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Entry  Mon Sep 20 12:20:31 2021, Paco, Summary, SUS, PRM and BS Angular Actuation transfer function magnitude measurements PRM_PIT_ACT_TF.pdfPRM_YAW_ACT_TF.pdfBS_PIT_ACT_TF.pdfBS_YAW_ACT_TF.pdf
    Reply  Mon Sep 20 14:22:00 2021, rana, Summary, SUS, PRM and BS Angular Actuation transfer function magnitude measurements 
       Reply  Thu Sep 23 15:29:11 2021, Paco, Summary, SUS, PRM and BS Angular Actuation transfer function magnitude measurements BS_PRM_ANG_ACT_TF.pdf
          Reply  Fri Oct 1 14:25:27 2021, yehonathan, Summary, SUS, PRM and BS Angular Actuation transfer function magnitude measurements MICH_PRM_-0.34.pngMICH_PRM_-0.1.png
          Reply  Mon Oct 4 16:00:57 2021, Yehonathan, Summary, SUS, PRM and BS Angular Actuation transfer function magnitude measurements BS_PRM_ANG_ACT_TF_20211004.pdfBS_out_mat_20211004.txtPRM_out_mat_20211004.txt
             Reply  Mon Oct 4 16:10:09 2021, rana, Summary, SUS, PRM and BS Angular Actuation transfer function magnitude measurements 
             Reply  Tue Oct 5 20:04:22 2021, Paco, Summary, SUS, PRM and BS Angular Actuation transfer function magnitude measurements 
                Reply  Wed Oct 6 15:39:29 2021, Anchal, Summary, SUS, PRM and BS Angular Actuation transfer function magnitude measurements 
             Reply  Tue Oct 12 11:32:54 2021, Yehonathan, Summary, SUS, PRM and BS Angular Actuation transfer function magnitude measurements modified_output_matrices_radar_plots.pngnormal_output_matrices_radar_plots.png
                Reply  Tue Oct 12 16:39:52 2021, rana, Summary, SUS, PRM and BS Angular Actuation transfer function magnitude measurements 
                   Reply  Thu Oct 14 13:40:49 2021, Yehonathan, Summary, SUS, PRM and BS Angular Actuation transfer function magnitude measurements BSPRM_Actuation_Radar_plots.pngITM_Actuation_Radar_plots.png
Message ID: 16358     Entry time: Thu Sep 23 15:29:11 2021     In reply to: 16345     Reply to this: 16371   16374
Author: Paco 
Type: Summary 
Category: SUS 
Subject: PRM and BS Angular Actuation transfer function magnitude measurements 

[Anchal, Paco]

We had a second go at this with an increased number of averages (from 10 to 100) and higher excitation amplitudes (from 1000 to 10000). We did this to try to reduce the relative uncertainty a-la-Bendat-and-Pearsol

\delta G / G = \frac{1}{\gamma \sqrt{n_{\rm avg}}}

where \gamma, n_{\rm avg} are the coherence and number of averages respectively. Before, this estimate had given us a ~30% relative uncertainty and now it has been improved to ~ 10%. The re-measured TFs are in Attachment #1. We did 4 sweeps for each optic (BS, PRM) and removed the 1/f^2 slope for clarity. We note a factor of ~ 4 difference in the magnitude of the coil to angle TFs from BS to PRM (the actuation strength in BS is smaller).


For future reference:

With complex G, we get complex error in G using the formula above. To get uncertainity in magnitude and phase from real-imaginary uncertainties, we do following (assuming the noise in real and imaginary parts of the measured transfer function are incoherent with each other):
G = \alpha + i\beta

\delta G = \delta\alpha + i\delta \beta

\delta |G| = \frac{1}{|G|}\sqrt{\alpha^2 \delta\alpha^2 + \beta^2 \delta \beta^2}

\delta(\angle G) = \frac{1}{|G|^2}\sqrt{\alpha^2 \delta\alpha^2 + \beta^2 \delta\beta^2} = \frac{\delta |G|}{|G|}

Attachment 1: BS_PRM_ANG_ACT_TF.pdf  59 kB  Uploaded Thu Sep 23 16:38:04 2021  | Hide | Hide all
BS_PRM_ANG_ACT_TF.pdf BS_PRM_ANG_ACT_TF.pdf BS_PRM_ANG_ACT_TF.pdf BS_PRM_ANG_ACT_TF.pdf
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