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Hello
Here is an uniform E filed distribution aperture antenna E and H far filed euations
2204887800_1448824658.png

and here is directivity calculation approach
6234799200_1448824658.png
my problem is why don't we calculate D with both E(theta) and E(phi)? My mean is:
instead of using
.latex?U%3Dr%5E2.P_%7Bave%7D%3Dr%5E2%28%5Cfrac%7B%7CE%28%5Ctheta%29%7C%5E2%7D%7B2%5Ceta%20%7D%29.gif
we should use
3Dr%5E2%28%5Cfrac%7B%7CE%28%5Ctheta%29%7C%5E2+%7CE%28%5Cphi%29%7C%5E2%7D%7B2%5Ceta%20%7D%29.gif
because both of them are not zero in far-filed zone and not zero at theta=pi/2
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