Equation (4.24) expresses the scattered (and thus the total) monochromatic field in terms of the incident monochromatic field (we remind the reader that the incident field is the total field in the absence of the scattering object). However, neither field can be measured directly with conventional optical instruments, which obviously calls for the derivation of the corresponding relationships between observable characteristics of the total and incident fields. In view of the discussion in Chapter 8, all such relationships should be particular cases of a general expression of the PST of the total field in the presence of the scattering object in terms of that of the incident field. This general expression will be derived below.

There are two other important practical issues to consider. Indeed, our previous discussion of electromagnetic scattering has been based on the assumptions that: (i) the electromagnetic field is purely monochromatic, and (ii) the scattering object does not change with time. However, in the majority of actual applications the electromagnetic field is polychromatic and the scattering object changes in time randomly or quasi-randomly. Furthermore, the temporal variability of the object can be rapid enough to affect the result of averaging an actual optical observable over the time interval required to take a measurement.