ABSTRACT
The Doppler effect is named after the Austrian scientist Christian Doppler, who first noticed the effect in relation to the apparent change in pitch of sound waves that were emitted first from a stationary source and then from the same source but now in motion relative to the listener. His early experiments apparently involved placing musicians armed with brass instruments onto a moving railway bogey and asking them to play a fixed note whilst approaching and then passing a platform on which listeners were stationed. The effect is also readily audible to the casual listener who listens to the change of pitch of an ambulance siren or similar; the pitch audibly drops when the vehicle passes by and begins to recede from the listener. Essentially the same effect occurs with light waves, namely that the optical frequency increases (i.e. the wavelength falls) when a source of light approaches an observer and conversely the optical frequency falls (i.e. wavelength increases) when it recedes. Although some modifications to the basic theory of optical Doppler shifts were made by Einstein in his Special Theory of Relativity, the corrections are not of practical importance when applied to everyday situations, and so Doppler’s original formula remains valid; namely, that if light of frequency f0 and wavelength λ is reflected (i.e. backscattered) from a moving object whose speed, along the line of sight is V, then the frequency f of the backscattered light will be changed to
(1)
where V is positive if the object is approaching the observer and negative if it is receding. The optical carrier frequency f0 is of the order 10
16 Hz. Typical values of 2V/λ in a clinical setting are about 104Hz and so the fractional change in frequency is very
f = f0 + fDoppler = f0 + 2V λ
small. Laser Doppler techniques, including D-OCT, thus rely on the generation of a beat-frequency 2V/λ, by mixing the Doppler-shifted signal with a reference signal of frequency f0. In conventional LDF, this reference signal is often derived from backscattering from static cells within the tissue itself; in D-OCT the signal is generated in the reference arm of the interferometer. In both cases an optical detector then produces an output signal that oscillates at the Doppler frequency 2V/λ.
