It has for sure a very obvious answer, but I must admit I find it very difficult to visualize how a linear phased array can focus the beam with a sinc pattern. I'm not talking about the mathematical proof of the array factor shape, which can be easily found everywhere on the web, but just the intuitive analysis.
Let's consider the following picture:
It says the main beam of the sinc array factor points along the array normal direction. It appears to justify this by saying the single radiating elements spherical wavefronts are aligned in such a direction. However, I do not understand that. Why is the main beam direction orthogonal to the horizontal line connecting the single spherical wavefronts?
Will there be another constructive interference along the following direction in blue?
Why are there the side lobes? How can we visualize their cause?