Transition between paraxial and Helmholtz Fourier spaces

Different correction methods for paraxial solutions have been used when such solutions extend out of the paraxial regime. Mapping functions play a fundamental role in them. This paper analyzes how to translate directions of paraxial wavevectors into Helmholtz wavevectors. Two possible mappings that are commonly used are examined, and a new mapping is proposed. The three mappings are classified in the framework of the full wave correction schemes.