the sum of all contributions to the wave function is: Again noting that is small, so , we have: Now, we can use the following identity Substituting into our equation, we find: We now make our substitution as before and represent all non-oscillating constants by the variable as in the 1-slit diffraction and bracket the result. Remember that This allows us to discard the tailing exponent and we have our answer: General case for far field In the far field, where is essentially constant, then the equation: is equivalent to doing a Fourier transform on the gaps in the barrier. See also Diffraction grating Envelope (waves) Fourier analysis N-slit interferometer Radio telescopes References Equations of physics Wave mechanics