Depth of Field and Field of View

I had a friend question my comment in another post about focal length not being a factor in controlling depth of field.

Let's start with a definition of depth of field (DOF): The area of a photograph that is reasonably sharp (in focus) from front to rear. A lens focuses on one plane. Everything in front of or behind the focus plane is out of focus and imaged as a circle, called a circle of confusion (insert joke here that a circle of confusion is a group of photographers sitting around a table discussing depth of field).

There is a lot more detail and math behind this than I and many of you won't want to get into. I am providing a simplified description of depth of field as knowing the math doesn't help us in making photographs. There are books, articles, and websites that carry all that information available via your favorite search engine.

When we focus a camera at an object a definite distance from the camera lens there is a finite range of distances within and beyond the focused object in which everything appears acceptably in focus, while outside that range everything becomes progressively more blurred at increasing distances from the plane of best focus. The actual extent of this range depends mainly on the distance of the object from the lens, the aperture of the lens, and the manner in which we look at the final print.*1

These circles are tiny just in front of and behind the focus plane and grow larger the farther away they are from the focus plane. Our eyes have a threshold beyond which we no longer resolve the circles as circles and they look like points, which we accept as being in focus. Depth of field comes from the range in front of the plane of focus where the circles get small enough out to the range behind the focus plane where they again get large enough to be recognized as circles. The control over the size of these circles is the aperture in the lens. As the aperture or f/stop is closed down (f/8, f/11, f/16, f/22, etc.) a greater range of the circles are imaged small enough to be seen as in focus. As you open up the lens (f/2.8, f/2.0, f/1.4, f/1.2, etc.) the circles get larger and we have less depth of field. Notice that focal length is not mentioned in the quote above.

Acceptably sharp circles of confusion indicated by the green shading.

Acceptably sharp circles of confusion indicated by the green shading.

With the camera focused on a certain subject-distance all objects lying in a flat plane at that distance will be sharply imaged on the film (sensor) as this plane is actually the image of the film plane carried into the object space. An object-point lying beyond or within this focused plane will be projected by the lens into that plane as a small "circle of confusion…

"The lens will now image that circle upon the film (sensor) just as if it were a real object lying in the focused plane. The important thing to notice is that the limit of acceptable depth of field will be reached when this circle of confusion becomes large enough to (be seen as a circle instead of a point). *1

The other control the photographer has over depth of field is the magnification of the subject of the photo. The less the magnification, the deeper the depth of field. The greater the magnification the shallower the depth of field. I started by saying that the focal length of the lens is not a factor in depth of field. However, focal length, when combined with camera to subject distance, determines magnification, which is a factor. But on its own, focal length is not a determining factor.

From the same camera position a shorter focal length lens does give us more depth of field than a longer lens does. But the subject is smaller in the frame. The longer lens from the same camera position has less depth of field, but a larger subject taking up more of the frame. If you take the camera with the shorter lens on it and move in so the subject is the same size in the frame as it was with the longer lens the depth of field with the short lens shrinks down to be the same as it was with the long lens at the same f/stop. If you use the short lens at the original distance and crop it to the same subject size as the photo with the long lens you do have more depth of field, but you lose resolution. Everything is a trade-off.

I am going to politely bow out of the discussion over print sizes and viewing distances today.

Let's go to the photos

Here we see three matchsticks at different distances from the camera photographed at 1:1 magnification and manually focused on the middle match with three different macro lenses: A Tamron SP 90mm f/2.8 Macro lens, a Sigma 105mm f/2.8 DG Macro HSM lens, and a Sigma 180mm f/3.5 APO Macro lens. The first set has all three lenses set to f/4 and you can see that despite the three different focal lengths the depth of field is the same in all three. The second set is at f/8 and you see that again the depth of field is the same with all three different focal lengths. The third set is at f/22 and, what do you know!?! The depth of field is the same.

matches_f4_widex1500.jpg

matches_f8_widex1500.jpg

matches_f22_widex1500.jpg

In the series at f/22 it is easier to see what IS different between the three focal lengths—or technically what is different between the three different camera to subject distances. The 90mm lens has a wider field of view and lower magnification so is positioned closer to the matchsticks to get the 1:1 reproduction. Being closer to the subject makes the background look smaller. In the photo we start to see the magenta color square behind the matchsticks. Changing to the 105mm lens the camera had to be backed up a little bit and now the background shows out to only part of the blue square. With the 180mm lens the camera had to be moved back a greater distance and now we see only out to the red square, with just a tiny hint of the blue square. This is where the misconception about "telephoto compression" comes from. It is really the change in camera position or viewpoint that compressed the image (made the background appear to be larger or closer to the subject). See the recent post about lenses and perspective for more about compression.

Not only for macro

I know that someone is going to ask if the above only applies to macro photography. The answer is no. Here we have a pair of photographs made with a 35mm and a 135mm lens at f/4 where the subject is about the same size in the frame and is the same distance from the background.

35vs135_dof.jpg

Again, the DOF is virtually the same, despite the big difference in focal length. There is a difference in the size relationship (perspective) between the subject and the background elements. With the 135mm being used at a greater distance from the subject the chart in the background looks either larger or closer.

"That is, in fact, a general rule. When the image size on the film (sensor) is the same,
the depth of field is the same at any given f/number…" *2

Depth of Field vs Depth of Focus

And this brings us to another term: Depth of Focus. Much too often I hear photographers interchange the terms depth of field and depth of focus. These are NOT the same thing. Depth of field happens outside the camera at the subject or focus plane. Depth of focus happens inside the camera at the film or focal plane.

"Care should be taken to distinguish between Depth of Field and its image in the camera called "Depth of Focus." The latter term, depth of focus, represents the acceptable degree of out-of-focus permitted in the camera itself." *1

DOF_vs_DOF2.jpg

In the above illustration we see the depth of field out in front of the camera where the subject gradually fades into focus and then back out of focus represented by the color objects at the focus plane. Then we see the depth of focus inside the camera as the yellow range in front of and behind the red focal plane. Basically, it represents the mechanical precision necessary in focusing the camera and/or how "off" the placement of the sensor can be from the actual focal plane.


*1 quotes and paraphrasing from the book Lenses in Photography: The Practical Guide to Optics for Photographers by Rudolf Kingslake, Director of Optical Design for the Eastman Kodak Company published by The Case-Hoyt Corporation for Garden City Books in 1951.

*2 quotes and paraphrasing from the book Zoom and Special Lenses by Leonard Gaunt published by Focal Press 1981