FoV, DoF, perspective, and distortion...

[ebann]

Ok... I just spent this morning trying to understand more intimately the differences between shooting with different lenses I'll start off with my findings and then I'll end with a question:

A 50mm lens has a horizontal FoV of 39.6 degrees.
A 85mm lens has a horizontal FoV of 23.9 degrees.

Considering a upper-body portrait scenario with a 85mm on a full-frame camera standing 5' away from a model:

85mm at f/1.4 has about 1" of DoF, 0.5" in front and 0.5" behind.
At this distance, the lens is capturing a 25.3" horizontal stretch.

In order to keep the same framing, the 50mm lens has to capture the same 25.3" horizontal stretch. The result is that the camera should be 35.2" away from the model.

At this new distance from the model, the 50mm at f/1.4 has about 1" of DoF, 0.5" in front and 0.5" behind.

THEREFORE:

Question 1: Is it correct to conclude that the 85mm@f/1.4 and 50mm@f/1.4 maintaining the same framing will yield the same DoF, i.e. getting closer with the 50mm will only change perspective but DoF won't change.

Question 2: Does getting closer with the 50mm add distortion to the subject? In other words, is it possible that while the framing is identical, the two subjects can be "rendered" differently? How close can a 50mm get without adding distortion.

Question 3: People mention the ability of long lenses to "compress" the scene, does that have anything to do with distortion?

[SkipD]

A decent depth of field calculator will confirm your DOF values. Without testing the numbers, I do believe that you will find that using various focal lengths (at the same f-stop settings) with the same framing of a primary subject (at varying distances to control the framing), the depth of field remains roughly the same.

Regarding perspective, "distortion", and focal lengths, please read our "sticky" tutorial titled Perspective Control in Images - Focal Length or Distance?.

[ebann]

Thanks for the link!

[ebann]

The reason for all this is simple: I was planning to buy either the 135/2L or 85/1.2L and was curious to know if the larger aperture of f/2 on the 135 would produce equal DoF of the 85 at f/1.2 being the longer lens that it is. Many people say the 135 produce equally pleasing results as the 85.

The truth is that the 135 @ f/2 at 7.9' away has a DoF of +/- 0.7" for the same framing.

The 85 @ f/1.2 at 5' away has a DoF of +/- 0.42".

The 50 on a crop camera @ f/1.4 at 5' away has a DoF of +/- 1.5"

The 85/1.8 @ f/1.8 at 5' away has a DoF of +/- 0.64".

Conclusion:

For a normal half-body portrait, the thinnest DoF that can be obtained is (all with the same framing):

FF and 85/1.2 (DoF of +/- 0.42")

Followed by in increasing DoF:

85/1.8 and FF (DoF of +/- 0.64")
135 and FF (DoF of +/- 0.7")
50/1.4 and crop camera (DoF of +/- 1.5")

[RDKirk]

Those of us who have been using multiple formats discovered long ago:

Question 1: Is it correct to conclude that the 85mm@f/1.4 and 50mm@f/1.4 maintaining the same framing will yield the same DoF, i.e. getting closer with the 50mm will only change perspective but DoF won't change.

Remember that the final variable in depth of field is the enlargement of the original image size to the final image display size. As you increase the enlargement to the final image display size, the apparent depth of field decreases. I make that statement here to explain what happens when you crop an image to equate framing between images shot with different focal lengths at the same subject distance.

Changing your distance will change depth of field at a given aperture. Distance and aperture are the two fundamental variables of the depth of focus at the sensor plane (focal length does not change depth of focus). A depth of focus change will always change the corresponding depth of field in the final image.

Question 2: Does getting closer with the 50mm add distortion to the subject? In other words, is it possible that while the framing is identical, the two subjects can be "rendered" differently? How close can a 50mm get without adding distortion.

Perspective will change when you change the distance to the subject, and as you get closer to the subject to maintain framing with a shorter lens, you may incur an appearance of exaggerated perspective.

How close you can get before it becomes objectionable in traditional terms depends on how "deep" the subject is. That is, the proportion of the depth of the subject to the distance to the subject is important. For instance, in a tight headshot, you may see only the face (depth of subject only 2-3 inches) and that might not be objectionalble.

But if you use a wider lens at the same distance that now includes a shoulder that projects closer to the camera, the depth of the subject has increased to 16 or so inches--a much greater proportion of the subject distance, and that shoulder projected toward the lens is now exaggerated in size. If the person projects her hand toward the camera, now the subject's depth is about three feet, and that projecting hand appears even more exaggerated.

In my experience, it's best to keep the distance to the subject no less than 10 times the depth of the subject, as a rule of thumb. This means that in close quarters, you would pose the subject as "flat" as possible to the camera. You don't have to get out a measuring tape--just be aware of the phenomenon and eyeball it.

Question 3: People mention the ability of long lenses to "compress" the scene, does that have anything to do with distortion?

Apparent perspective "compression" is what you may see when you move away from the subject to retain framing with longer lenses. Unlike the exaggerated perspective seen with shorter lenses, compression is not as acutely noticeable as exaggerated perspective.

For instance, if you have pleasant perspective at six feet from the subject with a 50mm lens, the compressed perspective you see moving 12 feet away and using a 100mm lens is less visually jarring than the exaggerated perspective you see moving three feet away with a 24mm lens.

[toxic]

Originally Posted by ebann

The reason for all this is simple: I was planning to buy either the 135/2L or 85/1.2L and was curious to know if the larger aperture of f/2 on the 135 would produce equal DoF of the 85 at f/1.2 being the longer lens that it is. Many people say the 135 produce equally pleasing results as the 85.

DoF is not everything when it comes to subject separation. 25mm at f/4 has approximately the same DoF as 50mm at f/4, which is the same as 100mm at f/4, for the same framing - the inherent smaller DoF of the longer lens is offset by the greater subject distance. However, the longer the lens, the more diffuse the background, leading to more subject separation.

The "equally pleasing results" of the 135 compared to the 85 probably has to do with more background diffusion (making up for the DoF difference) and a slightly different look from the greater distance.

[ebann]

Originally Posted by toxic

DoF is not everything when it comes to subject separation. 25mm at f/4 has approximately the same DoF as 50mm at f/4, which is the same as 100mm at f/4, for the same framing - the inherent smaller DoF of the longer lens is offset by the greater subject distance. However, the longer the lens, the more diffuse the background, leading to more subject separation.

The "equally pleasing results" of the 135 compared to the 85 probably has to do with more background diffusion (making up for the DoF difference) and a slightly different look from the greater distance.

Interesting... so there are TWO variables that leads to a creamy bokeh? DoF *AND* background diffusion?

How does background diffusion happen?

[sued5320]

This was posted in another thread about DoF. It seems to confirm a "yes" for the OP's question 1.

http://www.luminous-landscape.com/tutorials/dof2.shtml

[toxic]

Originally Posted by ebann

Interesting... so there are TWO variables that leads to a creamy bokeh? DoF *AND* background diffusion?

Bokeh, by definition, is a result of lens design. Subject separation is a function of DoF and background diffusion.

How does background diffusion happen?

In the context of this thread (shorter vs longer focal length), as you move farther away, the subject looks larger relative to the background (or the background looks larger relative to the subject). This means a smaller portion of the background has to be enlarged more, making it appear more diffuse.

Another way of saying this is if, say, you took an image with a wide-angle lens at whatever exposure settings. If you take the same image with a telephoto (with the same f-stop), only a portion of the original background is still in the image - say that portion was 400x600 pixels in the wide-angle shot, and the camera records at 1600x2400. That means in the telephoto shot, it was enlarged 4 times more than with the wide-angle, and more enlargement = less sharpness (more diffusion).