The pupil function or aperture function describes how a light wave is affected upon transmission through an optical imaging system such as a camera, microscope, or the human eye.
More specifically, it is a complex function of the position in the pupil[1] or aperture (often an iris) that indicates the relative change in amplitude and phase of the light wave.
[2] Imperfections in the optics typically have a direct effect on the pupil function, it is therefore an important tool to study optical imaging systems and their performance.
is the phase change (in radians) introduced by the optics,[3] or the surrounding medium.
Such change in amplitude of the light wave is described by the factor
[2][5] In a homogeneous medium, a point source emits light with spherical wave fronts.
A lens that is focused onto the point source will have optics that change the spherical wave front into a planar wave before it passes through the pupil or aperture stop.
Often, additional lens element refocus the light onto a sensor or photographic film, by converting the planar wave front to a spherical wave front, centered onto the image plane.
Such a variation in optical path length will create an image that is blurred only in one dimension as is typical of systems with astigmatism.