Photoacoustic Doppler effect

To be simple, consider a clear medium firstly. The medium contains small optical absorbers moving with velocity vector ${\displaystyle {\vec {v}}}$. The absorbers are irradiated by a laser with intensity modulated at frequency ${\displaystyle f_{0}}$. Thus, the intensity of the laser could be described by:

${\displaystyle I={I}_{0}\left[1+cos\left(2\pi f_{0}t\right)\right]/2}$[2]

Figure 1: Overview of PAD Effect[2]

When ${\displaystyle {\vec {v}}}$ is zero, an acoustic wave with the same frequency ${\displaystyle f_{0}}$ 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 ${\displaystyle {\vec {v}}}$, the angle ${\displaystyle \alpha }$ between the velocity and the photon density wave propagation direction, and the angle ${\displaystyle \theta }$ between the velocity and the ultrasonic wave propagation direction. The frequency shift is given by:

${\displaystyle f_{PAD}=-f_{0}{\frac {v}{c_{0}}}cos\alpha +f_{0}{\frac {v}{c_{a}}}cos\theta }$[2]

Where ${\displaystyle c_{0}}$ is the speed of light in the medium and ${\displaystyle c_{a}}$ 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.[2]

In practice, since ${\displaystyle {\frac {c_{0}}{c_{a}}}\sim 10^{5}}$ and ${\displaystyle v\ll c_{a}}$, only the second term is detectable. Therefore, the above equation reduces to:

${\displaystyle f_{PAD}=f_{0}{\frac {v}{c_{a}}}cos\theta ={\frac {v}{\lambda }}cos\theta }$[2][3]

In this approximation, the frequency shift is not affected by the direction of the optical radiation. It is only affected by the magnitude of velocity and the angle between the velocity and the acoustic wave propagation direction.[2]

This equation also holds for a scattering medium. In this case, the photon density wave becomes diffusive due to light scattering. Although the diffusive photon density wave has a slower phase velocity than the speed of light, its wavelength is still much longer than the acoustic wave.[3]

Figure 2: Average Photoacoustic Doppler Shift vs. Velocity for a Scattering Medium [3]

In the first demonstration of the Photoacoustic Doppler effect, a continuous wave diode laser was used in a photoacoustic microscopy setup with an ultrasonic transducer as the detector. The sample was a solution of absorbing particles moving through a tube. The tube was in a water bath containing scattering particles[2]

Figure 2 shows a relationship between average flow velocity and the experimental photoacoustic Doppler frequency shift. In a scattering medium, such as the experimental phantom, fewer photons reach the absorbers than in an optically clear medium. This affects the signal intensity but not the magnitude of the frequency shift. Another demonstrated feature of this technique is that it is capable of measuring flow direction relative to the detector based on the sign of the frequency shift.[2] The reported minimum detected flow rate is 0.027 mm/s in the scattering medium.[3]

One promising application is the non-invasive measurement of flow. This is related to an important problem in medicine: the measurement of blood flow through arteries, capillaries, and veins.[3] Measuring blood velocity in capillaries is an important component to clinically determining how much oxygen is delivered to tissues and is potentially important to the diagnosis of a variety of diseases including diabetes and cancer. However, a particular difficulty of measuring flow velocity in capillaries is caused by the low blood flow rate and micrometre-scale diameter. Photoacoustic Doppler effect based imaging is a promising method for blood flow measurement in capillaries.

• Photoacoustic spectroscopy
• Photoacoustic imaging in biomedicine
• Photoacoustic tomography
• Doppler effect
• laser Doppler imaging
• Doppler optical coherence tomography