rsc_wp¶
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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
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).