Fraunhofer approximation ($D\gg a^2/\lambda$)

The far-field approximation neglects quadratic variation of propagation phase across an aperture of characteristic size a at observation distance D. For two narrow slits separated by s, their path difference remains $s\sin \theta$ at a finite observation angle. The additional substitution $\sin \theta \simeq Y/D$ requires a small observation angle; it does not follow from the Fraunhofer approximation itself.