added 22 November 2002
The Ultimate Depth-of-Field Skinny
an article by Jeff Donald
Jeff is one of our primary moderators at the DV Info Net Community. In his spare time he teaches photography and digital photography.
Arguably, more has been written about Depth of Field (DoF) on the DV Info Net Comunity than any other discussion topic. This is my attempt to provide the ultimate discourse and treatment of the subject. By posting all of the variables and examples in one place, novices and old hands can benefit and apply the newly gained knowledge in the field. I’ll begin with the formula for DoF as it appears in the “American Cinematographers Manual,” 8th edition, pages 698-699.
Hyperfocal Distance: h = f2 / ac
f = focal length of lens
a = aperture diameter (f/stop number)
c = circle of confusion
Depth of Field, Near limit: hs / h + (s – f)
Depth of Field, Far limit: hs / h – (s – f)
h = hyperfocal distance
s = distance from camera to object
f = focal length of lens
What is Depth of Field?
Depth of Field (DoF) is the distance range between between the nearest and farthest objects that appear to be in acceptably sharp focus within the image plane. DoF involves one image plane, and the area between two target planes (in front of the lens).
What is Hyperfocal Distance?
Hyperfocal Distance is the distance of the nearest object in sharp focus, when the lens is focused on infinity. It varies with each f/stop number. When the lens is focused on that distance, everything from one-half the distance from the camera to infinity will be sharply focused.
A. The focal length of the lens.
B. The diaphragm opening (effective aperture).
C. The distance from the lens to the object that is focused on.
D. The distance from which the image is viewed.
E. The viewer’s personal standard of the permissible degree of sharpness (or unsharpness).
Other variables in the formula remaining constant, it follows that:
A. The shorter the focal length of the lens, the greater the DoF.
B. The smaller the diaphragm opening (larger f/stop number), the greater the DoF.
C. The greater the distance to the object being focused on, the greater the DoF.
D. The greater the distance from which the image is viewed, the greater the “apparent” DoF.
E. An often-used standard of acceptable sharpness is the reproduction in the image of a small point in the object plane by means of a “Circle of Confusion,” or disc not greater than 1/100 of an inch. This is often expressed as 1/1000 of the focal length. Sometimes a figure of 1/300 of an inch or 1/3000 of the focal length is used.
At this point in the discussion, the image size will not remain constant. If you change the focal length in the above example, the subject (Target Size) will get larger or smaller depending upon the change in focal length.
How do I apply this in the real world?
Much of what is written above is common practice for many of us. If I want more DoF, then I can increase my f/stop number to f/11 or f/16 or even higher. If I want less Dof, I can lower the f/stop number, add Neutral Density filters or a polarizer to reduce the light, thereby forcing the f/stop number lower.
Move the camera closer for less depth of field, further away for more. But if you zoom the lens at the same time (to maintain a constant subject size), then the depth of field will stay the same. If the Target Size remains the same, by moving the camera all you have done is change perspective. In the real world (such as a news anchor person behind a desk), the Target Size needs to consistently remain the same size. As you move closer to decrease DoF, the image size will increase, so you must decrease the focal length to maintain the same Target Size. The two variables (lens-to-subject distance and focal length) cancel themselves out due to the Law of Reciprocity.
What about 1/3 inch CCD’s having more DoF than 35mm film?
Just as the Target Size can vary as in the above paragraph, so can the size of the film stock or the size of the CCD image sensor. If the Target Size in front of the lens is to remain the same when we change CCD sizes, then DoF will indeed change.
What happens when we change chip (format) sizes?
If the focal length of the lens stays the same (such as a 100mm lens on 1/3 inch CCD, and a 100mm lens on 35mm film), then the Target Size will increase 7.2 times, because a 1/3 inch CCD is 7.2 times smaller than the 35mm image plane. To maintain the same Target Size, either the lens-to-subject distance must be 7.2 times greater, or you must reduce the focal length 7.2 times. By either increasing the lens-to-subject distance, or by reducing the focal length, the DoF is increased. If all formula variables stay the same and the Target Size (CCD) behind the lens changes, then DoF will not change. If the Target Size changes in front of the lens (by changing focal length or len-to-subject distance), then DoF will change.
Bring me back to the real world. What does all this mean to me?
The real world experience is that under most conditions (a TV set, some product shots, a speaker at a podium), the subject must consistently remain the same size due to the basic rules of image composition, head room for subject, or because the Art Director says the box will must appear so big. The Art Director also wants less DoF. So you move the camera closer. Now the AD says the box is too large. So you zoom the lens wider to make the box appear smaller. Then the AD says hey, you’ve got too much DoF again. By moving closer and zooming wider, you’ve cancelled out the change in DoF. This is the Law of Reciprocity. The only effective way to reduce DoF while maintaining the Target Size is to lower the f/stop number (f/2.8, f/2.0 etc.). In a well-lit scene, you’ll need to use Neutral Density filters to reduce DoF.
I want to play with DoF but I don’t have a Palm Pilot. How about a link?
So, what’s next?
That’s really all there is to it. You may need to read this pages several times to fully grasp it. Reread both sets of A-to-E points above. Remember, in the A-to-E examples the Target Size will change. In the real world, Target Size usually needs to stays the same.
Questions that may come up would concern Circles of Confusion (Cc) and proper viewing distance of a TV monitor. Viewing distance affects the “apparent” DoF. Factors affecting Cc are human visual acuity, sharpness at DoF limits, diffraction, lens aberrations and film properties (and in the case of film, film flatness).
Several of these factors can be measured with Modular Transfer Function (MTF), which is not the same as film grain. Grain is analogous to noise in video terms. MTF is more like bandwidth in video. The greater the bandwidth, the greater the resolution. Resolution is the ability to distinguish line pairs per length. Certainly grain and perceived sharpness go hand in hand.
The easiest way to think of viewing distance is the image on a billboard. When viewed up close, the image is clearly lacking apparent sharpness and appears to be low resolution and lacking in detail. It may look out of focus. But when viewed from the proper distance, the scene appears to be in focus. Pick up an 8×10 photo and view it held just inches from your face. The image will not appear to have good sharpness or resolution. It looks out of focus. Now put the picture on the wall and stand back five or six feet and look at it. There’s a remarkable difference. All you did was change the viewing distance.
The three basic things (A, B, C above) that affect DoF are focal length of the lens, taking aperture and distance to your subject. In some cases, focal length of the lens and the distance to subject cancel each other out. How do they do that? By picking up your camera and moving it further away from your subject, you increase depth of field. However, your subject size may now appear too small. That’s only common sense and easy to demonstrate with your camera. But how do we get the subject back to the same size as it appeared prior to moving the camera? We typically zoom the lens until the subject is larger. By zooming and making the subject larger, we have decreased the DoF (longer focal length, therefore less DoF). The Law of Reciprocity cancels the two changes out (longer focal length equals less DoF and moving away from subject equals more DoF). Your DoF stays exactly the same if the subject size is the same.
How do I change DoF?
In most cases, if your subject size has to remain the same size (say a model’s head size), then decreasing the aperture (a smaller numerical f/stop number) will decrease the DoF. Use an aperture size of about f/1.6, f/2, or f/2.8 to achieve a shallow DoF. If your scene is too bright, using a Neutral Density (ND) filter will decrease the light entering the lens, which forces the aperture to go numerically smaller.
The subject size does not always stay the same size. If you just move the camera further from the subject (without zooming back in), then DoF will increase. If you zoom in (without moving the camera back), then DoF will decrease. Combine these changes with changes to your aperture, and large changes in DoF can be made.
Why do you dwell so much on subject size?
In the real world, the subject size (persons head size) is dictated by the TV set or the script for the movie. Who would watch the news if the persons face was the size of a quarter? Or who would be afraid of Dirty Harry is his face were small on the screen? So, in conclusion, size does matter.
Please direct questions to the DV Info Net Community Forums.