Analysis of linear, area and volume distortion in 3D ultrasound imaging

We have developed a three-dimensional (3D) ultrasound imaging system that uses a side-firing probe, axially rotated under computer control, to acquire a series of 2D images, from which the 3D image is reconstructed. For an undistorted reconstruction, the inner radius R0 of the 2D images and the total scanning angle theta must be known accurately. Here, we describe (a) a theoretical analysis of the relative distortion in image shape, length, area, and volume due to an error delta R in R0 or delta theta in theta; (b) measurements of these in simulated and real 3D images; and (c) a method to calibrate R0, theta, and image scale accurately. Theoretically, all four relative distortions vary as P delta R/R + Q delta theta/theta, where magnitude of P < or = 1, magnitude of Q < or = 1, and R is the average distance of the object from the axis. In every case, the simple theoretical formulas for P and Q agree with image measurements to within the measurement uncertainty.