rsc_wp

pyrost.bin.rsc_wp(double complex[::1] u0, double dx0, double dx, double z, double wl)

Wavefront propagator based on Rayleigh-Sommerfeld convolution method [RSC]. Propagates a wavefront u0 by z distance downstream.

Parameters
  • u0 (numpy.ndarray) – Initial wavefront.

  • dx0 (float) – Sampling interval at the plane upstream [um].

  • dx (float) – Sampling interval at the plane downstream [um].

  • z (float) – Propagation distance [um].

  • wl (float) – Incoming beam’s wavelength [um].

Returns

u – Propagated wavefront.

Return type

numpy.ndarray

Notes

The Rayleigh–Sommerfeld diffraction integral transform is defined as:

\[u^{\prime}(x^{\prime}) = \frac{z}{j \sqrt{\lambda}} \int_{-\infty}^{+\infty} u(x) \mathrm{exp} \left[-j k r(x, x^{\prime}) \right] dx\]

with

\[r(x, x^{\prime}) = \left[ (x - x^{\prime})^2 + z^2 \right]^{1 / 2}\]

References

RSC

V. Nascov and P. C. Logofătu, “Fast computation algorithm for the Rayleigh-Sommerfeld diffraction formula using a type of scaled convolution,” Appl. Opt. 48, 4310-4319 (2009).