** Next:** 4.2.1 Defocus
**Up:** 4. Aerial Image Simulation
** Previous:** 4.1.5 Vector-Valued Extension

The operation of an ideal lens is only diffraction limited, i.e.,
the lens catches rays only up to a certain degree of obliquity, but
otherwise the image is composed in an ideal way.
In reality fabrication imperfections of the lens degrade the image quality
as the image composition is distorted by phase errors occurring
during the passage of the ray through the lens. Such imperfections are
commonly called *lens aberrations* and can be modeled by
introducing a general phase factor
**exp(***jk*_{0}(*n*, *m*)) in the pupil function.
Phase manipulations or even amplitude modifications can also be
intentional as the depth of focus of the imaging system might be increased.
These techniques are commonly referred to as in-lens filtering
and have been sketched in Section 2.5.2.
The filter operation can be modeled by adding a general
transfer function *F*(*n*, *m*) to the pupil function. Hence, the ideal pupil
functions (4.53) and (4.58) of the scalar
and vector theory, respectively, are modified to:
In the following three sections we present models for the phase
aberration function **(***n*, *m*) and for the filter function *F*(*n*, *m*).

** Next:** 4.2.1 Defocus
**Up:** 4. Aerial Image Simulation
** Previous:** 4.1.5 Vector-Valued Extension
*Heinrich Kirchauer, Institute for Microelectronics, TU Vienna *

1998-04-17