P010010-00-R - LIGO - California Institute of Technology

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103 each other, such that a single mode cleaner can be used after modulation but before they are input into the RSE interferometer. Given this design, analytical formulas were derived to generate the matrix of discriminants. These were used, along with the Twiddle model, to derive the matrix of discriminants for the 5 × 5 cross-coupled system. This was done for both the optimized broadband and the 1 kHz narrowband RSE interferometers design in Chapter 2. Variation of the asymmetry was used as a tool to improve the diagonality of the matrix. One positive aspect of this design is that the power and signal cavity submatrix could be diagonalized, with no coupling from the arm cavity degrees of freedom. The Michelson degree of freedom, however, remained strongly coupled with the arm cavity common mode, and so a gain hierarchy needs to be used. Furthermore, in the narrowband interferometer, the Michelson signal port is dominated by signals from both the arm cavity common mode and the signal cavity. It was found that a reasonable double gain hierarchy could be established which did not significantly degrade the performance of the Michelson degree of freedom. Although two designs were “successfully” implemented, the success largely de- pended on using the asymmetry as an optimization tool. In both cases, the optimal coupling asymmetry presented an ill-conditioned matrix, which was subsequently im- proved by increasing the asymmetry. It’s very difficult, however, to quantify this technique. In particular, some cases were found (specifically with Tprm < Tsem) in which variation of the asymmetry did very little to improve the conditioning of the matrix. Clearly, in these types of cases, a much more careful analysis would need to be taken to determine whether some type of gain hierarchy could be established to provide a stable system which provides the necessary performance.
Chapter 4 104 The RSE Tabletop Prototype Experiment An experimental verification of the proposed signal extraction scheme was demon- strated on an RSE interferometer which was prototyped on an optical table. This chapter describes the experiment and its results. Section 4.1 will describe the physi- cal design of the experiment. Section 4.2 describes the conditioning of the laser light for the interferometer, while Section 4.3 describes the characterization of the arm cavities. The RSE interferometer is a very complicated system, and locking it in the desired state is a difficult task. Section 4.4 describes the process through which the interferometer is aligned and finally locked, with some confidence that the interferometer is in the correct state. Section 4.5 reports the data from the locked RSE interferometer, including the matrix of discriminants and the RSE transfer function. 4.1 Prototype Design Figure 4.1 shows the optical layout of the RSE tabletop prototype experiment. The placement of the optics in the figure is fairly close to scale. A brief description of the layout is given here, with a more detailed description of the hows and whys of the various optics, lengths, and other components involved in the following subsections. All of the optics are located on a single optical table, a 5’ by 12’ Newport RS-4000 optical table on Newport I-2000 vibration isolator legs. A free standing clean room cover surrounds the table. The air flow from the HEPA filters in the ceiling of the clean room were turned off for the running of the experiment due to the noise they generated. A patch panel located on the table is the point at which all electronic signals are passed to three racks of electronics and diagnostic equipment (oscilloscopes, spectrum analyzers, etc.). In between the laser and the power recycling mirror (PRM) are all the conditioning
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Signal Extraction and Optical Desig
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Abstract iii The LIGO project is tw
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v Of course, one couldn’t last si
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vii 2.3.2 Optimized Broadband . . .
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ix 5.7.2 Narrowband RSE . . . . . .
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xi 3.11 Signal cavity spectral sche
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xiii D.7 Michelson compensation boa
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xv 4.2 Effective response of the mi
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2 into which a stone has been dropp
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4 but no smoke). These tricks have
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6 At the heart of passive technique
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8 The various terms are defined as
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Pendulum Thermal Noise 10 The test
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12 back-action force on the inciden
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14 Scatter and absorption of coatin
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16 Another feature of signal tuned
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18 A scheme for controlling the fiv
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Laser PD1 PD2 ¦¡¦ ¥¡¥ PRM +
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22 known as the detuning phase. The
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24 cavity induces a phase shift upo
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26 of the first cavity, then for a
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Frequency (Hz) 5000 4000 3000 2000
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0.8 0.6 0.4 0.2 0 −4 φ sec 1 6 5
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the mirror is 32 i2k(l+δl/2 cos(ω
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The shot noise current spectral den
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36 depends on the choice of ITM, up
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38 mirror is calculated based on th
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40 This is not the transmissivity o
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Cavity reflectivity 1 0.9 0.8 0.7 0
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44 For high frequency response, bot
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46 Although this is a tiny signal,
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Strain sensitivity (h(f)/rtHz) 10
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50 sources the interferometer would
Page 67 and 68: Chapter 3 Signal Extraction 52 The
Page 69 and 70: photodiode is proportional to 54 |E
Page 71 and 72: 56 The demodulation phase β = 0 is
Page 73 and 74: 58 to the difference in the rates o
Page 75 and 76: 60 out of the amplitude of the audi
Page 77 and 78: 62 is non-zero. This is the basic f
Page 79 and 80: 64 further to generate the second o
Page 81 and 82: The source amplitude is set by the
Page 83 and 84: 68 of their sum and difference, or
Page 85 and 86: however, is given by 70 φ− = Ω
Page 87 and 88: 72 transmittance is then higher tha
Page 89 and 90: 74 resonance, for both upper and lo
Page 91 and 92: 76 due to the fluctuating length of
Page 93 and 94: 78 the hash marks corresponding to
Page 95 and 96: sensitive to differential signals,
Page 97 and 98: Laser �§�� §� rp
Page 99 and 100: compound mirror. The derivatives of
Page 101 and 102: freedom. 86 N ′ = 1 ∂rc −irc
Page 103 and 104: 88 The φs degree of freedom is qui
Page 105 and 106: care must be applied to this questi
Page 107 and 108: 92 The magnitude likewise doesn’t
Page 109 and 110: 94 Φ+ Φ− φ+ φ− φs Refl 81
Page 111 and 112: 96 10 more than this. With a transm
Page 113 and 114: 98 factor to Φ+, which was ∼ 500
Page 115 and 116: 100 Degree of freedom Residual leng
Page 117: 3.5 Conclusions 102 Designing the R
Page 121 and 122: 106 Two input test masses (ITM) and
Page 123 and 124: 108 a CVI W1-1064 window, AR coated
Page 125 and 126: 110 order diffracted beam. Although
Page 127 and 128: 112 Reflected 81 Reflected 54 Picko
Page 129 and 130: 114 combination of the PRM and SM1
Page 131 and 132: 116 from ETM2 and SM5. A box of ele
Page 133 and 134: 118 output roughly +18 dBm, while t
Page 135 and 136: 120 The reflected powers are used t
Page 137 and 138: 122 Waist size (mm) Waist position
Page 139 and 140: 124 characterized mirrors, alignmen
Page 141 and 142: 126 completely different mixer, and
Page 143 and 144: 128 on with minimal gain and using
Page 145 and 146: 130 for the φ− servo, hand tunin
Page 147 and 148: 132 matrix to imperfections in thes
Page 149 and 150: RF photodiodes L.O. BLP-5 5 MHz low
Page 151 and 152: 136 modeled matrix are the demodula
Page 153 and 154: 138 the dual-recycled Michelson. Th
Page 155 and 156: 140 4.5.3 Gravitational Wave Transf
Page 157 and 158: Relative Magnitude Relative Phase (
Page 159 and 160: 144 an offset can be estimated. The
Page 161 and 162: 146 Many aspects of the process of
Page 163 and 164: 148 the detuned case is more compli
Page 165 and 166: 150 different, and these terms do n
Page 167 and 168: 152 where there (ideally) is no car
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154 equivalent to shot noise, isign
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156 The laser field can be expanded
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Φ+ = φ3 + φ4 Φ− = φ3 − φ4
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160 Eq. (5.15) will then be evaluat
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DC Carrier Term 162 It’s useful t
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164 of interest, then, the noise si
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166 transmissivity terms. Eq. (5.15
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168 match the detuning phase for th
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170 A second subscript, I or Q, wil
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each noise source. 5.7 Analysis 172
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174 the demodulation phase. This is
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176 noise, the frequency noise spec
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Amplitude noise (arb. units) Freque
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180 ferential length RMS fluctuatio
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182 characterizes the fringe width
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A.1.1 Cavity Coupling 184 One of th
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186 A.1.2 Cavity Approximations The
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esonance. 188 rcanti−res. = rf +
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190 where the primed parameters ref
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Magnitude Phase (degrees) 10 0 10
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194 The magnitude of the transmitte
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196 Where As is 1 − Ls, or one mi
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198 The beamsplitter is typically v
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200 closed loop gain of the control
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202 Substitution and some algebra m
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204 Defining the phases for the RF
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Appendix C 206 Cross-Coupled 2 × 2
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208 the coupling due to the second
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to the disturbance at d1. 210 ⎛
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212 The measurement is also assumed
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214 is replaced with a 1 µF capaci
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216 Figure D.2: PZT compensation sc
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Input Test In 1 kΩ 1 kΩ − + 1
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Figure D.10: RF frequency generatio
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Bibliography 226 [1] J. Weber. Dete
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228 [19] Yuk Tung Liu and Kip S. Th
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230 [38] T.T. Lyons, M.W. Regehr, a
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232 [60] J.E. Mason. Noise coupling
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