Fresnel Diffraction

Fresnel diffraction (also called near-field diffraction) is the diffraction pattern observed when the source or observation screen is at a finite distance from the diffracting aperture.

Fresnel Approximation

The Fresnel approximation uses a quadratic phase approximation:

$$ \gamma_z \approx 1 - \frac{1}{2}(\gamma_x^2 + \gamma_y^2) $$

valid when $\gamma_x \ll 1$ and $\gamma_y \ll 1$ (small angles).

Fresnel Condition

The Fresnel approximation is valid when:

$$ z \ll \frac{a^4}{\lambda^3} $$

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

Key Properties

• Pattern changes shape with propagation distance
• More complex than Fraunhofer diffraction
• Involves Fresnel integrals or quadratic phase factors

Related Topics

• Fraunhofer diffraction (far-field limit)
• Fresnel zones
• Fresnel zone plate