Detailed analysis of MSE spectra

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Figure 14: Bessel functions J 0 , J 1 , and J 2 . The nominal retardance of the pems is R = π. There is a zero of J 0 at 2.405 and a zero of J 1 at 3.832 so if the actual retardance of one or both pems deviates from the nominal value by about 0.7 we would see unusual ratios of the 22 kHz to 20 kHz. 16
δ (degrees) I 40 /I 20 I 22 /I 20 5 26.8 0.72 30 4.6 0.72 60 2.6 0.72 R MSE (cm) 86.8 3.5 0.029 85.3 4.4 0.023 83.7 3.9 0.024 82.1 4.4 0.036 78.5 4.4 0.018 76.6 5.0 0.059 74.6 5.9 0.086 72.5 7.5 0.15 70.9 7.5 0.21 67.1 2.7 0.16 Table 2: Comparison of expected intensity ratios (for different assumptions about the phase shift imposed by the mirror) to the observed intensity ratio on calibration shot 1030521013. Note that the intensity ratio I 40 /I 20 is matched only if we assume a very large phase shift of order 30 o , whereas from the mirror specs we expect a phase shift of less than a degree or so. However, we observe very little intensity at 22 kHz, e.g. in the outer channels the observed intensity in the 20 kHz component is 25-50 times larger than the 22 kHz component, whereas we expect them to have roughly the same intensity if the pem retardances are at their nominal values, R 1 = R 2 = π. So imperfect mirrors that impose a large phase shift of order 30 o would be consistent with our data only if the retardance is also off. I ω2 = 0. I 2ω1 = (I b + I 0 )J 2 (A 1 )(1 − r m ) 2 √ − I 0J 2 (A 1 )(1 + r m ) 2 2 √ cos(2γ) 2 I 2ω2 = 0. (5) Note that the intensities for ω 1 and 2ω 1 are just the same as when both pem#1 and pem#2 are operating. Also note that there will be a nonzero intensity at frequency ω 1 only if the mirrors introduce a phase shift, i.e. if mirrors were perfect (δ = 0), there would be no intensity at ω 1 . Similarly, we we turn off pem#1, then which yields I net = M p · M P EM2 · M m · S v . (6) 4I net = (I 0 + I b )(1.707r m + 0.2929) +I 0 cos(2γ)(1.707r m − 0.2929) +I 0 sin(2γ)(cos(δ) cos(B) − sin(δ) sin(B)). (7) 17
Page 1 and 2: From: Steve Scott To: Howard Yuh, B
Page 3 and 4: Figure 1: Computed fft spectrum for
Page 5 and 6: Figure 3: fft spectrum for mse oper
Page 13 and 14: Figure 11: Computed ratio of fft am
Page 15: Figure 13: fft spectrum for mse ope
Page 19: Figure 15: fft spectrum for mse ope
Page 22 and 23: Figure 18: fft spectrum for mse ope
Page 24 and 25: Figure 20: fft spectrum for mse ope
Page 26 and 27: Memo #7 computed the effect of impe
Page 28 and 29: Figure 23: Calculated time dependen
Page 30 and 31: Figure 25: Calculated time dependen
Page 32 and 33: Figure 27: Computed ratio of signal
Page 34 and 35: Figure 29: Computed ratio of signal
Page 36 and 37: Figure 31: Calculated ratio of fft
Page 38 and 39: Figure 33: Calculated ratio of fft
Page 40: Now we make use of the expansions c

Detailed analysis of MSE spectra

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