Hang, Gabriele, TVo, Amber, Stefan, Danny
This morning we measured, using the AS_A and AS_B DC SUM, MICH dark and estimate 9 counts with 50 mW CO2 central heating on ITMY and 8000 counts for MICH bright (with no CO2) which leaves us with about 0.1% contrast defect.
We followed up the measurement by estimating the amount of sideband power we could be seeing :
Where P_f is the power of the sidebands of frequency f at the Michelson output, P_o is the input power to the Michelson, Gamma_f is the modulation depth of the sideband of frequency f, and t_f is the amplitude transmission coefficient of the sideband frequency f for the Michelson.
P_9MHz: 3.77*10^(-2) counts (0.4% of what we see when dark)
P_45MHz: 1.3 counts (14.4% of what we see when dark)
Hang and TVo also thought about low frequency movement of the beamsplitter and how this could introduce higher order misalignment modes. We looked at the power spectrum of the beamsplitter oplevs below 0.5 Hz and estimate 10*10^(-9) radians (in both pitch and yaw) is dominant at those frequencies. We estimate the amount of HOM misalignment mode that could be contributing:
Where P_o is the input power to the Michelson, alpha is the beamsplitter misalignment (in rad), w(z) is the beam size at the misaligned optic, and lambda is the wavelength of the carrier. (The factor of 2 is added to include both pitch and yaw)
P_HG01 = 14.4*10^(-2) counts (1.6% of what we see when dark)
The model for differential lensing in a single bounce Michelson contrast defect should be simple conceptually. After the beamsplitter, the phase change that the X and Y beams see is dominated by the prompt reflection off the HR surface of the ITM as well as the double passing static substrate lens from the compensation plate+ITM substrate.
Using the galaxy page numbers:
Converting this to the required ring heater power to get this effect is the along the same lines of logic but the ring heater will change the substrate (double pass) as well as the HR surface (single pass) and of course, because the ring heater is annular heating instead of central, we will want to try this on ITMX ring heater.
We can try to run the ring heater over the weekend as Sheila suggested and see if this improves the Michelson contrast over time. The loops that Hang and Gabriele designed seem to be stable enough to run for many hours.
Correction
The previous estimate of the actuation calibration for the CO2 lasers on the substrate was off by a factor of 3, this was due to the changing out the mask:
Old: 6.23e-5 diopters/watt
New: 2.50e-5 diopters/watt
So the estimate of the CO2 power for the best simple Michelson contrast defect is:
which still fits with our measurement.