Aperture (draw here)
Diffraction Pattern |FT|²
The Fraunhofer diffraction pattern is the squared magnitude of the 2D Fourier transform of the aperture function:
I(u,v) = |∬ A(x,y) e^{−2πi(ux+vy)} dx dy|²
Narrow aperture → wide pattern (uncertainty principle: σ_x · σ_u ≥ 1/4π).
Single slit: sinc² envelope. Double slit: sinc² × cos² (Young's fringes).
Circle: Airy disk pattern ∝ [J₁(r)/r]², radius ∝ λ/D. Draw any shape to see its Fourier transform!
Narrow aperture → wide pattern (uncertainty principle: σ_x · σ_u ≥ 1/4π).
Single slit: sinc² envelope. Double slit: sinc² × cos² (Young's fringes).
Circle: Airy disk pattern ∝ [J₁(r)/r]², radius ∝ λ/D. Draw any shape to see its Fourier transform!