Photoacoustic Doppler effect

The photoacoustic Doppler effect, as its name implies, is one specific kind of Doppler effect, which occurs when an intensely modulated light wave induces a photoacoustic wave on moving particles with a specific frequency. The observed frequency shift is a good indicator of the velocity of the illuminated moving particles. A potential biomedical application is measuring blood flow. The photoacoustic Doppler effect, as its name implies, is one specific kind of Doppler effect, which occurs when an intensely modulated light wave induces a photoacoustic wave on moving particles with a specific frequency. The observed frequency shift is a good indicator of the velocity of the illuminated moving particles. A potential biomedical application is measuring blood flow. Specifically, when an intensity modulated light wave is exerted on a localized medium, the resulting heat can induce an alternating and localized pressure change. This periodic pressure change generates an acoustic wave with a specific frequency. Among various factors that determine this frequency, the velocity of the heated area and thus the moving particles in this area can induce a frequency shift proportional to the relative motion. Thus, from the perspective of an observer, the observed frequency shift can be used to derive the velocity of illuminated moving particles. To be simple, consider a clear medium firstly. The medium contains small optical absorbers moving with velocity vector v → {displaystyle {vec {v}}} . The absorbers are irradiated by a laser with intensity modulated at frequency f 0 {displaystyle f_{0}} . Thus, the intensity of the laser could be described by: I = I 0 [ 1 + c o s ( 2 π f 0 t ) ] / 2 {displaystyle I={I}_{0}left/2} When v → {displaystyle {vec {v}}} is zero, an acoustic wave with the same frequency f 0 {displaystyle f_{0}} as the light intensity wave is induced. Otherwise, there is a frequency shift in the induced acoustic wave. The magnitude of the frequency shift depends on the relative velocity v → {displaystyle {vec {v}}} , the angle α {displaystyle alpha } between the velocity and the photon density wave propagation direction, and the angle θ {displaystyle heta } between the velocity and the ultrasonic wave propagation direction. The frequency shift is given by: f P A D = − f 0 v c 0 c o s α + f 0 v c a c o s θ {displaystyle f_{PAD}=-f_{0}{frac {v}{c_{0}}}cosalpha +f_{0}{frac {v}{c_{a}}}cos heta } Where c 0 {displaystyle c_{0}} is the speed of light in the medium and c a {displaystyle c_{a}} is the speed of sound. The first term on the right side of the expression represents the frequency shift in the photon density wave observed by the absorber acting as a moving receiver. The second term represents the frequency shift in the photoacoustic wave due to the motion of the absorbers observed by the ultrasonic transducer. In practice, since c 0 c a ∼ 10 5 {displaystyle {frac {c_{0}}{c_{a}}}sim 10^{5}} and v ≪ c a {displaystyle vll c_{a}} , only the second term is detectable. Therefore, the above equation reduces to: f P A D = f 0 v c a c o s θ = v λ c o s θ {displaystyle f_{PAD}=f_{0}{frac {v}{c_{a}}}cos heta ={frac {v}{lambda }}cos heta }