Fourier Transform of a Bessel Function

Hi all,

I'm working on a project (imaging) where I have a Bessel function that I need to take the Fourier Transform of. I looked the transform up in a table, and was given:

W(q) = J1(2*pi*a*q)/(pi*a*q) <=> w(r/2a) = {1 if r < a, 0 if r > a}

Where q is a radial distance in the starting plane, and r is the radial distance in the end frame. So, basically, the transform of a Bessel function of the first kind (n=1) is a window function. What I am confused about is the the parameter "a." I know that I can use it to vary the "width" of the Bessel function (another thing I am slightly confused about, how is the "width" of a Bessel function formally defined?), but what does w( r/2a ) mean? I would like to be able to predict for a given "a" the width of the window function produced from the above transform (or is it as simple as the window has width a?).

Thanks for your consideration of this issue.

Dillon