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