[by everyone involved in IMC commissioning]

This post explains how the two IMC-X and IMC-F channels are generated and calibrated. As of the date of this post, this has been made uniform between the two sites.

NOTES:
- here the term "IMC length" is used to indicate the round trip length (~32 m). Because the IMC is a very squeezed triangle, there is sometimes a tendency to refer to half of this value (~16 m) as "the length of the IMC" (assimilating it to a linear cavity); this has been a source of misunderstanding in the past. Here, the change in half-round trip length is called IMC-X and is equivalent to the displacement of the MC2_M3 optic.
- there may or may not be other filters present in the filter banks cited below. This additional filters are temporary, for testing purpose, or leftovers from old tests, and are supposed to be disabled. Only the filters explicitly mentioned in this post should be engaged for the calibration to work.


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            IMC-X (DAQ channel IMC-X_DQ)
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The displacement of MC2_M3 is read by the OSEMs and recorded as MC2_M3_L_OUT_DQ; however, the sensitivity of the OSEMs is not sufficient to measure the motion of the IMC when locked, so IMC_X needs to be estimated from the lock feedback signal sent to the various MC2 stages. Note that this is independent from how the lock signal is filtered and distributed to the various stages of the suspension.

M1:
M1_LOCK_L goes into the IMC_X_M1 filter bank, where the following filters are enabled:
    "dc_cal": converts counts into displacement at DC (thus including counts->force calibration and the dc value of the force->displacement TF for M1). LLO measured value: 8.2e-13. LHO is using the same value.
    "white": whitening filter to compensate for rounding errors of the digital system. Double zero at 0.2 Hz, double pole at 1 kHz, dc gain = 1.
    "wresg1" and "wresg2": transfer function from "force on M1" to "displacement on M3", assuming the resonant gain damping filter is enabled (as it should be), and normalized to 1 at dc (the dc gain is absorbed in "dc_cal"). Two filters are necessary because the expression is too complex to be represented by a single foton filter.
    "to_um": converts the channel into um for convenience.

M2:
Same as M1 (appropriately replacing M1 with M2), except:
    "dc_cal" value is 1.75e-11 (measured at LLO, copied at LHO)
    "wresg1" and "wresg2" are replaced by a single "wresg" filter, as the expression is simple enough that it doesn't need to be split.

M3:
Same as M2 (appropriately replacing M2 with M3), except:
    "dc_cal" value is 1.75e-9 (measured at LLO, copied at LHO)

IMC-X is obtained by summing the outputs of these three filter banks (IMC_X_M1/M2/M3).

NOTES:
- it is calibrated in um
- remember that it needs to be "de-whitened"


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            IMC-F (DAQ channel IMC-F_OUT_DQ)
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The "fast output" of the common mode board used for IMC locking is digitized and sent into the IMC-F filter bank, where the following filters are enabled:
    "cts2V": to convert ADC counts into volts. Both sites use the value of 0.000610016 V/cts.
    "InvGenFilt":  invert common mode board "generic filter". It is a double pole at 10 Hz, double zero at 100 Hz, 0.5 DC gain (to account for differential output fo the board).
    "VCO": control signal --> frequency shift calibration; it accounts for the VCO gain, an internal filter and the double pass into the AOM. Zero at 40 Hz, pole at 1.6 Hz. DC gain (2*measured VCO gain) is 496900 V/Hz at LLO, and 536604 V/Hz at LHO.
    "tokHz": converts the output in kHz for convenience.

To be "calibrated" in meters and plotted together with IMC-X (MC2 displacement = delta(IMC length)/2), IMC-F needs to be multiplied by 5.85e-14 m/Hz, according to the formula:

delta(IMC-X) = delta(IMC-F)*lambda/(2*FSR)