Fourier Transformation of Array Factor [exp(cos(t))]

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I have a following issue. I have a formula of Array Factor. It looks like:

$$AF (\phi) = I_{0} \cdot \exp[j\cdot b\cdot\omega_{0}\cdot(\cos(\phi-\phi_{0}) - \cos(\phi_{w}-\phi_{0}))]$$

$I_{0}, b, \phi_{0}, \phi_{w}$ are constants.

Now i need to calculate Fourier transform of it (transition from "angle" domain to "frequency" domain).

I know a correspondent of $exp(j\cdot\omega_{0}\cdot t)$ (that's a two Dirac functions) - in my case i use angle instead of time, but it doesn't matter.

But the problem is that in my case i have deal with $exp(j\cdot\cos(\phi)\cdot \omega)$ and can't see a possible way to solve it.

Any suggestions?

Thanks for your help

Mikka