This paper discusses fundamental questions of the study of the diffraction processes of scalar waves in the Kirchhoff approximation, using the concept of a delta perturbation. The method is convenient for investigating the field of ultrashort pulses in linear systems. Simple relationships are presented that describe the diffraction field in the near and far zones. The main features of the field structure and approximate methods for describing it are shown. It is established that the method developed here corresponds to the classical relationships for monochromatic vibrations. Previously unknown conservation laws for diffracted waves are derived. © 2005 Optical Society of America