2
Chapter 1. Introduction
1.1.1 Error signals
The key common feature of feedback control is that the error signal
used for control should reverse sign as the laser frequency shifts
above or below the setpoint, as in figure 1.2. From the error signal,
a feedback servo or
compensator
generates a
control signal
for a
transducer in the laser, such that the laser frequency is driven to-
wards the desired setpoint. Critically, this control signal will change
sign as the error signal changes sign, ensuring the laser frequency
always gets pushed towards the setpoint, rather than away from it.
Error
Error
Frequency
f
Frequency
f
f
0
ERROR OFFSET
∆
f
Figure 1.2:
A theoretical dispersive error signal, proportional to the dif-
ference between a laser frequency and a setpoint frequency. An offset on
the error signal shifts the lock point (right).
Note the distinction between an
error signal
and a
control signal
.
An error signal is a measure of the difference between the actual
and desired laser frequency, which in principle is instantaneous and
noise-free. A control signal is generated from the error signal by
a feedback servo or compensator. The control signal drives an ac-
tuator such as a piezo-electric transducer, the injection current of
a laser diode, or an acousto-optic or electro-optic modulator, such
that the laser frequency returns to the setpoint. Actuators have
complicated response functions, with finite phase lags, frequency-
dependent gain, and resonances. A compensator should optimise
the control response to reduce the error to the minimum possible.
