How does crop factor affect perspective?

Question

I have a question about crop factor and how it affects the perspective.

Suppose you have one Super 35 camera and one APS-C camera. As far as I understand, to photograph the same image on the APS-C camera as on the Super 35 camera, you need to use a wider lens, with the focal length needed being determined by the crop factor. Using a wider lens though, this would affect how the depth is perceived, e.g. background objects appear further away than they do when using a longer lens. Therefore, this would not result in the ‘same’ image. Is that correct?

An alternative would then be to move further away from the subject and use the same focal length. I would assume this would capture the same field of view, but would it have an effect on the perspective? I.e. would objects in the background appear the same size as photographed on a Super 35 camera? How can we ensure an equivalent image is captured, both in terms of field of view and perspective?

Answer 1

When I started photography, this one took me ages to figure out, because people tend to explain it with a lot of math, or in a way that makes sense once you already grasp the principle but not before.

How does crop factor affect perspective?

It doesn't.

Not at all, in the slightest.
The only way you change perspective is to move the camera.
Changing the body or the lens has no effect at all on perspective.
What it affects is only how much of the overall image you can see through the viewfinder.

He was such a hit last time he appeared, I'm bringing him back for an encore.
The toy bear... & the bookshelf

^{I cheated making these so they don't actually overlay perfectly; I used a zoom lens, matched by eye in the viewfinder & later cropped to fit as best as possible - call it artistic license just to quickly demonstrate a point ;)
Click any image for larger version.}

Here's our hero on a crop frame camera with an 85mm lens

Without changing the camera position at all, swap out the camera but not the lens.
85mm on full frame

OK, it looks completely different - but this is not a change of perspective, you can simply see more because the sensor is bigger.

Prove it by overlaying one image on the other...

Again without moving the camera, swap to a 120mm [approx] on the FF camera. You will see an identical image to our first shot - except for difference in depth of field, which will be slightly shallower. The framing & perspective will be identical.

Overlay darkened to show inset 120mm image on top of our 85mm image from above - it's hard to tell, but this is not a perfect overlay from the previous image, probably due to the very approximate nature of my method as well as the DOF change.

Then, to complete the experiment, swap back to the 85mm lens on the FF.
Now we can move the camera until we re-frame the bear as he was in the 'hero' shot from the beginning.

Now we've changed perspective, by moving the camera.
Even though we re-framed to match the bear in our original shot - the bear will almost perfectly overlay the first shot, except for the perspective change - the background is now totally different.

Answer 2

Not correct. Perspective (referring to the size and spacing of background objects relative to subject) is determined by only the distance of camera to subject. This is the geometry drawn from the camera position, regardless of any camera details.

Another focal length or another camera crop size (and subsequent enlargement to equivalent size) can "magnify size of everything seen", but can only see the same view with the same perspective if standing in same location at the same distance. Thinking just a second will conclude that this is obvious. We cannot see two different views from the same one location. Perspective depends only on where we stand to see it.

We do imagine that long lenses compress the distance, if we also change where we stand, to stand far back, at a different distance. But if standing in the same spot, enlarging an image from any shorter focal length necessarily can only see the same exact view from that same location. That one view is all that can be seen from that one spot.

Relative to the subject, standing at one spot with one lens, vs standing back 3x further with a lens 3x longer, will both see the same subject view and field (at the subject). We call that an Equivalent view (speaking of the subject and its distance and its field area at its distance). However the more distant background seen will depend on where the camera stands. Standing back further with a longer lens will see less background, even if the view is the same field at the subject. This is a very valuable property to know for outdoor portraits, to crop and minimize distracting backgrounds (it also provides a bit more depth of field at the subject distance).

Saying again, perspective depends only on the camera distance, i.e., depends on where you stand to see it.

Answer 3

1. Perspective is the size of the objects in the image relative to each other - it is determined by their distance from the camera and from each other in the scene.

2. Composition is the totality of the contents of the image, the location of objects and their sizes relative to the size of the image, some also include perspective as a subset of composition.

3. Focal length is a geometric/optic property of a lens, measured in units of distance.

4. Frame size a.k.a. "the format" is a property of the camera (and also informs lens design since a lens needs to be able to satisfy it by projecting a large enough image) -it is measured along the image diagonal in units of distance.

5. Cropping is the act of changing the frame size, either by using a different camera, sensor area, digital back, film, or digitally cropping a larger image.

6. Field of view and its corresponding angle of view are determined by the focal length relative to the frame size - it can be altered by altering either of the two relative to the other.

7. Changing the field of view (by either un/cropping or by focal length change a.k.a. zooming) without moving the camera or the scene doesn't affect perspective, it does affect composition as objects are included or excluded from the frame and the size of existing ones relative to the size of the image changes.

8. To maintain a given composition under a field-of-view change (if one does not include perspective in the definition of composition otherwise we say that's impossible and skip to 9.), say to keep the frame filled with the subjects face one needs to move the camera further from or closer to the subject - this alters the perspective and in case of portraits the perceived proportions of facial features.

9. To create an image that is identical in both perspective and composition (an "equivalent" image) with different frame sizes the same field of view needs to be maintained, since the frame sizes are given that means changing the focal length. By how much ? By multiplying it by the ratio between the old and the new frame sizes, that's the crop factor and thats's why it is also known as the "focal length multiplier" - it does not multiply the focal length of a given lens, the focal length of a given lens is multiplied by it to obtain a new focal length needed for an equivalent image to be created on a different frame size.

Answer 4

“How does crop factor affect perspective?”

Super 35 film generally has a frame size of 24.89mm x 18.66mm which is smaller than a FF still camera (36mm x 24mm), but larger than a Canon crop camera (22.5mm x 15mm), or Nikon crop camera (24mm x 16mm).

This assumes 3:2 aspect ratio for stills but DSLR video uses a 16:9 aspect ratio and I am unsure of the exact image size used in 16:9 videos.

Video image size and crop factor is going to change considerably depending on which camera and resolution you are shooting with. (The Canon 5D Mk IV has a 1.74 crop factor when shooting 4K video)

Image Source

In general, if you are using a smaller image sensor (crop sensor) then you must either stand farther back, or use a wider lens (shorter focal length) to get the same subject framing.

Standing farther back will change the perspective but by using a wider lens and standing closer, you should be able to match the perspective.

I would think that in most cases, Super 35 and APS-C video are close enough that the average person could not tell the difference.

Answer 5

Perspective in terms of the camera – more to it than you might think:

First a qualification -- Except for special circumstances, proper (correct) perspective is unimportant for the vast majority of pictures taken. However, it is the perspective property of the two dimensional image that allows the viewer to make judgements as to the distances encompassed. For some imagining, correct or nearly correct perspective is essential. We are talking scientific imaging and flattering imagining of faces etc.

Correct perspective: If you gaze out a window at a vista, you can trace with wax pencil, the outlines of objects, on the glass pane. Such a trace divulges “correct” or the “human perspective”. We can duplicate this outlook if we replace the human eye with a camera. It makes no difference what size (format) camera or what focal length lens combination is used.

We can view this photograph as it will deliver a “correct” perspective if viewed same size (contact print or image the same size as the imaging chip), from a distance equal to the focal length of the taking lens. In modern times, such a viewing distance is problematic because our cameras make miniature images and the focal length used is likely shorter than our natural reading distance. It is therefore likely that the resulting image will enlarged. Suppose we enlarge to 8 X 12 inches for viewing. This will require 8 ½ X magnification if the camera is a full frame 35mm. If the camera is a compact (APS) digital, the magnification required will be 12 X. In other words each and every different format size dictates the magnification required to make a final size displayed image.

Now back to “correct” perspective: If the camera image is not enlarged and viewed from a distance equal to the focal length of the taking lens, the perspective realized is “correct”. If enlarged, we must revise the viewing distance based on the magnification applied. Suppose 50mm lens is mounted on a full frame and an 8 X 12 image is displayed by enlarging the camera image 8.5X. Now the viewing distance is 8.5 X 50mm = 425mm = 17 inches. If these conditions are achieved, the viewer is presented with “correct” perspective.

Suppose the same vista is imaged using a compact digital with a 30mm lens mounted. The magnification to achieve a 8 X 12 image is 12X. The viewing distance that delivers “correct” perspective is 33 X 12 =396mm = 16 inches.

Bottom line: It makes no difference what format or what focal length provided the image is viewed from a distance equal to the focal length of the taking lens multiplied by the degree of enlargement.

A key point: Most images are viewed from a distance about equal to their diagonal measure. This fact is taken into account by the industry custom of assigning the “normal” focal length for a format based on the diagonal measure. For the full frame this value is 45mm but usually rounded up to 50mm for convince. For the compact digital (APS) this value is about 33mm

One last point: Over the years camera sizes have shrank due to technological improvements in film and imaging sensors. This trend will continue. The focal length of the lens consigned also reduced proportionally. Thus the final perspective of the image is an intertwining of format size, focal length, viewing distance and magnification to create the image that will be viewed.

Answer 6

It doesn't.

PERSPECTIVE IS ALWAYS ABOUT CAMERA POSITION RELATIVE TO THE SUBJECTS VISIBLE IN THE FIELD OF VIEW. IT IS NEVER ABOUT LENS, SENSOR SIZE, OR ANYTHING ELSE.

As far as I understand, to photograph the same image on the APS-C camera as the Super 35 camera you need to use a wider lens, with the focal length needed being determined by the crop factor. Using a wider lens though, this would affect how the depth is perceived e.g. background objects appear further away than they do when using a longer lens. So this would not result in the ‘same’ image. Is that correct?

NO IT IS NOT. IF THE CAMERA IS IN THE SAME POSITION THEY HAVE THE SAME PERSPECTIVE. PERIOD.¹

Parts of the scene that are visible in one image will be visible in the other. Parts of the scene hidden by other objects in the scene will still be hidden by those other objects. This is because the lines from the camera to each object are always the same and are always straight. What may change is the way those objects are projected by the lens which will affect the shape of those objects as projected onto the focal plane, but the same parts of each object will be visible and the same parts will not be visible as long as the camera and the objects are all in the same position. That is what perspective is!

Any difference between two images made with different lenses shot from the same position and with the same field of view will NOT be due to differences in perspective. They will be due to the differences between the two lenses in terms of geometric projection caused by the way each lens refracts the light passing through it, by the different absolute resolution of the two lens/camera systems, by the difference in color and light transmission between the two camera/lens systems, etc. But there will be no difference in perspective if both photos are taken from the exact same position.

The difference between an image taken with an 8mm fisheye and an image taken with an 8mm rectilinear lens is not a difference in perspective if both images are taken from the same shooting position. It is a difference in the geometry of projecting a 3D world onto a 2D sensor (or film). If there are two objects there with part of one object in front of part of the other object, as long as you shoot from the exact same spot the exact same parts of the rear object will be seen and the exact same parts of the rear object will be hidden by the nearer object. That is what perspective is!

The difference in how those two objects are shaped differently in the two photos is not one of perspective, it is one of geometry of projection. Two totally different things. Perspective distortion is a result of shooting position. Geometric distortion is a result of the different ways different lenses project the same perspective onto a flat imaging sensor or piece of film.

For more, please see this answer to a different but related question: Is there a difference between taking a far shot on a 50mm lens and a close shot on a 35mm lens?
See also this answer to: Does wide angle equivalent in crop sensor skew image?

Perspective is dependent only upon shooting distance - both the distance from the camera to the subject and the distance from the camera to the foreground/background, and the ratios between them all. If you shoot from the same distance with two different sensor sizes or different focal lengths and crop the wider shot to match the narrower angle of view perspective is identical.

If you shoot from the same position with both cameras, then taking the Super 35 camera and crop it to the same angle of view of the APS-C sensor that will give you pretty much the same picture, other than the differences in optical quality between the two sensors and the resolution lost to cropping.

But even if you were to shoot with the same camera, shooting from a different distance will give a different perspective. This is because shooting distance is the only thing that determines perspective. The focal length and sensor size then determine the angle of view and framing from that shooting distance. So backing up with a crop sensor to get the same framing of the subject as a larger sensor would at a closer shooting distance also gives a different perspective: The relative sizes and shapes of items closer and further away from the camera will shift as the ratio of the distances of the various items to the camera changes.

_{Image copyright 2007 SharkD, licensed CC-BY-SA 3.0}

Here's an extreme example of the effect differences in shooting distance have when using different focal lengths to get the same framing from different distances. The change in perspective is due to the change in shooting distance and the different distance ratios between the various elements in the scene and the camera as the camera moves forward and back to preserve framing of the subject at various focal lengths.

https://i.stack.imgur.com/WV9tD.jpg

How can we ensure an equivalent image is captured, both in terms of field of view and perspective?

Shoot from the exact same position with a lens+camera combination that gives the same angle of view. It's that simple. If you want the same depth of field, also apply the ratio of the sensor sizes/lens focal lengths to the f-number used.

_{¹ The reason we think a wider focal length causes objects in the background to be smaller than they would be if we had used a longer focal length lens is because when we use a wider lens we move closer to the subject. This changes the ratio of the camera-subject distance and the camera-background distance. If we shoot a subject from 15 feet and the background is another 15 feet behind the subject,the ratio of the distances from the camera is 1:2 (15 feet/30 feet). If we use a wider lens and move to within 5 feet of the subject the ratio is now 1:4 (5 feet/20 feet).}

For further related reading, please see:
Why do you need to change your position rather than just focal length to affect perspective?
What is the difference between perspective distortion and barrel or pincushion distortion?
Is there a difference between taking a far shot on a 50mm lens and a close shot on a 35mm lens?
Does wide angle equivalent in crop sensor skew image?
Focal length on Full frames and cropped sensors
Can a telephoto lens have a wide field of view?
How does focal length change perspective?
Why is the background bigger and blurrier in one of these images?
What does it really mean that telephoto lenses "flatten" scenes?

Myth Busting: Focal Length & Perspective