OPTIMAL BEAM FORMING FOR LASER BEAM PROPAGATION ...

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AcknowledgementFirst and foremost, I would like to thank my advisor Dr. Timothy Schulz, forhis support, guidance, and encouragement in the Ph.D program. He showedme the way to approach research problems and taught me how to express myideas. I am deeply impressed by his inspiring and encouraging way to guideme to a deeper understanding of knowledge. I am grateful for his advise andcomments in this dissertation.I also would like to thank the rest of my thesis committee: Dr. MichaelRoggemann, Dr. Jeffrey Burl, and Dr. Mark Gockenbach, for their kindhelp and valuable comments on this work. Thanks also go to my friends andcolleagues, who give me help and have fun with me. I really enjoy the lifewith them in the beautiful Keweenaw Peninsula.Last, I wish to thank my parents, my sister, and my brother, for theircontinued support and encouragement. I am also very grateful to my wifeLing, for her love and patience during the Ph.D period.v
Page 6 and 7: ContentsAbstractAcknowledgementList
Page 8 and 9: 4.3.1 Averaged kernel for the phase
Page 10 and 11: List of Figures3.1 The scalar diffr
Page 12 and 13: 5.2 Scintillation index for transmi
Page 14 and 15: 5.15 Monte-Carlo simulated performa
Page 16 and 17: 5.6 Optimal weighting α p , scinti
Page 18 and 19: Free space optical communicationsBe
Page 20 and 21: man-made sources such as laser guid
Page 22 and 23: Historically, most of the original
Page 24 and 25: Chapter 2BackgroundBecause of its i
Page 26 and 27: and included the effect of absorpti
Page 28 and 29: agation cases, the experimental dat
Page 30 and 31: the naked eye: bright stars close t
Page 32 and 33: Chapter 3Mathematical ModelsIn this
Page 34 and 35: yields the Huygens-Fresnel diffract
Page 36 and 37: we find that paraxial waves satisfy
Page 38 and 39: withH 0 (x) = 1, and H 1 (x) = 2x.
Page 40 and 41: Figure 3.3: Laguerre Gaussian beams
Page 42 and 43: tion f(⃗r, t) is also an analytic
Page 44 and 45: YYu 1v 1u 2oXXAv 2ZZ = 0Z = dFigure
Page 46 and 47: It has been shown that the cross-sp
Page 48 and 49: process. The fluctuations about the
Page 50 and 51: where κ 0 = 2π/L 0 and κ m = 5.9
Page 52 and 53:
3.5.2 Born approximationIn the Born
Page 54 and 55:
ewritten as∇ 2 ψ s + 2∇ψ 0 ·
Page 56 and 57:
of the inhomogeneous wave equation
Page 58 and 59:
AZAZ(a)(b)Figure 3.5: Turbulence la
Page 60 and 61:
intensity fluctuations:S I = var[I]
Page 62 and 63:
−0.2−0.2−0.1−0.1(meter)0(me
Page 64 and 65:
10.90.80.70.60.50.40.30.20.10−4
Page 66 and 67:
discussed and complete solutions ar
Page 68 and 69:
where 〈H(⃗u 1 , ⃗u 2 )〉 is
Page 70 and 71:
where D φ (⃗u 1 , ⃗u 2 ) is th
Page 72 and 73:
−10.9−10.4(meter)0.500.80.70.60
Page 74 and 75:
equation is correct to all orders i
Page 76 and 77:
This result is not unexpected becau
Page 78 and 79:
the received intensity is|g(v)| 2 =
Page 80 and 81:
4.4.2 Two dimensional experimentAs
Page 82 and 83:
improvement space for it. Short ter
Page 84 and 85:
5.1 Optimal Pupil Plane Mutual Cohe
Page 86 and 87:
intensity are needed:〈〉 I2−
Page 88 and 89:
5.2.1 First moment of the integrate
Page 90 and 91:
optimal pupil plane coherence.It wa
Page 92 and 93:
The term C in the above equation ha
Page 94 and 95:
5.4.1 Scintillation reduction by us
Page 96 and 97:
m I m µ m S m0 0.9249 0.6419 0.130
Page 98 and 99:
N = 1 2 3 4 5 6 7 8α 0 1.0000 0.17
Page 100 and 101:
p ξ p µ p S p0 0.8981 0.6296 0.12
Page 102 and 103:
screen in the pupil plane according
Page 104 and 105:
Scintillation index of single mode0
Page 106 and 107:
0.4r 0= 0.050.8r 0= 0.050.35r 0= 0.
Page 108 and 109:
0.90.80.7r 0= 0.05 mr 0= 0.1 mr 0=
Page 110 and 111:
Physical parameter Symbol Value(s)t
Page 112 and 113:
0.6C n2 = 2x10−16C n2 = 5x10−16
Page 114 and 115:
0.70.6m=1m=2m=3m=40.450.40.35N=1N=2
Page 116 and 117:
3. We have shown that the optimal c
Page 118 and 119:
Appendix AGlossary of SymbolsAa(x)c
Page 120 and 121:
τ Time shift = t 2 − t 1θ Propa
Page 122 and 123:
[8] M. Beran. Propagation of a fini
Page 124 and 125:
[27] R. M. Gagliardi and S. Karp. O
Page 126 and 127:
[45] A. N. Kolmogorov. Turbulence,
Page 128 and 129:
[63] Timothy J. Schulz. Optimal bea
Page 130:
[82] H. T. Yura. Mutual coherence f
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