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I've been pondering this problem for a while but am daunted by the maths I suspect is required.

Consider the irradiance from a diffraction grating:

I=I0(sinB/B)^2 . (sin Na/sin a)^2

where a=0.5kdsin(theta)

b=0.5kwsin(theta)

I0= max irradiance

N= No of slits

k= wavevenumber

d= distance between adjascent slits

theta= angle of diffraction

w= width of anyone slit

My question is how to derive a similar equation for a grating in which the slit separtion is not uniform but is instead, a function of y (the distance along the length of the grating).

Any help would be grately appreciated.

Many thanks