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Fresnel Diffraction


Fresnel Diffraction

Definition

Fresnel diffraction is the diffraction of light in which the source and screen are at finite distances from the diffracting obstacle or aperture.

Theory

Fresnel diffraction is based on the Huygens–Fresnel principle. According to this principle, every point on a wavefront acts as a source of secondary wavelets. These wavelets spread into the region behind the obstacle or aperture and interfere with one another.

In Fresnel diffraction, the incident wavefront is generally spherical or cylindrical. Therefore, the curvature of the wavefront cannot be neglected.

Fresnel Half-Period Zones

The wavefront is divided into a number of zones called Fresnel half-period zones. The path difference between waves reaching the observation point from two consecutive zones is:

Δl = λ/2

Therefore, the waves from successive zones reach the observation point with a phase difference of:

Δφ = π

Hence, the contributions of successive zones are opposite in phase and partially cancel each other.

Resultant Amplitude

The resultant amplitude at the observation point is:

A = a1 - a2 + a3 - a4 + …

where a1, a2, a3, … are the amplitudes contributed by successive Fresnel zones.

Since the amplitudes decrease gradually:

a1 > a2 > a3 > a4 > …

the resultant amplitude is not zero.

Characteristics

  • The source and screen are at finite distances.
  • The incident wavefront is generally spherical or cylindrical.
  • Lenses are generally not required.
  • The diffraction pattern depends on the distance between the source, obstacle, and screen.
  • It is also called near-field diffraction.
  • It is explained using Fresnel half-period zones.

Examples

  1. Diffraction by a straight edge
  2. Diffraction by a narrow slit
  3. Diffraction by a circular aperture
  4. Diffraction by a circular disc

Fresnel Number

F = a2 / (λD)

where:

  • a = size of the aperture or obstacle
  • λ = wavelength of light
  • D = distance between the aperture and screen

For Fresnel diffraction:

F ≥ 1

Conclusion

Fresnel diffraction is the diffraction phenomenon observed in the near field, where the curvature of the wavefront is significant.