Abstract

A spherical wave field is exactly represented by the angular spectrum of the plane waves with the limited bandwidth. It is given by superposing the minimum amount of plane waves which really contribute to the wave field. This representation is reduced to the circular plane-wave (CPW) expansion with a good approximation, if a distance from the source to an observation point is larger than a few wavelengths. The band-limited angular spectrum representation of the diffracted wave field is also obtained from the Fresnel-Kirchhoff diffraction formula by applying the CPW expansion of the spherical wave. The bandwidth is W = 2(r0λ)−1/2 + ρmaxcos(k,n)/r0λ[(r0λ)1/2 > ρmax] or W = 2(r0λ)−1/2 [(r0λ) ≫ ρmax], where r0 is the distance from the center of the aperture to the observation point, and ρmax is half of the maximum of the linear dimension of the aperture.

© 1978 Optical Society of America

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