ray 546 beam quality 106 bending a lens 217 f, 226 f, 243, 250, 262 bending parameter 41 bi-blaze structure 524 binodal astigmatism 560 blazed diffractive element 500 Bociort s method 362 ff bonding tolerances 639 Bossung plots 171 Brent s method 304 broken contact 266, 285 bubbles 601, 615 c cemented surface 217, 223 centering tolerance 598, 630 ff asphere tolerances 613, 636 bonding tolerances 639 corner cube 710 lens wedge 638 mounting tolerances 640 play mounting error 642 prism angles 690 ff pyramidal error 698 ff rolling angle 644 roof-angle 706 tilt angle 631 centroid 78, 102, 135 chromatic aberrations 2, 13, 187 ff, 268 ff, 489 Abbe number 490 achromat 231, 248, 260,, 269 ff, 339 apochromat 273 axial chromatic aberration 13 axial color 13, 269 chromatic aberrations of grin media 489 chromatic difference in magnification 13, 187, 280 correction 268 ff diffractive hybrid lens 505 lateral chromatic aberration 13, 188, 280 lateral color 13, 188, 280 partial dispersion 217, 222, 274, 491 partial dispersion of a diffractive element 502 primary chromatic aberration 13 ff relative partial dispersion 217, 222, 274 secondary spectrum 269, 272 f spherochromatism 13, 283, 508, 515 superachromat 273 chromatic difference in magnification 13, 187, 280 clocking 654, 664 Coddington equations 552 coherent transfer function 156 coma 13, 24, 558 correction 242 ff elliptical coma 52 inner coma 25 linear coma 51 longitudinal coma 26 on-axis coma 656 outer coma 25 pupil coma aberration 49 sagittal coma 24, 59 f tangential coma 24, 60 vectorial 558 compensator 652, 663 concentric surface 65 conic sections 434 conjugate gradient method 323 conjugate parameter 41 constraints 296, 309 ff, 347 ff contrast 127, 133, 147, 162 control function 300 f convergence 318 corner cube 710 correction 13 aspherical surface 217 astigmatism 250 chromatic 268 ff coma 242 ff curvature 252 ff diffractive element 217, 242 distortion 261 ff field flattener 226, 254 field lens 217, 226, 253

3 751 flattening lens 226, 254 flattening mirror 258 gradient media 217, 242 lens bending 217 f, 226 f, 243, 250, 262 spherical aberration 226 ff strategy 401 symmetry principle 18, 217, 225 f, 249, 262, 280 correlation 181 correlation length 207 cost of tolerances 650 covariance matrix 304 crown glass 231 cylindrical irregularity 608 d damped least squares 320 damping 318, 320 f Davidon-Fletcher-Powell method 324 defocussing 89, 124 ff, 135, 155 depth of focus 124 diameter 111 beam diameter 111 energy diameter 112 entropy diameter 113 Gaussian diameter 112 Petermann diameter 112 threshold diameter 111 diffraction efficiency 519 diffraction orders 498 diffractive elements 224, 495 ff Abbe number 502 aspherical carrier surface 517 athermalization 528 bi-blaze structure 524 blazed diffractive element 500 correction 217, 242 diffraction efficiency 519 diffraction orders 498 equivalent refractive lens 500 Fresnel zone plate 499, 503 f hybrid lens 505 kinoform lens 500 multi-material 524 f multi-order 509, 523 f nearly index match 526 f partial dispersion 502 quantization 535 Seidel coefficients 511 f stray light 521, 542 Sweatt model 501 tolerances 533 ff diopter 5 discretization 207 dispersion ratio 506 displaced energy 178 distortion 13, 46, 182 ff, 562 barrel distortion 184, 265, 562 correction 261 ff keystone distortion 185, 550, 562 line bowing 562 pincushion distortion 184 tv distortion 182 distributions 667 double plane symmetric system 544 Duffieux integral 133, 142 e edge 163 ff edge defect 168 edge steepness 167 edge width 163 Thomas criterion 164 efficiency of diffraction 519 efficiency of variables 305 f elliptical coma 52 encircled energy 175 energy 175 ff displaced energy 178 encircled energy 175 ensquared energy 177 power in the bucket 175 ensquared energy 177 equivalent passband 180 equivalent refractive lens 500 escape function 365 expert system 359 f fidelity 180 field curvature 13, 28, 252 ff correction 252 ff field flattener 226, 254 flattening lens 226, 254 flattening mirror 258 meniscus lens 253 Petzval curvature 30, 221, 252 ff primary image surface curvatures 40 thick meniscus 253 field flattener 226, 254 field lens 217, 226, 253 fifth-order aberration 50 figure tolerance 598 finish error 611 Fisher criterion 130 flattening lens 226, 254

4 752 flattening mirror 258 flint glass 231 form tolerance 598, 605 ff free-form aspheres 456 Fresnel zone plate 499, 503 f g Gaussian aberration 189 Gaussian image height 2 Gaussian image plane 2 Gaussian image point 2 genetic optimization 335 ff geometrical spot 77 geometrical transfer function 142 Glatzel s method 368 global explorer 365 ff global optimization methods 330 ff golden section 303 gradient index media 463 ff Abbe number 490 axial gradient 465, 472 chromatic aberrations 489 correction 217, 242 GRADIUM media 222, 482 ff parabolic profile 469 partial dispersion 491 radial gradient 465 Seidel coefficients 475 ff selfoc lens 222, 467 Wood lens 470 gradient of the merit function 296 GRADIUM media 222, 482 ff h head-up display 584 Hektor lens 541 Herschel condition 60 Hessian matrix 296 high frequency range 611 high-order aberration 50, 53 ff, 265 Hopkins factor 153 human eye 152 hybrid lens 505, 515 f i illumination 49, 191 image quality 20 image rotation 703 image tilt 549 immersion 386 imperfection tolerances 615 inclusions 601 inhomogeneity 602 inner coma 25 inner scale 206 inverse tolerancing 685 irregularity 605, 608 ff ISO standard 600 ff isoplanatism 61 Isshiki s method 365 ff j Jacobi matrix 295 k Karman scale 206 keystone distortion 185, 550 kinoform lens 500 Kolmogorov range scale 206 Kuhn-Tucker conditions 312 Kurtosis parameter 104 l lateral chromatic aberration 13, 188, 280 lateral color 13, 188, 280 lens bending 217 f, 226 f, 243, 250, 262 lens wedge 638 Levenberg-Marquardt method 325 f line 170 Bossung plots 171 line resolution 168 line spread function 170 Struve criterion 170 line bowing distortion 562 line resolution 168 linear coma 51 local grating of a diffractive element 496 local minimum 294 longitudinal aberration 20 longitudinal coma 26 longitudinal magnification 60 low Fresnel number 96 lsf 170 m M-square 104 Marechal approximation 91 Marechal criterion 96 Marquardt method 325 f material tolerance 598, 604 meniscus lens 253 merit function 295, 349 f Merte surface 221, 267 f micro-objective lens 382 ff, 542 microroughness 611 mid-frequency range 87, 611

5 753 mirror 224, 258 mirror symmetry 18 ff modulation transfer function 20, 132, 196 moments 78, 102, 107 monochromatic aberrations 2, 20 Monte Carlo simulation 677 Morse index 363 motion blur 208 mounting play error 642 mounting tolerances 640 multi-material diffractive element 524 f multi-order diffractive element 509, 523 ff n nearly index match diffractive element new achromat 260 Newton method 302, 319 nodal points 557 ff non-axisymmetric system 543 ff normal matrix f o object shift 45 objective function 295 oblique spherical sagittal aberration 51 obscuration 46 offense against the sine condition 51, 57 ff on-axis astigmatism 654 on-axis coma 656 OpTaliX 718 ff command line 719, 732 export of data 739 global surface references 737 import of data 739 lens database 720 macro language 719 menu entry 731 surface apertures 728 surface data 724 system data 722 user interface 718 optical path 6 optical path difference 7 optical sine theorem 57 optical transfer function 89 optimization 293 ff adaptive method 368 barrier function 315 f Bociort s method 362 ff Brent s method 304 conjugate gradient method 323 constraints 296, 309 ff, 347 ff control function 300 f damped least squares 320 damping 318, 320 f Davidon-Fletcher-Powell method 324 efficiency of variables 305 f escape function 365 expert system 359 genetic optimization 335 ff Glatzel s method 368 global explorer 365 ff global methods 330 ff Isshiki s method 365 ff Kuhn-Tucker conditions 312 Levenberg-Marquardt method 325 f local minimum 294 merit function 295, 349 f Newton method 302, 319 normal matrix 320 objective function 295 orthogonalization method 326 f over-determined 297 penalty function 313 f rate of convergence 318 saddle point method 362 ff simplex method 327 ff simulated annealing 332 ff, 365 starting solution 353 ff steepest descent method 317 f under-determined 297 weighting factors 295, 305 orthogonalization method 326 f outer coma 25 outer scale 206 over-correction 21, 42 p parasitic light 209 partial dispersion 217, 222, 274 grin media 491 diffractive element 502 peak to valley 81 penalty function 313 f periodicity 18 Petzval curvature 30, 221, 252 ff phase transfer function 144 pincushion distortion 184 ping-pong distribution 669 piston 56 pitch length 467 plane symmetric system 544 play mounting error 642 point resolution 113 point spread function 88, 99, 196 polar coordinates 10

6 754 polarization 209 polychromatic transfer function 141 polynomial aspheres 436 polynomial expansion 80 power combination 217 ff, 231 f, 262 power in the bucket 175 power series expansion 7, 46 power spectral density 86, 200, 619 power splitting 217 ff, 229 f, 246 primary aberration coefficient 13, 16 ff, 29 primary angular aberration 39 primary chromatic aberration 13 ff primary fractional aberration 40 primary image surface curvatures 40 primary longitudinal aberration 40 primary monochromatic aberration 13 ff primary transverse aberration 39 prism tolerances 690 ff production yield 678 pseudo inverse 297 psf 88, 99, 196 pupil 3 meridional pupil section 4 pupil aberration 10, 45 pupil coma aberration 49 pupil grid 3 sagittal pupil section 4 tangential pupil section 4 pyramidal error 698 ff q quantization of a diffractive element 535 quasi symmetry 225, 262 r radial gradient media 465 radius tolerance 606 rank of matrix 298 ray aiming 48 Rayleigh criterion 90, 96, 114, 119 Rayleigh limit 6 reference sphere 6, 82 relative ceiling 179 relative partial dispersion 217, 222, 274 resolution 113 ff, 147 lateral resolution 114 line resolution 168 point resolution 113 resolution chart 157 total resolution 121 retrofocus lens 262 reversed telephoto lens 262 ripples 611 rms value 82 rod lens 465 rolling angle 644 roof-angle 706 rotational symmetry 18 ff Räntsch superposition 674 s saddle point method 362 ff sagittal coma 24, 59 f sagittal field 31 sagittal structures 141 Scheimpflug condition 549 ff Schiefspiegler telescope 544, 571 ff Schmidt mirror 239 Schupmann lens 278 Schwarzschild telescope 440 scratches 615 secondary aberration 50 secondary spectrum 269, 272 Seidel 13 Seidel aberration 13 Seidel coefficient 13, 31, 84, 218, 392 Seidel coefficients of aspheres 443, 447 Seidel coefficients of diffractive elements 511 f Seidel coefficients of gradient media 475 ff Seidel eccentricity 37 Seidel sum 29 ff, 38 selfoc lens 222, 467 sensitivity analysis 671 Shafer approach 355 f Siemens star 159 simplex method 327 ff simulated annealing 332 ff, 365 sine condition 51, 57 ff, 441 singular value decomposition 298 slope tolerance 613 small angle scatter 630 Sparrow criterion 115, 120 spatial frequency 85, 132, 200, 610 spatial moments 102 spherical aberration 13, 21, 64 f, 226 correction 226 ff oblique spherical sagittal aberration 51 spherochromatism 13, 283, 508, 515 spherochromatism 13, 283, 508, 515 spot diagram 3, 77 standard radii 379 standard tolerances 600 starting solution 353 ff statistical aberrations 199 statistical distributions 667

7 755 statistical transfer function 204 steepest descent method 317 f stop position 217 ff, 245, 250, 250, 261 stop shift 36, 217 stray light 162 stray light of a diffractive element 521, 542 Strehl ratio 85, 87 ff, 134, 195 stress birefringence 601 striae 602 structural changes 377, 358 structural content 180 structure function 620 Struve criterion 170 super gaussian profile 104, 108 superachromat 273 surface contribution 34 surface texture 618 surface tolerance 598, 605 ff Sweatt model 501 symmetry parameter 373 symmetry principle 18, 217, 225 f, 249, 262, 280 t tangent condition 46 tangential coma 24, 60 tangential field 31 tangential structures 141 Tatarski scale 206 telephoto lens 262 telescope 572 anastigmatic 572 Schiefspiegler 544, 571 ff Schmidt 239 Schwarzschild 440 Yolo 579 Tessar 260 test charts 157 ff, 187 test-plate radii 379 thermo-optical coefficient 528 thick meniscus 253 thin lens aberration 41, 218 thin lens starting system 354 f third-order aberration 13 threshold modulation 151 through focus spot diagram 3 tilt angle 631 tolerances 597 ff adjustment 652 asphere tolerances 613, 636 asphericity 608 astigmatism of prisms 712 axial run-out 645 bonding tolerances 639 bubbles 601, 615 centering tolerance 598, 630 ff compensator 652 corner cube 710 cost 650 cylindrical irregularity 608 distributions 667 figure tolerance 598 finish error 611 form tolerance 598, 605 ff high frequency range 611 lens wedge 638 microroughness 611 mid frequency range 611 Monte Carlo simulation 677 mounting tolerances 640 spatial frequency 610 image rotation 703 imperfections 615 inclusions 601 inhomogeneity 602 inverse tolerancing 685 irregularity 605, 608 ff low frequency range 610 material tolerance 598, 604 play mounting error 642 prism tolerances 690 ff production yield 678 pyramidal error 698 ff radius tolerance 606 Räntsch superposition 674 ripples 611 rolling angle 644 roof-angle 706 scratches 615 sensitivity analysis 671 slope tolerance 613 standard tolerances 600 statistical distributions 667 striae 602 surface texture 618 surface tolerance 598, 605 ff tilt angle 631 total indicator runout 632 waviness 611 top hat profile 104 total indicator runout 632 total integrated scatterer 626 total resolution 121 transfer function 89 area criterion 155 coherent transfer function 156

8 756 geometrical transfer function 142 optical transfer function 89, 110, 132 ff modulation transfer function 20, 132, 196 phase transfer function 144 polychromatic transfer function 141 statistical transfer function 204 system contribution 154 transverse ray aberration 2, 4, 76, 127 tv distortion 182 u undercorrection 21, 42 w wave aberration 5, 14 ff, 80 ff wavefront 6 waviness 611 wedge of a lens 638 weighting factor 295, 305 wide angle scatter 630 Wood lens 470 working distance 390 y yield of production 678 v vector aberration theory vignetting 122 visibility 133 visual detection ff z Zernike coefficients 54, 83 zero power operations 378 zonal 216, 231, 265

Handbook of Optical Systems

Handbook of Optical Systems Edited by Herbert Gross Volume 3: Aberration Theory and Correction of Optical Systems Herbert Cross, Hannfried Zügge, Martin Peschka, Fritz Blechinger BICENTENNIAL BICENTENNIA