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A recent Letter [Opt. Lett. 40, 3420 (2015) [CrossRef] ] reported a modified angular spectrum method that uses a sampling scheme based on a compact space–bandwidth product representation. That technique is useful for focusing and defocusing propagation cases and is generalized here for the case of propagation between two defocus planes. The proposed method employs paraxial spherical phase factors and modified propagation kernels to reduce the size of the numerical space–bandwidth product needed for wave field calculations. A Wigner distribution analysis is carried out in order to ensure high accuracy of the calculations in the entire computational domain. This is achieved by analyzing the evolution of the generalized space–bandwidth product when passing through the propagation algorithm for various space–frequency constraints. The results allow the derivations of sampling criteria, and, despite this, also show that a small amount of space/frequency zero padding significantly extends the capability of the recently reported modified angular spectrum method. Simulations validate the high accuracy of that method and verify a computational and memory gain of more than two orders of magnitude when comparing this technique with the conventional angular spectrum method.
© 2016 Optical Society of America
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