Originally posted by Big G My question is: what makes a fish eye at 10mm different from a non fish eye at 10mm? Is the fish eye deliberately distorted? Is it something to do with the lens element setup?]
A fisheye lens needs that kind of distortion to achieve its 180 degree fielf of view. The point is, if you compare the images of the fisheye versus the Sigma 10mm ones (that's a rectilinear lens), you will find some more differences, not just the barrell distortion:
A fisheye uses a special projection (most use the equisolid angle projection) to fit the 180 degrees view into the image frame. So the "barrell distortion" is not a fault of the lens, but a design goal.
Rectilinear lenses, like the Sigma 10-20mm zoom aim to prevcent the curved lines and produce no or less visible distortion. BUT at the expense of a changing projection ratio, which gets very visible (and annoying) near the edges. Photograph a person with a rectilinear lens, which is placed near the frame edge and you'll distort the person's head to some ugly egg-form. BUT this is usually not or hardly noticeable in landscapes.
A short wrap-up cayn be found here:
Fisheye Projection - PanoTools.org Wiki
Some people use software tools to "correct" the distortion of the fisheye lens, which is counterproductive. You not only interpolate many pixels (which reduces resolution), but also end up with a much diminished angle of view, which a rectilinear lens provides anyway.
Simply think of a fisheye lens versus a rectlinear lens as two very different lenses, which serve different purposes.
Ben