Hamilton’s Mixed and Angle Characteristic Functions and Diffraction Aberration Theory

The use of Hamilton’s mixed and angle characteristic functions in wave and diffraction aberration calculations is theoretically examined. The relation of Hamilton’s mixed and angle characteristic functions to a new wave-aberration function is shown. This aberration function is to be used in the Luneburg–Debye diffraction integrals. The mixed and angle characteristic functions as utilized in diffraction theory via the Luneburg–Debye integrals are examined. The mathematical and physical approximations are discussed. The use of the Luneburg–Debye diffraction integrals for image evaluation is examined and some difficulties are pointed out. It is concluded that the above methods should not be used for microwave and radio-frequency imaging systems; they are of limited validity for optical imaging systems.