“…The direction of vector ( x p − x 0 , y p − y 0 , H + B ) is (cosϕ 0 cosγ 0 , cosϕ 0 sinγ 0 , sinϕ 0 ), so we can easily get,
Then equation (37) becomes
and
In most situations, the first term in equation (40) can give an accurate sensitivity estimation for the standard region, and the second term can be used to calculate the relative error. The first term of equation (40) is identical to equation (19) in (Wieczorek and Goedicke 2006) and to equation (24) in (Accorsi et al 2008). When the point source is in the principal line, the sensitivity formula is the geometric mean of the sensitivity for pinhole and cone-beam collimators (Metzler et al 2006, Cherry et al 2003).…”