Doppler Speed Projection Cross Scan - Biophysical Ultrasound: Echo Timing and Acoustic Interfaces Step by Step

Doppler shift changes with speed and along-beam projection. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Doppler shift has speed and projection factors

The transmit frequency and sound speed stay fixed while speed or projection changes.

\Delta f={2 f_{\text{tx}} v p\over c}

Speed and projection both move the frequency shift

The first group changes speed; the second group changes the along-beam projection.

\begin{array}{c|c|c|c}\text{scan}&v&p&\Delta f\\v\ \text{changes}&1&\frac{1}{2}&2\\v\ \text{changes}&2&\frac{1}{2}&4\\v\ \text{changes}&3&\frac{1}{2}&6\\p\ \text{changes}&2&\frac{1}{4}&2\\p\ \text{changes}&2&\frac{1}{2}&4\\p\ \text{changes}&2&1&8\\\end{array}

The middle speed row gives a four-hertz shift

The same equation cites speed, projection, and sound speed before accepting the shift.

2\cdot6\cdot2\cdot\frac{1}{2}/3=4