Gabriele, Sheila

The message:

We had a look at the upconversion we would expect from the quadratic response of DC readout.  The message is that the large DARM residual at around 3Hz (due to our LSC feedforward) limits our noise near 10Hz, and upconversion around the calibration lines is about a factor of 4 below DARM at 40 Hz. 

Details:

The DCPD photocurrent is proportional to the power on them:

P_DC offset current (20mA),  G_opt is the optical gain (3.3 mA/pm), and x_0 is the darm offset (12 pm).

If we inject a line we expect to see upconversion at the second harmonic, the amplitude of the second harmonic (seen in the DCPDs) over the fundamental should be:

This is the explanation for the upconversion mentioned in alogs 25001 and 21240 .

Since the quadratic term should be small we can approximate the DARM residual, and use it to predict the noise in the DC PDs due to upconversion:

We took the data from a time when I was injecting a 6 Hz line into DARM and made this projection.  The upconversion of the 6 Hz peak predicts the 12 Hz peak well. 

The rms of our DARM residual is dominated by bad feedforward around 3 Hz, this is upconverted and limits our sensitivity at around 10 Hz.  There is also upconversion around the calibration lines that is about a factor of 4 below DARM near 40 Hz.