Pulsed Doppler depth-velocity tradeoff

The pulsed Doppler depth-velocity tradeoff is the restriction linking uniquely localized depth and unaliased beam velocity in a simple repeated-pulse Doppler ultrasound acquisition. Deeper echoes take longer to return, leaving fewer distinct pulse observations per second. Fewer observations reduce the unaliased Doppler ultrasound frequency interval.

For maximum depth $d$, speed of sound $c$ and pulse repetition frequency $f_r$, the ideal nonoverlapping timing restriction is $f_r\le c/(2d)$. The Nyquist frequency is $f_r/2$. Combining this with $f_D=2f_{0}v\cos \theta /c$ givesThe strict inequality excludes the ambiguous Nyquist endpoint. For beam-parallel motion, $|\cos \theta |=1$. At a right angle there is no first-order Doppler sensitivity to the motion; the apparent divergence of the formula does not provide unlimited useful velocity measurement.

For an original calculation, let $c=1540$ m/s and $f_0=2.5$ MHz. A 15 cm depth allows at most approximately 5133 pulses/s in this idealization, with axial Nyquist speed about 0.791 m/s. At 30 cm these bounds fall to approximately 2567 pulses/s and 0.395 m/s. Doubling the transmitted frequency to 5 MHz halves the axial velocity limits at either depth.

These are timing and sampling bounds, not a specification for a particular instrument. Pulse duration, scheduling and processing can lower the usable limit. Moving a spectral baseline changes the displayed signed interval but does not increase its total sampled-frequency width. Continuous-wave Doppler echocardiography avoids this pulse-rate restriction while sacrificing unique depth selection; high-pulse-rate acquisition instead accepts Doppler range ambiguity.^[ref] The acquisition choice determines which ambiguity remains.