The representation of the electromagnetic field as an angular spectrum of plane waves is becoming increasingly popular in the treatment of certain problems in physical optics. In this paper the equivalence of the angular-spectrum representation and of one of Rayleigh’s integral transforms is demonstrated. Making use of conditions under which the Rayleigh integral formula exists as the unique solution to a certain class of boundary-value problems, conditions under which the angular-spectrum representation is valid are discussed.
ÉAMON LALOR, "Conditions for the Validity of the Angular Spectrum of Plane Waves," J. Opt. Soc. Am. 58, 1235-1237 (1968)