Afterword
From the early ground-and-polished prism facets of glass lighthouse Fresnel lenses
to modern microreplicated flexible Fresnel lenses for solar concentrators, new
applications of prismatic optical components for light control are constantly being
developed. In addition, innovations utilizing single and compound prismatic and
reflective optical components are emerging in the fields of metrology, polarization
control, projection systems, and illumination and display lighting, among others.
Several significant applications which may indicate future trends are:
• In the field of electronic projection, handheld LCOS-, DMD-, and LCDbased “cell phone” projectors (picoprojectors) require compact optical systems.
Large-screen projection displays are being developed using colored laserdiode sources. Complex monolithic optics (CMO) optical engines are being
investigated for digital cinema projectors.
• For screen illumination of large flat-panel LED televisions, there are LED lightguiding optics and new types of color-combining prisms for flat-panel OLED
(organic light-emitting diode) displays.
• In the field of direct-view microdisplays, LED backlighting optics for handheld
devices such as cell phones, digital cameras, and tablet-type personal computers
is an area of continuous development. There are new designs for LCOS-based
near-to-eye (NTE) miniature displays.
• Ranging from observation of the very large to the very small, there are giant
segmented mirror telescopes (GSMTs) and new high-contrast stereo prism
microscopes.
• Beam-shaping prisms are being designed for high-power lasers.
• New-generation Fresnel lens–based solar concentrating photovoltaic systems
(CPVs) are being designed and sold by several manufacturers.
• In the field of machine vision and image processing, multispectral prism-based
smart cameras are being developed.
• Microstructured metamaterial prisms exhibiting negative refractive index are
being fabricated, and applications are being proposed.
The techniques and examples presented in this book were intended to provide
a good background to analyze, evaluate, and understand these types of optical
applications, among others. It is further hoped that the material in this book may
have inspired readers to create novel and useful devices utilizing prismatic and
reflective optical components.
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Index
angular
accuracies, 131
dispersion, 34
annealing, 130
antireflection coatings, 9
aplanatic
prism spectrograph, 152
refractions, 152
aspect ratio, 115, 198
astigmatism, 16, 177
reduction, 177
autocollimator, 131
automated defect inspection, 159
axicon prism, 116
azimuth angle, 80, 89
2D tracking, 258
45-deg Bauernfeind prism, 53
60-deg Bauernfeind prism, 46
90-deg
beam-deviating prism, 28
polarization-rotating prism, 92
total-internal-reflecting prism array,
250
A
Abbe
number, 2
prism, 35
Abbe, Ernst Karl, 35
accumulated phase shift, 85
achromatic
compound beam expander, 113
Fresnel lens, 265
N-prism beam expander, 111
retarder, 77
afocal telescopic system, 161
air-spaced prism pair, 111
Amici prism
double, 97
roof, 40, 131, 137
Amici, Giovanni, 40
anamorphic
beam expander, 107
expansion, 30
prism
magnification, 104
pair, 108
system, 103
B
backlighting, 206, 208
device, 202
Bartholinus, Erasmus, 61
base-angle tolerance, 131
Bauernfeind prism
45-deg, 53
60-deg, 46
beam
combiner, 222
catadioptric, 222, 227
compression factor, 105
compressor, 105
expander, 104, 106
achromatic compound, 113
anamorphic, 107
N-prism, 111
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Index
beam, (continued)
fill fraction, 226
steering, 107
beam-deviating prism, 90-deg, 28
beamsplitter, 222
beam-splitting
coating, 162
film, nonpolarizing, 74
prism, 116
biaxial birefringent polymer layers, 70
binocular
head-mounted display, 159
surgical loupe, 160
birefringence, 61
birefringent
film, 220
polarizing film, 71
blaze
angle, 271
wavelength, 273
blind spot, on-axis, 144
block polishing, 135
Brewster’s angle, 6, 44, 64, 68, 104,
216
Pellin–Broca prism, 37
wedge, 42
Brewster, David, 6
brightness enhancement, 210
film, 210, 213
dual, 217
Broca, André, 36
C
calcite, 61
Cartesian polarizing beamsplitter, 176
wide-angle, 72
catadioptric
beam combiner, 222, 227
Fresnel lens, 261, 267, 270, 271
prism, 113
change in parity, 19
charge-coupled device matrix array,
153
chromatic dispersion, 264, 272
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288
chromosome, 281
clean-up polarizer, 176
close-packed hexagonal array, 248
coaxial output, 99, 105
cold-cathode fluorescent tube, 210
collinear output, 98, 106
wavelength tuning, 99
color-corrected Fresnel zone plate,
274
coma, 16
complex reflection coefficient, 87
compound parabolic
concentrator, 215
reflector, 183
illuminator, 184
compound-wedge Risley-type prism,
144
compression molding, 265
concentration ratio, 258
constant deviation
angle, 37
dispersing prism, 36
critical angle, 7
cube-corner
reflector
hollow, 56
solid-glass, 58
retardance, 80
cumulative dispersion, 109
curved
catadioptric Fresnel lens, 262
linear Fresnel lens, 255, 257
D
deceptive attractors, 127
degree
of freedom, 137
of polarization, 90
depolarization effect, 169
deviation angle, 33, 237, 238
diamond-turning machine, 228
dichroic layer, 165
dielectric optical materials, 3
differential interference contrast, 67
289
diffraction
compensation, 276
efficiency, 273
diffractive
groove period, 271
structure, 271
digital
light processing, 170
projector, 170
micromirror device, 170
direction
angles, 19, 52
cosine, 11, 187
directional output, 202, 203
direct-view
display, 159
system, 47
direct-vision prism, 97
dispersing prism, 33, 152
dispersion equations, 2
divergence angle, 197
double
Amici prism, 97
Dove prism, 44
Fresnel rhomb, 77
Fresnel rhomb polarization rotator,
93
isosceles total-internal-reflecting
prism, 124
refraction, 61
double-pass
laser interferometer, 149
projection, 168
Dove prism, 42, 157
double, 44
roof, 43
rotating, 131
Dove, Heinrich Wilhelm, 42
dual-brightness-enhancement film,
217
dual-element Fresnel lens, 242
dual-grooved Fresnel lens, 273
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Index
E
echelle spectrograph, 137
edge-ray principle, 257, 258, 260, 264
effective
aperture, 56
f /#, 9
electric field vectors, 4
elliptical light guide, 199
ellipticity, 89, 168
entrance aperture
hexagonal, 230
equilateral
prism, 33
triangle-entrance aperture, 228
e-rays, 61
étendue, 183
preservation, 184
evolutionary prism design, 126
exit pupil, 159
experiential design, 124
external reflection, 5
extractor, 196, 202
extraordinary refractive index, 61
eyepiece, 159–161
F
f /#, 9
fabrication
error, 229
methods, 135
of a Penta prism, 135
Fermat’s principle, 1
field of view, 160
figure, 130
film
birefringent, 220
polarizing, 71
brightness-enhancement, 210, 213
dual-brightness-enhancement, 217
multilayer polarizing beamsplitter,
176
multilayer thin, 9
nonpolarizing beam-splitting, 74
reflecting polarizer, 70
turning, 206
Index
fire polishing, 137
Fizeau interferometer, 136
flare reduction, 160
flatness, 130
flexible linear refracting Fresnel lens,
260
fluorescent tube, cold-cathode, 210
four-mirror
90-deg polarization rotator, 94
beam-displacing prism, 25
fourth-order reflection matrix, 25,
125, 189
Fresnel
lens
achromatic, 265
catadioptric, 261, 267, 270, 271
collimator, 240
curved catadioptric, 262
curved linear, 255, 257
doublet, 242, 244, 245
dual-element, 242
dual-grooved, 273
flexible linear refracting, 260
inflatable flexible, 260
meniscus, 248
phase-optimized, 277, 278
planar circular, 248
positive aspheric, 237
reflective, 245
reflective linear, 250
reflector, 247
refractive, 237, 264
total-internal-reflecting, 261, 264
reflection, 4
reflector, linear, 250
rhomb, 76
double, 77
quarter-wave double, 77
rhomb polarization rotator
double, 93
zone plate, color-corrected, 274
Fresnel, Augustin Jean, 4, 76
frustrated total internal reflection, 53,
73, 157
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290
G
Gaussian-light-beam profile, 162
gene, 280
genetic algorithm, 126, 280
geometric
concentration ratio, 257, 259
efficiency, 56
Glan–Foucault prism, 63
Glan–Taylor prism, 64
Glan–Thompson prism, 64
glass cube-corner prism, 126
glass plate, tilted, 13
goniometer, 131
gyroscope, ring-laser, 153
H
half-wave
plate, 176
rhomb retarder, 77
Harting–Dove prism, 42
hemispheric model, 190
hexagonal
aperture, 58
array, close-packed, 248
entrance aperture, 230
high-reflectance surfaces, 9
histogram, 255
hollow
cube-corner reflector, 56
light pipe, 179
homogeneous transformation matrix,
125
I
image contrast, 166, 169
index-matching fluid, 159
indicatrix, 61
inflatable flexible Fresnel lens, 260
injection molding, 137, 265
interference, thin-film, 73
interferometer
Fizeau, 136
laser, 150
Nomarski polarized, 151
polarization, 149
291
Index
internal reflection, 6
intersection coordinate, 13
matrix, 19
inversion, 18
inverting prism, 19
irradiance, 90
isosceles
roof prism, 187
total-internal-reflecting prism, 122
isotropic, 61
liquid crystal polymer plate
compensator, 175
Littrow
30/60/90-deg reflecting prism, 47
laser-dispersion prism, 47
prism, 46
Littrow, Joseph Johann, 46
Littrow-type prism, 104
longitudinal spherical aberration, 16
loupe, binocular surgical, 160
K
Kessler direct-vision prism, 98
kinematic mount, 137
Knoop test, 130
M
MacNeille
pair, 217
polarizing beamsplitter, 175
polarizing beamsplitter cube, 69
stack, 71
master die, 228, 229
material properties, 130
matrix
array, charge-coupled device, 153
fourth-order reflection, 25, 125, 189
homogenous transformation, 125
intersection coordinate, 19
methods for design, 125
system, 28
transposed reflection, 23
meniscus Fresnel lens, 248
meridional plane, 10
merit function, 103
micrometer eyepiece, 132
micromirror, 170
microprismatic
array, 187
light homogenizer, 181
microreplication, 228
microscope, 67
microstructured anisotropic layer, 220
minimum deviation, 34, 101, 243,
255, 260
angle, 119
mirror, roof, 25
moiré pattern, 211
mounting tolerance requirements, 121
L
ladar guidance, 145
laser
diode, 106
interferometer, 150
double-pass, 149
laser-dispersing prism, 44
law of reflection, 17
LCD projection displays, 166
least-squares fit, 243
LED light source, 278
left handedness, 90
Leman prism, 27
Leman–Sprenger prism, 27
light
pipe, 179, 195
transporter, 196
tube, 197
light-directing total-internal-reflecting
prism, 171
light-guide luminaire, 202
light-guiding prism, 158
linear
Fresnel reflector, 250
scanner, 146
linear-focus solar concentrator, 250
liquid crystal on silicon
imager, 160, 173
spatial-light modulator, 166
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Index
multilayer
polarizing beamsplitter film, 176
thin films, 9
multipass optical cell, 150
multiprism dispersive compressors,
109
N
negative
dispersion, 101
group velocity dispersion, 101
uniaxial calcite, 61
Nicol prism, 61
Nicol, William, 61
Nomarski
polarized interferometer, 151
prism, 67
Nomarski, Georges, 67
nonbirefringent glass, 72
noncubic polarizing beamsplitter, 167
nonkinematic mount, 137
nonpolarizing beam-splitting film, 74
nonsequential ray tracing, 180, 191
normalized
output, 203
transmission, 191
numerical aperture, 168, 183
O
OASIS coating, 53
oblique rays, 10
occlusions, 130
off-axis rear projection, 265
on-axis blind spot, 144
optical
cell, multipass, 150
disk reader, 155
lighting film, 195
path distance, 116
o-rays, 61
ordinary refractive index, 61
orientation of viewed images, 18
orthogonal output, 104
overhead projector, 226, 242, 245,
262, 273
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292
P
paraxial approximation, 143
Pechan
prism, 53, 124, 126
roof prism, 54
Pellin, Phillippe, 36
Pellin–Broca prism, 36, 124
Penta prism, 38, 124, 125, 131, 135
phase
conjugate mirror, 149
difference, 155
quadrature, 149
shifter, 43
phase-coated total-internal-reflecting
retarders, 80
phase-compensation coating, 89
phase-correction coating, 55
phase-optimized
coating, 159
Fresnel lens, 277, 278
phase-shift
coating, 169
compensating coatings, 173
phase-shifting prism, 116
Philips prism, 165, 166
photoreplication, 221, 265
Pierre de Fermat, 1
planar
circular Fresnel lens, 248
polarization converter, 227
plane of incidence, 1
polar tracking, 259
polarization
beamsplitters, wire-grid, 178
converter, 75, 226
ellipse, 76
interferometer, 149
pupil map, 78
recycling, 219
rotating prism, 90-deg, 92
rotation, 167
rotator, four-mirror 90-deg, 94
wavelength shift, 170
polarization-preserving prism, 82
293
polarized backlight, 219
polarizer, wire-grid, 72, 177
polarizing beamsplitter, 159
Cartesian, 176
cube, 68
wire-grid, 73
film, multilayer, 176
MacNeille, 175
noncubic, 167
wide-angle Cartesian, 72
wire-grid, 178
Porro prism, 40
Type I, 41
Type II, 41
Porro, Ignazio, 40
Porro–Abbe prism, 41
positional mountings, 138
positive
aspheric Fresnel lens, 237
dispersion, 101
p-polarized light, 4, 64
prepolarizer, 159, 178
pressed-glass optical prism, 137
primitive sections, 127
principal
axis, 61
plane, 61
section, 65
prism
45-deg Bauernfeind, 53
60-deg Bauernfeind, 46
90-deg beam-deviating, 28
90-deg polarization-rotating, 92
Amici
double, 97
roof, 40, 131, 137
array, 90-deg
total-internal-reflecting, 250
axicon, 116
beam-splitting, 116
Brewster’s-angle Pellin–Broca, 37
catadioptric, 113
design, evolutionary, 126
direct-vision, 97
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Index
dispersing, 33, 152
constant deviation, 36
double isosceles
total-internal-reflecting, 124
Dove, 42, 157
double, 44
roof, 43
rotating, 127, 131
equilateral, 33
four-mirror beam-displacing, 25
Glan–Foucault, 63
Glan–Taylor, 64
Glan–Thompson, 64
glass cube-corner, 126
Harting–Dove, 42
isosceles
roof, 187
total-internal-reflecting, 122
Kessler direct-vision, 98
laser-dispersing, 44
Leman, 27
Leman–Sprenger, 27
light-directing
total-internal-reflecting, 171
Littrow, 46
30/60/90-deg reflecting, 47
laser-dispersion, 47
reflecting, 124
Littrow-type, 104
magnification, anamorphic, 104
Nicol, 61
Nomarski, 67
pair
air-spaced, 111
anamorphic, 108
refracting/total-internalreflecting,
113
Pechan, 53, 124, 126
roof, 54
Pellin–Broca, 36, 124
Penta, 38, 125, 131, 135
Philips, 165
polarization-preserving, 82
Index
prism, (continued)
Porro, 40
Type I, 41
Type II, 41
Porro–Abbe, 41
pressed-glass optical, 137
quality, 130
reflective dispersing, 98
reflector,solid-glass cube-corner, 58
reversion, 125
rhomboid, 127
right-angle, 39, 161
Risley, 144
Risley-type
compound-wedge, 144
roof, 54
rotationally symmetric, 116
Schmidt, 49
Schmidt–Pechan, 54
sections, right-angle, 124
spectograph, aplanatic, 152
spectroscope, 35
Sprenger–Leman, 27
switch, 153
system, anamorphic, 103
three-mirror beam-displacing, 21
total-internal-reflecting, 113
double isosceles, 124
light directing, 171
trichroic separation, 165
wedge, 107, 155
anamorphic compressor, 107
as scanners, 143
Wollaston, 66, 125, 150, 151
x-cube, 168
prismatic
hollow light guide, 195, 197
sheets, 187
prism-based readout, 154
pyramidal
angle tolerance, 131
error, 133
faceted scanner, 141
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294
Q
QuadCubeTM architecture, 174
quarter-wave
double Fresnel rhomb, 77
retarder, 175, 227
rhomb retarder, 77
R
randomly polarized light, 89
ray tracing, nonsequential, 191
readable image, 19
rear-projection displays, 264
reflecting
Littrow prism, 124
polarizer
film, 70, 217
sheet, 220, 228
reflection
and translation of skew rays, 17
coatings, 9
coefficient, complex, 87
phase shifts, 7
reflective
axicon, two-piece, 87
dispersing prism, 98
Fresnel lens, 245
LCD imager, 166, 174
linear Fresnel lens, 250
reflector, hollow cube-corner, 56
refracting/total-internal-reflecting
prism pair, 113
refraction
and translation of skew rays, 10
matrix, 24, 187
refractive
Fresnel lens, 237, 264
index, 1
extraordinary, 61
ordinary, 61
relative phase shift, 8, 85
retarded stack filter, 176
retarder, 75
achromatic, 77
quarter-wave, 175, 227
295
Index
retrace interval, 141
retroreflection, 191
efficiency, 57
reversion, 19
prism, 125
rhomb retarder
half-wave, 77
quarter-wave, 77
rhomboid prism, 127
right handedness, 90
right-angle prism, 39, 161
sections, 124
right-handed image, 19
ring-laser gyroscope, 153
Risley prism, 144
scan patterns, 144
Risley-type prism
compound-wedge, 144
Risley-type prism, compound-wedge,
144
Rochon, Alexis Marie, 67
roof
Dove prism, 43
mirror, 25
prism, 54
Amici, 40, 131, 137
array, 190
array, 90-deg, 192
isosceles, 187
rotating
Dove prism, 127, 131
refracting square plate, 146
rotationally symmetric prism, 116
semiconductor laser light source, 155
semikinematic mount, 137
Sherman-type prism, 98
sidelighting, 213
skew rays, 10
reflection and translation of, 17
refraction and translation of, 10
skew-ray depolarization, 166, 175
Snell, Willebrord, 1
Snell’s law, 1
solar
collimation acceptance angle, 258
concentrator, 250
linear-focus, 250
furnace, 248
simulator, 248
solar-energy concentration, 248
solid light pipe, 180
solid-glass cube-corner reflector, 58
spatial coherence length, 276
spectograph, aplanatic prism, 152
spherical aberration, longitudinal, 16
spinner, 141
s-polarized light, 4, 64
spot-focus concentrator, 253
Sprenger–Leman prism, 27
square plate, rotating refracting, 146
Stokes parameters, 89–91
Stokes, George Gabriel, 89
stress birefringence, 130
striae, 130
surface quality, 130
system matrix, 28, 189
S
sagittal
plane, 16
ray, 52
Schmidt prism, 49
Schmidt, Bernhardt Woldemar, 49
Schmidt–Pechan prism, 54, 160
scratch and dig standard, 130
sectional element, 122
T
tabletop lectern projector, 127
tangential
plane, 15
ray, 50
telescopic laser range finders, 161
test plate, 130
thermal environment, 121
thin-film interference, 73
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Index
three-mirror beam-displacing prism,
21
tilted glass plate, 13
total internal reflection, 6
frustrated, 53, 157
phase changes, 76
total-internal-reflecting
deviator, 122
extractor, 208
Fresnel lens, 261, 264
prism, 113
array, 90-deg, 250
double isosceles, 124
isosceles, 122
light-directing, 171
retarders, phase-coated, 80
touch switch, 157
transmissive extractor, 207
transport
efficiency, 198
factor, 198
transposed reflection matrix, 23
trapezoidal
microprism, 208
prism, 161
triangular aperture cube-corner, 57
trichroic separation prism, 165
tunnel
diagram, 30, 43
integrator, 179
turning film, 206
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296
two-piece reflective axicon, 87
Twyman-Green interferometer, 133,
137
Type I Porro prism, 41
Type II Porro prism, 41
U
uniaxial stretching, 70
V
variable achromatic beam deviator, 39
virtual image display, 267
W
wavelength-compensation plates, 167
wedge prism, 107, 155
anamorphic compressor, 107
as scanners, 143
wet out, 212
wide-angle Cartesian polarizing
beamsplitter, 72
wire-grid
polarizer, 72, 159, 177
polarizing beamsplitter, 178
cube, 73
Wollaston prism, 66, 125, 150, 151
Wollaston, William Hyde, 66
X
x-cube prism, 168
ν-number, 2
Dennis F. Vanderwerf has been involved in the fields of optics
and optical engineering for over 35 years. He has held technical
positions at the Roswell Park Cancer Institute, Buffalo, New
York, the NASA John H. Glenn Research Center, Cleveland,
Ohio, and the 3M Company in St. Paul, Minnesota and Austin,
Texas. He has worked in the areas of crystallography, solar
radiometry, flow visualization optics, optical solar concentrator
design, lens and projection systems optical design, new product
development, quality assurance, and intellectual property management. He has
received the NASA Apollo Achievement Award and the 3M Corporate Circle of
Technical Excellence Award. He holds a BS in physics from Canisius College,
Buffalo, New York, an MS in physics from Ohio State University, Columbus,
Ohio, and an MBA from the University of St. Thomas, St. Paul, Minnesota.
He has numerous optical journal, trade magazine, and conference proceedings
publications, and is a named or sole inventor on 29 U.S. patents in the fields of
optics and optical design. His current interests lie in scientific writing, novel optical
technology applications, and science and math education. Dennis F. Vanderwerf
resides in Austin, Texas.
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