Diffraction algorithm suitable for both near and far field with shifted destination window and oblique illumination

Abstract

We propose a method for diffraction simulation with both shifted destination window and a large oblique illumination. Based on the angular spectrum theory, we first derive a generalized transfer function (GTF) and a generalized point-spread function (GSPF) suitable for free-space diffraction simulation when both a shifted destination window and a large oblique illumination are taken into account. Then we analyze the sampling error caused by sampling of the GTF and the GSPF for numerical simulation based on fast Fourier transform (FFT), and find out an analytical formula for determining a criteria distance of Zc. Theoretical analysis and simulation results prove that the FFT-based GTF sampling algorithm is valid for diffraction simulation with a diffraction distance less than or equal to Zc, while the FFT-based GSPF sampling is only suitable for the simulation with a distance larger than or equal to Zc. Based on theoretical analysis, we propose the hybrid GTF-GSPF algorithm suitable for simulation of both near- and far-field diffractions with shifted destination window and large oblique source illumination at the same time. Finally, some simulation results are given to verify the feasibility of the algorithm.

Angular spectrum-based wave-propagation method with compact space bandwidth for large propagation distances

“…Properties of RS and AS methods have been investigated by many authors [5][6][7][8][9][10] concluding that AS and RS is accurate for shorter and longer propagation distances, respectively. A recent algorithm [11] was proposed for both short and long propagation distances, which selects either an AS or an RS solver for a given distance. In this work, we propose a novel scalar AS approach that minimizes the sampling requirements of diffraction calculations and allows extending the AS capability to larger propagation distances, i.e., z ≥ N Δ 2 λ −1 1 − λ 2 Δ −2 ∕4 1∕2 where N is number of samples, and Δ sample size.…”

“…However, this rectangular space-frequency-shaped sampling strategy is very inefficient: high resolution and large distance propagations require a large SW with large empty space-frequency regions. This casts particular doubt on the utility of the RS method, as it is only accurate for large propagation distances [5,11].Several authors recognize the major downside of rigorous approaches that use the same sampling frequency of input and output fields. Harvey [13] proposed an AS approach for diffracted field calculation on a hemisphere.…”

Modified shifted angular spectrum method for numerical propagation at reduced spatial sampling rates

“…For a given bandwidth of the input wave field a given size of the sampling window and a given offset between the sampling windows, the propagation can only be done up to a certain distance limit without loss of accuracy. Detailed discussions on this limit for the angular spectrum and shifted angular spectrum method, which is also true for this modified method, can be found for example in [4][5][6]17]. To enable propagation for distances above the distance limit one has to choose another method for example [4][5][6].…”

“…Detailed discussions on this limit for the angular spectrum and shifted angular spectrum method, which is also true for this modified method, can be found for example in [4][5][6]17]. To enable propagation for distances above the distance limit one has to choose another method for example [4][5][6]. Or, one has to increase the size of the sampling window, which according to Eq.…”

“…In [4], a similar approach applicable to oblique illumination with plane waves is used. Compared to that, the method presented in section 2 is directly applicable for more general wave fields under the conditions given in section 4, and thus for example illumination with spherical waves, which is also shown in section 5.…”