= Fresnel half-period zone
{c}
A <Fresnel half-period zone> is a region of an aperture whose optical path to an observation point differs from the axial path by an interval of half a <wavelength>. For an axial <optical point source> a distance $s$ before the aperture and an axial observer a distance $r$ beyond it, the paraxial path excess at aperture radius $u$ is $u^2(s^{-1}+r^{-1})/2$. The outer radius of zone $n$ is therefore
$$
u_n^2=\frac{n\lambda sr}{s+r}.
$$
Successive zones contribute approximately opposite <phases> to the <Huygens-Fresnel principle> integral. The finite source distance matters: using the plane-wave formula $u_n^2=n\lambda r$ requires $s\to\infty$.
Back to article page
