Distortion with Nikkor 14-30 f4 S

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It is my understanding that the considerable distortion from the 14-30 f4 S lens is automatically corrected in Lightroom and Photoshop. I have been taking fall foliage pix and am appalled by the distortion I'm seeing in both LR and PS! LR's Lens Correction module says "Built In Lens Profile Applied". Since, with this software, one cannot see the uncorrected image, I am assuming that the profile IS applied by the software. Looks the same in both LR and PS. In the attached photo at 14mm, the camera is level and the trees on both sides are vertical in real life. Also, the earth is flat.
Am I expecting too much?
I can improve it with vertical transform in LR, but at the penalty of severe cropping.
Your comments please.
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I think what you're seeing is what's called 'keystoning'. A wide angle lens exaggerates perspective, so lines above and below the horizon line seem to converge. I don't think it's really distortion, per se. This is what tilt-shift lenses (and view cameras) are good for. Raising and lowering the front element has the effect of eliminating this. (The distortions wide angle lenses are prone to are what are called 'barrel distorion' and 'pincushion' distortion, and I think this lens has both, depending on the focal length, but LR does a good job of eliminating it.

All told, I think this is really an excellent lens for landscapes, especially at the price.
 
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1. Do you think LR did a good job of correcting it in my photo? I do not. I think it's horrible actually with the trees on each side leaning in, and the ground convex!
2. Doesn't keystoning pertain to tilting the lens up? I thought so, but could well be wrong. Nevertheless, I think this is distortion. No?
 
I was wondering whether the automatic correction software included in the lens was failing because the photo looked so bad.
My previous widest lens was 16 - 30. Never saw this. 4 Perhaps this is normal behavior for 14 mm. My understanding was that if the camera/lens were level that one would not see this distortion, that the lens was rectilinear i.e. straight lines stay straight , but FOR THIS LENS that is made possible by "corrective " software transmitted from this lens to LR and PS and others.
 
You can manually correct in LR in Optics/ Disortion, allowing correction in vertical and horizontal planes, separately and manually. ….at the expense of a heavy crop as others have noted.
 
The images is clearly presenting keystoning, which for my understanding is not a distortion.
Pincushion or Barrel distortion is a effect seen in most lenses, but especially in zoom lenses. By analyzing images taken with the lenses the software manufacturer can make a profile for the lens that automatically can remove the 2 effects. The image above is not likely to show trace of these effects as no lines seems to be parallel with the top-bottom edge.

I have not seen any automatic handling of keystoning, maybe because distance to the subject has an influence on the amount of keystoning in the image. So we will have to use tools to manually fix keystoning - if we don't like it as an artistic effect - and get lines parallel again. This will naturally need to crop away some parts of the image.

I use Darktable in it's crop-rotate filter there is handling of keystoning (both vertical and horizontal) just need to drag 4 points on guidance lines into right position and click OK, then the image i straight and smaller
 
I believe 'rectilinear' designs are intended to keep straight lines straight, but I've noted the proviso on several definitions that extremely wide angle lenses still show increasingly exaggerated perspective effects. I suspect that's what you're seeing at 14mm. The lens is rectilinear by design, though the technical reviews do say that it has a fair amount (something like 3% is quoted) of barrel distortion uncorrected. Lines would appear to curve outward without correction.
 
This is very normal with wide angle lenses. To see the most extreme examples, look at images made with a fisheye lens. Here is a short article that explains:


As you noted, correction in Lightroom requires quite a bit of cropping. That is, however, the only way to make the correction you are looking for.
 
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