It is often advantageous to consider spatially incoherent optical information processing systems in terms of general remote sensing systems. Each remote sensing system has as its goal the detection or estimation of some unknown object-related quantity. This quantity could be as specific as object range or as general as object spatial intensity. In many problems interesting complications arise because of incomplete knowledge of object or system parameters that are not directly desired but contribute negatively to the estimation of the parameters that are of interest. For example, lack of knowledge of the range, or misfocus state, of a planar target increases the difficulty of accurately estimating the spatial intensity of the target. By combining spatially incoherent optical system modelling with information theory, application-specific design goals for optimum systems can be formulated.
Consider an spatially incoherent optical information processing system, one that physically begins in the free space immediately in front of some target, and ends with a optical detector or CCD array, as an information channel. As can be imagined, some channels are better suited for certain types of information transmission than others. Exactly which type of channel is the optimum for a particular application? This is the answer that can be provided through information theory. By modelling the system, or channel, including all unknown signal-influencing parameters, a design goal for the optimum system can be produced. Since spatially incoherent optical systems are only indirectly controlled, through modification of the pupil function, a system that meets the information theory design goal may be difficult to acquire. This is a challenging aspect of the use of information theory typical in many fields. Information theory does not lead the way. It merely determines the destination.
In the following sections a brief review of the information theory concepts of Fisher Information and the Cramer-Rao bound is offered. Application of these information theory concepts are then applied to three specific information processing systems. These systems are passive, single-lens, single-image, range estimation, range-invariant imaging, and orthogonal passive range detection systems.