I am trying to understand a sentence on section "The blazed reflection grating" of The Observation and Analysis of Stellar Photospheres.

After saying a large part of light is lost to zero order of maximum, and we want to use higher order, it states that

To solve this problem, the diffraction envelope must be shifted relative to the interference pattern to those $\theta$ value where we wish to work. The Fourier shift theorem tells us that we can accomplish this by introducing a phase term in $B_1(x)$. When this is done the grating is said to be blazed.

In previous section it is proven that the resultant waves behind the grating can be written as the Fourier transform of grating transmission $G(x)$. The function of facets is to change the direction of light, then shine it into the place of higher order.

But what I don't understand here is that how the facets "introducing a phase term in $B_1(x)$"?


For normal gratings, $B_1(x)$ is real and binary, "1" for transmission and "0" for non-transmission. But a blazed grating will introduce a tilted surface of each rectangular function, as a result, introducing a phase term of something like "$exp(-ikx)$", now $B_1(x)$ will become complex.


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