Modelling sky noise using a 2D array with plane waves I have a question about modeling sky noise which should be filtered by a spatial filter 4f system. My approach for this task is to use a 2D array with random amplitude values and another 2D array that simulates different phases based on the directional cosine of a plane wave. So my code should create a 2D array where each element is a different plane wave with a different amplitude and direction of propagation. These plane waves should hit the aperture of the first lens of the spatial filter at different angles at different positions (so that they are focused on different positions in the Fourier plane).
This is my approach:
$$
Noise(x,y) = A(x,y)\cdot e^{-i(k_xx + k_yy)}
$$
Where:
$$
k_x = \frac{2\pi}{\lambda_0}cos(\alpha(x,y)) \\
k_y = \frac{2\pi}{\lambda_0}cos(\beta(x,y))
$$
My question here is: Is my approach right, or did I miss something here?
Edit: I want to use this noise 2D array for a spatial filtering siumlation of a 4f system by using Fourier optics, and my initial field has a Gaussian field distribution superimposed with noise. The goal is to see how much noise is filtered after the system, when diffraction is taken into account. But at the moment I'm not sure how I can simulate the noise that should represent sky noise.
Here is also an image of the problem that I want to simulate (Taken from: Gruneisen, Adaptive spatial filtering of daytime sky noise in a satellite quantum key distribution downlink receiver, Optical Engineering 55(2), 026104 (2. February 2016))

Thanks in advance!
 A: Welcome to Physics SE!
First step: have you checked the literature? I saw  some interesting stuff with a quick Google search. Compare the data and approaches to your own. If yours is good/reasonable, only experiment can tell. Gaussian noise, however, is a common standard. As far as I know, your approach seems to be fair enough. If I were going to model sky noise in the simplest naive physicist-appealed way, I'd use the Rayleigh distribution, since (1) it is almost equivalent to Maxwell-Boltzmann, (2) It is related to distance distributions (density of gas molecules in the atmosphere, which correlate with scattering intensities) and (3) people actually use it in wind-speed modelling. Obviously related is Rayleigh sky model.
In any case, I strongly suggest working with some real-world data. Perhaps try to fit your parameters (essentialy alpha, beta and lambda_0 (?)) via, I don't know, simple linear regression methods? Maybe you'll actually find that the fit is superfluous: uniformly distributed random parameters might do the job already for a statistically relevant dataset.
A nice thing to do would be training a Neural Network to find optimal parameter distribution. Could be accurate but hard to interpretate. Check this Kaggle competition, you'll probably find a good model already, plus the always nice discussions.
