focal length ≠ perspective (optics 101)

[arachnophilia]

from here: http://forums.dpreview.com/forums/read.asp?forum=1030&message=31330339

i contend that perspective is simply a matter of distance, and focal length is irrelevant. to prove such a point, i invite anyone to do the following demonstration.

set up two targets such that both can appear in the same frame, and you can gauge the relative size of each. separate the two by several feet, in the direction of the camera.

find a telephoto lens and a wide angle lens.

make two exposures, taken at the same distance, one with each lens. crop the two so that the foreground target is the same size in each frame, for easy comparison. the background target should be the same size, relative to the foreground.

if you'd like, make another two at a new distance, using the same technique. bonus points if you can get new tele to have the same foreground composition as the wide. the two wide shots should now have completely dissimilar perspective, as should the two teles, but the two shot at the same distance will still look the same.

this is why "crop factor" or "lens equivalence" works. to maintain the same angle of view on a smaller frame, you need a shorter focal length -- a 28mm lens on DX (normal) will yield the same perspective as a 43mm lens on FX (also normal), or a much much shorter focal length on a P+S. it's all equivalent, relative to the size. the only thing that makes a wide lens "wide" is the angle of view -- perspective has nothing to do with any of the physical properties of the lens.

perspective, afterall, is the apparent compression of space relative to distance. so this whole thing is kind of tautological and "duh" if you know what you're talking about. our eyes see with perspective (though not the rectilinear projection photographs entail -- which is not perspective, but rather projective distortion). looking down a road, the lamp posts near the end of the street should seem closer together than the lamp posts on your end. zooming in, and magnifying that section of the street does nothing particularly special -- the apparent spatial compression happens because of the distance. and that part of the street looks exactly the same in the wider view of the same scene. if you walk in closer to get a better view, you get a different perspective.

but photonut2008 contends differently. and he posted pictures to "prove" it. of course, using perspective control lenses to, you know, correct the perspective, is sort of cheating. wouldn't you say? would anyone ELSE like to explain to him why he's wrong? with pictures, if you'd like. i've shown him some (pretty bad) test samples, but maybe i'll go take some prettier real-world examples.

i realize this can be a little counter-intuitive, when we're taught things about flattering perspective and longer lenses for portraits, but that's just a product of the working distance, thanks to the tight framing. we're photographers; we should know about these things and get our optical facts straight. right?

 

[rriveros]

perspective is simply a matter of distance, and focal length is irrelevant.

Absolutely correct.

but contends differently
would anyone ELSE like to explain to him why he's wrong?

Not interested in educating others, especially those who are not willing to learn.

Photography is a visual medium. These types of discussions can be argued and proven with visual aids (photos). But people still get confused/stubborn.

I run into these types all the time, and not just in the photography field. The worst thing is that they believe what they say, and are spreading misinformation and confusing those who really want to learn.

 

[arachnophilia]

Not interested in educating others, especially those who are not
willing to learn.

Photography is a visual medium. These types of discussions can be
argued and proven with visual aids (photos). But people still get
confused/stubborn.

well, i showed him. but as you say. stubborn. i guess you kind of have to do it yourself or you think the other guy is trying to pull a fast one on you. when it's your camera and your lenses and your eye and your targets, then you know for sure.

I run into these types all the time, and not just in the photography
field. The worst thing is that they believe what they say, and are
spreading misinformation and confusing those who really want to learn.

i was once confused by this too, and helped spread some misinformation. but then someone showed me. and i tried it myself. and lo and behold, it's true.

he said he'll do some more tests. we'll see if he has anything to contribute.

 

[LandoftheCleves]

"make two exposures, taken at the same distance, one with each lens. crop the two so that the foreground target is the same size in each frame, for easy comparison. the background target should be the same size, relative to the foreground."

I wonder if maybe the cropping portion of this test is what directs the results the way you want them to.

How is this different than, say, a one-point perspective drawing on a horizontally-oriented rectangular-shaped piece of paper? The closer to the periphery you get, the more dramatic the angle objects take to the vanishing point, and it's there that the perspective feels the most exaggerated. Crop that drawing so that you lose what's going on in the periphery and you lose the feeling of exaggerated perspective.

Exaggerated perspective, to me, seems less a matter of the actual distance between things in a 2D picture than a matter of the effect of 1) a fixed perspective in 2) a widened field of view, and how that compares to our every day experience of looking at the world around us.

 

[BackInTheGame]

and I am no closer to understanding this than before I started. I don't have the photos on the web, and I'm at work, but let me give you a scenario that I ran into.

There is a red horse barn about a quarter mile off the highway that I photographed with an 85mm lens on my D300. I did it again with a 200mm lens. In the foreground was freshly planted crops with the rows cultivated in the direction of the barn. In the 85mm photo the rows are clearly very long in relationship to the barn, giving more of a sense of distance. In the 200mm photo the rows look very short, as if the field is only a short distance across. The rows don't look distorted or sqeezed, just short. Granted, if your focus is simply the barn and you crop both photos so that only the barn is left they will look pretty much the same, but it is the other stuff in a photo that is most affected by focal length, not the subject (if the subject is flat), I think. If the subject is three dimensional all bets are off. I guess that is why pros like long tellies for portraits, to flatten out the subject. There is quite a difference in a human head shot from an 85 and a 300mm.

 

[FuzzTheKingOfTrees]

I guess that is why pros like long tellies for
portraits, to flatten out the subject. There is quite a difference
in a human head shot from an 85 and a 300mm.
--

Yes but the point is that to get a head shot at 300mm you have to stand a lot further away than you would do to get a head shot at 85mm and a lot lot further away than you would to get a head shot at 35mm.

It's this change in distance from the subject that causes the change in perspective.

If I had a D700 (which would be nice) and I shot a picture with a 150mm lens, then switched to DX mode and shot the same picture from the same location using a 100mm lens, viewed at the same size the pictures would look very nearly the same (bar the FX picture having better resolution). The perspective in those pictures would be very similar.

This is a similar point to where people say that DX has greater depth of field than FX. Technically this is wrong because DX actually has less depth of field, it's just that with DX you use wider lenses or stand further away from the subject which gives you more depth of field.

 

[arachnophilia]

I wonder if maybe the cropping portion of this test is what directs
the results the way you want them to.

sort of. cropping is equivalent to zooming, except in terms of resolution. which is what i'm trying to show. longer focal length lenses, in essence, make larger image circles, a smaller portion of which is recorded by sensor. rectilinear distortion, as you mention below, is controlled by the relationship of the flat image plane with the spherical "shell" of the projection. for a longer focal length, thus a larger sphere, a flat plane is a closer approximation than it is for a smaller sphere/shorter focal length. rectilinear distortion, coincidentally, is also then a factor of distance and sensor size, but to some degree, focal length as well.

this could be what's tripping people up. people (including you, below) often call this "perspective." it's not. perspective is the apparent compression of space relative to distance.

How is this different than, say, a one-point perspective drawing on a
horizontally-oriented rectangular-shaped piece of paper? The closer
to the periphery you get, the more dramatic the angle objects take to
the vanishing point, and it's there that the perspective feels the
most exaggerated. Crop that drawing so that you lose what's going on
in the periphery and you lose the feeling of exaggerated perspective.

i assure you, unless you're m.c. escher and capable of making curved lines look straight, the triangles are always similar. the angles are always the same. always. the APPARENT DISTANCE, however, changes as a function of the of proximity to the vanishing point. which was always the hard part of making those drawings -- getting the scale right. here's an old film photo i took, in rather one-pointed perspective.



pay attention to ties on the left side of the tracks. they're easier to see. the line is straight, and the ties are always horizontal. all of the angles are the same. that was shot at 28mm. but if i cropped it in towards the end of the track, it might has well have been a telephoto. the only thing that changes is the compression of the space, and it changes as a function of the distance from the observer.

Exaggerated perspective, to me, seems less a matter of the actual
distance between things in a 2D picture than a matter of the effect
of 1) a fixed perspective in 2) a widened field of view, and how that
compares to our every day experience of looking at the world around
us.

well, it's kind of a standard function of optics that wider focal length lenses have shorter focusing distances. the OTHER side of the spherical projection is also shorter. so the wide lenses we've all get can get more exaggerated perspective than our longer lenses, strictly because we can get in closer.

but, yes, by all mean. compare it to the world around us. keeping in mind, of course, that we will not see the artifacts of rectilinear projections (no stretchy edges) because our retinas are not flat. but look for that compression of space. do the experiment in my OP without a camera, if you'd like. you should be able to see the same effect with your eyes.

and in analog, too. not just two pictures. you can watch the background target slowly get bigger in relation to foreground target as you slowly pull away. it's not a camera trick. it's a property of lenses in general, even the ones in our eyes.

 

[arachnophilia]

Granted, if your focus is simply
the barn and you crop both photos so that only the barn is left they
will look pretty much the same, but it is the other stuff in a photo
that is most affected by focal length, not the subject (if the
subject is flat), I think.

that's stuff that's affected by angle of view. one lens simply crams more picture into the same space. if you had enough space to show the similar angle of view on that 200mm lens, it'd look the same. this is precisely why we can say stuff like "35mm (52mm equivalent)." on an 8x10 view camera, that 200mm would be a wide angle lens!

If the subject is three dimensional all
bets are off.

no no, this is precisely about 3-dimensionality. space looks more compressed at a distance. meaning that if i take a headshot, and i stand 5 feet away from the model, her face will look flatter than if i stood 1 foot away -- where i crop that image is irrelevant to the perspective that the distance creates.

I guess that is why pros like long tellies for
portraits, to flatten out the subject.

pros like teles for portraits because of the working distance. the distance provides a more flattening/flattering perspective. they choose the focal lengths based on how they want to frame the shot at their preferred distances (whether they know it or not).

There is quite a difference
in a human head shot from an 85 and a 300mm.

at the same distance, there isn't. try it! you'll just get more than just a head at the 85mm. the reason for the difference you're thinking of is that the shot is framed the same way, and the portrait photog BACKED UP to take the 300mm shot.

 

[slimandy]

Another test with the same two objects. Take a picture using the tele lens. Replace the lens with the wide angle and start walking forward. Keep going until the viewfinder image matches the framing of the first shot. NO cropping allowed! Keep moving forward until you reach the same framing. Take the shot.

The difference in perspective will be obvious even though the subject fills the frame in the same way on both shots.

 

[arachnophilia]

It's this change in distance from the subject that causes the change
in perspective.

man, i was starting to think i was the only person around here that understand this. of course, i invite anyone to try for themselves.

If I had a D700 (which would be nice) and I shot a picture with a
150mm lens, then switched to DX mode and shot the same picture from
the same location using a 100mm lens, viewed at the same size the
pictures would look very nearly the same (bar the FX picture having
better resolution). The perspective in those pictures would be very
similar.

interestingly enough, i believe that at the same aperture, you might see some difference in DOF. but barring factors of individual lens optics such as field flatness etc, they'd look very nearly identical. and for those reading who don't believe me, try it.

This is a similar point to where people say that DX has greater depth
of field than FX. Technically this is wrong because DX actually has
less depth of field, it's just that with DX you use wider lenses or
stand further away from the subject which gives you more depth of
field.

well, not to get too far into this one. the dof calculator http://www.dofmaster.com/dofjs.html indicates that a 50mm lens at f/2 on a d300, with the subject at 5 feet, will have 0.24 ft DOF. a 75mm lens at f/2 on a d3, same subject distance, will have 0.15 ft DOF. so larger format will have LESS DOF and smaller format will have MORE DOF for equivalent lens focal lengths.

this would back up my experience with medium format (i shot 6x7 very briefly). you can get very small DOF even though the lenses are like f/3.5 at the fastest. even more so with large format, whose lenses are often even slower. DOF is a product of many things, and i admit i don't fully understand it.

i think what's happening is that people are using DOF backwards a lot of the time. instead of meaning the actual depth of what's in focus, they mean the stuff that's out of focus, so shallow DOF to them is "more DOF."

 

[arachnophilia]

Another test with the same two objects. Take a picture using the tele
lens. Replace the lens with the wide angle and start walking forward.
Keep going until the viewfinder image matches the framing of the
first shot. NO cropping allowed! Keep moving forward until you reach
the same framing. Take the shot.
The difference in perspective will be obvious even though the subject
fills the frame in the same way on both shots.

correct, and that change will have come from the change in distance.

but i feel this is less illustrative because you've changed two factors, the focal length and the distance. however, it is incredibly illustrative if you take a whole series of shots in between, starting with one at the same distance. or if you actually watch the perspective change in real time. the proportions of the two targets will be the same in the wide and tele at the same distance (the crop is just for illustrative purposes), but as you approach the foreground target, you can watchi the perspective change very dramatically.

even better, do it without any camera at all.

 

[slimandy]

but i feel this is less illustrative because you've changed two
factors, the focal length and the distance.

Surely that's the point? You want to see how changing focal length affects perspective. If you stay in the same place you are seeing how focal length affects FOV.

 

[arachnophilia]

but i feel this is less illustrative because you've changed two
factors, the focal length and the distance.

Surely that's the point? You want to see how changing focal length
affects perspective.

right, but... see, this is the source of confusion. the focal length hasn't changed anything here. the distance has. the person in the other thread even had an example much like this one. when you change the working distance, you change the perspective. the different focal length changes the perspective IF AND ONLY IF you change the working distance to result in a similar framing. and it's not a result of the focal length (as the crops show), it's the result of you moving.

what you and i just described is actually a somewhat common effect in films. it's called a "dolly zoom." you may have seen in hitchcock's "vertigo" or, well, about a thousand other movies. it looks like this:

http://www.youtube.com/watch?v=Y48R6-iIYHs

the effect is not caused by the zooming, it's caused by the dolly. the zoom is only there to accomodate the same framing.

this was confusing and new when hitchcock did it, because zooms weren't really commonplace in 1958. but they are today. you'll be hard pressed to find someone with a camera who doesn't also own at least one zoom lens. and these days, you're hard pressed to find someone without a camera. we all use zooms. so why is this so hard to understand?

stand in one place, and zoom in. we've all done it several thousand times. but watch closely: does the perspective change? no. only when we move.

 

[bclaff]

John,

FWIW, and this only matters for close-ups, it's the distance from the entrance pupil to the subject as opposed to the total distance that determines perspective.

Bill (visit me at http://home.comcast.net/~NikonD70/ )

 

[BackInTheGame]

at the same distance, there isn't. try it! you'll just get more than
just a head at the 85mm. the reason for the difference you're
thinking of is that the shot is framed the same way, and the portrait
photog BACKED UP to take the 300mm shot.

That might be right. I have actually done this with an 85 and a 135 for a portrait. They looked pretty much the same, although the 85 was much higher quality of course. Guess you are right.

 

[DominicNguyen]

Perspective will change if the angle has changed between the camera and the subject. Think geometry: length of hypotenuse has changed, so has perspective.

E.G.

S1
I
I
I
S2..........................C1......................C2

If C1 and C2 are camera positions, the perspectives are different when focusing on "S1". However, if S2 is the subject, then cropping C1 "might" give you the same result as C2 (ignoring individual lens characteristics such as distortion, etc).

Dominic

 

[Jeff Klofft]

i contend that perspective is simply a matter of distance, and focal
length is irrelevant.

Yes, this is 100% true. However there is the matter of framing, which is FL dependent. So if I stand 2 feet away from the subject and use two different lenses (say a 20mm and a 50mm), the persective will be the same, but the framing with differ greatly. Likewise if I use the same two lens and take two shots with the exact same framing, the perspective will be different because I was closer with the 20mm. It is the interplay of these two concepts that I think trips people up.

--
Jeff

Check out my gallery at http://www.theexpressivemoment.com

 

[LandoftheCleves]

"pay attention to ties on the left side of the tracks. they're easier to see. the line is straight, and the ties are always horizontal. all of the angles are the same. that was shot at 28mm. but if i cropped it in towards the end of the track, it might has well have been a telephoto. the only thing that changes is the compression of the space, and it changes as a function of the distance from the observer."

The effect I was talking about was the effect of the triangle formed by the rails appearing to have an angle of a lesser degree at the vanishing point than the triangle formed by the right side of the rail and the (presumably) straight line further to the right. An effect that is increased with a wider field of view as well as a closer proximity to the vanishing point.

If that is not properly called perspective, but rather distortion, or something else, I stand corrected.

 

[arachnophilia]

The effect I was talking about was the effect of the triangle formed
by the rails appearing to have an angle of a lesser degree at the
vanishing point than the triangle formed by the right side of the
rail and the (presumably) straight line further to the right. An
effect that is increased with a wider field of view as well as a
closer proximity to the vanishing point.

the lines are still straight. the effect is not increased by a wider field of view. it is increased by distance. think about the image as if there were rows on parallel lines on the ground. the ones further left and right will appear to compress for the same reasons the space in the distance (say bwteen the ties) appears to compress. this makes the angles at the vanishining point appear to compress as well, to infinity. if the crop contains the vanishing point, nothing has changed because we've changed the field of view, regarding those angles.

the only thing the focal length changes is the magnification of the image, which portion you're seeing.

 

[arachnophilia]

FWIW, and this only matters for close-ups, it's the distance from the
entrance pupil to the subject as opposed to the total distance that
determines perspective.

i believe it's distance from the subject to the central point of the lens, where the image is flipped. but i could be wrong here -- that presumes all lenses are simple, which is very much not the case. perhaps the center of the front element.