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Paraxial rays:
computations for, 302–304
for mirrored surfaces, 43
through several surfaces, 34–38
in third-order aberrations, 329
Paraxial region, 22, 32–34
Path length in fiber optics, 282
Pattern-generating surfaces, 297
Peak-to-valley (P-V) OPD, 356
Peaking-up characteristics, 572–573
Pechan prisms, 112
Pellicles, 114–115
Penta prisms, 113–114
Pentac anastigmats, 460
Perfect optical systems, 22
Periscopes, 256–257, 401
Petzval curvature, 70–71
in Cooke triplets, 418, 422
in eyepieces, 440
manual correction of, 427
in meniscus camera lens, 395–396, 400
Petzval lenses:
for photographic objectives, 465–467
with split elements, 522, 524
Petzval sum, 420
Petzval surfaces, 71, 423
Phase shifts, 287, 379
Phase transfer function (PTF), 372
Photoelectric effect, 16–17
Photographic density of filters, 175
Photographic depth of focus, 156–157
Photographic objectives, 453
afocal attachments, 470
airspaced anastigmats, 459–464
meniscus anastigmats, 453–459
Petzval lenses, 465–467
reverse telephoto lenses, 468–470
telephoto lenses, 467–468
Photographic triplet lens, 342–345
Photometry, 219–220, 237–243
Photopic curve, 134
Pincushion distortion, 72, 440
Pipes, light, 279–280
Pitch in blocking, 551
Planck’s law, 232–235
Plane mirrors, 116–117
Plane parallel plates, 100–104
Plane surface reflections, 97–100
Plane waves, 2
Plasmat lenses, 455
Plastic cements, 214
Plastic fibers, 283–285
Plastic optical materials, 188–192
Plate glass, 183
Ploessl eyepieces, 443–444, 509
Point spread functions (PSFs), 361–362, 
385–391
Polarizing materials, 197–200, 209
Polishing, 554–556, 558
Porro prisms, 109–110
Portrait lenses, 465
Position in image formation, 24–26
Power:
in anamorphic systems, 287, 289
in Cooke triplet anastigmats, 419–421
in design, 426
of field lenses, 261–262
of lenses, 24
of microscopes, 267–270
radiated into hemispheres, 222–223
of searchlights, 245
in telescopes, 251, 253, 259, 
263–267, 585
of two-component systems, 47
Precision bevels, 436
Precision in computations, 301–302
Presbyopia, 137
Pressing, 549
Primary aberrations, 64
manual correction of, 426–428
point spread functions for, 385–391
Principal planes, 45–46
Principal points, 22, 39–42
Principal rays, 69, 142, 329
Prisms, 91
achromatic and direct vision, 94–96
in anamorphic systems, 287, 290–291
designing, 117–122
dimensions and angles for, 95, 567–568
diopter, 126
dispersing, 91–92
erecting systems for, 108–111
in eyepieces, 440
inversion, 111–113
minimum deviation of, 94
mounting, 580
Penta, 113–114
plane parallel plates in, 100–104
polarizing, 199
in rangefinders, 272–273
reflection from plane surfaces in, 97–100
rhomboids and beam splitters, 114–116
right-angle, 104–107
roof, 107–108
thin, 92–94
total internal reflection in, 96–97
wave fronts affected by, 8–11
PRK technique, 136
612
Index
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Projection condensers, 245–247, 
470–471
Projection screens, 195–198
Projection TV objectives, 542
Protars, 454
Protected glasses, 183
Pulfrich refractometers, 598
Pupils:
and aperture stop, 142–143
eye, 126
in magnifiers, 444
in optical devices, 257–267
in telescopes, 254, 260
zones of, 588–589
Purkinje shift, 134
Purple optical glass filters, 194
R-Biotars, 525
Radial energy distribution, 383–385
Radial gradients, 187
Radial keratotomy, 136
Radial test targets, 593
Radiant intensity, 240
Radiation:
blackbody, 231–237
glasses for, 183
into hemispheres, 222–223
reducing, 148–150
Radiometers, 274–281
Radiometry and radiance, 219–220
blackbody radiation, 231–237
conservation of, 225–230
and diffuse sources, 223–225
and hemispheres, 222–223
of images, 225–230
inverse square law for, 220–221
and Lambert’s law, 221–222
spectral, 230–231
Radius in unknown optics 
analysis, 597
Ramsden eyepieces, 441–442
Rangefinders, 271–274
Rapid estimation of blur size, 491–496
Rare earth glasses, 179, 183, 423
Ray heights in raytracing, 37–38
Ray refraction at single surface, 30–32
Ray slope-index product, 319
Rayleigh limit (RL), 355–357
Rayleigh’s criterion, 161–162
Rays, 4
intercept curves for, 65, 83–89
through lenses, 10
meridional, 69, 304–308
paraxial (see Paraxial rays)
Raytracing:
in aberration measurements, 585
computer effects on, 394
graphical, 306–307
in optical computations, 302
through several surfaces, 34–38
for spot diagrams, 360–361
Real angular field of view, 253
Real images, 10
Rear meniscus camera lens, 400, 434
Rear projection screens, 198
Reciprocal relative dispersion, 93–94, 178
Red optical glass filters, 194
Reduction of residual aberrations, 429–430
Reflectance levels of natural sources, 
239–240
Reflecting microscope objectives, 452–453
Reflecting systems, 474
Bouwers system, 488–491
conic sections through origins in, 
484–485
ellipsoid and hyperboloid, 477–484
Mangin mirrors, 487–488
paraboloidal reflectors in, 476–477
Schmidt system, 485–487
spherical mirrors in, 474–476
Reflection, 173–175
dielectric, 200–209
in fiber optics, 282
with immersion lenses, 278
in prisms, 96–100
Reflectors, 117–122, 209–211
Refracting prisms, 290–291
Refraction:
equations for, 302, 305, 309
law of, 5–8
at single surface, 30–32
for skew rays, 315–317
Regions of solution, 427–428
Reinforced waves, 14
Relative apertures, 152
Relative dispersion, 7, 178
Relay systems, 256–257
Replication, plastics for, 191
Residual aberrations, 80–83, 429–430, 462
Resistance of optical glass, 181
Resolution:
of compound microscopes, 270–271
in diffraction-limited systems, 379
of eyes, 258
in fiber optics, 283
in modulation transfer function, 
367–368, 376
in optical devices, 257–267
Index
613
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Resolution (Cont.):
of optical systems, 160–163
tests for, 592–594
Reticles, 211–213
Retina, 127–128
Retrofocus lenses, 468–470, 513
Reverse telephoto lenses, 468–470, 513
Reversed Tessars, 519
Rhomboid prisms, 114–116
Right-angle prisms, 104–107
Ritchey-Chretien objective, 479–480
RMS (root-mean square) OPD, 355–356
Rod-lens endoscopes, 257
Rods, 127–128
Ronchi grating tests, 557
Roof prisms, 107–108, 112
Rough shaping, 550–551
Sagittal coma, 69, 103, 323
Sagittal curvature of field, 317
Sagittal height, 16
Scaling of aberrations, 79
Scheimpflug condition, 55–57
Schlieren test, 592
Schmidt cameras, 333
Schmidt prisms, 111–112
Schmidt systems:
blur size estimation in, 493, 498
Cassegrains, 487
in reflecting systems, 485–487
Schwarzchild configuration, 452
Scotopic curve, 134
Scratch and dig specifications, 436
Searchlights, 243–247
Second-surface mirrors, 116–117
Secondary spectrum (SS), 82
in achromatic telescope objectives, 
409–410
in diffractive surface design, 416
Seidel aberrations, 62–72
Seidel coefficients, 331
SELFOC rods, 285
Sellmeier dispersion equation, 176–177
Semi-coherent illumination, MTF with, 
380–383
Semireflecting mirrors, 210
Sensitivity of eyes, 131–134
Separated component systems, 45–49
Seventh-order aberrations, 88
Sheet polarizers, 199
Short-pass transmission filters, 207
Sigmoidoscopes, 284
Sign conventions, 25, 30–31, 57–58
for mirrored surfaces, 43
for telescopes, 253
Simple lenses:
blur size estimation in, 494
meniscus camera, 395–401
wave fronts affected by, 8–11
Simple microscopes, 267–269
Simultaneous design techniques, 432
Sine wave response, 369
Sine-wave targets in MTF, 375–376
Single-lens elements, blur size estimation 
in, 499
Single-lens reflex (SLR) cameras, 274
Single-material catadioptric systems, 533
Single-point diamond turning, 414, 
483, 559
Single refracting elements, blur size 
estimation in, 498
Single surface, ray refraction at, 30–32
Singlet correctors, 531
Size in image formation, 26–30
Skew rays, 69
aspheric surface computations, 312–317
spherical surface computations, 308–312
Slits in MTF tests, 594–596
Slope angles in paraxial raytracing, 38
Snell’s law of refraction, 5–8
Sonnar anastigmats, 456, 528
Spacing:
in Cooke triplet anastigmats, 419–421
in design, 426
in microscope objectives, 452
in telescopes, 263–265
in unknown optics analysis, 597
Sparrow’s criterion, 160
Spatial filtering, 168
Special glasses:
gradient index, 187
infrared transmitting, 186–187
low-expansion, 185–186
Spectral radiometry, 230–231
Speed of systems, 152
Spheres, integrating, 247–248
Spherical aberration, 64–67
in anastigmats, 424, 458, 461
in blur, 364–365, 492
computations for, 322
in condenser systems, 472
in Cooke triplets, 421–422
in diffraction-limited systems, 379–381
in diffractive surface design, 416
in eyepieces, 440
fifth-order, 352–354
geometric spot size due to, 362–366
and lens shape, 75
manual correction of, 427
in meniscus camera lens, 395, 399
614
Index
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Spherical aberration (Cont.):
in optical path difference, 349–355
in Petzval lenses, 467
in plane parallel plates, 103
in point spread functions, 386–387, 
390–391
Rayleigh limit in, 358
in reflecting systems, 474–476, 
479–480
in telescope objectives, 402, 405–409
third-order, 335, 351–352
wave aberration polynomial for, 
354–355
Spherical gradients, 187
Spherical mirrors, 474–476, 493, 497
Spherical reflectors, 473
Spherical surfaces, general and skew rays
on, 308–312
Spherical test plates, 561
Spherochromatism, 82
computations for, 325
in diffractive surface design, 416
in residual aberrations, 429
in telescope objectives, 406–409
Spherometers, 597
Spike filters, 207
Spinning shoulders, 578
Split elements, 462–463
Split-front triplets, 526, 529
Split-image rangefinders, 274
Split-rear crown double Gauss, 536
Spot diagrams, 360–361
Spot size due to spherical aberration, 
362–366
Spread functions, 361–362
Spreading of gaussian beams, 165–166
Sprenger prisms, 112
Spurious resolution, 379
Square-wave targets in MTF, 375–376
Star test, 587–588
Statistical combination, 570
Stefan-Boltzmann law, 232, 235
Steinheil form, 405
Steradians, 220
Stereo vision, 131
Stokes lenses, 289
Stop shift equations, 335–345
Stops (seeApertures)
Stray radiation, 148–150
Strehl definition, 368
Strehl ratio, 356–359, 385
Styrene plastic, 191
Subtended angles, 251, 253, 268
Superachromat lenses, 411
Surface curvature in eye, 127
Surfaces:
diffractive, 296–297
specifications and tolerances for, 
560–564
in third-order aberration computations, 
328–335
Surveying instruments, 258, 446
Sweatt model, 414–415
Symmetrical eyepieces, 443–444, 509
Symmetrical principle, 401
Synthesis of optical systems (see Optical
systems design)
Systems of separated components, 45–49
T-stops, 153
Tangential coma, 69, 322–323, 358, 417
Tangential curvature of field, 317
Tangential images, 69
Tangential rays and planes, 69
Targets in MTF, 366–367, 375–376
Telecentric stops, 150–151
Telephoto lenses, 467–468, 515
Telephoto ratio, 467
Telescope systems and eyepieces, 251–255, 
439–441, 508
brightness in, 247
diopter adjustment of, 445
erector systems, 445
Erfle eyepieces, 444
Huygenian eyepieces, 441
Kellner eyepieces, 442
magnification, 52
magnifiers, 444–445
objective systems in, 252, 254, 402–413,
445–447
orthoscopic eyepieces, 442–443
power measurements, 251, 253, 259, 
263–267, 585
Ramsden eyepieces, 441–442
Rayleigh limit in, 358
symmetrical eyepieces, 443–444
Temperature:
in blackbody radiation, 232, 234
and telescope objectives, 412
Terrestrial telescopes, 252
Tessar anastigmats, 459, 518
Test plates, 561, 574
Theodolites, 446
Thick lenses:
in Cooke triplets, 422
in design, 435–436
Thickness, 564–565
apparent, 29
of filters, 194
magnification of, 27
Index
615
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Thickness (Cont.):
in paraxial raytracing, 37–38
in unknown optics analysis, 597
Thickness fits, 575
Thin elements, 435
Thin-edged elements, 435
Thin-film computations, 205–209
Thin lenses:
aberration expressions, 428
blur size estimation in, 494, 500
in image formation, 42–43
stop shift equations, 335–345
for telescope objectives, 402–404
Thin prisms, 92–94
Third-order aberrations, 64, 88, 351–352
in Cooke triplets, 422
in diffraction-limited systems, 379–381
in geometric spot size, 362–363
in meniscus camera lenses, 396–398
Rayleigh limit in, 358
in reflecting systems, 479–480
in residual aberrations, 429
surface contribution in, 328–335
thin lenses, 335–345
Third-order theory, 88
35-mm camera objectives, 535
Three-dimensional vision, 131
Three-hole masks, 585–586
Topogon lens, 454
Toroids, 557
Total curvature of thin lenses, 42
Total emissivity, 235–236
Total internal reflection (TIR), 96–97, 
283–284
Transfer equations, 302–303, 305, 309, 311
Transformation temperature in glass, 181
Transmission:
calculations for, 174–175
in radiance of images, 226
Transmitting diffusers, 197–198
Transverse aberrations, 64–66, 322, 358
Transverse magnification, 26
Triangulation rangefinders, 271
Trigonometric correction, 428–429
Trigonometric functions, 301–302
Triplet achromats, 410
Triplets:
with aspheric field correctors, 541
Cooke (see Cooke triplet anastigmats)
Truncation, beam, 166
Tunnel diagrams, 105
Twisting in lens mounting, 579
Two-component systems, 47–49
Ultraviolet region, 2
Undercorrected astigmatism, 70
Undercorrected spherical aberrations, 65
Underspecification, 559–560
Unfolding prisms, 104–105
Unknown optics analysis, 596–599
USAF1951 resolution test target, 593
V-number, 94, 178–179, 183
Variable-power systems, 291–296
Velocity of propagation, 3
Vernier acuity, 131
Vertex length, 424, 456
Viewer lenses, 444–445
Vignetting, 143–147
Virtual images, 10
Visible spectrum, 1
Visual acuity, 128–130
Visual centering, 555
Visual resolution of microscopes, 270–271
Vitreous humor, 126
Waists, 165–168
Warping in lens mounting, 579
Watts, 219
Wave aberration polynomial, 354–355
Wave fronts:
aberration, 79–80, 88–89, 326–327
simple lens and prism affects on, 8–11
Wavelength, 1–3
in blackbody radiation, 232–234
and dispersion, 176
and emissivity, 236
and eye sensitivity, 133–134
in fiber optics, 287
in radiometry, 219
Wide-angle design, 539
Wide-angle lenses, 154
Wide-angle photography, 455
Widely airspaced doublets, 411
Wien’s displacement law, 232, 235
Wind-tunnel applications, 592
Window glass, 183
Wood lenses, 286
Working f-numbers, 152
Wratten filters, 193
Y-ybar diagrams, 55
Ynu raytraces, 34
Young’s experiment, 12–13, 15
Zeiss Protars, 454
Zero-power meniscus elements, 429
616
Index
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Zonal aberrations, 81
in anastigmats, 424
computations for, 322
in diffractive surface design, 416
with point spread functions, 390
Rayleigh limit in, 358
Zonal aberrations (Cont.):
in residual aberrations, 429
in telescope objectives, 
407–409
Zones of pupils, 588–589
Zoom systems, 291–296
Index
617
ABOUT THE AUTHOR
Warren J. Smith, chief scientist at Kaiser Electro-
Optics and an independent consultant, is one of the
most widely known writers and educators in the field
of optical design. He is the author of Modern Optical
Engineering, Modern Lens Design, and Practical
Optical System Layout.
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