Generalized optical theorem for reflection, transmission, and extinction of power for scalar fields

A derivation of the optical theorem that makes it possible to obtain expressions for the extinguished power in a very general class of problems was presented. The optical theorem related the power extinguished from a plane wave incident on an object to the scattering amplitude in the direction of the incident field. The theorem implied that the total power extinguished from the incident was removed from the incident field by means of interference between the incident field and the forward scattered field. The results show that the extinguished power is a meaningful measure of object structure for certain forms of the incident field.