4.2 Lens Aberrations and In-Lens Filter

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(jk₀$\Phi$(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:

 

$$\begin{aligned}P_{\mathrm{real}}(n,m) &= P_{\mathrm{ideal}}(n,m)\... ...\mathbf{P}_{\mathrm{ideal}}(n,m:p,q)\, F(n,m)\, e^{jk_0\Phi(n,m)}.\end{aligned}$$

In the following three sections we present models for the phase aberration function $\Phi$(n, m) and for the filter function F(n, m).