Perspective - and focal length

We often hear about perspective in connection with photography. We hear (incorrectly) that a change in focal length changes "the perspective" of the image. In a related area, we hear (incorrectly) that an increase in focal length causes the appearance of "compression" of the distances between objects at different distances.

"Perspective" in general language

In general language, we can take "perspective" as meaning "how we look at something". This actually dovetails well with its technical significance.

"Perspective" in a technical sense

In such fields as engineering drawing, technical illustration, landscape sketching, and photography, and in fact in regular human vision, perspective refers to the phenomenon by which objects in the scene of the same actual size will appear in the drawing or image with different sizes, depending on their distance (don't worry for now from what).

In fact, in photography, this inherently happens (with some very rare exceptions).

The properties of a perspective image

In a true perspective image (and we get that in photography if the lens is "rectilinear"):

• For scene objects of the same real size, their size in the image is inversely proportional to their distance (in the scene) from a certain point, called the point of perspective.

• For points in the scene that lie along a line passing through the point of perspective, their images will fall at exactly the same point in the image.

The point of perspective is in fact the point from which the scene is "seen"; it is the location of the camera (the lens entrance pupil, to be precise) or of the "sketch artist" (human or virtual).

What will change "the perspective" of the image

We of course cannot answer this unless we know what is meant by "the perspective" of the image.

• Some people think that this "property" is given by the size of an object on the image. (Is that in pixels, or millimeters on the sensor, or fractions of the frame diagonal size, or what?)

• Some people think that this "property" is given by the field of view of the camera.

• Some people have some notion of "the perspective" that does not lend itself to description in any technical way, as we might speak of "the feel" of an image.

Any of these people should not expect to be comfortable with the remainder of this note.

The technical concept of perspective leads to a worthwhile definition.

Let me, however, put aside for a moment the matter of "an indicator" of "the perspective" of an image. We will sneak up on it by saying, "We have two images. How could we tell that they had 'the same perspective'?"

An outlook that fits well with the technical notion of perspective is this:

Two images would have "the same perspective" if:

• The relative sizes of the images of various objects (for objects appearing in both images) are the same in both images.

• The relative positions of of the images of various objects (for objects appearing in both images) are the same in both images.


Now, when will this happen? If, and only if the point of perspective is the same for the two images. Thus, the location of the point of perspective, and nothing else, determines "the perspective" of an image. (We assume that the aiming directions are generally consistent.)

Focal length

We hear often that "the perspective" of an image is varied if we vary the focal length of the lens used for the shot.

Now, if this is so, and we increase the focal length from one case to another, in which direction does that change "the perspective" of the image? Does it make it "greater" or "lesser"? Does it make it "hotter" or "cooler"? This conundrum should make us suspicious of the notion.

In fact, the focal length makes no change in the perspective of the image. That is only affected by the location of the point of perspective - by the location of the camera.

Why do so many people think that the focal length affects the perspective? Because the focal length that we choose may be determined by the distance to the subject, or vice versa.

Here's an example. We set up to do a portrait, and put a 35 mm lens on the camera. We place the camera where the subject will properly fill the frame, and shoot. We don't like the result, from a "perspective" basis (the nose looks too big, the ears are hidden, etc.)

We remember reading that many portrait photographers like an 85 mm lens, so we put one on. Well, now only part of the subject is in the frame. So we roll the camera back until the framing is essentially as it was with the 35 mm lens.

We shoot, and the result is very nice. "Wow!, we say. "That longer focal length really did the trick!"

No, it didn't. What did the trick was to roll the camera back. The point of perspective was now farther back from the subject, with a corresponding effect on the perspective effects.

Now suppose we didn't have an 85 mm lens, but kept the 35 mm lens on and moved the camera back as before. We shoot.

Of course, the subject is rather small in the frame. so we crop the image in post. And guess what! The image, with respect to perspective, is just like the one done with the 85 mm lens from that same point.

Now of course this is not necessarily an attractiveness technique. The image quality may be worse, because of the "fewer pixels for any object". But we see that is is not the focal length, as such, that controls the perspective effect.

These two images illustrate the situation. They were taken from the same point. The first one was shot with a focal length of 105 mm, the second with a focal length of 47 mm. I have only presented here a crop from the second shot that covers the same scope as the first image, and present them here at the same size to facilitate comparison.


There is no difference in "the perspective" of these two images in any way I understand that.

In the next part of this series, I will discuss the concept of "perspective angle" encountered in connection with CAD and technical illustration systems.

In the third part of this series, I will discuss the matter of the "visual compression" of objects said to be a result of the use of a greater focal length.

Best regards,

Doug

Perspective - Perspective angle

Sometimes colleagues talk to me about the "perspective angle", and angle they say characterizes "the perceptive" of an image. There are typically people who have worked with CAD systems or certain kinds of technical illustration system.

Suppose that in such a system we have defined a three-dimensional part or assembly. We now want to the system to prepare a perspective view of the "scene".

To do that, we must tell the system where to put the point of perspective, and what should be the "direction of view".

It is easy to describe the direction of view. It may well be along one of the axes of the coordinate system.

We can also describe the wanted point of perspective with respect to the coordinate system. But often the operator has no good basis to choose the point on that basis.

Thus, these systems generally allow the operator to define the location of the point of perspective, along the direction of view, in a more intuitive way. The operator enters what is usually labeled the "perspective angle".

This is the angle that would be subtended (from the point of perspective) by the left and right boundary of the "scope" of the drawing as is defined on a plane passing though the origin of the coordinate system.

The trigonometry of the situation is such that this defines where the point of perspective must be, and the system places it there before constructing the perspective "view".

That's all very handy, but it does not mean that this angle (by itself) defines the perspective situation of the view.

Best regards,

Doug

The flea on the back of the bird on a fence in a flower garden!

Hi Doug,

Your essay is worthy of being read in its entirety. Still, just to simplify. If we stay in one place and just change lenses, what happens? All a different focal length will do is alter the DOF and the extent of extra subject material extending from the center of the field.

Considering a flea on the back of a bird on a fence in a flower garden and that the flea is the star of the show!

A wide angle lens will take in the entire scene. However few pixels or a small film area will be devoted to the bird and less to the flea!

The right telephoto lens could assign all its pixels or film area to that one bird and its friendly flea!

A much longer telephoto lens would just cover the flea!

In each case, the flea enlarged to the same size would have similar geometry and appearance and so its perspective would be the same. The differences would be only in the DOF and the detail of the final image!

Asher

Hi Doug,

We shall start again.

Three dimensional talk is wrongly confusing the issue on a printed photograph that is only composed of two dimensions.

Let me repeat..A printed photograph on a sheet of , say, 8 X 10 inch paper does not have the third dimension. There is no z-axis. No i-axis. Just the x and y axis. Period.

Perspective does not depend on the Focal Length of a lens ONLY when an object is kept the same size on sensor ( or film ) when alternate lenses are used.

On the contrary to what the OP has suggested, it is important to know that in practical photography a tele lens will appear to have compressed the spaces between objects, and a wide angle lens shall appear to widen the distance between objects.

Let me state that generally photographers do not run around using geometry or make scientific calculations when taking photographs. They might do so in their homes or academia.

In the field, what one needs is to create a sense, a feel of space and how it relates to objects.
Use a tele if you want to make a photograph appear to have compressed distances. Use your wide angles to create an impression of space between objects.

Move around to change your point of view..for example so that a pole is not sticking out of a head.
Or if you work only with primes, zoom with your feet to create the ' perspective , that suits you.

Remember that the human brain and vision act together. Points in sharp focus shall draw the eye
towards them. OOF areas are just that, out of focus.

You control the depth of field, the distance in front and behind the subject that is in sharp focus by the distance between the camera and the subject, the focal length and the aperture.

I rarely use aperture to let in more or less light. I use aperture to control the dof.

Full frame 35mm ( that's all I have ) has a smaller dof than a small sensor camera for an equivalent focal length lens. P&S cameras generally have huge dof. That is why subject isolation is a bit difficult with the cheaper variety of P&S.

It might be scientifically wrong, but perspective to me is how I view an image. My perspective. The view I want the viewer to see when I have taken the photograph and show it to him or her.

Again, I use wide angle lenses and Tele lenses to expand and/or compress the spatial relationships that shall appear to the viewer of my photographs.

It is the perspective, my perspective, that I want the viewer to see in my photographs.

Visual compression

We often here discussions of how the use of a lens of long focal length can cause the distances between objects at different distances "seem less that they really are". We have all seen shots of a line of telephone poles, taken from quite a distance with a long focal length lens that, indeed, "look really close together"

To understand this, we must first look into what is the actual phenomenon in play.

Suppose that we have two telephone poles, 25' tall and separated by 132' along the side of the road (the standard spacing, by the way - 40 to the mile). Suppose we visually observe them from a point 50' in front of the nearer one.

Essentially, the second one looks to us to be 0.27 times the height of the first one (50/182). We take this as meaning the the second is indeed farther away than the first.

The smaller the ratio, the more obvious it is that the second pole is quite a way behind the first.

Now we drive to a location 1000' from the nearer pole. The second one now looks as if it is 0.88 times the height of the first one (1000/1132). But by now they both look so small that we can't really draw any conclusion from that.

But suppose that I took a photo from each of those two locations, with the same focal length lens (maybe 35 mm). Of course in the second position case, the poles are pretty small, so for the delivered image, we take a crop (and see them at a greater reproduction magnification).

I look at the two images in the studio. Now, since I are not standing out in the road, I am not in the overall context of the two situations. To me, in the second shot, the nearly-one ratio of the heights (0.88) makes it look to us as if the second pole is not nearly as far behind the first pole as it looked in the first position shot (where the ratio was quite a way from one - 0.27).

And this in is fact the concept of "visual compression of distance".

But note that I didn't do anything to the focal length to do this. What did I do? Drove back 850 feet!

If in fact the intent was indeed just to mainly show the telephone poles in the delivered image, for the second shot I wouldn't want to do it by cropping an image taken with the 35 mm lens, for reasons of image resolution. So instead I use a longer focal length lens (maybe a 600 instead of a 35).

Afterward, somebody says, "Look at that visual compression. What a neat artistic effect. Did you use a telephoto lens to do that?"

No, I did it with a Jeep.

Moving back gave us the "visual compression". And we then used a longer focal length for best resolution.

We can in fact see this principle illustrated by the images in part one of this series. There we have mailbox columns rather than telephone poles.

The two images were done with different focal lengths, yet the apparent spacing of the objects is the same.

Best regards,

Doug

There is a neat video effect that I've seen most recently in advertisements for the "new" Dodge Durango...

The main subject (the Durango) is at medium distance and is held fixed in the center of the frame. Then the background is zoomed to look smaller and appears to be pushed "back" in the frame while the subject retains its original size and "perspectives" or shape.

If I were to attempt this, I would move toward the subject as I zoomed the lens, thus keeping the subject at the same size in the frame while producing the effect in the background. I don't know if this is how it is done or if there is special equipment involved.

What I do know is that I find the effect interesting and sensational at the same time. By sensational I mean over done and slightly annoying.

Perhaps this effect, if you are familiar with it, makes a good illustration of zoom lenses and perspective?

Hi, Edward,

Edward Bussa said:

There is a neat video effect that I've seen most recently in advertisements for the "new" Dodge Durango...

The main subject (the Durango) is at medium distance and is held fixed in the center of the frame. Then the background is zoomed to look smaller and appears to be pushed "back" in the frame while the subject retains its original size and "perspectives" or shape.

If I were to attempt this, I would move toward the subject as I zoomed the lens, thus keeping the subject at the same size in the frame while producing the effect in the background. I don't know if this is how it is done or if there is special equipment involved.

Click to expand...

Indeed, that's called a "zoom and truck". I don't know what kind of gear is used for it these days.

Best regards,

Doug