Approximations to the Huygens-Fresnel principle

Since U(x1,y1)= 0 outside of Σ (see figure III-1), we can rewrite the integral defined in Eq. II-2A by integrating from to :

General approximations:

• distance z >> the largest linear dimension of Σ.

• distance z >> the largest linear dimension of the region of observation.

With those two hypothesis, we obtain:

The term r01 in the exponent cannot be replaced by z as it is done in the denominator because the error which would result from this approximation would be multiplied by and would lead to errors on the phase far larger than radians.