# Difference between Fast Fourier transform of a 2D lattice image and its reciprocal lattice image

I have constructed an image of nXn pixels with each pixel having values either 0 or 1. I have added circles in the form of square lattice with definite period a.

The image basically looks like (a).

If I perform Fast Fourier Transform I get this image (b).

The zoomed-in image looks like this (c).

My questions are,

1. Are FFT of the square lattice obtained above same as reciprocal lattice of the same square lattice?

2. Assuming that the spacing between neighbouring points in square lattice is a, what is the spacing between neibouring points in reciprocal lattices? is it 1/a or 2$\pi$/a?