What is depth of field?

A photographic lens renders a sharp image of points at one given distance, measured along the lens axis. This distance can be adjusted (the process of focusing). Any points at a different distance will be rendered more or less unsharp, and this unsharpness increases gradually as we move away from the "sharp" focus plane. Within some limits it will be small enough to consider the image of our point "sharp enough" for a given purpose.

We are talking here only about the unsharpness due to the subject being out of the focused distance. Other sources of unsharpness are possible: camera shake, dirty lens, atmospheric conditions, and various optical flaws of the lens among others. These reasons remain outside of the scope of this article.

The term depth of field (DOF) is often used to refer to the fact that points not exactly in focus are rendered acceptably sharp in the image. Quantitatively, DOF is often defined as the distance between the closest acceptably rendered point on the lens axis and the furthest such point. Obviously, this value will depend on how much unsharpness we are willing to accept.

Is it good or bad for your pictures?

For many types of photography we would like to have everything in the frame as sharp as possible. This includes, but is not limited to, landscape, architecture, documentary, and vacation/family snapshots. Usually the more DoF the better for these applications.

In some cases, however, we may want to use a more creative approach, with the main subject of the picture being sharp, while the background (and, if applicable, the foreground) is fuzzy, out of focus. With the main subject "standing out" from the surroundings, the picture may have more impact, being generally more pleasing to the eye. In such cases we want to minimize the depth of field. This approach is especially useful in portraits, but not only.

What is "acceptably sharp" — circle of confusion

The extent of the depth of field depends on what we understand as "acceptably sharp" in the definition above. If we are willing to accept more unsharpness, the depth of field (or whatever we accept as depth of field) will extend more. For sharpness-critical applications, it will be very shallow.

A (hypothetical) lens without any optical flaws, placed at a given distance from the image plane (film or digital sensor) will create point-like images only for point subjects at one given distance (as measured along the lens axis).

For a point subject at any other distance, its image will be a circular spot, referred to as circle of confusion.

The acceptable size (diameter) of the circle of confusion depends on how the photographic image will be magnified in the printing or viewing process, and from what distance it will be viewed — plus of course, on what you mean by "acceptable" in the magnified (printed, displayed) image.

Obviously, a smaller image created by the lens has to undergo stronger magnification to be viewed.

This is why, from the DoF standpoint, it does matter on what size camera a lens of a given focal length is used.

For example, a frame from a 35 mm camera has the size of 24×36 mm. To be printed as a typical 30×40 cm (12×16 inches) enlargement, or viewed on a 20" (diagonal) screen, it has to be magnified 12.5 times (note that because of a different aspect ratio, the usable part of the frame is only 24×32 mm).

For the same print size, an image created on the 2/3" sensor of a typical non-SLR digital camera (6.6×8.8 mm) will require a magnification of about 50×. The circle of confusion has to be five times smaller to result in similar perceived sharpness of the viewed image.

The human eye has a resolving power of about 1/1000 of a radian. This means that we can see detail of the size of about 1/1000 of the viewing distance. A typical viewing distance for a 30×40 cm print is 40 cm or more; this results in an acceptable circle of confusion of 0.4 mm (about 1/60" of an inch). Reduced into the film plane (divided by 12.5) this translates itself into a CoC diameter of 0.032 mm for 35-mm film. For a Four Thirds digital sensor, with the sensor two times smaller (diagonally), the CoC will have to be two times smaller: close to 0.016 mm.

Various sources a value varying from 0.025 mm to 0.033 mm for the 35-mm film. This is already hairsplitting; I will be using a value of 0.03 mm, a little bit more conservative than one shown above.

To account for differences in format size and aspect, it is handy to define the size of the circle of confusion as a fraction of the diagonal of the film (sensor) frame. For the 35 mm format, the value of 0.03 mm equals to 1/1440 of the diagonal.

Still, designers of mass-market cameras often assume that 1/1000 will be enough for their intended users, while in scientific and technical photography the value of 1/3000 is not uncommon.

Basic facts

Assuming the image frame size (film, sensor) stays the same, the following is true:

1. At any given focal length depth of field increases as the lens is closed down (i.e., the F-number increases).
2. At the same lens aperture and the same subject distance, depth of field is greater for short focal lengths (wider lenses) than for long ones. This difference is quite dramatic.
3. At the same lens aperture and image magnification (i.e., width of the frame, measured in the subject plane), depth of field remains approximately constant for various focal lengths.
4. At the same focal length and aperture, depth of field increases with the subject distance (even if measured as a percentage of that distance).

While points (1), (2), and (4) are getting quite a lot of exposure in photography books and articles, (3) is mentioned rather rarely. Some people may even think that it contradicts (4), which is not the case: both statements are valid. (On another extreme, some authors stress (3) and claim that (2) is not true. Once again, all depends what are the other controlled variables kept equal.)

Note, however, that using a longer lens will not lead to shallower DOF in portrait shots, assuming the subject is identically framed in both cases; this is a direct consequence of (3).

Anyone who wants to use and control the depth of field creatively in his/her photographs must realize and understand the points (1-4) above; without that all process will be reduced to a guesswork. Therefore if you are not sure, go back to the beginning of this section and read it again. No instant gratification here.

The formulae leading (directly or indirectly) to these conclusions can be found near the end of this article, so can be graphs illustrating them.

What's so special about digital cameras?

Actually, not much, except that most have sensors smaller (or much smaller) than the 35-mm film frame. Therefore the CoC size used to define "acceptably sharp" also has to be proportionally smaller.

This would, seemingly, lead to less DoF in small-sensor cameras, if not for one additional fact: for the same image angle (field of view) a smaller sensor requires also a proportionally smaller lens focal length.

For example, a 100 mm lens on a 35-mm film camera gives the same field of view as a 25 mm (approximately) lens on a digital camera with a 2/3" sensor. This is why we often say that the EFL (equivalent focal length, implying the 35-mm film as a reference) of the latter lens is 100 mm. The ratio of these two values (here: 4.0) is often referred to as focal length equivalence ratio, or focal length multiplier. In this article I will denote this ratio as simply M.

Some writers refer to M as crop factor, which is a wrong term. It suggests that the optics of a digital camera is the same as of the film one, except that we are using just a part of the frame. This is not the case: for the same sharpness of the final picture, a digital lens with a given M should have the absolute resolution (measured in the image plane) M times higher than a corresponding 35-mm film lens. On the other hand, it needs to deliver acceptable images only within an image circle which is M times smaller than in the other case. Would you say that a 35-mm camera has a crop factor of 2.5× compared to a 6×9 cm, medium-format one?

Here we are for some surprise. Even if the acceptable CoC size in digital cameras is M times smaller, the actual unsharpness of the image drops even faster because of the focal length being M times shorter (for the same field of view). As a result, cameras (digital or not) with smaller frames show more depth of field!

This can be seen in the comparison of Figs. 1 and 1a showing DoF for two cameras with different sensor sizes, but even more clearly in Fig. 3.

The M×A Rule

The relationship turns out to be quite simple. It can be summarized as

For example: you are using a Four Thirds camera (M = 2) with a zoom lens set to the focal length of 25 mm (EFL = 50 mm) at the F/2.8 aperture. The depth of field you will be getting will be identical to that obtained with a 35-mm film camera using focal length of 50 mm, providing the same image angle, closed down to F/5.6 (as 2.8×2=5.6).

This has nothing to do with your camera being digital — it is entirely a result of smaller frame size. Digital cameras come with differently sized sensors; the rule of thumb is that entry-level models have smallest ones (i.e., larger M), and for those models the effect is, obviously, strongest.

This, by the way, is a lucky coincidence: the users of small-sensor cameras will usually be concerned in getting most depth of field, to get everything sharp in the picture. They usually tend not to worry about creative, out-of-focus background, and these cameras, usually are lacking direct control over the aperture, therefore providing no control over depth of field. As a result, switching from film to digital resulted in millions of vacation snapshots becoming sharper than before.

On the other extreme, discerning photographers may want to control the DoF. This is one of the reasons why the so-called full-frame (M = 1) digital SLR are so common among professionals. Medium-format digital backs or cameras are also available, with M less than 1.

For example: the Mamiya ZD digital SLR has the frame size of 36×48 mm, which translates into M = 0.72. To get an EFL of 100 mm you will have to use a focal length of 140 mm, and at F/2.8 the DoF will be comparable to that at F/2.0 on a 24×36 mm camera using a 100 mm lens. You can focus on your model's eyes, keeping her ears out-of-focus.

Frame sizes and equivalence ratios

Various digital camera models use sensors of varying sizes. These are usually denoted in terms of "inch fractions", a holdover from fifty years ago, when such a value actually corresponded to the outer diameter of a glass tube holding the image sensor in TV cameras. The glass tube is gone, the notation remains.

Here is a sample of typical sensor sizes (nominal and actual), with the corresponding values of M, the focal length multiplier. The M values as shown are more than good enough for any practical use.

Notes:

1. Canon publishes the efective size of image (as opposed to the overall sensitive area, part of which does not fit into the final image frame). This makes sensor size estimation easy and reliable.
2. Nikon, I believe, lists the overall sensor size, including the pixels (photosites) not used in the final image. This makes the estimate harder to do.

   The Nikon values in our table are based on indirect information on the D300. It uses a 12 MP Sony CMOS sensor with the pixel pitch of 5.49 micrometers (according to Sony). Multiplying that by the image pixel dimensions of 4288×2848 pixels, we arrive to the effective frame size of 15.6×23.5 mm.

   It is possible that Nikon frame sizes subtly change from one model to another. The reasons for secrecy (and hence confusion) are unknown.

3. The frame size I'm listing for 4/3 sensors is the area from which the image is collected, not the overall photosensitive size, which is 13.5×18 mm.

For the whole discussion of DoF to have sense, the pixel pitch (i.e., distance between centers of neighboring pixels) has to be smaller than the accepted CoC size. This is true for all cameras of two megapixels or more: even in a 2 MP sensor (1200×1600) pixel pitch is 1/2000 of the diagonal; less than the CoC of 1/1440.

Good news and bad news

For most photographers the vastly increased depth of field in digital cameras is good news. Too many pictures taken with our 35 mm cameras were not quite good, running out of the depth of field. Especially in landscape photography it is very nice to have sharp foreground.

In 1932 a group of American photographers, including Ansel Adams, founded Group f/64. The name was derived from the small aperture opening the group members deemed necessary for achieving acceptable depth of field with use of large-format view cameras.

Now, you may think that F/64 gives you a huge depth of field. Let us have a closer look. A full-format view camera has a frame of (approximately) 8×10 inches (20×25 cm), with a diagonal of 32 cm. This means, that for a given image angle, it needs a focal length 7.5 times larger than that for a 35-mm camera, or 30(!) times that for 2/3" sensor digitals.

A quick application of the M×A rule brings us the bare truth: from the viewpoint of DoF, F/64 on an 8x10 camera is equivalent to F/8.5 on your 35 mm SLR, to F/2.1 on the E-10/E-20 (2/3"), or even wider apertures on most other non-SLR models!. In other words, the depth of field attained by closing a view camera lens all the way (with the resulting multi-second exposure times) is matched or exceeded by your digital camera's lens fully open!

Being able to work with wider apertures (smaller F-numbers) allows us to use higher shutter speeds, thus eliminating another source of image unsharpness.

Needless to say, most digital camera manuals do not mention anything on the subject: remember, we are just mass-market customers, a bunch of illiterate idiots! Still, program modes in such cameras are aware of that, clearly favoring wide apertures and high shutter speeds. Let us also remember, that with more DoF there is less need for accurate autofocus, especially if the sensor is really small (1/2.5" or less).

Even with a Four Thirds camera, M = 2: shooting at F/4 results in DoF like at F/8 on a 35-mm film (at the same image angle), a considerable advantage — if you are after more DoF. Now, whenever I'm shooting in aperture or shutter priority, I have to break my long-embedded SLR habits, and use apertures much wider than I'm used to. Usually there is no sense in using openings smaller (F-numbers greater) than F/5.6, when shooting at the wide-to-medium lens angle.

Small apertures, i.e., large F-numbers, may lead to image degradation due to diffraction effects. While for a given image size it is the relative aperture (F-number) what counts here, small frames need more magnification for the same final (printed or viewed) image size; this is why diffraction is more painful with digital cameras, especially those with smallest sensors. This is one of the reasons the digital camera makers limit themselves to F/8 or F/11 on sensors of 2/3" and smaller, although greater DoF (greater F-numbers) could be quite useful in macro applications. The topic, however, is out of the scope of this article.

The bad news is that it is much more difficult, using a digital camera, to blow the background out of focus, which is a pleasing effect in portrait and nature photography. You will have to use the longest possible focal length, and keep your lens wide open. Well, there is no free lunch. I would love to see a 50 mm, F/1.4 Four Thirds lens, capable of DoF as shallow as a 100/2.8 lens on my film SLRs. (The 30/1.4 lens from Sigma comes close, but may be a tad too wide for portraits. 50 to 60 mm would be perfect!)

Computing depth of field

The near and far distance values defining the limits of acceptable sharpness can be calculated as

with plus in the denominator used for the near (d₁), and minus — for the far (d₂) value. The notation is:

• d₁ or d₂ — the minimum or maximum subject distance in acceptable focus (measured from the lens, or, more exactly, from its front cardinal point, see below)
• d — the focused subject distance
• f — lens focal length
• a — aperture (or F-number) value, e.g., 2.8
• c — the diameter of the acceptable circle of confusion.

The value of c should be set to the 1/1440 of the frame diagonal: for example, 0.03 mm for 35 mm cameras, 0.0061 mm for ones with 1/1.8" sensors (Olympus C-series from C-2000Z to C-7070WZ), 0.0077 mm for 2/3" ones (E-10/E-20), or 0.015 mm for the Four Thirds system, and so forth.

As mentioned above, you may use another fraction, like 1/2000 or 1/1000, as long as you know what are the implications, and if you use the same value for all comparisons.

You may like more the same formula re-shuffled to a slightly different form, proving exactly the same results:

where h = f²/ac is close (but not equal) to the hyperfocal distance, described in a section that follows.

Negative results for the far limit (i.e., with a '–' in the denominator) mean that it reaches the infinity. Remember that all lengths have to be expressed in the same units (whatever they are: millimeters, inches, or nautical miles).

Instead of using the above formula to compute d_i, some people prefer to compute the absolute value of Δd_i = |d–d_i|. It can be computed from this definition, or from another, equivalent, form:

In other words, if your camera is focused at d, acceptable circle of confusion will be achieved for subjects ranging in distance from d₁ to d₂, or from d–Δd₁ to d+Δd₂.

Nitpicker's notes

While the general dependencies outlined in the first half of this article work for any lens type and distance range, the numeric results of the formulae [1..3] are approximate. They are good enough for any practical use when the subject distance is much greater than the focal length (say, ten times or more); at lower distances they may start becoming inaccurate, especially for some types of lenses. Therefore using the formulae as they are needs some caution. Here is why.

(The remainder of this section can be skipped, if you wish, without a harm to the general understanding of the DOF issues. This is for nitpickers only!)

1. In all these considerations the object distance is measured from the front cardinal plane, or front nodal plane (these two differ only if the medium on both sides of the lens is not the same, as in underwater photography). For an ideal lens, consisting of a single, symmetrical element, this plane passes through the lens center; for more complex lenses it may be elsewhere: within the lens barrel, or even outside of it; some (true) telephoto lenses have the front cardinal plane well ahead of the front element.

   The camera makers, however, usually define the object distance as measured from the image plane. This is, obviously, larger by a value of the distance between that plane and the front cardinal one. This distance depends on the lens design, its focal length, and often even on the object distance. There is no easy way of knowing it for a particular lens. (For a simple, idealized, lens the difference equals just the image distance, close, in turn, to the focal distance.)

   The difference between these two ways of defining the object distance can be neglected if that distance is much larger than the focal length; usually a factor of ten is enough.

2. In many lenses (especially longer ones) the focal length starts to change as you focus closer, with the photographer being unaware of the fact. One more reason not to publish any tables for distances below 10× focal length (nominal, that is).

   For example, at larger subject distances (say, three meters or more) the field of view of the Olympus 15-54 mm ZD lens fully zoomed out is about 20% narrower than that of a 14-45 mm ZD; this reflects the 20% difference in the maximum focal length. When the focus is at 50 cm or so from the camera, however, the first lens covers slightly wider field than the second one, a surprise. This means that the focal length of the first lens decreases when focused close (this may be the case with both lenses, but in the second one the effect is less strong.)

3. There is another, much less-known reason why the equations shown above are only approximate. This happens for asymmetric lenses, characterized by the so-called pupil magnification being different than one. That magnification is the ratio of the apparent aperture size seen from the lens rear to that size seen from the front. (You may also define the pupil magnification as the distance between the rear principal plane (with focus at infinity) and image plane, divided by the focal length.)

   The best known cases of such lenses used in film photography are the true telephotos, with the elements shifted significantly to the rear, or wide-angle lenses (using the inverted telephoto design), where these elements are shifted to the front, usually to make enough room for an SLR mirror.

   Lenses used in digital photography almost always use the inverted telephoto design, for a number of reasons, at least in the wide-angle to normal range.

   Once again, these deviations from our equations tend to disappear as the object distance increases; ten focal lengths is usually considered to be a reasonable limit of applicability. This is why my tables do not go below this value.

   The issue of asymmetric lenses is usually neglected even in advanced sources on photographic optics. The best description I was able to find is in the very informative article by Paul van Walree.

The exact formula which should be used to account for lens asymmetry, is

with Q = (P-1)/P, where P is the pupil magnification mentioned above. Note that this formula differs from [2] in just one detail: the Qf(d–f) term in the numerator.

Unfortunately, I'm not aware of any manufacturer who would publish data on lens asymmetry, therefore we have no choice but ignore this correction. On the other hand, DoF tables published for some particular lenses may have the asymmetry accounted for (this, for example, seems to be the case for Olympus; I am not sure about other makers).

The hyperfocal distance

Have another look at the formula [1] above. The far DoF limit (the one with a '–' sign used) becomes infinity for a single value of the subject distance, which is

(You may often neglect the final f, as it is usually much smaller than f²/ac, and then d_H becomes identical to h used in [2].)

This is the so-called hyperfocal distance, and, as you can see, for any given focal length f it depends on the used aperture, a.

Also note, that when we use d = d_H in the DoF formula to compute the near DoF limit, the result will be d_H/2.

Thus, another handy thing to remember:

Digital cameras, with their shorter focal lengths, have much smaller hyperfocal distances. For the common focal length ratio, N=5, the "normal" focal length (EFL = 50 mm) is 10 mm. Using this value (with c=0.0061mm), for the aperture of F/4 we arrive to d_H=4.1 m. Set your focus manually to this value, and you can take sharp pictures from two meters to infinity!

Experienced photographers know and use this rule, which allows them to skip autofocus, and shoot reliably and quickly, without any autofocus lag. This works best for short and normal focal lengths; with longer lenses the hyperfocal distance may be too large for most applications.

On the other hand, under many circumstances we are more willing to accept some unsharpness in closer subjects than in more distant ones. This is why some photographers prefer to set the focus to infinity (even if some DOF is "wasted" in the process).

If the lens is focused at infinity, the near DOF limit becomes close to the hyperfocal distance; more exactly, d₁=d_H–f, or just h.

In my own practice, I often use a mixed approach, setting the focus to the hyperfocal distance computed for an aperture one stop (sometimes even two stops) wider than the one actually used.

The tables

Here are depth-of-field tables for four groups of Olympus digital cameras with different sensor sizes:

• Four Thirds system SLRs: from Olympus E-1 to E-30 and E-620, Panasonic L-1 and L-10, Leica Digilux 3; also Micro Four Thirds EVF cameras, like the Panasonic G1. The tables cover focal lengths from 7 to 500 mm.
• C-series (C-30x0Z, C-40x0Z, C-5050Z), EFL = 35-105 mm or 32-96 mm (1:4.93); nominal sensor size: 1/1.8";
• The C-5060WZ and C-7070WZ with the EFL of 27-105mm (1:4.80 focal length ratio); sensor, I believe, just about 3% larger than 1/1.8"; sorry for hairsplitting;
• E-series (E-10, E-20), with the EFL = 35-140 mm (1:3.89); sensor size of 2/3";

The tables are also applicable to other cameras of similar sensor sizes, and therefore M, see the Appendix below.

For comparison, and for those who may need them, here are

• Tables for cameras with the 24×36 mm frame (digital or film)

To automate the calculations, I wrote a simple program, Doffy, which generates an HTML page with tables for user-defined values of apertures, distances, and focal lengths; you can then view or print that page with any Web browser.

As soon as I have Doffy nicely packaged (including user documentation), I'll include the download in my Works section; if you need it before that, let me know.

DoF graphs

Some of the readers of earlier versions of this article asked for graphs, especially, if not only, to illustrate points [1..3] in the Basic Facts section. Here let me just illustrate the above points with some graphs.

In all these graphs the horizontal axis shows the subject distance (meters). The vertical one shows how much depth of field extends ahead (negative values) and beyond (positive values) the subject, expressed as a fraction of the subject distance.

For example, the values of -0.2 and +0.6, at the subject distance of 5 meters, mean that DoF extends from 1 m ahead of the subject (0.2×5) to 3 m beyond the subject (0.6×5), of from 4 to 8 m counted from the lens.

An example of how to read this graph: let us find the DOF for the focused subject distance of 5 meters at F/2.8. That aperture corresponds to the second pair of lines (counted from inside), shown in purple. The lower purple line crosses x=5 at about -0.25; the upper one at 0.5. This means that DOF extends from 25% of the (5 m) distance ahead to 50% beyond the 5-meter plane; in other words, from 3.75 m to 7.5 m.

Other graphs should be interpreted in a similar way, except that various lines correspond to another controlled variable.

Appendix: sensor sizes for selected cameras

Here is a partial list of sensor sizes used in some cameras from major makers. The list does not pretend to be a complete reference and I am not planning to maintain it, as new models are showing up all the time. If in doubt, check the inch sensor size as given by the manufacturer and use the table above. Cameras with sensors smaller than 1/2.5" are not included at all.

Further reading

There are hundreds, maybe thousands, articles on DOF available on the World Wide Web. Some of them are worthless, some — extremely useful, informative and interesting. This one, I hope, falls somewhere in the middle.

Here is a list of references I found useful, interesting, and free of factual or interpretational errors. This is the cream of the crop of I could find.

1. Understanding Depth of Field by Sean McHugh at his ever-expanding Cambridge in Colour site. This is an easy (but not shallow!) introduction into the topic, from a photographer's perspective. Some DOF-related issues are also discussed in Sean's Digital Camera Sensor Sizes, another highly recommended reading.
2. Depth of Field and Derivation of the DOF Equations by Paul van Walree at Van Walree Photography & Optics.

   The rest of Paul's site is also definitely worth reading (not to mention his photography galleries); articles are mostly on various aspects of photographic optics; well-written and informative. This is what the Web was supposed to be about before it fell to cheap commercialization.

3. An Introduction to Depth of Field and Depth of Field in Depth by Jeff Conrad, PDF files posted at the Large Format Photography site.

   This is one of the most interesting and useful photography sites on the Web. While it does not deal expressly with digital-specific issues, it provides information which will make everyone (at least everyone willing to do some reading) a better, more technically skilled photographer. The site is entirely non-commercial and has a number of knowledgeable contributors. Check it out now and thank me later.

4. A comprehensive article on DOF on Wikipedia;

Thanks are due to the Readers who made suggestions or corrections to this page. In particular, Marc-Andre Lafortune was kind enough to point out the exact M×A Rule, while Erik Ekholm and Jon Baber found a few typos in the camera sensor list.