A method is proposed to calculate the amplitude on the reference sphere due to a non-uniform transmission filter. The method may be divided into two stages: imaging of the filter plane, and projection of the filter image plane on the reference sphere. In this way we deduce some expressions which relate the coordinates on the filter plane to those on the reference sphere. Although the method is approximate, it has the advantage of saving computing time, since it is only necessary to trace two rays for each considered field. The accuracy of the method is studied by applying it to different real systems. © 1989 Taylor and Francis Ltd.