Summary

I calibrated the JAC WFS A/B RF signals into the complex misalignment amplitude at the JAC waist, using four angular calibration lines at 62 W (measurement of Aug 14). The sensing matrix agrees with the one measured on Aug 12 and with the layout. Converting the two WFS signals into the real and imaginary parts of the misalignment (δ^r = lateral shift at the waist, δⁱ = tilt), the displacement part dominates by a factor of 4–5, which is consistent with the dominant jitter source being the PSL which is far (~90 deg of Gouy phase) from the JAC waist.

One question remains: the locked WFS DC does not sense on the plane 90 deg from the RF where it should; the unlocked DC does. Second-order modes are the prime suspect and analysis ongoing.

1. Measurement

With the cavity locked at 62 W we injected four angular calibration lines and recorded WFS A and B (RF I/Q of all segments, and the DC segments). The raw spectra are in wfs_spectra_0814.png. Three records were taken: all lines on ("LAline"), length lines only ("Lline"), and no lines ("noline"), plus a dark record for the sensor floor. The line list is as follows:

The length lines are not for this post: they provide the demodulation reference for the double-demodulation signal, to be reported separately.

2. Sensing matrix in the actuator basis

From the heights of the four lines in each sensor we built the two 2x2 sensing matrix (actuator basis). The sensing-matrix vector figure is wfs_sensing_vectors_0814.png; it also carries the same measurement taken on Aug 12 and the layout-model prediction. The two measurement days agree very well. The model deviates by a few degrees per head (up to ~10 deg, table below), which we do not worry about, since WFS placement uncertainties and the actuators' own Gouy-phase uncertainties are of this order.

3. Sensor Gouy phases and the delta plane

The delta plane is the complex amplitude of the TEM10/01 content referenced at the JAC waist (accumulated Gouy phase = 0 there): the real axis is the waist lateral shift, the imaginary axis the tilt. An actuator kicking by an angle at accumulated Gouy phase η_a drives this amplitude with phase i·e^iηa; a sensor reads the projection of the amplitude onto its own axis.

Actuator parameters taken from the layout model (accumulated Gouy referenced to the JAC waist):

Solving each head's sensing axis from its response to the two actuators of its plane:

The actuator vectors and sensor axes on the delta plane are drawn in wfs_delta_plane_0814.png.

4. Calibrated input jitter

With these calibration I got the main plot(wfs_delta_spectra_0814.png.)  The two WFS signals inverted into the calibrated complex misalignment at the JAC waist, δ^r (lateral shift) and δⁱ (tilt).

• δ^r dominates δⁱ by 4–5x. This makes sense: the dominant jitter source is the PSL, in air and far away (about 90 deg of Gouy phase), so its angular jitter, entering as i·e^iη, lands on the real (displacement) quadrature.
• The structures above 100 Hz are coherent with the PSL periscope accelerometers, so they are caused by the PSL periscope.
• The broad bump below 10 Hz is most likely caused by air convection inside the PSL enclosure.
• The WFS picks up only about 5% of any post-JAC jitter (to be reported separately), so what is shown here is essentially the input jitter.

5. the locked DC

Calibrating the WFS DC the same way should give a sensing plane rotated 90 deg from the RF: the RF reads the tilt-like quadrature at its axis, the DC reads the beam position. But actually, tt does not. In wfs_sensor_gouy_states_0814.png the cyan/orange lines (locked-DC sensing axes) should lie on the blue/red dash-dotted lines (the RF axes rotated by 90 deg), but  they point 30–70 deg away. The same solve on an unlocked, clean beam lands within about 10 deg of the expectation, so the sensors themselves are fine: something in the locked field is doing it, and the second-order (mode-mismatch) content is strongly suspected.

The analysis of this signal is in progress and will be posted shortly. Stay tuned.