Derivation of correlation coefficient formula for determination of Doppler angle using time domain correlation ultrasonic flowmeter.

Calculation of the Doppler angle from the correlation coefficient of two aligned windowed data sets of two echoes in the time domain correlation method has been demonstrated. By assuming ideal sound and velocity fields, it is shown that the Doppler angle can be obtained from the statistics of the reflected ultrasonic signals in time domain correlation ultrasonic flowmeter. The resolution cell is chosen to be much longer than the impulse response of the system in order that the signals reflected from the scatterers preceding and following the resolution cell will be sufficiently small that they do not contribute to the resolution cell. Hence, the truncation effects of the resolution cell on the nearby scatterers may be ignored. The mathematical derivation of correlation coefficient is presented clearly. The measurement method of Doppler angle is given from the position of two aligned resolution cells.