I modified filiters for LSC_MICH and LSC_PRCL.
Although modes we can see at POP and AS look still bad, error signals are less glitchy than I see before (elog #6886).

Measured power recylcing gain for PRMI was 1.6 (??)

Openloop transfer function for LSC_MICH:
  UGF ~130Hz, phase margin ~30 deg
  550 usec delay


APOLOGIES: I forgot "pi" in previous delay calculation. (I put notes on elogs #6940 and #6941)

Openloop transfer function for LSC_PRCL:
  UGF ~130Hz, phase margin ~30 deg
  550 usec delay
  A bump cam be seen in ~200 Hz. Coupling of DOFs?


Beam shape and motion:
   Below left is the Sensoray capture of AS/REFL/POP when PRMI is carrier locked.


  Beam spot motion looks less bouncy than before, but it still shows motion mostly at ~3.3Hz. This might be from PRM motion. Above right is uncalibrated spectra of POPDC and REFLDC. You can see 3.3 Hz peak. This peak has some coherence with PRM motion measured by oplevs. I centered BS/PRM oplev to do this measurement.

Power recycling gain:
 - Definition and designed value
  Power recylcing gain is

G = (PRC intracavity power) / (incident power)

  When MI is perfectly symmetric, this can be written as

G  = (t_PRM/1-r_PRM*r_ITM)**2

  where t_i, r_i is amplitude transmissivity, reflectivity. Inserting the designed values;

 t_PRM = sqrt(0.0575)
 r_ITM = sqrt(1-0.014)

  designed power recycling gain for PRMI is

G = 44

 - Measurement
  POP power when PRM is misaligned and MI is locked at dark fringe is

P_mis = P_in * T_PRM * (1-T_PR3) * (1-T_ITM) * T_PR3

  POP power when PRMI is locked is

P_PR = P_intra * T_PR3

  So,

G = P_intra / P_in = (P_PR / P_mis) * T_PRM * (1-T_PR3) * (1-T_ITM) ~ (P_PR / P_mis) * 0.06

  I measured power of POP using C1:LSC-POPDC_OUT. It was 268 when PRM is misalined and MI is locked at dark fringe. Also, it was ~850 when PRMI is carrier locked. When closing PSL shutter, it was ~246. So,

G_PR = (850-246)/(268-246) * 0.06 = 1.6

  It looks too small.