2D Fourier Optics Simulator
2D Fourier Optics Simulator computes the 2D diffraction pattern of an aperture using the Fourier transform. Enter aperture dimensions \\( a, b \\) (or diameter for circular), wavelength \\( \lambda \\), focal length \\( f \\), and select aperture type (rectangular or circular).
2D Fourier Optics Model
The diffraction pattern is the squared magnitude of the 2D Fourier transform of the aperture function. For a rectangular aperture of size \\( a \times b \\):
\\[
U(u,v) = \frac{ab}{\lambda f} \text{sinc}\left(\frac{a u}{\lambda f}\right) \text{sinc}\left(\frac{b v}{\lambda f}\right), \quad I(u,v) = |U(u,v)|^2
\\]
For a circular aperture of diameter \\( d \\):
\\[ U(u,v) = \frac{\pi d^2}{4 \lambda f} \frac{2 J_1\left(\frac{\pi d \sqrt{u^2 + v^2}}{\lambda f}\right)}{\frac{\pi d \sqrt{u^2 + v^2}}{\lambda f}}, \quad I(u,v) = |U(u,v)|^2 \\]Where:
- \\( a, b \\): Aperture width and height (mm) (or \\( d \\) for circular)
- \\( \lambda \\): Wavelength (m)
- \\( f \\): Focal length (m)
- \\( u, v \\): Spatial coordinates in the Fourier plane (m)
- \\( U(u,v) \\): Complex amplitude
- \\( I(u,v) \\): Intensity
- \\( \text{sinc}(x) = \sin(\pi x)/(\pi x) \\)
- \\( J_1 \\): First-order Bessel function of the first kind