This calculator assumes the the input file is on a flat surface, and by default at 555nm for monochromatic mode and at the F,d,C lines for polychromatic mode. This calculator rescales all files to 512x512. This calculator is for educational purposes only.

There exist several propagation methods for propagating scalar fields in optics. The most common of which are based on finite difference methods (FDTD) and spectral methods (FFT BPM). There are a few other methods which also just integrate the Rayleigh Sommerfeld integral or Fresnel Integral as well. All of these approaches have pros and cons. But for simplicity we will offer just FFT BPM for the time being. For advanced propagation effects, checkout KostaCLOUD WaveTracing.

FFT BPM is a spectral method, which is based on taking the wave equation and calculating from the following PDE an ODE in the spectral domain:

uₜₜ = c² Δu

To make this an ODE we simply take the spatial Fourier Transform, we also treat this as a planar surface:

ûₜₜ = - c² k_{z}² û

If we integrate this twice we get the following solution:

û = C_{1} sin ( |k_{z}| c t) + C_{2} cos ( |k_{z}| c t)

Applying boundary conditions, substitutions of ct = z and Maxwell's Electric field is divergence free we can eventually arrive at at the well known Angular Spectrum method: