The fine structure of the annular images of circular gratings is analyzed in terms of diffraction patterns of axicon pairs. Each image arises substantially from only one converging and one diverging axicon of equal deflection angle. Single main lobe, symmetric double main lobe, and various intermediate asymmetric double lobe structures are obtained depending on the phase relationship and strengths of the two axicon beams, which in turn depend on the design of the circular grating. Approximate expressions are derived for the intensity distribution and energy content of the symmetric single and double lobe images.
Andre Fedotowsky and Kurt Lehovec, "Far Field Diffraction Patterns of Circular Gratings," Appl. Opt. 13, 2638-2642 (1974)