Fourier Optics Simulator 1D
Fourier Optics Simulator computes the diffraction pattern of a 1D aperture using the Fourier transform. Enter aperture width \\( a \\), wavelength \\( \lambda \\), focal length \\( f \\), and select aperture type (rectangular or Gaussian).
Fourier Optics Model
The diffraction pattern is computed as the squared magnitude of the Fourier transform of the aperture function. For a rectangular aperture:
\\[
U(u) = \frac{a}{\sqrt{\lambda f}} \text{sinc}\left(\frac{a u}{\lambda f}\right), \quad I(u) = |U(u)|^2
\\]
For a Gaussian aperture with width \\( a \\):
\\[ U(u) = \frac{a}{\sqrt{\lambda f}} \exp\left(-\frac{\pi^2 a^2 u^2}{(\lambda f)^2}\right), \quad I(u) = |U(u)|^2 \\]Where:
- \\( a \\): Aperture width (mm)
- \\( \lambda \\): Wavelength (m)
- \\( f \\): Focal length of the lens (m)
- \\( u \\): Spatial coordinate in the Fourier plane (m)
- \\( U(u) \\): Complex amplitude in the Fourier plane
- \\( I(u) \\): Intensity (diffraction pattern)
- \\( \text{sinc}(x) = \sin(\pi x)/(\pi x) \\)