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The 18-55 also has strong distortion. In Iridient Developer you can turn off the correction that's embedded in the RAW file (you can't in Lightroom). Maybe this strong -varying along the zoom range- distortion makes the field curvature less predictable.
Ken Rockwell says this about the 18-55
"Distortion as shot on the X-E1 is completely invisible, except for moderate to minor pincushion distortion at 23mm, whoo hoo! (I'm pretty sure that the X-E1 is correcting this automatically.)"
Photographyblog.com review says this
"At the wider end, the Fujifilm XF 18-55mm F2.8-4 R LM OIS has some barrel distortion, as you can see in the photo above, but it's no worse than you would expect from a 27mm lens."
Ephotozine says this
"Just over 0.2% barrel distortion is present throughout the zoom range. Not only is this remarkably consistent performance for a zoom lens, but the level is so low that it will be very difficult to spot."
Imagingresource says this
Low geometric distortion with the 18-55mm kit lens in JPEGs, though strong distortion in uncorrected raw files.
When shooting JPEGs, the Fuji X-E1's 18-55mm kit lens produces about 0.3 percent barrel distortion at wide angle, which is much less than average and just slightly noticeable in its images. It isn't very symmetrical though. Pincushion distortion at full telephoto is just over 0.1 percent, also much lower-than-average and hardly noticeable. This is the tendency for the lens to bend straight lines outward (like a barrel -- usually at wide-angle). The Fuji X-E1 compensates for most distortion, though. "
My conclusion is that there is some distortion, but that the lens does very well compared to other zooms. It is almost as good as some primes. The camera corrects some of the distortion automatically with jpg shooting.