Bernie’s Better Guide to Depth of Field for Geeks Who Want to be Digital Artists

Being a guide to portrait photography cleverly masquerading as a technical analysis

Like the topics we covered in the beginner's guide last month, depth of field might initially seem complex, but behind it is some relatively simple logic and maths. Don't worry if maths isn't your strong point: long equations are the crutch of the inarticulate, and there's nothing in this article more complicated than division.

Speaking of division, I like to divide photography into two broad disciplines. Portraits are photos of a particular object (not necessarily a person), designed to capture something about that object. Landscapes are photos of a scene (not necessarily outdoors), designed to capture the sensation of being in a place. I say that this is a disguised guide to portrait photography because mastering depth of field is one of the main skills you need to take great portraits. Whether you're keeping the whole scene in focus for an environmental portrait, or using a very shallow depth of field to emphasise just the eyes of your subject, you need to understand how to get exactly the right depth.

Depth of field terminology

The following image depicts a (fake) flower about 50cm away, with a hedge around 5 meters behind it. This is an example of narrow depth of field: notice how some of the petals are sharp, others are slightly soft, and the hedge is almost blurred out of all recognition. Move your mouse over the photo to see a version with very wide depth of field.

Wide aperture photo

A photo taken at wide aperture

Narrow aperture photo

A photo taken at narrow aperture

Depth of field
The range of distances in a photo within which the image appears sharp. In this photo the depth of field is about 49cm to 51cm: 2cm in total. Any point outside of this range appears blurred into a disc.
Blur
The size of the blur discs as measured in the real world. This is tied to depth of field: the larger the blur, the narrower the depth of field.
Circles of confusion
The size of the blur as measured on the photographic image.

Blur vs circles of confusion: Consider the rightmost petal and the leaves in the bottom right. The blur - measured in the real world - is around 2mm and 20cm respectively, and the circles of confusion - measured on the image - are around half a millimetre and 5mm respectively. When measured in the real world the leaves are 100 times more blurred than the petals, but measured on the actual photo they are only 10 times more blurred. This is because of perspective: the leaves are 10 times further away from the camera than the petals are, so the ratio of the two kinds of blur are different by a factor of 10.

I just measured those circles of confusion by counting pixels in the above image. This is valid, but inconvenient because the values would change if I altered the size of the image. For this reason, circles of confusion are usually measured on the camera's sensor.

Over the rest of this article I'll explain the physics behind blur and sharpness, so that you can learn to precisely control the look of your photos. An explanation of depth of field often starts with a list of rules. These do exist, and I list them at the end of the article, but the whole premise of a Geek's Guide is that the rules are easier to learn if you understand the mechanism behind them first.

Onwards...

What causes blur in a photo?

First of all, consider a pinhole camera with no focusing capability and infinite depth of field:

DoF diagram

Light from each point in the scene enters the pinhole, forming an upside-down image on the sensor. Unfortunately, the vast majority of the light is wasted. Each point on the vase is emitting light in every direction, but only the light that happens to be emitted exactly in the direction of the pinhole will be captured. So little light comes in through the pinhole that you need long shutter speeds to expose the image. Also the small pinhole creates a very soft image due to diffraction. In order to allow more light in, the pinhole is replaced by a wide aperture and a glass lens to bend the light so that it still forms a sharp image on the sensor:

DoF diagram

The lens works by bending light so that the rays emitted from any point on the subject have a larger target to hit, but still form a sharp image on the sensor. So far so good, but there is a cost. In the pinhole camera, all objects are equally in focus. With the lens, the focus must be adjusted for a subject. You tell the lens how far away the subject is, and it will make sure that light radiating from that distance is brought back to a single point on the sensor. The slice of the world that is in focus is called the focal plane.

So what about objects that are not on this focal plane? Light rays from points on these other objects will still be bent back to a single point by the lens, this point will be slightly in front or behind the sensor. If the object is in front of the focal plane then the light rays will not have enough distance to converge; if the object is behind the focal plane the rays will converge before the sensor and cross over. Either way they appear in the image as a blurred disc the same shape as the aperture. This disc is called a circle of confusion.

DoF diagram

I find this model a bit hard to use to visualise the depth of field in a photo, but fortunately there is a much simpler one for predicting the size of the blur: imagine a pair of imaginary lines starting at the aperture and crossing over at the plane of focus. Any object not on the plane of focus will be blurred into a disc the size of the distance between the lines.

DoF diagram

An example

Port bottle

A lovely bottle of port. 1977 is just perfect for consumption now.

This photo was taken with an 85mm lens at f/1.8, which means that it has an aperture width of 47mm.

The bottle is one meter from the camera, and half a meter behind the bottle are two candle flames which are blurred into discs.

According to the simple model above, since the candles are half as far from the focal plane as the camera is the circle of confusion should be half the aperture width, or 23.5mm. Measuring the discs in Photoshop, I find them to indeed be just over 23mm wide. Not bad.

The rule for calculating the blur according to the model in figure 4 is that if your subject is x meters away, an object that is x meters away from the subject will be blurred into a disc the size of the aperture, an object 2x meters behind the subject will be twice the size of the aperture, etc...

The size of the circle of confusion created by the candle flames is 2.14mm measured on the camera's 35mm sensor.

Obtaining sharp images

So far we've been talking about the size of the blur in the out of focus areas, now lets turn to the sharp area.

Firstly, we need a definition of what qualifies as 'sharp'. Technically speaking, only the 2D slice of the world lying exactly on the plane of focus is perfectly sharp (and even then, only if the lens is a perfect optic, which it isn't). However, since our eyes are even less perfect, we can use the more useful definition that a part of an image appears sharp when its resolution exceeds that of the human eye.

So what is the resolution of the human eye?

DoF flower photo

Depth of field at f/1.4

In this image you can see a band crossing the flower petals and rising up the side of the vase in which everything seems to be sharp (it is clearer in the large version - click to open it). This is the range either side of the focal plane where the circles of confusion are so small that they appear as points.

How small do the circles have to be before they look like a single point? In an exhaustive analysis, Wikipedia tells me that assuming that you're going to make 25cm wide prints and view them from a distance of 25cm, then you will perceive any circle less than 0.2mm wide as a single point.

This means that a circle of confusion must be no bigger than 1/1250 of the image width if the image is to appear sharp. This translates into a minimum circle of confusion of 1/1250th of the sensor size. For 35mm cameras, the value 0.03mm is often used.

Note that this is the minimum acceptable sharpness. If you're a perfectionist or plan to make larger than A4 sized prints, you should strive to get your images even sharper.

Visualising the depth of field

It's imaginary line time again. Picture a cone extending from your lens to infinity, always 1/1250th the width of your image. I'll call this the sharpness cone because as far as I know there's no accepted name for it. If the blur discs are smaller than this cone, the image appears sharp. Using a 24mm lens which has a 72 degree angle of view on a full frame DSLR, this cone will be around a millimetre wide one meter from the camera, and a meter wide one kilometre from the camera.

DoF diagram

Between the near and far boundaries where the blur is smaller than the sharpness cone, the image will be perceived as sharp. The distance between the two boundaries is the depth of field.

Calculating the size of the depth of field

There are equations for calculating the near and far boundaries, which I shall include here even though I don't fully understand them so that we may share a sigh of relief when I introduce a nifty gadget that calculates them for you:

DoF equation

Yuck. Since pausing for a minute to use a calculator interrupts the creative process a bit, people use depth of field charts. I might not fully understand the above equation, but I can count that it has 4 variables. A single chart applies to one combination of focal length (f) and sensor size (c), leaving two variables left: subject distance (s) and aperture (N). The chart is a grid of the result of the above equations for every permutation of subject distance and aperture.

Go generate charts for all your lenses here: www.dofmaster.com/doftable.html. You use the chart by finding the row representing the subject distance, then selecting an aperture from that row that gives you the depth of field you need.

Nice laminated depth of field charts

For extra geek points, get them laminated!

If you look at the bottom row of these charts, you will see that they have a figure for each f-number called hyperfocal distance.

Hyperfocal distance

Sometimes, especially during landscape photography, you want the whole of a scene to be in focus. In order to do this you use hyperfocal distance focussing. This can be explained in terms of concepts already covered in this article: the hyperfocal distance is the closest distance you can focus on at which the blur discs behind the plane of focus are always smaller than the sharpness cone. In other words, the red and grey lines in figure 5 never cross over and there is no far focus boundary: very distant objects are in sharp focus.

When you are focussed on the hyperfocal distance, everything from half that distance to infinity will be sharp. For example, the hyperfocal distance for an 85mm lens at f/8 is 30 meters; focus on 30 meters and everything from 15 meters to infinity will be sharp.

Bear in mind when using hyperfocal focussing that it will produce "acceptably sharp" images according to the 1/1250th rule. However, if you don't actually need all that depth of field it is possible to get sharper images. If the subject you're shooting with the 85mm lens is 100 meters and there is no foreground that needs to be sharp, just focus on the subject!

The aesthetics of depth of field

The effect of focal length and aperture on depth of field has been mentioned above but a picture, as they say, is worth a thousand words.

The effect of focal length

Assuming that you change position to keep the subject filling the frame, focal length does not affect depth of field. However, the perspective causes the image to look different.

Flower 1

30mm @ f/2, taken from 40cm

Flower 2

85mm @ f/2, taken from 110cm

Look at these two photos large (click them to view the large size). At first glance the 85mm one looks like it has a thinner depth of field, but in fact this is not the case: in both photos the sharp area is about two squares of tablecloth thick, just enough to get the petals and the leaf sharp. In the second shot the perspective compresses the scene, causing the same depth of field to take up less space on the image.

Likewise the flower in the background is just as blurred in the second shot, but the circles of confusion are larger because the flower is larger. If you resize the flowers to compensate for perspective, you can see that the blur is identical.

See? Just the same.

The effect of aperture

DoF flower photo

30mm focal length, f/1.4 aperture

DoF flower photo

30mm focal length, f/4 aperture

DoF flower photo

30mm focal length, f/16 aperture

'nuff said.

The natural laws of depth of field...

There are some laws governing the relationship between these factors, which I shall call the Natural Laws of Depth of Field, highlighted in bold to convey an appropriate sense of gravitas. If you are one of those people who imagines the author speaking as they read an article, you may cast my voice in an "Ian McKellen as Gandalf" tone for this section.

Each of these rules explained in terms of the grey and red lines in figure 5, so here it is again for reference:

DoF diagram
1. Larger apertures cause narrower depth of field
Increasing the size of the aperture increases the angle of the grey lines.
2. Closer subjects cause narrower depth of field
Bringing the subject closer to the lens increases the angle of the grey lines. Remember: Ian McKellen voice.
3. Cameras with larger sensors give more blur with a given focal length and f-number
This is a corollary of the previous rule: because full fame DSLRs have a wider angle of view than cropped DSLRs, you have to get closer to the subject to take the same picture with a particular lens.
The other way of looking at it is that with a full frame DSLR you have to use a longer focal length lens to get the same angle of view as a cropped DSLR, and that longer lens will have a physically larger aperture. Either way the effect is the same.
4. As long as your subject fills the frame, depth of field depends only on f-number, not focal length.
Increasing the focal length and then moving back to keep the subject filling the frame keeps depth of field and blur constant, but increases the size of the circles of confusion because of perspective. Increasing the focal length increases the physical size of the aperture, but at the same time you move backwards, so the angle of the grey lines in figure 5 does not change.
This is why telephoto lenses are good for background control in portraits: they make the background appear more blurred without sacrificing depth of field on the subject. (Also, because the telephoto lens includes less of the background, it is easier to select a less complicated bit of background for the composition)
5. Zooming in on a subject (increasing focal length while maintaining the same position) massively narrows the depth of field
Two effects combine to produce this: the longer focal length has a physically wider aperture (hence the angle of the grey lines in figure 5 becomes steeper) and the longer focal length magnifies the image (so the angle of the red lines becomes narrower)

... and how to break them

So now you know the rules of depth of field.

[Morpheus voice:] What you must understand is that these rules are no different than the rules of any computer system. Some of them can be bent, others can be broken.

Focus stacking

A technique called focus stacking can be used on macro photographs to increase the depth of field beyond the limits of optics. You take a series of exposures, changing the focal plane by a tiny amount each time so that every point on the subject is sharp in at least one exposure.

You then run the series of images through some software that generates a composite image made from the only the sharp parts of each image.

Focus stacking example

The first photo, with only the antennae sharp

Focus stacking example

The last photo in the stack

Focus stacking example

The resulting image, obtained from stacking the above two with 35 other exposures in Helicon Focus. There is an excellent page of samples here.

images copyright Charles Krebs, 2005, taken from heliconsoft.com.

Helicon Focus is commercial software that makes it very easy to create your own focus stacks. The best free program to do the same is probably CombineZM, and there are some more listed on Wikipedia.

Tilt-shift miniature fakes

If your aperture is big relative to your subject then you will get a narrow depth of field, and if not then you won't. Since diffraction prevents you from having microscopically sized apertures, macro photographs have a narrow depth of field relative to the subject size. Likewise, since they don't make lenses with apertures a meter wide, you won't get a narrow depth of field when you shoot something the size of... well, a field.

This rule is so engrained in the minds of people who look at photographs that you can actually make a scene look like a tiny architectural model by adding fake depth of field. Your mind tells you that it must be small, because large subjects never have a narrow depth of field. This effect is called a 'tilt-shift miniature', because it was first done using tilt shift lenses that can tilt their plane of focus to achieve this effect without digital processing.

First take an image shot from above. The higher the better, since you normally look down on a model. Then use a fake blur - for greatest realism a lens blur like the one in Photoshop - and selectively blur the regions behind and in front of an imaginary plane of focus. Here are some I found earlier, click on them to see the large versions:

Cars and racetracks are great subjects for this effect, since its easy to believe they you're looking at a hobbyist's model. I find the bushes particularly amusing.

Without the fake depth of field added to the original photo, the huge hand added in Photoshop would have looked (even more) out of place! Note how the artist has also changed the white balance of the original. The warmer tone makes the scene look as if it was shot under indoor lighting; very clever.

Images by Dingo2494 and Photo Munki Deluxe on flickr. Hooray, for Creative Commons and for silly usernames.

The end!

That was my second photography article, I hope it was a better sequel to its predecessor than the Matrix Reloaded was. Feel free to post comments or ask questions below.

To subscribe to future photography articles, add this link to your RSS reader.

26 Responses to Bernie’s Better Guide to Depth of Field for Geeks Who Want to be Digital Artists

  1. Ronald Olszewski says:

    Just wanted to say “Thanks!” for the excellent depth of field article; I learned a lot from it. Got a new Rebel XTi on the way, so hopefully I’ll be able to put your knowledge to use soon. Take care!

  2. Axel says:

    *Great* article!

  3. Kate says:

    Just finished reading this and the beginner’s guide, you are a very talented gentleman and were you not apparently married already, i would have to propose to you. Purleeeeeaaaase could you do something on macros, i’d like to get a little closer than the 40″ (or something similarly poor) minimum focus distance on my kit lense, but am confused to death about macro lenses, “close up filters”, “extension tubes” and various methods mentioned on flickr which seem to be suggesting sticking a lense on backwards. Ideally, illustrated with pictures of the kit concerned and how you plug it all together, too (i know, i don’t ask much..)

  4. bernie says:

    Aw shucks. I don’t get comments like these for my computer programming articles :)

    In order to use the kit lens for macro work, you could buy the Canon 12mm extension tube which will allow you to get right up close to a subject so it will appear larger. However, you will only have a few centimetres between the lens and your subject, so photographing skittish insects is out.

    Personally I use a 500D close-up attachment on a 70-300 telephoto zoom. It’s basically a magnifying glass that screws onto the front of the lens and allows you to focus close. You can get good pictures of insects from a couple of feet away. If you can afford a 70-300, this is the most comfortable way of shooting macro, and allows you to do stuff like this:

    The extension tubes work for normal and wide lenses like your kit lens, the 500D works for telephoto lenses.

  5. dan says:

    Thanks for the article. Its rare to find something so well written that has good depth. I often find the web full of ultra basic or ultra geeky stuff with no in-between like yours.

    dan

  6. Clay says:

    I read the line about casting your voice as that of Ian McKellen in my head and instantly reverted…it really was perfect. Thanks for such a well-written article! If only college textbooks were this clear! :P

  7. Chris Trott says:

    Great Job on the SLR’s beginners guide. Almost all online introductions I read leave me “What the $#@” after reading it. Your article has been printed and put in my camera bag. I’m just looking at getting into the photography field (I am already a Geek) to enhance my print/graphics business. Thanks for the comic relief throughout!!

  8. Elliott says:

    Thanks for the in-depth (pun intended) explanation! I am going to go play with all of these new ideas.

  9. Jesper says:

    Thanks for a great article. I just bought my first SLR and probably spent more on it than is healthy but I really wanted something to grow into, and I’m very happy with the Nikon D300 I bought. Finding good guides has been hard but I really think you have done a superb job. Keep up the good work and thanks for alleviating my growing pains ;)

  10. Simon Watson says:

    Thanks for a couple of superb articles ! I have your first one and the depth of field one, and they are superb !!! Keep up the good work !

    Simon – Selkirk, Scotland !

  11. Hey just wanted to say thank you for taking the time to write this informative and in depth article!! I have only really begun to get into digital photography since March when I bought my Nikon D300 and definitely still learning. My pursuit of this material started with a question that came to mind as I am reading about a digital point-and-shoot that I am considering. It has a max aperture of f2.8, the same as my much larger Nikon 70-200mm f2.8 lens. That struck me as confusing so I looked for an answer. You article helped me understand! Thanks

    Kyle

  12. Ajith says:

    I was going through the beginner’s guide to photographic technique for geeks. This is the kind of information I was looking for a long long time.

    Thanks a lot.

    Ajith

  13. Amanda says:

    Wow! Thank you so much for this depth of field article and your beginners guide. It is exactly what I needed! The depth *haha pardon the pun* was amazing and you explained everything very clearly.

    Thank you thank you!!

  14. sino says:

    hi bernie

    fist thanks for the time and the effort you put in explaining all the subject related to photography.

    i m new in landscape photography , i m interested in hyperfocal distance. after reading your blog and others i started to understand this concept , but what confuses me more is the chart from http://www.dofmaster.com/doftable.html could you please explain to me what is the relation between , distance , near , far, and hyperfocal distance. and what distance this chart refer to 1….100

    thanks

  15. Hey superb post, i recognize that this is a little bit of off topic however is the Telephoto EF 100mm f/2.8 USM Macro Autofocus Lens worth it? i’ve read a few reports but on the other hand i wouldn’t like to throw away $480 on it. also are there any beneficial message boards that i could possibly participate in photography thanks Charles in the the united kingdom…english is not my first language

  16. Charlotte Wedding Photography says:

    I’m going on my 2nd yr in the photography field & I am discovering new stuff all the time, such as this posting – many thanks for this blog. Jennifer

  17. Kim Pham says:

    Thanks very much for your method of explaining things, very easy to understand the most complicated subject. I am just a happy single mom, had to learn to record golden moments of my two children about 6 years ago. I took a basic class at a local college at that time, and took good pictures with film / luck more than skill, then bought a few more P&S digital camera for my kids, canon G9 is one of them, it is traveling to my son to Ghana right now-it takes good pictures. I finally bought a Canon 7D for my trip-visit and watch my daughter performing on the stage at her university next month. I started searching and your site popped up and thanks again. Good luck for your trip.

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  19. Alex says:

    Great article! It is suitable for anyone from beginners to those sophisticated guys.

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  23. Liza Q. Delgado says:

    hey! nice article. I was wondering though, can the blur still be measured when you already used a software on the image? example, helicon focus. or adobe photoshop. how can you say that it has a greater depth of field than the image which is not edited? you can’t just say it’s clearer, too. is there any way to measure depth of field when a software has already edited it?

    • bernie says:

      Good question. Depth of field is really a property that applies to optical systems and the images that they produce. Once you’ve edited an image or combined several images together then all statements about depth of field no longer have their strict technical meanings. You could go by aesthetics and say “This edited photo seems to have half the depth of field of the original”, but that’s a human judgement, not a technical statement.

  24. Liza Q. Delgado says:

    i wanna ask again, how exactly do you get the value for the minimum circle of confusion? i kinda don’t get it. there’s the 0.2 mm, then the 25 cm, then suddenly there goes the 1/1250. please enlighten me! thanks vm

  25. Les says:

    Good article. But, I’d should like to clarify one point. . .
    When you speak of measuring blur in the real world, you are not really measuring in the real world, but are extrapolating the amount of blur you see in the image to how large that would be given the actual size of the subject or object being blurred in the image. Is that correct?

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