electromagnetic wave propagation in turbulence: evaluation and application of mellin transforms, 2nd...
TRANSCRIPT
This page has been reformatted by Knovel to provide easier navigation.
INDEX
Index Terms Links
A
adaptive optics 4
filter function 83
focal anisoplanatism 80 195
variance 114
Zernike anisoplanatism 188
anisoplanatism
angular 225
beam shape 345
centroid 103
chromatic 228
cone 195
displacement 225
focal
distributed source 200
offset source 204
point source 195
focus 186 195
scintillation 184
Strehl ratio 219
tilt 164
outer scale 314
time delay 226
Zernike 188
annulus
piston
filter function 77
Index Terms Links
This page has been reformatted by Knovel to provide easier navigation.
annulus (Cont.)
variance 153
tilt
filter function 76
variance 153
aperture averaging
filter function 78
Gaussian beam 80
scintillation 176
Appell function 310
asterisk notation 10
asymptotic series
N complex planes 295
complex parameter 253
Poincaré 130
positive parameter 126
asymptotic solutions 126 253 295
atmospheric density 229
B
beam movement 107
beam shape 57 337
anisoplanatism 345
general solution 337
tilt jitter 342
uncorrected turbulence 340
beam wave
filter function 264
phase 261
power spectral density 267
scintillation 261
Index Terms Links
This page has been reformatted by Knovel to provide easier navigation.
Bessel function 10
complex argument 252
integrals 69
modified 260
third kind 12
Born approximation 39
Buckingham’s Pi theorem 27
Bufton wind model 227
C
Cauchy residue theorem 119
N complex planes 284
characteristic sizes
aperture 178
coherence diameter 97
isoplanatic angle 97
source angle 181
tilt anisoplanatism 171
time 227
coherence diameter 97 211
spherical wave 210
convergence of power series 279
convolution
N complex planes 14
one complex plane 13
correlation
beam wave 265
correlation function
density 37
focus 187
inner and outer scale 328
refractive index 37
Index Terms Links
This page has been reformatted by Knovel to provide easier navigation.
covariance function
filter function 55
D
diffraction
tilt 160
diffraction parameter 44
digamma function 133
distributed source 78 176
E
Euler’s constant 133
F
filter function 69
adaptive optics 83
anisoplanatism 54
annulus 75
beam wave 264
covariance function 55
finite aperture 78
focal 78
general formula 51
piston 72
annulus 77
power spectral density 56
beam wave 267
servo 57
single wave 52
tilt 72
annulus 76
Index Terms Links
This page has been reformatted by Knovel to provide easier navigation.
filter function (Cont.)
gradient 75
Zernike modes 71
focal anisoplanatism 195
focus 186
Fourier transform
definition 29
Fox H-function 17 120 123 212
Fresnel number 161
Fried’s coherence diameter 97
G
gamma function
definition 8
duplication formula 9
Gauss-Legendre formula 9
recursion relation 9
residue 8
Stirling’s formula 10
Gauss hypergeometric function
definition 15
examples 22
Gaussian beam
tilt 106
Gaussian beam 41 105
aperture averaging
filter function 80
piston 105
Strehl Ratio 64
Gegenbauer polynomials 220 356 361
generalized hypergeometric function 15
Greenwood frequency 114
Index Terms Links
This page has been reformatted by Knovel to provide easier navigation.
Greenwood spectrum 33
guidestar 195
H
Heaviside function 10
Hesse’s determinant 301
Hill spectrum 33
Horn function 280
Hufnagel-Valley turbulence 96
Huygens-Fresnel approximation 58
hypergeometric function
examples 22
Gauss 15 22
generalized 15
I
incomplete gamma function 96
inner scale 26 33 181 317
correlation function 328
definition 33
scintillation 176
tilt 152 317
intermittency 38
isoplanatic angle 97 225
K
Karhunen-Loève polynomials 74
Kolmogorov spectrum 31
L
Legendre function 220
Index Terms Links
This page has been reformatted by Knovel to provide easier navigation.
log-amplitude 46
log-polar transform 8
M
Macdonald function 12
Maréchal approximation 64
extended 64
Maxwell’s equations 38
Meijer G-function 17 212
Mellin convolution theorem 13
N complex planes 14
Mellin transform
N complex planes 277
definition 7
properties 7
Mellin-Barnes integral 16
complex parameter 251
Miller-Zieske 98
mirages 25
moment
temporal 227
turbulence 96
velocity 114
N
Navier-Stokes equations 27
O
outer scale 33 317
correlation function 328
definition 31
Index Terms Links
This page has been reformatted by Knovel to provide easier navigation.
outer scale (Cont.)
spectrum 33
tilt
Greenwood spectrum 150
von Kármán spectrum 146
turbulence spectrum 31
P
paraxial assumption 42
phase 46
beam wave 261
covariance function 55
piston
annulus 153
Gaussian beam 105
infin ite beams 99
Pochhammer symbol 15
Poincaré series 130
polylogarithm 132
power spectral density
beam wave 267
filter function 56
tilt 172 321
propagation parameter 43
psi function 133
R
Radar effects 26
refractive index 25 229
resolution 211
Reynolds number 28
Index Terms Links
This page has been reformatted by Knovel to provide easier navigation.
Riccati equation 39
Rytov approximation 37
S
scintillation 110
adaptive optics 114
anisoplanatism 184
aperture averaging 176
beam wave 261
covariance function 55
finite apertures 176
finite sources 176
focused beam 112
infinite beam 112
inner scale 181
saturated 38 41
servo system 57
beam wave 267
variance 113
SLCSAT Day turbulence 98
SLCSAT Night turbulence 98
steepest descent 126
N complex planes 296
complex parameter 253
Stirling’s formula 10
Strehl Ratio
Gaussian beam 64
top-hat beam 62
Strehl ratio 57 209
anisoplanatism 219 225
angular 225
chromatic 228
Index Terms Links
This page has been reformatted by Knovel to provide easier navigation.
Strehl ratio (Cont.)
combined effects 232
displacement 225
time delay 226
beam jitter 214
outer scale 213
tilt removed 234
uncorrected turbulence 209
Structure function 84
outer scale 214
structure function 55
density 28
inner and outer scale 328
log-amplitude 55 62
phase 55 62 328
velocity 27
T
Taylor frozen turbulence 56
temporal moment 227
thermal blooming 38
tilt
angle-of-arrival 108
anisoplanatism 164
outer scale 314
annulus 153
collimated 101
diffraction 160
focused 101
Gaussian beam 106
gradient 102
Greenwood spectrum 150
Index Terms Links
This page has been reformatted by Knovel to provide easier navigation.
tilt (Cont.)
inner and outer scale 317
inner scale 152
power spectral density 172
outer scale 321
von Kármán spectrum 146
Zernike 99
top-hat beam 42
transform
Fourier 29
log-polar 8
Mellin 7
trigamma function 133
turbulence
Strehl ratio 209
turbulence models 96
Hufnagel-Valley 96
SLC Day 98
SLC Night 98
turbulence moments 96
full 96
partial 96
turbulence spectra
Greenwood 33
Hill 33
Kolmogorov 31
Tatarski 33
von Kármán 31
modified 33
turbulence strength 28
two-thirds power law 27
Index Terms Links
This page has been reformatted by Knovel to provide easier navigation.
V
velocity moment 114
von Kármán spectrum 31 146
W
wind model 227
Z
Zernike anisoplanatism 188
Zernike modes 70 104
focus 186
piston 72
tilt 72 99