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Entry  Fri Jul 6 01:39:56 2012, yuta, Update, Locking, MI + Y arm ALS succeed, but not both FPMIALStrial20120706.pngnewALSMEDMscreen.png
    Reply  Fri Jul 6 14:10:31 2012, yuta, Summary, LSC, calculation of FPMI using ALS 
Message ID: 6931     Entry time: Fri Jul 6 14:10:31 2012     In reply to: 6925
Author: yuta 
Type: Summary 
Category: LSC 
Subject: calculation of FPMI using ALS 

From calculation, phase fluctuation of reflected beam from length stabilized arm is not disturbing MI lock.

Easy calculation:
  The phase PD at AS port sense is

phi = phi_x - phi_y = 2*l_MICH*omega/c + (phi_X - phi_Y)

  where l_MICH is the Michelson differential length change, omega is laser frequency, phi_X and phi_Y are phase of arm reflected beam. From very complicated calculation,

phi_X ~ F/2 * Phi_X

  at near resonance. Where F is arm finesse, Phi_X is the round trip phase change in X arm. So,

phi = 2*l_MICH*omega/c + F/2 * 2*L_DARM*omega/c

  Our ALS stabilizes arm length in ~ 70 pm(see elogs #6835#6858). Finesse for IR is ~450. Considering l_MICH is ~ 1 um, MICH signal at AS port should be larger than stabilized DARM signal by an order of magnitude.

Length sensing matrix of FPMI:
  Calculated length sensing matrix of 40m FPMI is below. Here, I'm just considering 11 MHz modulation. I assumed input power to be 1 W, modulation index 0.1i, Schnupp asymmetry 26.6 mm. PRM/SRM transmissivity is not taken into account.

[W/m]     DARM      CARM      MICH
REFL_I    0         1.69e8    0
REFL_Q    7.09e1    0        -3.61e3
AS_I      0         0         0
AS_Q      1.04e6    0         3.61e3


  Maybe we should use REFL_Q as MICH signal, but since IQ separation is not perfect, we see too much CARM. I tried to lock MI with REFL11_Q yesterday, but failed.

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