Focal length on Full frames and cropped sensors

Yes, this subject again. But I have a slightly different question and I was unable to find an answer here or anywhere else.

I understand a 50mm lens is a 50mm lens ALWAYS. I understand that "equivalent focal length" is a theoretical thing that is more about comparing field of view between different sensors. I understand that a 50mm DX on a cropped sensor and a 75mm FX on a FF have the same field of view. What I would like to know is: Do they have the same perspective? If you take a photo with a FF camera and 75mm DX lens and compare that image with another shot of same subject made by a cropped camera and a 50mm lens what will you see? Can they be superimposed without any deviation?

Another experiment: Two shots of same subject, one in a FF/50mm FX and another in a cropped camera/50mm DX. In this case, the image produced by the FF camera is large than the other. Fine. But if you superimpose the image produced by 50mm DX on the central region of the image produced by 50mm FX what will you see? Any deviations? Or a perfect match?

So far, I understand the first experiment will result in a slight deviation because one is a 75mm lens and another is a 50mm - they are two completely different things, only with a similar field of view, and so they have different perspectives.

In the second experiment, I expect a perfect match on the central region, because they have the same geometry and perspective.

Also, based on the geometry, I expect that deviation would be larger in short focal lengths (50mm and below) and they may be irrelevant on longer focal lengths (100mm and above).

Am I right ?

PS: This is a theoretical discussion about ideal lens, about geometry and perspective. Please, ignore chromatic aberrations, construction, design, makers, technology, coats, whatever.

I appreciate your patience on this subject.

best regards,

Keeping in mind that you are asking about a perfect, theoretical lens:

What I would like to know is: Do they have the same perspective? If you take a photo with a FF camera and 75mm DX lens and compare that image with another shot of same subject made by a cropped camera and a 50mm lens what will you see? Can they be superimposed without any deviation?

I assume that you actually mean "full frame camera and full-frame lens".¹

In this case, if you:

• print or enlarge to the same size, and
• also compensate for depth of field by adjusting the aperture, and
• and put the camera in the exact same place, and
• have theoretically ideal lenses and sensors,

then, yes, you'll get indistinguishable results. They have the same perspective, because you're taking the photograph from the same location, and perspective literally means the appearance of objects from a certain location.

This will also be the case if you put the 50mm lens on the full-frame camera, keep everything else in mind above, and then crop away the edges keeping only the center.

Another experiment: Two shots of same subject, one in a FF/50mm FX and another in a cropped camera/50mm DX. In this case, the image produced by the FF camera is large than the other. Fine. But if you superimpose the image produced by 50mm DX on the central region of the image produced by 50mm FX what will you see? Any deviations? Or a perfect match?

Right — if you follow the rules above, this will be a perfect match.

In a theoretical universe, zooming in is exactly the same as cropping. This is why the "digital zoom" feature common on compact cameras works, and how you can "zoom in" on a cell phone which has only a fixed lens.

1. If you put a DX lens — a Nikon lens designed for APS-C — on a FX Nikon camera, the image will be cropped effectively turning the FX camera into a DX camera. If you disable this, or use a lens designed for a crop sensor on a camera without a similar feature, the full image will be captured, but there may be significant vignetting (or even complete blockage) at the corners, because the lens design may not project an image circle large enough to cover the whole of the larger sensor.

• Postscript: Although you say I have a slightly different question, this really, really, is exactly the same question as all of the others. Dec 22, 2016 at 12:59

If you take a photo of a FF camera and 75mm DX lens and compare that image with another shot of same subject made by a cropped camera and a 50mm lens what you will see ?

But to be able to see the "same subject size" in the pictures, the longer lens must stand back further. So that is a difference in what the lens will see there, at that new location.

So the perspective will be different, because perspective is determined simply by where the camera stands. Any lens on the camera standing in the same spot obviously can only see the same scene as any other lens sees there, specifically with the same perspective. There can be only one view to see from that one spot. But if you move the camera, you see a different scene (a different perspective).

Focal length can enlarge and crop, but of the same scene and perspective, if standing in the same place. There is only one view to see from that one spot. Perspective is NOT about focal length, it is only about where the lens stands, and the view it sees there. Perspective is the relationship of objects in the scene, how they appear from the spot that you are standing to view them. The lens cannot change the perspective it sees there, but it can affect your choice of where to stand.

If you stand in the same place, but later crop the full frame image to match the cropped frame, then the pixel count will be less, but they will be the same image if from the same spot (assuming all else the same, including enlarging the smaller picture more to show and compare at the same viewed size).

The DX frame is a simple crop of the FX frame, simply due to the smaller sensor. With the same lens standing in the same place, there is no other difference, just sensor size. It is called a "crop factor". The smaller image is simply cropped from the larger image that the lens might show. Some properties like depth of field appear different, merely because those numbers are computed from the sensor size, and in practice, that the smaller image is enlarged more to view it. Enlarging it more simply better shows any blurriness due to depth of field (therefore Circle Of Confusion for Depth of Field is computed from sensor size, typically CoC = frame diagonal / 1500.)

• uhh..something is not quite right. Consider the perspective distortion that occurs at focal lengths as small as 8mm. Nearby objects appear much larger than slightly distant objects.So, focal length plays a role here. Is that effect that I am interested in understand. A 50mm lens has a different perspective distortion than a 75mm lens, isn´t ? So they are not equivalent, although they have the same field of view. Dec 20, 2016 at 10:55
• No, think it out. That perspective change is ONLY because the short lens must stand much closer to see the same size subject. Stand much closer, and yes, the perspective will change. But if you stand in the same place, then there is only one view possible to be seen there. The lens has no ability to make close things larger, and distant things smaller, Only where we stand to look can do that. Any lens just sees what it sees there. You will see the SAME perspective change with the SAME LENS standing up close, and standing far distant. Perspective seen is only about where we chose to stand. Dec 20, 2016 at 15:26
• The main emphasis of this answer is absolutely correct, but there's an incorrect assertion in the first paragraph. You can either stand farther back with the longer lens to get the same subject size, or you can crop the shorter lens so the subject takes the same proportion of the total picture. If the crop camera with short lens and FF camera with long lens have the same pixel dimensions, the pictures will be identical. Dec 20, 2016 at 20:13
• OK, but distortion of a 50 or 75 mm lens should be nearly nothing, compared to a wide angle lens where it becomes a problem. You did not mention "portraits", but portraits is where I think of perspective. 50mm is too short for portraits anyway. Portraits (excepting groups or full length views) ought to be more like 70mm DX or 105 mm FX. That simply to forces us to stand back at least 6 or 7 feet or more, for proper portrait perspective. For portraits, first of all, stand back properly, and then zoom in all you want, for the view you want. But stand back some, for proper portrait perspective. Dec 21, 2016 at 16:19
• @MichaelClark sorry, I'm not familiar with the Nikon terminology, so I missed that little nuance. Of course that changes everything and my comment is no longer relevant. Dec 21, 2016 at 19:23

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.

So far, I understand the first experiment will result in a slight deviation because one is a 75mm lens and another is a 50mm - they are two completely different things, only with a similar field of view, and so they have different perspectives.

NO THEY DON'T. IF THE CAMERA IS IN THE SAME POSITION THEY HAVE THE SAME PERSPECTIVE. PERIOD.

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 distortion 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?

• Note to casual / drive-by readers: Michael is not shouting at OP per se; "perspective being a function of the lens" is a common misconception that is repeatedly corrected and restated here at Photo.SE.
– scottbb
Dec 19, 2016 at 20:17
• In my hypotetical experiment, both the lens and camera body were changed ! Please, read my question again. I am interested in find differences between images taken with a FF/75mm and a APS/50mm. I am thinking in that perspective distortion that is obvious at short focal lengths like 8mm (not fish eye). That perspective distortion is present in a 35mm, but in a lesser extent. It is still present at ANY focal length but is smaller as the focal length increases.So, a 50mm has a certain degree of perspective distortion which is greater than in a 75mm lens. So they are not equivalent, isn´t ? Dec 20, 2016 at 11:18
• Even more, the bokeh is not the same, the DoF is not the same. Only the field of view. So why people says they are equivalent ? There are more differences than similarities !In the other hand, a 50mm DX on a APC body and a 50mm on a FF body produces images with only one thing different: the field of view. And the perspective distortion will be the same, the DoF will be the same, and the bokeh will be the same (I hope, this is why I am here). Dec 20, 2016 at 11:18
• The diameter of aperture is given by d=f/n where f is the focal length of lens and n a number (2.8, 4, 5.6 etc).Two lens said equivalents, a 50mm on APS and a 75mm on a FF don´t have the same aperture in diameter at same f number. Lets says they are both in f/4. One will have d=50/4=12.5mm and another will have d=75/4=18,75mm which explain the difference in DoF and bokeh, at least is how I understand this. Please correct me if I am wrong. Dec 20, 2016 at 11:18
• @MiguelRozsas geometric distortion is dependent upon individual lens design, not focal length. You could have two different 50mm lenses and one would shape the FoV differently than the other. It is true that it is harder to make a flat field, low distortion wide angle lens than it is to make a flat field, low distortion narrow angle lens. But by about 35mm and longer even lower priced consumer grade primes are generally very low distortion. With zooms it is much harder, especially the wider the ratio is between the shortest and longest focal lengths... Dec 21, 2016 at 18:41

I always get the impression that people like to explain this the hard way.

Let me try explain it how I understand it, the easy way, & see if it gets up or down-votes.

[For this entire explanation, let's just ignore everything not related to the actual 'view of the scene' as it arrives on the CCD. Let's imagine both cameras have the same 'dpi' but different sized sensors]

Imagine you set your lens on a stand, rather than the camera body, so it becomes the fixed entity.
You attach a FF body & take your picture.
You remove that & put an APS body on instead & take another.
You touch nothing else.
You print both pictures at the same 'image size'/DPI, rather than fill the same amount of paper ...I did mention we needed to ignore all other considerations, so you have to bear with me on this

Then, you take the printed image from the crop body... which will have a lot of white paper round the edges compared to the one from the FF... & you cut off the white edges.
You put that picture right over the FF pic, so it fits inside it.

What you have is a seamless [still ignoring other stuff;) version of the photo from the FF body, it just doesn't extend as far so the outer edges are missing.
They overlay perfectly, but the APS gives a smaller picture.

Any other explanation is just trying to confuse you (or me ;)

Edit:
Let me make another, really simple comparison.
Close one eye, look at something with foreground & background.
Don't move.
Roll one hand into a tube shape [halfway to making a fist] & look through it like a child pretending he has a telescope. What can you see?
Close your hand still further. Now what can you see?

Did the perspective change, or only the 'crop size'?

The more open the hand - size of sensor - the more you can see [we're not dealing with aperture here, this fakes sensor size, not aperture].
The perspective doesn't change, only the amount of the scene that you can see through the hole.

You can repeat the experiment by walking away/towards what you were viewing & trying to re-frame to give the same view in both cases.
This time your perspective changes. You will see more or less of the background compared to foreground subject depending on distance, not 'tube' size.

• @MichaelClark - I did reiterate 'assuming you don't actually move anything' but it does seem it cannot be emphasised too strongly. I'm really not sure why it causes so much confusion. I'm far from the most experienced photographer, still really a newbie, but I got it the first time it was ever mentioned, even before the full explanation. It crops up [pardon the pun] so frequently that I've been trying to find other ways to explain it. Dec 20, 2016 at 16:38
• Yeah, it's not hard at all. I think where most people get off track is either 1) mistaking geometric distortion or differences in how a lens projects an image (rectilinear vs. fisheye, for example) for differences in perspective or 2) mistaking the different results from using different focal lengths at different shooting distances as a result of the different focal lengths rather than the different shooting positions. Dec 20, 2016 at 16:47
• @Tetsujin Ohh my ! Sorry. I didn´t know the correct term; I meant "geometric distortion" when I said "perspective" ! I was talking about differences in how a lens projects an image. I know there is always a geometric distortion involved in any focal lens and it is more strong on short focal lengths than is longer ones. This is way I believe a 50mm lens on a APS body would not produces the same image a 75mm on a FF body ! That geometric distortion is greater on a 50mm lens than on 75mm and the images will be different ! Dec 21, 2016 at 11:25
• @MiguelRozsas That all depends on the two lenses in question. A lens such as a 50mm Zeiss Planar very likely shows much less geometric distortion than a lens such as a consumer grade 85mm f/1.8... Dec 21, 2016 at 18:52
• @MiguelRozsas I'm afraid that it sounds like now you actually mean perspective distortion, are just as confused as before, but are adding the additional confusion of calling it "geometric distortion". Dec 21, 2016 at 19:08

In the first case you can imagine it as a pair of scissors. The long ones. Distance between your fingers is size of the picture taken and blades show you what area you are taking picture of.

If you want to shoot same image - say two trees, ground and branch creating the frame - using fullframe and cropped one, from very same spot you have fixed your fingers in different positions and to fit the frame you have different angle between two blades. In other words, you will have same frame, but different foreground and background.

For the second experiment, if you shoot the scene with everything untouched but the DX and FX body altered, after the crop you will get same pictures. One "frame" is wasted by sensor not being there, second one is wasted by cropping. If you compare, in case of Canon, D70 with EF lens and D700 with EF-S lens you may observe slight difference, because EF lens design must take care of near-frame regions, which are far beyond EF-S lens.

You may think of DX system as FX system with automatic crop and lenses adapted to it.