# Maximum Theoretical Angular Accuracy of Planer arrays

Hello,

in this link http://dtic.mil/dtic/tr/fulltext/u2/a028054.pdf a paper „Maximum Theoretical Angular Accuracy of Planer and Linear Arrays of Sensors“ can be found.

The accuracies are given in equations 19 (respect to the x axis) and 20 (respect to the y axis).

My question is: Shall the angle between the incoming ray and the normal direction to the planar array also play a role? I mean, the 90 degrees angle (along the normal direction) shall have the greatest accuracy. In example of line array on page 15 this angle (15 degrees there) is considered. Do I understand it correctly?

Senmeis

marcusl
Gold Member
I haven't read your link, but I can make some general comments about angular resolution. As the angle of incidence moves off of broadside, the apparent extent of the array normal to the incoming wave shrinks by cos(θ), due to simple geometry. This has two effects. First, the angular resolution suffers since it varies inversely proportional to the aperture length. Second, the SNR drops for the same reason. In fact, the electrical gain of the array drops more quickly than cos(θ) because the antenna elements become mismatched (no longer 50 ohms, e.g.) due to varying phase shifts in the mutual antenna coupling terms as the angle increases. It is common to approximate the rolloff in antenna gain (hence SNR) as cos(θ)^1.5, though this is just an approximation. Both of these effects will reduce the resolution and accuracy.

Thank you. Can I understand what you are saying as following in simple words?

1. For a planar array the best accuracy and resolution can only be achieved if the incidence ray is on the normal direction.

2. The accuracy and resolution are different with different directions of incidence (different elevation and azimuth angle).

Senmeis

marcusl