The
light frequency, f, that we want to determine is
too high to be measured directly. Instead we have
to use an indirect technique by which we compare
the unknown frequency to a measuring stick – the
frequency comb. The comparison between two light
frequencies is made with a beat technique that shows
the difference in frequency low enough to be measured.
We create this
frequency comb by means of a mode-locked laser that
emits a train of very short pulses of light. The laser
light consists of a long series of different frequencies,
like the teeth of a comb. The distance between two
teeth, f_{p}, is determined by the time between the pulses.
What we measure are the beats, f_{b}, between the unknown
light and the closest tooth on the comb. By approximately
determining the optical frequency we can also find
out which tooth lies closest (n=5). For the measurement
to be good, the measuring stick, that is, the frequency
comb, has to be carefully calibrated. Unfortunately,
the first tooth on the comb is not at the frequency
of 0 Hz but at the distance f_{0}. The first three teeth
in the schematically drawn frequency comb (numbered
0, 1 and 2; in practice there can be a million teeth)
contain no light, so a trick is needed to measure
f_{0}. Take the first tooth with light (No. 3) and double
the frequency. It then stands at the distance f0 from
the tooth with twice the number (No. 6), and it is
that distance that can be measured.
We then get the
unknown frequency: f = n · f_{p} + f_{b} + f_{0} |