Justification of the use of scalar theory in optics is discussed. Although it is difficult to relate the scalar quantity V (t) commonly used in the scalar theory with the components of the electric field vector E (t), we show that there exists a simple relationship between the corresponding quantities quadratic in the field variables. Thus a scalar theory based on this identification can be used to obtain correct answers for the measurement of irradiance when the description of polarization is not of primary interest.
A. S. MARATHAY and G. B. PARRENT, JR., "Use of Scalar Theory in Optics," J. Opt. Soc. Am. 60, 243-245 (1970)