#format jsmath
= 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 position dither function to try:

||<:-3> $  D = L/2 $ ||<:-3> $  k = 2 \pi / N * L $ ||
|| $ \Delta x = D * ( \sin( k z ) + \cos( k y ) ) $ || ||<-2> $ \Delta y = D * ( \sin( k x ) + \cos( k z ) ) $ || || $ \Delta z = D * ( \sin( k y ) + \cos( k x ) ) $ ||

... or some variation of that ( I originally tried $ D = \lambda/2 $ , with little effect).  This assumes the spacing $ L >> \lambda $, a sparse array, so that the antennas do not couple (much).
Try scaling D and k, and also modifying amplitudes across the array like a Hamming window, and see how that changes the sidelobes. 

This happens on top of the array of perhaps hundreds of emitters on the thinsat itself, which beamforms to a few degrees of angle,
reducing power splattered far from the target.

The signal is broadband, so there is not a well defined $ \lambda $.   We may end up making k a function of x, y, and z as well.

== 5x5x5 skewed, dithered array ==

{{ attachment:a4d21.png | | height=768 }}

Annotated version with explanation coming soon.


== 16x16x16 skewed, dithered array ==

{{ attachment:a4d21-16.png | | height=768 }}

Annotated version with explanation coming soon.

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