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:
Δ = λ/2
Therefore, the waves from successive zones reach the observation point with a phase difference of 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.