Fraunhofer Diffraction

Fraunhofer diffraction (also called far-field diffraction) is the diffraction pattern observed when both the light source and observation screen are effectively at infinite distance from the diffracting aperture.

Fraunhofer Condition

The Fraunhofer approximation is valid when:

$$ z \gg \frac{a^2}{\lambda} $$

where $z$ is the propagation distance, $a$ is the aperture size, and $\lambda$ is the wavelength.

Key Properties

• The diffraction pattern is the Fourier transform of the aperture function
• Pattern shape is independent of distance (only scales)
• Intensity distribution: $I(f_x, f_y) \propto |T(f_x, f_y)|^2$ where $T$ is the aperture transmittance

Examples

• Circular aperture → Airy disk
• Rectangular aperture → sinc$^2$ pattern
• Diffraction grating → discrete diffraction orders

Related Topics

• Fresnel diffraction (near-field)
• Plane wave