I made some simulation to study the change that the heater setup can induce on the Radius of Curvature of the ETM.
**Heat pattern**
First, I used a non-sequential ray tracing software (Zemax) to calculate the heat pattern. I made a CAD of the elliptical reflector and I put a radiative element inside it (similar to the rod-heater 30mm long, 3.8mm diameter that we ordered), placing it in such a way that the heater tip is as close as possible to the ellipse first focus. (figure 1)
Then, by putting a screen at the second focus of the ellipse (where we suppose to place the mirror HR surface), I could find the projected heat pattern, as shown in figure 2 and 3 (section). Notice that the scale is in INCH, even if the label says mm. As you can see, the heat pattern is pretty broad, but still enough to induce a RoC change.
**Mirror deformation**
In order to compute the mirror deformation induced by this kind of pattern, I used this map produced with Zemax as absorption map in COMSOL. I considered ~1W total power absorbed by the mirror (just to have a unitary number).
The mirror temperature and deformation maps induced by this heat pattern are shown in figures 4 and 5.
**RoC change evaluation**
Then I had to evaluate the RoC change. In particular, I did it by fitting the Radius of Curvature over a circle of radius:
where is the waist of tha Gaussian mode on the ETMY (5mm) and *n* is the mode order. This is a way to approximately know which is the Radius of Curvature as "seen" by each HOM, and is shown in figure 6 (the RoC of the cold mirror is set to be 57.37m). Of course, besides being very tiny, the difference in RoC strongly depends on the heat pattern.
**Gouy phase variation**
Considering this absorbed power, the cavity Gouy phase variation between hot and cold state is roughly 15kHz (I leave to the SURFs the details of the calculation).
**Unanswered points**
So the still unaswered questions are:
- which is the minimum variation we are able to resolve with our measurement
- how much heating power do we expect to be projected onto the mirror surface (I'll make another entry on that) |