Fan Beam Angle

For these divergent beam geometries, the fan beam angle needs to be calculated. For real-world CT scanners, this is fixed at the time of manufacture. CTSim, however, calculates the fan beam angle, alpha, from the scan diameter and the focal length as alpha = 2 x asin ( (Sd / 2) / f)

Empiric testing with CTSim shows that for very large fan beam angles, greater than approximately 120 degrees, there are significant artifacts. The primary way to manage the fan beam angle is by varying the focal length since the scan diameter is usually fixed at the size of the phantom.

To illustrate, the scan diameter can be defined as

Sd = Sr x Vr x Pd

Further, the focal length can be defined as

F = FR x (VR x Pd)

Substituting these equations into the above equation, We have,

alpha = 2 sin (Sr / Fr)

Since in normal scanning s_r = 1, alpha depends only upon the focal length ratio in normal scanning.