I trained a deep neural network (DNN) to reconstruct MICH and PRCL degrees of freedom in the PRMI configuration. For details on the DNN architecture please refer to G1701455 or G1701589. Or if you really want all the details you can look at the code. I used the following signals as input to the DNN: POPDC, POP22_Q, ASDC, REFL11_I/Q, REFL55_I/Q, AS55_I/Q.
Gautam took some PRMI data in free swinging and driven configuration:
In contrast to the Fabry-Perot cavity case, we don't have a direct measurement of the real PRCL/MICH degrees of freedom, so it's more difficult to assess if the DNN is working well.
All MICH and PRCL values are wrapped into the unique region [-lambda/4, lambda/4]^2. It's even a bit more complicated than simpling wrapping. Indeed, MICH is periodic over [-lambda/2, lambda/2]. However, the Michelson interferometer reflectivity (as seen from PRC) in the first half of the segment is the same as in the second half, except for a change in sign. This change of sign in Michelson reflectivity can be compensated by moving PRCL by lambda/4, thus generating a pi phase shift in the PRC round trip propagation that compensate for the MICH sign change. Therefore, the unit cell of unique values for all signals can be taken as [-lambda/4, lambda/4] x [-lambda/4, lambda/4] for MICH x PRCL. But when we hit the border of the MICH region, PRCL is also affected by addtion of lambda/4. Graphically, the square regions A B C below are all equivalent, as well as more that are not highlighted:
This makes it a bit hard to un-wrap the resonstructed signal, especially when you add in the factor that in the reconstruction the wrapping is "soft".
The plot below shows an example of the time domain reconstruction of MICH/PRCL during the free swinging period.
It's hard to tell if the positions look reasonable, with all the wrapping going on.
Here's an attempt at validating the DNN reconstruction. Using the reconstructed MICH/PRCL signal, I can create a 2d map of the values of the optical signals. I binned the reconstructed MICH/PRCL in a 51x51 grid, and computed the mean value of all optical signals for each bin. The result is shown in the plot below, directly compared with the expectation from a simulation.
The power signals (POP_DC, AS_DC, PO22_Q) looks reasonably good. REFL11_I/Q also looks good (please note that due to an early mistake in my code, I reversed the convention for I/Q, so PRCL signal is maximized in Q instead than in I). The 55MHz signals look a bit less clear...