Complete far-field asymptotic series for free fields.

The closed form of the complete far-field asymptotic series is provided for the scalar and electromagnetic monochromatic fields in free space whose angular spectrum is smooth over the sphere of directions. The first few terms of this series are also shown to give corrections to the Fraunhofer diffraction formula. The application of this series is illustrated with two examples corresponding to a highly focused radially polarized field and to the scalar diffraction from a circular aperture.

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