The set-up deviation as determined from portal image i is defined as Rmv,i = (Ui,Vi,Wi), where Ui and Vi lie in the plane of the imager and Wi is perpendicular to the plane of the imager. Therefore, only Ui and Vi can be determined from the portal image. In the patient coordinate system (x,y,z) the positive x-direction corresponds to the left, the positive y to the dorsal and the positive z tot the cranial direction. The set-up deviation in the patient coordinate system R = (x,y,z) is related to Rmv,i by an isocentric table rotation Φi and a gantry rotation Φi:

for a patient in supine position with the head in the direction of the gantry. Eq. 1 can be solved for ≥ 2 portal images with different gantry angles θi and θj. We have implemented the matrix transformation in an Microsoft Excel spreadsheet for n portal images and used the Microsoft Excel Solver (Microsoft Corporation, Redmond, WA) to find the solutions for Wi that minimize the function Cn(W):

The iteration process was performed with a convergence of 0.001 and a maximum of 100 iterations