Doppler principle
Nico A.M. Schellart, Dept. of Med. Physics, AMC

Basic principle

The Doppler effect, discovered by Christian Doppler in 1842, is the apparent change in frequency (and wavelength) of a wave that is perceived by an observer moving relative to the source of the waves. The waves can be electromagnetic (visible light, X-ray, radio-waves, gamma, etc.), sound waves, gravity waves, surface waves at a liquid (water) etc. For sound waves, the velocity of the observer and the source are reckoned relative to the transmitting medium.

Fig. 1 Sound waves emanating from an ambulance moving to the right.

The total Doppler effect results from either motion of the source or motion of the observer. Each of these effects is analyzed separately. For waves which do not require a medium (such as light) only the relative difference in velocity between the observer and the source needs to be considered. Fig. 1 visualizes how the sound of an ambulance are compressed (perceived frequency increase) in front of the ambulance and ‘diluted’ (frequency decrease) behind it.

Remind that the frequency of the sounds that the source emits does not actually change.

The following analogy helps to understand the Doppler principle. Someone throws one ball every second in your direction. Assume that balls travel with constant velocity. If the thrower is stationary, you will receive one ball every second. However, if he is moving towards you, you will receive balls more frequently than that because there will be less spacing between the balls. The converse is true if the person is moving away from you. So it is actually the wavelength, which is affected; as a consequence, the perceived frequency is also affected.

If the moving source is emitting waves through a medium with an actual frequency f₀, then an observer stationary relative to the medium detects waves with a frequency f given by:

(1)

where c is the speed of the waves in the medium and v_s is the speed of the source with respect to the medium (negative if moving towards the observer, positive if moving away), with the observer on the pathway of the source (radial to the observer). With v_s is<<c and Δf, the frequency shift, is f−f₀, and applying (1) Δf is:

(2)

A similar analysis for a moving observer and a stationary source yields the observed frequency (the observer's velocity being represented as v_o):

(3)

A stationary observer perceives the moving ambulance siren at different pitches depending on its relative direction. The siren will start out higher than its stationary pitch, slide down as it passes, and continue lower than its stationary pitch as it recedes from the observer. The reason the siren slides is because at the moment of passing there is some distance between the ambulance and you. If the siren approached you directly, the pitch would remain constant (as v_s is only the radial component) until the vehicle hit you, and then immediately jump to a new lower pitch. The difference between the higher pitch and rest pitch (v=0) would be the same as the lower pitch and rest pitch. Because the vehicle passes by you, the radial velocity does not remain constant, but instead varies as a function of the angle between your line of sight and the siren's velocity:

(4)

where θ is the angle between the object's forward velocity and the line of sight from the object to the observer.

Applications

The Doppler effect is broadly applied to measure the velocity of bloodstream in vessels and the heart with ultrasound. A limitation is that the ultrasound beam should be as parallel to the blood flow as possible. Other limitations are absorption at interfaces and scatter (e.g. on blood cells). Δf, the Doppler shift is 2 times that of 2) since the emitted ultrasound beams impinges and reflects on the blood cells. Δf is generally some hundreds of Hz and can directly made audible by a microphone.

Contrast enhanced ultrasound using gas-filled microbubble contrast media can be used to improve velocity or other flow-related medical measurements.

However, "Doppler" has become synonymous with "velocity measurement" in medical imaging. But in many cases it is not the frequency shift (Doppler shift) of the received signal that is measured, but the phase shift (when the received signal arrives).

Velocity measurements of blood flow are also used in other fields of echography (obstetric, neurological).

Instruments such as the Laser Doppler velocimeter (LDV), and Acoustic Doppler Velocimeter (ADV) have been developed to measure velocities in a fluid flow. The LDV (also known as laser Doppler anemometry, or LDA) is a technique for measuring the direction and speed of fluids like air and water. In its simplest form, LDV crosses two beams of collimated, monochromatic light in the flow of the fluid being measured. A microscopic pattern of bright and dark stripes forms in the intersection volume. Small particles in the flow pass through this pattern and reflect light towards a detector, with a characteristic frequency indicating the velocity of the particle passing through the probe volume. LDV may be unreliable near solid surfaces, where stray reflections corrupt the signal. The ADV emits an acoustic beam, and measure the Doppler shift in wavelengths of reflections from particles moving with the flow. This technique allows non-intrusive flow measurements, at high precision and high frequency.

Measurement of the amount of gas bubbles in the venous system is performed in diving medicine. They are generally measured subclavicular in the pulmonary artery. Gas bubbles in the circulation may result in decompression sickness.

"Doppler" has become synonymous with "velocity measurement" in medical imaging. But in many cases it is not the frequency shift (Doppler shift) of the received signal that is measured, but the phase shift (when the received signal arrives).

More info

The echo-Doppler technique The description of velocity measurement holds for a continuous emitted ultrasound. With pulsed Doppler, short periods of emitting and receiving are alternated. By adjusting the period length the depth of reflection can be selected. In this way, motion of deeper layers is not disturbing the analysis.

The Doppler method and echography are combined in one apparatus, the echo-Doppler and yields a duplex image. In the black and white echo-image, direction and velocity are depicted in red for approaching the probe and blue for leaving. The more blue or red the higher the speed. The most common application is echocardiography.

The Doppler effect is also a basic ‘tool’ in astronomy (red shift, temperature measurements by line broadening) and daily life radar (navigation, speed control).