Irradiance distribution of an optical system with Gaussian source using fft functions

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I am trying to create (in matlab) an irradiance distribution in a 2-D array, using the exact scalar method. As of now I have a 2-D array defined as my aperture function and I also have a 2-D array defined as a Gaussian function (light source).

I believe that I know how to do this with a uniform input due to some simplifications in the mathematics, however I'm not sure how or where to include the Gaussian input. My intuition says that there should be a convolution included somewhere, but I'm not quite sure. Any help would be greatly appreciated. I'm not necessarily looking for any specific code, just the correct way to go about solving or incorporating the Gaussian source.

I am not sure if there is enough detail in this post, if not please let me know and I will post whatever more necessary.

Thanks!
 

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