Optical Communications, 2nd Edition

2.1 FIELD FOCUSING

The focusing of fields by an optical lens can be described using the diagram in Figure 2.1. The field collected at the lens input is defined in the aperture (receiver) plane, and the focused field is defined in the focal (detector) plane. The focal plane is located at distance f_c behind the aperture plane, where f_c is the focal length of the lens. The optical lens, physically placed in the aperture plane, redirects the incoming light field on to the focal plane, where the photodetector is located. The field produced in the focal plane is often called the diffracted field.

A well-designed receiver lens allows for Fraunhofer diffraction [1, 2] in the focal plane. Thus, if f_r(t, r) is the received field over the aperture lens and if f_d(t, u, ν) is the diffracted field in the focal plane, then the two are related by

Figure 2.1. Imaging geometry of the optical receiver.

where

is a phase factor, r = (x, y) are the field coordinates in the aperture plane, and (u, ν) are the field coordinates in the focal plane, as shown in Figure 2.1. Equation (2.1.1) describes the manner in which the received and focal plane fields are related. Note that f_d(t, u, ν) is also related to ...