Doppler shift or Doppler effect is defined as the change in frequency of sound wave due to a reflector moving towards or away from an object, which in the case of ultrasound is the transducer.

Terminology

When sound of a given frequency is discharged and subsequently reflected from a source that is not in motion, the frequency of the returning sound waves will equal the frequency at which they were emitted. 

However, if the reflecting source is in motion either toward or away from the emitting source (e.g. an ultrasound transducer) the frequency of the sound waves received will be higher (positive Doppler shift) or lower (negative Doppler shift) than the frequency at which they were emitted, respectively ².

• positive Doppler shift

  • frequency of received sound waves > frequency of emitted sound waves

  • source reflecting sound waves is moving toward the emitting source

  • depicted in colour flow Doppler as red

  • spectral envelope (in continuous and pulsed wave Doppler) above the baseline

• negative Doppler shift

  • frequency of received sound waves < frequency of emitted sound waves

  • source reflecting sound waves is moving away from the emitting source

  • depicted in colour flow Doppler as blue

  • spectral envelope (in continuous and pulsed wave Doppler) below the baseline

Doppler equation

F = 2f_o(v/c)cos(Q)

where:

• F is Doppler frequency shift

• f_o is transmitted frequency from ultrasound probe

• v is the velocity of moving reflector

• c is the velocity of sound in the medium

• Q is the angle between ultrasound beam and axis of flow

  • the Greek letter theta (θ) is also used

The above doppler formula is used because the transducer is not parallel to the axis of the moving object ⁴.

The magnitude of the Doppler shift is affected by the angle at which the reflecting source is travelling in relation to the transmitting source. This is accounted for in the Doppler equation with the "cosine(θ)" parameter; the maximum Doppler shift occurs when the relative motion occurs at a Doppler angle of 0 degrees (the cosine of 0 = 1) and no Doppler shift will be noted when the motion of the reflecting source is perpendicular (cosine of 90 = 0) ³.

History and etymology

Named after Austrian physicist, Christian Andreas Doppler (1803-1853) ¹.

See also

• Colour flow Doppler (ultrasound)

• Spectral Doppler (ultrasound)