# Array Phasing

When we randomly dither the position of the emitters in a 3 dimensional phased array, it smears out the grating lobes. I am looking for a better function.

A smear function to try:

D = \lambda/2 k = 2 \pi / N * L

\delta x = D * ( \sin( k z ) + \cos( k y ) ) \ \delta y = D * ( \sin( k x ) + \cos( k z ) )

\delta z = D * ( \sin( k y ) + \cos( k x ) )

... or some variation of that. This assumes the spacing L >> \lambda , a sparse array, so that the antennas do not couple (much). We can scale D and k, and also modify amplitudes across the array like a Hamming window, and see how that changes the sidelobes.

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