= Color Doppler
\b[Color Doppler] overlays spatially localized estimates of motion on an <ultrasound> image. In blood-flow imaging, the estimated quantity is related to the <Doppler ultrasound> shift of echoes from moving <red blood cells>. The color scale encodes motion relative to the beam, not the blood's oxygen content. The displayed legend and sign convention must be read with the image.<Recommendations for Quantification of Doppler Echocardiography by Miguel A. Quiñones and others>[General Principles, printed p. 167, multiple gates and color velocity estimates]{ref}
An important implementation estimates the phase change between repeated echoes using <autocorrelation>. <Chihiro Kasai> and coauthors demonstrated an autocorrelator combined with pulsed acquisition, testing scanners with phantoms as well as examining hearts. This made many localized estimates available fast enough for a changing two-dimensional image; it did not make each colored pixel an independent direct measurement of transported blood <volume>.<Real-Time Two-Dimensional Blood Flow Imaging Using an Autocorrelation Technique by Chihiro Kasai and others>[Abstract and Sections II–III, mean Doppler frequency, system and phantom experiments]{ref}
For an original single-frequency example, let successive complex echo samples be $z_n=Ae^{in\phi}$. Then
$$
z_{n+1}\overline{z_n}=A^2e^{i\phi},\qquad
\phi=\frac{2\pi f_D}{f_r}\pmod{2\pi},
$$
where $f_D$ is the <Doppler ultrasound> <frequency> shift and $f_r$ the <pulse repetition frequency>. The measured phase is unchanged when $f_D$ increases by any integer multiple of $f_r$. This is <aliasing> even for a noiseless signal.
With $f_r=4000$ Hz and transmitted <frequency> $f_0=2.5$ MHz, assume <speed of sound> $c=1540$ m/s and motion parallel to the beam. True <velocity> 0.80 m/s gives $f_D=2f_0v/c\approx2597.4$ Hz. Its principal sampled value is approximately $-1402.6$ Hz, corresponding to displayed beam <velocity> $-0.432$ m/s under the same conversion. A color sign change can therefore occur without physical reversal of <fluid flow>.
The example isolates <sampling (signal processing)>. Mixed moving scatterers, finite <spatial resolution> and <signal processing> add further limitations. A color image is useful for locating a jet or a changing flow pattern, while a <stroke volume> requires an appropriate spatial and temporal integration of <velocity>, not the apparent size or brightness of a colored patch.
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