Huygens-Fresnel principle

Let Σ be a diffracting surface (see figure II-1). The Huygens Fresnel principle can be expressed by :

where , is a unit vector (perpendicular) to Σ , , , dS is an elementary surface surrounding , and U(P1) and U(P0) are the field amplitudes in P1 and P0 .

Physical meaning of Eq. II-1 :

The field amplitude at a point P0 located after the aperture can be expressed as the superposition of all the diverging spherical waves emitted by the secondary sources P1 which constitute the diffracting aperture Σ.

Any secondary source located at P1 has the following properties:

• Its complex amplitude is proportional to the incident wave amplitude U(P1) .

• It is weighted by a cosθ term expressing its directivity with respect to the observation point, and by a term dS corresponding the elementary surface participating to the emission.

We can write:

where h est a weighting function defined by: