Depth of field (practical) theory

[alfake]

The depth of field in a photograph depends on two factors: 1) The aperture, 2) The magnification (or reproduction) ratio, ie, the relation between the size of the subject in reality and the size of its image on the sensor (or on the film). (For example, a magnification ratio of 1:1 means that the image on the sensor is the same size as the actual object .)

1) Aperture. The smaller the aperture, the greater the depth of field (distance between the near and far boundaries of the area in focus).
2) Magnification ratio. The bigger the magnification ratio (ie, the bigger the image in the sensor is in relation to the actual size of the object), the smaller the depth of field (for any given aperture).

Other factors (as lens-to-subject distance or focal length) affect the depth of field of the image by changing the magnitication ratio. If one gets closer to the subject (all else remaining the same), the magnification ratio gets bigger, so the depth of field is reduced. If the focal length is changed from 50mm to 100mm (all else remaining the same), again the magnification ratio gets bigger, and consequently the depth of field is reduced. As a result, you cannot obtain greater depth of field of a subject that fills the viewfinder by putting a shorter lens on your camera and moving it closer to the subject so the subject fills again the viewfinder. In that case the magnification ratio will equal that obtained with the longer lens, creating the same depth-of-field. (Of course, the different point of view will greatly change the picture itself, mainly the background).
The size of the sensor has no impact by itself on the depth of field of a picture. But if one takes the same image with a bigger and a smaller sensor camera, the magnification will be smaller in the smaller sensor camera, and therefore the depth of field will be larger. This is the reason why from a practical point of view smaller format cameras can be said to create larger depth of field than bigger format cameras.

I hope this helps (and complements Dr. Harout’s post on depth of field: http://www.photoclubalpha.com/forum/vie ... f=32&t=963).
Alfonso

[Dr. Harout]

I'm here to thank you the first, Alfonso, for this concise and excellent explanation .

[David Kilpatrick]

Alfonso'a explanation is mathematically correct (the magnification ratio is the critical factor). Depth of field is determined by the circle of confusion - the circle of blur created at the focal plane. This is always measured in the final print at a 'normal' viewing distance, and our old standard for d-o-f are based on looking at a 10 x 8 inch print held in the hand. Since small formats are enlarged more, smaller circles of confusion at the film plane are enlarged to equal those of larger formats where:

All distance conjugates are identical

That is: 50mm lens on 35mm film - subject 5 metres away
has the same conjugates as
25mm lens on 4/3rds format - subject 2.5 metres away

If you made the entire world miniature for the smaller format, the final print would show just the same depth of field. But of course we don't reduce the WORLD when we reduce the FORMAT size!

As you know from experience, depth of field is greater at a distance, than close-up. Well, with smaller formats, everything is relatively further away - so the apparent depth of field (which can be expressed in multiples of the focal length of the lens) for 3m high object at 3 metres away on a camera using a 7.2mm lens (KM A2) looks 'like' the depth of field for a 12m high building shot 12m away with a 28mm lens on full frame 35mm.

Depth of field (for a fixed circle of confusion figure and a fixed size of final print) is completely independent of format size, and scaleable, as long as you also scale all the distances and dimensions on the SUBJECT side of the lens too!

BUT - all our old ideas of d-o-f are failing, because we are now viewing our images much larger. Often we are viewing images as if they were not 10 x 8 inch prints, but 20 x 16s or 20 x 30s at arm's length. It is vital not to look too hard at 1:1 pixel views, especially from a camera like the Alpha 900. You can only judge d-o-f properly from an image which fits on your computer screen or on a suitable size of print.

David

[pakodominguez]

BUT - all our old ideas of d-o-f are failing, because we are now viewing our images much larger. Often we are viewing images as if they were not 10 x 8 inch prints, but 20 x 16s or 20 x 30s at arm's length. It is vital not to look too hard at 1:1 pixel views, especially from a camera like the Alpha 900. You can only judge d-o-f properly from an image which fits on your computer screen or on a suitable size of print.

David

Let's get back to the sources: photography is about the print. A monitor isn't the best support for enjoy a good image...

[01af]

Alfonso, your article on depth-of-field has several mistakes.

The depth-of-field in a photograph depends on two factors ...

Here's the first mistake. Actually, depth-of-field depends on five factors: (1) image size, (2) aperture, (3) focal length, (4) distance, (5) your idea of sharpness (= max. allowed diameter of circle of confusion).

It's a common misconception that the factors (3) and (4) could be mingled into one single factor, magnification. But they cannot. Depth-of-field will not be the same when only the magnification is the same, regardless of distance! Depth-of-field will be approximately proportional to magnification only if the angle-of-view is narrow (i. e. with telephoto lenses), or if the depth-of-field is small in relation the the linear size of the field-of-view (i. e. in macro photography).

The reason for this is the fact that magnification is not constant across the depth of the field. Instead, it's larger at the near border of DOF and smaller at the far border of DOF. This magnification gradient changes when shooting a wide-angle lens from a short distance or a telephoto lens from a long distance. If in the exact plane of focus the magnification is the same (and all other factors equal, too) then the telephoto shot will show more (!) depth-of-field towards the camera than the wide-angle shot, and less DOF towards the background---and the loss of DOF behind the plane of focus will be higher than the gain before the plane of focus so overall DOF will be less with the telephoto lens.

However when not comparing a wide-angle lens against a telephoto lens but a telephoto lens against a longer telephoto lens then the effect will become neglectible.

The smaller the magnification ratio is (i. e. the bigger the image in the sensor is in relation to the actual size of the object) ...

A bigger image size means larger magnification ratio, not smaller.

Other factors (as lens-to-subject distance or focal length) affect the depth of field of the image by changing the magnification ratio.

Mostly, yes. But not solely.

... you cannot obtain greater depth of field of a subject that fills the viewfinder by putting a shorter lens on your camera and moving it closer to the subject so the subject fills again the viewfinder. In that case the magnification ratio will equal that obtained with the longer lens, creating the same depth-of-field.

As explained above, the shorter lens will indeed give more depth-of-field ... at least in the background. After all, the background objects will be rendered smaller---which increases DOF there.

Still this doesn't mean there will be more visible detail in the background ... because the smaller rendition of the background details will counteract the increased DOF. So switching to a shorter lens in order to increase DOF is not a good idea, even though it will work---in a certain way. However the change in perspective caused by the shorter distance will affect the image in a much more significant way which (1) will render the gain of DOF useless and (2) is unwanted anyway when you only wanted to increase DOF (and change nothing else).

The size of the sensor has no impact by itself on the depth-of-field of a picture.

It does!

But if one takes the same image with a bigger and a smaller-sensor camera, the magnification will be smaller in the smaller-sensor camera, and therefore the depth-of-field will be larger.

Exactly.

This is the reason why from a practical point of view smaller-format cameras can be said to create larger depth-of-field than bigger-format cameras.

This applies not only to a practical point of view but it really is that way. On the one hand, the smaller-format camera requires a shorter focal length at the same distance and thus, a smaller magnification, to fill the frame with the same subject than a larger-format camera. This increases DOF. On the other hand, the smaller image format requires more magnification to arrive at the same print size and thus, a smaller circle of confusion. This decreases DOF. But these two factors don't cancel each other out! Instead, the shorter focal length goes into the DOF formula squared (i. e. twice) while the smaller COC goes linearly (i. e. once) into the formula. So in the end, the shorter focal length affects DOF more than the decreased COC does. That's why smaller-format cameras have more DOF than larger-format cameras.

If you made the entire world miniature for the smaller format, the final print would show just the same depth of field. But of course we don't reduce the WORLD when we reduce the FORMAT size!

Oh yes, indeed! This is an interesting way to look at this topic ... from 'The Far Side,' as cartoonist Gary Larson would say ...

By the way, the best article on depth-of-field (the only one free of errors I found so far on the Internet) is Paul van Walree's.

-- Olaf

[Dr. Harout]

How do you like it?
This site is gathering a big big info database, with your help of course.

[pakodominguez]

Let's get back to the sources: photography is about the print. A monitor isn't the best support for enjoy a good image...

Wrongo! My 32" HDTV displays some of the most brilliant still images I have ever seen, bar none!
-Sonolta

i understand the satisfaction your beautiful monitor gaves you, Don. But nothing better in this world than a beautiful print of your (or my) photographs. And ofering art quality pirnts is still less expensive than giving away digital frames
:-p

[alfake]

Thanks to everyone for the comments and links, and especially to Olaf, for chiming in and pointing out the inaccuracies and mistakes contained in my short and quick explanation. (Needless to say it was by no means intended as an ‘article’, but rather as a sort of quick reference field guide!) NOTE: I have edited the opening post to correct the ‘smaller-bigger’ lapse pointed out by Olaf.
Alfonso