grating lobe antenna

Hi, everyone. I have a simple question about avoiding grating lobes by arranging antenna array element spacing.

I remember that when the element spacing less than some value, theoratically only main lobe remains without grating lobe. But I cannot find the reference anymore.

Would you recommend some books chapters or reference online about that? Thanks.

Hi, Jay:

It should be slightly less than 1 wavelength in free space. If you have exact 1 wavelength in free space, you will have a grating lobe at theta = 180 degrees if your main beam is at theta = 0. You should try to reduce the spacing to be slightly smaller than one wavelength.

I think you can find it in most antenna books. However, if you can not find it, you can consider a uniform array of N elements in phi = 0 direction, its array factor is:

F = sum{i=0,1,2,..N-1}{ exp(j*k*r*sin(theta) } along phi.

You can derive a formula and you will see when kr=2*PI or r = one wavelength, you will have the grating lobe at theta = 180 degrees.

Regards.

it depends on the type of array?
linear/planner/circular..