Optimized heating profile for the CP, when CP and TM are infinitely distant

So far in our simulations for AdVirgo TCS, we always used, as a heating profile, the output of a Zemax simulation involving an AXICON to generate the pattern. In the past, both Vinet and Degallaix, found a different "optimzed" heating pattern to minimize coupling losses (see figure 1). Unfortunately, in both cases, they did not take into account the fact that the heating ring is partially compensating also wave-front distortions (figure 2).

So I set up an iterative linear optimization procedure, with the optical path length as the error signal, to generate a new optimized profile. As a starting point, I used the optical path length given by a test mass heated by the YAG and the ring heater and neglecting the radiative coupling between TM and CP. The procedure runs very fast on Matlab (less than 2 min) and converges very rapidly (circa 80 steps). Figure 3 compares three heating patters: AXICON, Vinet optimized and new optimized. The result is an optical path length which is flat over the whole CP diameter at the level of a few nanometers (figure 4).

Next step is to plug this heating pattern in Ansys to take into account the radiative coupling between CP and TM and see the real performances in terms of coupling losses.