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A diffraction envelope is the angular factor imposed by the shape and width of each opening in an interference pattern. For two equally illuminated rectangular slits of width $b$ and separation $s$, Fraunhofer diffraction gives $I(\theta )=4I_s{\mathrm{sinc}}^2(\pi b\sin \theta /\lambda ){\cos }^2(\pi s\sin \theta /\lambda )$, where $\mathrm{sinc}u=\sin u/u$ and $I_s$ is one slit's on-axis light intensity. The first factor limits the observable angular range even when the rapid interference fringes remain perfectly coherent.

Let each slit alone give local light intensity $I_s$, and assume equal coherent illumination. In Fraunhofer diffraction, the two wave amplitudes differ in wave phase by $\delta =2\pi s\sin \theta /\lambda$. Adding the wave amplitudes before squaring givesFor a flat screen, $\sin \theta =x/\sqrt{d^2+x^2}$. In the paraxial region $|x|\ll d$, the double-slit interference profile is thereforeThe given $d\gg s^2/\lambda$ justifies the far-field expansion. Slit widths have been neglected; a finite width multiplies this profile by the single-slit diffraction envelope. At large angles the one-slit light intensity and geometric spreading must also be retained, rather than treating $I_s$ as constant.