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Entry  Tue Mar 5 19:37:00 2013, Zach, Optics, Characterization, eLIGO OMC visibility vs. power measurement details eOMC_visibility_3_4_13.png
    Reply  Wed Mar 6 23:24:58 2013, Zach, Optics, Characterization, eLIGO OMC visibility vs. power measurement details TEK00005.PNGTEK00007.PNGeOMC_visibility_3_4_13.pngeOMC_AMTF_vs_power_3_6_13.png
Message ID: 67     Entry time: Tue Mar 5 19:37:00 2013     Reply to this: 68
Author: Zach 
Type: Optics 
Category: Characterization 
Subject: eLIGO OMC visibility vs. power measurement details 

EDIT (ZK): Koji points out that (1 - Ti) should really be the non-resonant reflectivity of the aligned cavity, which is much closer to 1. However, it should *actually* be the non-resonant reflectivity of the entire OMC assembly, including the steering mirror (see bottom of post). The steering mirror has T ~ 0.3%, so the true results are somewhere between my numbers and those with (1 - Ti) -> 1. In practice, though, these effects are swamped by the other errors.

More information about the power-dependent visibility measurement:

As a blanket statement, this measurement was done by exact analogy to those made by Sam and Sheon during S6 (c.f. LHO iLog 11/7/2011 and technical note T1100562), since it was supposed to be a verification that this effect still remains. There are absolutely better ways to do (i.e., ways that should give lower measurement error), and these should be investigated for our characterization. Obviously, I volunteer.

All measurements were made by reading the output voltages produced by photodetectors at the REFL and TRANS ports. The REFL PD is a BBPD (DC output), and the TRANS is a PDA255. Both these PDs were calibrated using a Thorlabs power meter (Controller: PM100D; Head: S12XC series photodiode-based---not sure if X = 0,2... Si or Ge) at the lowest and highest power settings, and these results agreed to the few-percent level. This can be a major source of error.

The power was adjusted using the HWP/PBS combination towards the beginning of the experiment. For reference, an early layout of the test setup can be seen in LLO:5978 (though, as mentioned above, the REFL and TRANS PDs have been replaced since then---see LLO:5994). This may or may not be a "clean" way to change the power, but the analysis should take the effect of junk light into account.

eOMC_visibility_3_4_13.png

Below is an explanation of the three traces in the plot. First:

  • TRANS: TRANS signal calibrated to W
  • REFL_UL: REFL signal while cavity is unlocked, calibrated to W
  • REFL_L: REFL signal while cavity is locked, calibrated to W
  • Psb: Sideband power (relative to carrier)
  • Ti: Input mirror transmission (in power)

Now, the traces

  1. Raw transmission: This measurement is simple. It is just the raw throughput of the cavity, corrected for the power in the sidebands which should not get through. I had the "AM_REF" PD, which could serve as an input power monitor, but I thought it was better to just use REFL_UL as the input power monitor and not introduce the error of another PD. This means I must also correct for the reduction in the apparent input power as measured at the REFL PD due to the finite transmission of the input coupler. This was not reported by Sam and Sheon, but can be directly inferred from their data.
    • trans_raw = TRANS ./ ( REFL_UL * (1 - Psb) * (1 - Ti) )
    • Equivalently, trans_raw = (transmitted power) ./ (input power in carrier mode)
  2. Coupling: This is how much of the power incident on the cavity gets coupled into the cavity (whether it ends up in transmission or at a loss port). Sheon plots something like (1 - coupling) in his reply to the above-linked iLog post on 11/8/2011.
    • coupling = ( REFL_UL * (1 - Ti) - REFL_L ) ./ ( REFL_UL * (1 - Psb) * (1 - Ti) )
    • Equivalently, coupling = [ (total input power) - (total reflected power on resonance) ] ./ (input power in carrier mode)
  3. Visibility: How much of the light that is coupled into the cavity is emerging from the transmitted port? This is what Sam and Sheon call "throughput" or "transmission" and is what is reported in the majority of their plots.
    • visibility = TRANS ./ ( REFL_UL * (1 - Ti) - REFL_L )
    • Equivalently, visibility = (transmitted power) ./ [ (total input power) - (total reflected power on resonance) ]
    • Also equivalently, visibility = trans_raw ./ coupling

The error bars in the measurement were dominated, roughly equally, by 1) systematic error from calibration of the PDs with the power meter, and 2) error from noise in the REFL_L measurement (since the absolute AC noise level in TRANS and REFL_L is the same, and TRANS >> REFL_L, the SNR of the latter is worse).

(1) can be helped by making ALL measurements with a single device. I recommend using something precise and portable like the power meter to make measurements at all the necessary ports. For REFL_L/UL, we can place a beam splitter before the REFL PD, and---after calibrating for the T of this splitter very well using the same power meter---both states can be measured at this port.

(2) can probably be helped by taking longer averaging, though at some point we run into the stability of the power setting itself. Something like 30-60s should be enough to remove the effects of the REFL_L noise, which is concentrated in the few-Hz region in the LLO setup.

One more thing I forgot was the finite transmission of the steering mirror at the OMC input (the transmission of this mirror goes to the QPDs). This will add a fixed error of 0.3%, and I will take it into account in the future.

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