Abstract
The shifted angular spectrum method allows a reduction of the number of samples required for numerical off-axis propagation of scalar wave fields. In this work, a modification of the shifted angular spectrum method is presented. It allows a further reduction of the spatial sampling rate for certain wave fields. We calculate the benefit of this method for spherical waves. Additionally, a working implementation is presented showing the example of a spherical wave propagating through a circular aperture.
Highlights
The propagation of scalar wave fields from one plane to a second parallel plane through free space is an important problem in the field of wave optics [1]
The shifted angular spectrum method allows a reduction of the number of samples required for numerical off-axis propagation of scalar wave fields
The Rayleigh-Sommerfeld diffraction integral can be evaluated directly in the spatial domain while the angular spectrum method requires a Fourier transform to obtain the angular spectrum of the wave field
Summary
The propagation of scalar wave fields from one plane to a second parallel plane through free space is an important problem in the field of wave optics [1]. The angular spectrum method and explicitly the band limited angular spectrum method [2] are well suited for numerical propagation in X-ray optics or generally in wave optics with similar conditions Another drawback of a plain numerical implementation of the angular spectrum method is that the input sampling window and the output sampling window have the same size and center. In [3], the shifted angular spectrum method is presented as a solution to this problem It allows for off-axis numerical propagation of scalar wave-fields by shifting the output sampling window relative to the input sampling window by using the Fourier shift theorem. To further reduce the spatial sampling rate that is needed, especially for off axis propagation, a modification of the shifted angular spectrum method ist presented. Further methods for numerical propagation, with shifted or tilted destination window or which try to reduce the computational demands, can be found in [10,11,12,13,14,15,16,17]
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