Airey Disk/Diffraction: Starting To Understand It.

I have read articles with nice diagrams outlining the problems with diffraction with photography. I know from experience a high F number is going to produce shots as soft as those taken with the aperture wide open. However I didn't really have more than a sort of academic understanding. For the last 2-3 weeks I have been playing with a 1975 vintage fisheye lens. The last couple of days I realised I was seeing real photographs of Airey( am I spelling it right) disks. The fish Eye lens I am using projects a 22mm diameter image on to my cameras sensor. If you ignore the picture in the centre and look at the black area you can see rings ( caused by diffraction) around the picture. The rings get fainter as you move out from the picture Its helped me understand it more! Its much more obvious on my computer screen looking at the origonal.