The Sigma 18-125mm is a "superzoom" lens, which means it focal range goes from wide angle to moderate tele (in 35mm equivalent, the range is somewhat like 28 to 200mm). This results in relativ strong distortion on both ends of the focal range.
The following images are taken with focal lengths trough the whole range of the lens, starting from 18mm. Some lengths I tried to use where exactly met, others differ slightly from the desired value (e.g. 34mm instead of 35mm). It is remarkable, that the lens has a relative low resolution in measuring the focal lengths in the short area: there are only values of 18, 21 and 23mm available, 20 or 22mm never occur.
Wide angle: barrel distortion in the center area, pincussion distortion at the corners.
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| 18mm (short end of focal range) | 21mm (should have been 20mm) |
Short normal focal lengths (28mm is the sensor diagonal): the barrel distortion in the center area begins to vanish, the pincussion distortion at the corners is still slightly visible.
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| 23mm (should have been 24mm) | 30mm (should have been 28mm) |
longer normal focal length to short telephoto: barrel distortion becomes invisible, the pincussion distortion starts to become very distorting in the corners.
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| 34mm (should have been 35mm) | 51mm (should have been 50mm) |
telephoto range: Here a pure pincussion distortion is found.
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| 67mm (should have been 70mm) | 98mm (should have been 100mm) |
longest focal range: The pincussion distortion continues.
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| 125mm (longest focal length) |