Calculation of the focus-width of a focused ultrasonic transducer
The focus depth of a lens-focused transducer is easily to calculate by the lens formula of the geometric optic. If we use the trigonometry we can calculate the focus-range (depending from aperture) using the formula F = R*(1 + 1/(squareroot((CLens*CLens)/(CMed*CMed)-(A*A)/(4*R*R))-squareroot(1-(A*A)/(4*R*R))), where R is the lens radius, A the aperture, F, the focus, CMed the longitudinal speed of sound in the medium and CLens the longitudinal speed of sound in the acoustic lens. If we calculate F for the border "sound beam" (at A) and F for the middle "sound beam" we get the focus range. For R >> A we get the common known lens formula and a single focus point.
But how can be calculated the sound beam width within the focus? I know from literature, that the focus area has a elliptic form. But I did not find a formular for calculating the beam width within the focus range of a lens-focused transducer. Does anyone know any paper containing the calculation of the elliptic focus zone and the way to get this calculation?