Here we go again!
First thing. Distortion and perspective are not the same. In lenses "distortion" is defined as an aberration where the corners of an image projected by the lens pull outward (pincushion) or the corners pull inwards (barrel). Distortion is independent of focal length. It is controlled in the design of the lens and is affected by the placement of lens elements and the placement of the aperture diaphragm inside the lens. It cannot be corrected by anything you do with your camera. It is built into the lens. Post-processing software often provides tools to help correct distortion. Most lenses are corrected as much as they can be for distortion. Rectilinear lenses attempt to keep straight lines straight across the image plane. Wide angle rectilinear lenses do have a characteristic of stretching objects at the edges of the frame. this comes from trying to fit a very wide almost unlimited view onto a fixed size image sensor (or film). This is usually most noticeable when the camera is in very close to the subject. The cure for this stretching is to use a fisheye lens! But that introduces a whole set of other issues for another discussion.
An interesting point about this "wide angle distortion" is that it only affects 3-dimensional subjects. Let's take an example of a tennis ball photographed with a wide angle rectilinear lens. If the tennis ball is in the middle of the frame it appears perfectly round. If it is move off to a corner of the frame you can see that it gets stretched out into an oblong shape. However, if you make a print of the centered ball and put the print in the corner of the frame in place of the actual tennis ball the ball in the print remains round.
But enough of that, it is just a distraction from what I want to talk about. If you want more information about lens distortion I invite you to take a look at this article from Zeiss.
On to Perspective!
I seem to be on a perpetual quest to help photographers understand the affect on perspective caused by camera to subject distance and how it is not related to focal length. Perspective here is defined as the relationship between objects in the scene. Objects closer to the camera appear larger than objects farther away. Objects closer to the camera also appear farther apart from each other than do the object farther away. It doesn't matter what focal length lens you use. All lenses show the same perspective from the same camera position.
So, you ask, what about telephoto compression? Isn't that caused by using a long lens? No! Go back to the previous paragraph. Looking at it from the other direction, it says that objects further away from the camera appear to be closer to each other than objects closer to the camera. Focal length doesn't affect that. Focal length affects magnification and the field of view (how much of the scene fits into the frame). You don't even need a camera to see how this works. Go someplace that has a series of similar items spaced out evenly in front of you. Maybe a long stretch of road with street lamps or something like that. Stand a foot or two from the first object and notice the distance to the second object. Pretty far apart. Now concentrate on the 8th and 9th objects. They look closer together and more similar in size. There is your compression. Of course, you took your camera with you anyway. So put the camera on a tripod and take a photo with a short lens and another photo with a longer lens.
Take those two photos into your favorite photo editor and crop the photo taken with the short lens to match the image taken with the long lens. You will see that for the area of the photo that is common to both focal lengths the perspective (and compression) are the same. When we want to show this compression we, of course, will pick a longer focal length lens as cropping optically maintains image quality as opposed to digital cropping or making an extreme enlargement from film. Changing the lens just changed the magnification, though, not the perspective.
Here is a set of images from a train station in Kyoto, Japan. All were made from the same camera position at various focal lengths rom 18mm to 400mm. Notice that perspective in the area outlined in purple, which is common to all of the photos, remains the same.
The same thing happens in our portrait work. From the same camera position your subject will look the same (except for size) if photographed with a 10mm lens or a 100mm lens. Take a look at the following image. It shows a studio scene made with a 10mm lens on a full frame (35mm) digital camera. The camera is fixed on a tripod at 58 inches from the mannequin. If you drag the slider from the right side to the left you will reveal an image taken with a 100mm lens and resized down to match the size from the 10mm lens. Notice that the perspective on the face is exactly the same from both lenses, despite the vast difference in focal length.
Here we see the same setup photographed with an 85mm lens next to the setup photographed with the 10mm lens. Again, the perspective is the same.
Here is a set of photos made with the following lenses: 100mm, 85mm, 50mm, 35mm, 24mm, 20mm, 16mm, 15mm fisheye, and 10mm. Despite the extreme barrel distortion bending everything but the center of the image, even the 15mm fisheye shows the same perspective on the face (see below).
Here are the 85mm and the 15mm fisheye cropped to the same framing...
This is also from Anatomy of a Studio Portrait.Can you tell what focal length lens was used for each of the above images?
From left to right, top to bottom: 200mm, 135mm, 105mm, 100mm, 70mm, 57mm, 38mm, and 24mm.
To round things out, all of the photos in this set were made with the same 24mm lens, but the camera to subject distance was changed attempting to maintain the same size head in each image. Distances are 20 inches, 24 inchces, 28 inches, 39 inches, 51 inches, and 60 inches.
What about full frame vs crop frame?
Easy enough. Same setup with two cameras. Full frame (Canon 5Diii) with a 50mm lens and a 1.6 APS-C (crop) frame (Canon EOS M5) with a 35mm lens. Camera to subject distance is the same (36 inches) in both photos. The facial features are the same.
Let's take it further and compare the 50mm lens on full frame with a 10mm lens on crop frame...
I hope this helps explain how distance affects perspective. Yes, you can get very widely different perspectives by using different focal lengths, but that is when and because you move the camera. Telephoto (long) lenses tend to make us back up away from our subjects making the scene look more compressed. Wide angle (short) lenses invite us to move in closer to our subjects making the scene feel more wide open. It is our moving in and out, though, that changes the perspective. The focal length of the lens then determines how much of the scene will be captured.
For even more on this topic, please visit the Understanding Camera Lenses article at Cambridge In Colour. And take a look at the other tutorials there. Sean McHugh does a great job at explaining photographic concepts with text, illustrations, and calculators.