A femtosecond optical frequency comb acts as a ruler in frequency space, with mode frequencies given by

f_m = m f_rep + f₀

where m is an integer. The spacing of the comb modes is equal to the repetition rate of the laser, f_rep, which can be accurately controlled using a microwave standard. Even without any knowledge of the offset frequency f₀, such a comb can be used to measure the difference between two optical frequencies, by observing the beat of each frequency with the nearest comb mode, and counting the number of modes between them.

The absolute measurement of an unknown frequency, however, requires a knowledge of f₀. This offset frequency can be measured by a self-referencing technique, which in its simplest form is illustrated below:

Self-referencing of an octave-spanning optical frequency comb

A mode with frequency f_n = n f_rep + f₀ at the low frequency (red) end of the comb is frequency doubled in a suitable non-linear crystal. If the frequency comb spans a full optical octave (i.e. a factor of two in frequency) then there will be a mode with frequency f_2n = 2n f_rep + f₀ at the high frequency (blue) end of the comb. The beat between this mode and the frequency-doubled mode will be at frequency 2f_n-f_2n, which is exactly the offset frequency f₀.