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The Ray-aiming algorithm is robust and can correctly aim rays for most aberrated and/or decentered/tilted pupils. However, it needs to first find a ray that reaches the stop surface in order to iteratively find the desired stop coordinate.  By default, the first guess is the center of the paraxial entrance pupil and launches rays in that direction. If the ray from the first guess does not reach the stop surface, it then attempts to find the stop surface by launching rays in different direction around the paraxial entrance pupil.  However, for extremely decentered/tilted and/or aberrated pupil the Ray-aiming will fail if it cannot find any ray that finds the stop surface. When this happens, ZEMAX will issue an error message as shown in the picture.



When ray aiming fails because of this (which is rare), you need to aid the Ray-aiming algorithm by providing a better first guess.  The Pupil Shift Factor specified under System >General>Ray-aiming is the measure of how much the initial guess XYZ coordinate should be shifted by, from the default (paraxial entrance pupil position).  The shift factor needs only be precise enough to help the algorithm find the stop surface. Once ZEMAX has successfully traced a ray it needs no further help.