If users introduce multiple identical slits so that the distance from slit center to slit center is “d” and if the number of slits is very large, then, because of phase relationships between the slits, light is restricted to very narrow lines called diffraction orders. These orders are located at: $\sin \left(\mathrm{\theta }\right)=\mathrm{m}\frac{\mathrm{\lambda }}{\mathrm{d}}\mathrm{ }$ (where m is an integer⁽¹⁾).

Changing the incident angle of the light simply slides the orders over to be centered on the principle ray. In other words the 0^th order moves and is also located at $\left({\mathrm{\theta }}_{\mathrm{r}}=\mathrm{ }{-\mathrm{\theta }}_{\mathrm{i}}\right)$ . Now the orders are located at: $\sin \left(\mathrm{\theta }\right)=\mathrm{m}\frac{\mathrm{\lambda }}{\mathrm{d}}-\mathrm{s}\mathrm{i}\mathrm{n}\left({\mathrm{\theta }}_{\mathrm{i}}\right)$ or $\mathrm{x}=\mathrm{m}\frac{\mathrm{\lambda }}{\mathrm{d}}-{\mathrm{x}}_{\mathrm{i}}$

The interesting feature of the resulting pattern is that the relative intensity envelope of these orders is just the intensity profile of a single slit. Notice that this is an envelope. Light is only allowed at the order locations but the relative intensity is obtained by the height of the Sinc² profile at the order location. The following link has a very good illustration: Multi-Slit Diffraction

Since the orders and the envelope move together with changing incident angle, the 0^th order and the peak of the Sinc² envelope are locked together. This means that the 0^th order receives more energy than any other order. How much more is determined by the width of the slits, “a”, relative to the spacing (pitch), “d”.

Again all of the light must be accounted for but now because of the discrete orders the equation becomes $\mathrm{A}\sum _{\mathrm{m}}{\mathrm{S}\mathrm{i}\mathrm{n}\mathrm{c}}^2\left(\mathrm{\pi }\frac{\mathrm{\lambda }}{\mathrm{a}}\left(\mathrm{m}\frac{\mathrm{\lambda }}{\mathrm{d}}-{\mathrm{x}}_{\mathrm{i}}\right)\right)\mathrm{ }=\mathrm{ }\mathbf{\Phi }$ for all orders such that $-1\mathrm{ }\le \left(\mathrm{m}\frac{\mathrm{\lambda }}{\mathrm{d}}-{\mathrm{x}}_{\mathrm{i}}\right)\mathrm{ }\le \mathrm{ }1$ .

In other words, only those orders that lie in the real space [+/- 90°] can receive light.