The ALS error (i.e. phase tracker output) is linear everywhere, but noisy.
The 1/sqrt(TR) is linear and less noisy but is not linear at around the resonance and has no sign.
The PDH signal is linear and further less noisy but the linear range is limited.
Why don't we combine all of these to produce a composite error signal that is linear everywhere and lessnoisy at the redsonance?
This concept was confirmed by a simple mathematica calculation:
The following plot shows the raw signals with arbitorary normalizations
1) ALS: (Blue)
2) 1/SQRT(TR): (Purple)
3) PDH: (Yellow)
4) Transmission (Green)
The following plot shows the preprocessed signals for composition
1) ALS: no preprocess (Blue)
2) 1/SQRT(TR): multiply sign(PDH) (Purple)
3) PDH: linarization with the transmission (If TR<0.1, use 0.1 for the normalization). (Yellow)
4) Transmittion (Green)
The composite error signal
1) Use ALS at TR<0.03. Use 1/SQRT(TR)*sign(PDH)*(1TR) + PDH*TR at TR>0.03
2) Transmittion (Purple)
