Fourier representation of aperiodic irregular function

MadMax
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We have

\epsilon(i f, r) = \epsilon_2(i f) when H + h_2(x) \leq z < + \infty
\epsilon(i f, r) = 0 when h_1(x) < z < H + h_2(x)
\epsilon(i f, r) = \epsilon_1(i f) when - \infty < z \leq h_1(x)

show the corresponding Fourier transform is

\frac{i}{q_z} \int d^2x e^{iq_\bot \cdot x}[\epsilon_2 e^{iq_z[H+h_2(x)]} - \epsilon_1 e^{iq_z h_1(x)}]

I've looked in a few books but tbh I have no real idea how to show this...

Any help/suggestions/tips would be much appreciated. Thanks.
 
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a small hint please?
 

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