OPTIMAL BEAM FORMING FOR LASER BEAM PROPAGATION ...

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ContentsAbstractAcknowledgementList of FiguresList of Tablesivvxivxvi1 Introduction 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Research Goals . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Dissertation Organization . . . . . . . . . . . . . . . . . . . . 72 Background 82.1 Reasons for Optical Disturbance in Random Medium . . . . . 82.2 Waves in Random Media . . . . . . . . . . . . . . . . . . . . . 112.3 Turbulence Effects on Beam Propagation . . . . . . . . . . . . 122.4 Adaptive Optics . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Mathematical Models 163.1 Scalar Diffraction in Homogeneous Medium . . . . . . . . . . 163.2 Optical Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . 19vi
3.2.1 Paraxial waves and Gaussian beam . . . . . . . . . . . 193.2.2 Hermite-Gaussian beams . . . . . . . . . . . . . . . . . 213.2.3 Laguerre-Gaussian beams . . . . . . . . . . . . . . . . 223.3 Optical Coherence . . . . . . . . . . . . . . . . . . . . . . . . 253.3.1 Mutual coherence function . . . . . . . . . . . . . . . . 253.3.2 Propagation of coherence . . . . . . . . . . . . . . . . . 283.3.3 Coherent mode representation . . . . . . . . . . . . . . 293.4 Statistical Model of Atmospheric Turbulence . . . . . . . . . . 303.4.1 Kolmogorov turbulence model . . . . . . . . . . . . . . 313.4.2 Power spectrum of refractive index fluctuations . . . . 323.5 Wave Propagation through Turbulence . . . . . . . . . . . . . 343.5.1 Inhomogeneous wave equation . . . . . . . . . . . . . . 343.5.2 Born approximation . . . . . . . . . . . . . . . . . . . 363.5.3 Rytov approximation . . . . . . . . . . . . . . . . . . . 373.5.4 Extended Huygens-Fresnel principle . . . . . . . . . . . 393.5.5 Turbulence layer model . . . . . . . . . . . . . . . . . . 413.6 Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . 423.6.1 Maximization of the integrated intensity . . . . . . . . 433.6.2 Minimization of the scintillation index . . . . . . . . . 434 Optimal Beam to Maximize the Integrated Intensity 454.1 Optimal Beam in Free Space . . . . . . . . . . . . . . . . . . . 494.2 Optimal Beam to Maximize the Average Integrated Intensity . 504.3 Averaged Kernel in Turbulence . . . . . . . . . . . . . . . . . 52vii
Page 5: AcknowledgementFirst and foremost,
Page 9 and 10: 6 Summary 996.1 Conclusions . . . .
Page 11 and 12: 4.2 Airy pattern: (a)Normalized Air
Page 13 and 14: 5.9 Monte-Carlo simulation by trans
Page 15 and 16: List of Tables4.1 Physical paramete
Page 17 and 18: Chapter 1Introduction1.1 Motivation
Page 19 and 20: eam due to turbulent media can, how
Page 21 and 22: the effects of refraction and diffr
Page 23 and 24: strate evident reduction of scintil
Page 25 and 26: are the most important causes of al
Page 27 and 28: mal blooming can be ignored and the
Page 29 and 30: centroid is caused by large eddies
Page 31 and 32: optics systems for laser beam contr
Page 33 and 34: YYouXθvXAZZ = 0Z = dFigure 3.1: Th
Page 35 and 36: When the propagation distance d is
Page 37 and 38: wherew(z) = w 0[1 +( zz 0) 2] 1/2,
Page 39 and 40: Figure 3.2: Hermite Gaussian beams
Page 41 and 42: 3.3 Optical CoherenceThe optical co
Page 43 and 44: where F (⃗r, ν) is the Fourier t
Page 45 and 46: from finite surfaces with small dif
Page 47 and 48: 3.4.1 Kolmogorov turbulence modelKo
Page 49 and 50: structure function of refractive in
Page 51 and 52: The wave number k(⃗r) can be expr
Page 53 and 54: An iterative method can then be tak
Page 55 and 56: We then get( ) aψ s (⃗r) = χ +
Page 57 and 58:
It can be seen that the ensemble av
Page 59 and 60:
3.6.1 Maximization of the integrate
Page 61 and 62:
Chapter 4Optimal Beam to Maximize t
Page 63 and 64:
A with aperture function⎧⎪⎨ 1
Page 65 and 66:
4.1 Optimal Beam in Free SpaceThe m
Page 67 and 68:
−0.132.5−0.052u’ (meter)01.51
Page 69 and 70:
plane as∫ z+∆zφ(⃗u) = k n(
Page 71 and 72:
−0.132.5−0.052u’ (meter)00.05
Page 73 and 74:
formh(⃗v, ⃗u) = 1 (jλd exp j 2
Page 75 and 76:
The transverse coherence length has
Page 77 and 78:
models - extended Heygens-Fresnel p
Page 79 and 80:
21.8free spaceturbulence10.91.60.81
Page 81 and 82:
2.5free spaceturbulence10.920.80.71
Page 83 and 84:
Chapter 5Optimal Beam to Minimize t
Page 85 and 86:
and the corresponding received inte
Page 87 and 88:
following two sections, we will dis
Page 89 and 90:
where Γ(⃗u 1 , ⃗u 2 ) = 〈φ(
Page 91 and 92:
intensity can be expressed as∫∫
Page 93 and 94:
5.4 Selection of coherent modesThe
Page 95 and 96:
m = 0m = 1m = 2222000−2−2−2
Page 97 and 98:
Scintillation Index0.140.130.120.11
Page 99 and 100:
p = 0p = 1p = 2420−2420−2420−
Page 101 and 102:
N 1 2 3 4 5 6 7 8α 0 1.0000 0.1177
Page 103 and 104:
120100TheoreticalSimulation1.21Theo
Page 105 and 106:
Scintillation Index0.40.350.30.250.
Page 107 and 108:
Scintillation index of single mode0
Page 109 and 110:
0.90.80.7r 0= 0.05 mr 0= 0.1 mr 0=
Page 111 and 112:
0.6C n2 = 2x10−16C n2 = 5x10−16
Page 113 and 114:
known fact that planets scintillate
Page 115 and 116:
Chapter 6Summary6.1 ConclusionsIn t
Page 117 and 118:
showed that increasing the receiver
Page 119 and 120:
L m p (x) Laguerre polynomialn Inde
Page 121 and 122:
Bibliography[1] L. C. Andrews and R
Page 123 and 124:
[18] D. deWolf. Strong irradiance f
Page 125 and 126:
[36] A. Ishimaru. Flucturations of
Page 127 and 128:
[54] C. Primmerman and D. Fouche. T
Page 129 and 130:
[73] V. I. Tatarski. Waves Propagat
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