I stepped the RC can temperature to see the response in the laser frequency. This gives a true measure of the thermal time constant of the RC. Its ~4 hours.

Since the RCPID screen now has a setpoint field, I can remotely type in 1 deg steps. The NPRO SLOW actuator locks the NPRO to the RC at long time scales and so we can use C1:PSL-FSS_SLOWDC to measure the RC length. By knowing what the step response time constant is, we can estimate the transfer function from can temperature to frequency noise and thereby make a better heater circuit.

 Does the observed temperature shift make any sense? Well, John Miller and I measured the SLOW calibration to be 1054 +/- 30 MHz / V.

We know that the thermal expansion coefficient of fused silica, alpha = 5.5 x 10^-7 (dL/L)/deg. So the frequency shift ought to be alpha * c / lambda = 155 MHz / deg.

Instead we see something like 110 MHz / deg. We have to take more data to see if the frequency shift will actually asymptote to the right value or not. If it doesn't, one possibility is that we are seeing the effect of temperature on the reflection phase of the mirror coatings through the dn/dT and the thermal expansion of the dielectric layers. I don't know what these parameters are for the Ta2O5 layers.

A more useful measure of the frequency noise can be gotten by just looking at the derivative in the first 30 minutes of the step, since that short time scale is much more relevant for us. Its 0.04 V / hour / (2 deg) =>  860 (Hz/s)/deg.

In the frequency domain this comes out to be dnu/dT = 860 Hz/deg @ 0.16 Hz or dnu/dT = 137 *(1/f) Hz / deg.

Our goal for the reference cavity frequency noise is 0.01 * (1/f) Hz/rHz. So the temperature noise of the can needs to be < 0.1 mdeg / rHz.