OPTIMAL BEAM FORMING FOR LASER BEAM PROPAGATION ...

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5.6 Optimal weighting α p , scintillation index S I , and the fractionalaverage integrated intensity µ when the first N Laguerre-Gaussian modes f p,0 (u) are used to generate the optimal pupilplane partially coherence. . . . . . . . . . . . . . . . . . . . . 855.7 Mean square error ɛ 2 of the Monte-Carlo simulation for differentperformance values: µ m , S m and 〈I m I n 〉. . . . . . . . . . . 895.8 Parameters used in the Monte-Carlo simulation of laser beamspropagate through multiple random phase screens. . . . . . . . 94xvi
Chapter 1Introduction1.1 MotivationPropagation of optical waves through random media such as the atmosphere,the ocean, and biological matter, is very important in many applications suchas optical communications and astronomical imaging. In these situations, thetemporally and spatially varying media change the amplitude and phase ofthe propagating optical fields in both time and space. These effects can causeattenuation or loss of the transmitted information and energy.Because of their directionality and high energy concentration, laser beamsare widely used in modern optical communications, remote sensing, and laserweapon systems. The performance of all these systems is limited by turbulenceeffects. Following is an introduction to some important applications ofwave propagation through random medium.1
Page 5 and 6: AcknowledgementFirst and foremost,
Page 7 and 8: 3.2.1 Paraxial waves and Gaussian b
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: List of Tables4.1 Physical paramete
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
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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−
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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
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known fact that planets scintillate
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Chapter 6Summary6.1 ConclusionsIn t
Page 117 and 118:
showed that increasing the receiver
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L m p (x) Laguerre polynomialn Inde
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Bibliography[1] L. C. Andrews and R
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[18] D. deWolf. Strong irradiance f
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[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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