Depth of Field

by Ashok Kandimalla

As per optical theory only one point (and all the points at exactly the same distance from the lens – often called a plane) can be in perfect focus. But in reality things on either side of this plane will also be in focus, that is, they will be acceptably sharp. Outside this zone they are definitely not sharp. This zone is called “Depth of Field” or in short DOF. Simply put DOF is a band of acceptable sharpness in a photograph. It is the distance between the nearest and farthest objects, which are in focus.

When needed, DOF is very desirable but can be a nuisance when one does not need it. As an example, if you are photographing a landscape, an accepted practice is to keep a foreground element in your composition to create a sense of depth. Here, you want the foreground and the background objects as sharp as possible or in other words you need a large DOF. On the other hand if you are taking the picture of a flower, you would like keep the cluttered background out of focus since it distracts the main subject, which is the flower. Here, you should opt for a shallow DOF. Thus, DOF is always important and hence you should know how to control it.

So what is acceptable sharpness? This is defined in terms of what is called the “Circle of Confusion (COC)”. When in perfect focus, a point subject will be reproduced as a point on the sensor. If not in perfect focus the point will become a disk on the sensor and this disk is called the COC. The size of the disk is a measure of what we can tolerate as acceptably sharp. The smaller the COC, sharper will be the picture and less will be the DOF.

COC varies for each format (frame size) and is lesser (more demanding) for smaller formats. The reason for this is that for the same size of print (enlargement), you need to enlarge a smaller format more. You can also easily see that, larger the print, higher will be the enlargement and hence smaller should be the COC. In other words a COC that is acceptable for a small print may not be good enough for a large print.

Also, we need to remember that in general, larger the print, greater will be viewing distance. This in turn puts less demand on the COC. The industry norm for viewing distance is generally taken as two times the diagonal of the print. Taking these factors into account, the COCs for different formats can be derived from a formula attributed to the famous optical company Zeiss. The formula is simple. The COC is taken as diagonal of the image (in mm) divided by 1730. The resulting values are given in Table below.

Format	Circle of Confusion in mm
4/3 System (13 X 17 mm)	0.013
APS Digital (18 X 24 mm)	0.017
35mm or digital FX (24 X 36 mm)	0.025
Medium (6 X 6 cm)	0.049

DOF depends primarily on four factors for a given format:

1. Print size
2. Viewing Distance of print
3. Magnification
4. Aperture size (f number)

If we use the COC given here for calculation of DOF, we can safely assume that the first two factors (print size and viewing) have been taken into account for all normal applications. In fact these two are not in the control of the photographer directly.

To proceed further you need to know what magnification means. To put it shortly, magnification is ratio of the size of the image to that of the real object. That is if one photographs a 1 centimeter (cm) line and it appears on the sensor as a half cm line, then we say the magnification is 1/2. The reproduction ration is now 1:2. If the image and the real object are of the same size then reproduction ratio is 1:1. Of the image is twice the size of the real object then magnification is 2 times and is reproduction ratio is 2:1. Remember that magnification increases with longer focal lengths and shorter subject distances. At high magnifications (as used in macro photography for e.g.)  the DOF will be very less, sometimes even less than a millimeter.

Many times in literature you might have seen that DOF is dependent of focal length. This is not correct in the strictest technical sense as DOF depends on magnification. That is, it depends on focal length and the distance of the subject. Contrary to the popular belief, a 105mm lens focused at infinity will have a lot more DOF than a 28mm lens focused very close to the subject since the magnification in the latter case is higher though the focal length is less, if aperture is maintained constant.

The aperture also has a significant impact on DOF. The DOF increases if you choose a narrow aperture (large f/ number). This is because as you make the aperture narrower the spread of light rays is contained making the image sharper. This is commonly known as “stopping down”. This in effect makes the DOF larger.

As a thumb rule remember that stopping down the aperture by two stops will double the DOF range.

However, it is not advisable to make the aperture very narrow beyond a certain point as diffraction effect sets in and reduces the sharpness. For small formats like 35mm and APS sized sensors this is normally around f/11 or f/16. If you stop down further, then the overall image sharpness may suffer though DOF may increase.

f/2.8

f/5.6

f/11

f/22

What was discussed so far is summed up as

We have seen that DOF is band that is in focus before and beyond the point of focus. At normal distances the DOF is distributed one third before and two thirds beyond the plane of focus. That is, if the focus plane is at 20 metres and DOF is at 9 metres, then the zone of focus (DOF) will extend from 17 metres to 26 metres. This however, changes when you focus very close (like macro photography). Here the DOF extends equally on either side of focus plane.
All fixed focus (prime) lenses have DOF scales on them. These are just below the distance scale and are marked as f-numbers on either side of focus mark.
You can align the farther distance point to the f-number being used on the DOF scale and get the closest point that will be sharp focus by reading off the distance scale opposite to the same f-number on the other side of the focus mark.

Similarly, one can also align the nearer point to the f-number being used on the DOF scale and get the farthest point that will be in sharp focus by reading off the distance scale opposite to the same f-number on the other side of the focus mark.

Modern zoom lenses do not have DOF scales on them. This is because it is difficult to mark DOF scales for different focal lengths in the limited space available on the lens barrel. Hence, you cannot follow the method described. However, you can check the DOF by using DOF preview button if the camera has this feature. When you press the DOF preview button, the cameras stops down (closes) the diaphragm blades to the aperture that has been chosen and you can actually see what is in focus and what is not. One consequence of stopping down is that this dims the viewfinder. If you find the image too dim, allow a little time for your eye to get used to it.

The DOF preview is also useful to check how out of focus the background is. This is particularly useful when photographing flowers, etc. By using DOF preview you can check if the distracting background elements are sufficiently out of focus.

Another concept that you should be aware of is the “Hyper Focal Distance” (HFD).

HFD is fixed for a particular COC, aperture and focal length and is the point at which DOF is at the maximum. If you set the focus of your lens at HFD, the near focus point of the DOF will be at the half the distance set and the far distance point will be infinity. In other words HFD is the point of focus where everything from half the distance of HFD to infinity falls within DOF. The HFD can be calculated by using the formula.

HFD (in mm) = L*L / (f*c)

Where L is the focal length in mm and f is the aperture that is the f-number and c is circle of confusion in mm. The resulting figure will be in milli-metres and dividing it by 1000 will give HFD in metres.

E.g. for a 24mm lens at f/8 the HFD will be 4.3 metres assuming a COC of 0.017mm (This value corresponds to  DSLRs using APC format sensors).

Here are some tips to help you set the HFD quickly.  In the case of fixed focal length lenses, the DOF scale can be used as before. First the aperture can be chosen and then the infinity mark can be set opposite to the f-number chosen on the DOF scale. The near focus point can be read opposite to the same f-number on the opposite end of the DOF scale. The point of actual focus will be exactly twice that of the nearer focus point.

In the case of zoom lenses most of which are without DOF scales, you can calculate the HFD using the formula given and place the resulting number on the distance scale opposite to the focus mark on the lens. Now, all the subjects from half that distance to infinity will be in focus, for that particular focal length and aperture that you have used in the formula.

Here is one point that you should be aware of. After setting the lens at HFD, if you look through the viewfinder the scene will look out of focus! This is because the viewing aperture is not the same as the (shooting) aperture at which the picture is taken. However, the resulting picture will be sharp so long as the HFD is set correctly for the particular aperture and focal length you have chosen. You can check this by pressing the DOF preview button.

The following table gives HFD for different focal lengths and f-numbers in metres. This table has been calculated using a COC of 0.017mm and is suitable for DSLRs with APC sized sensors.

HFD Table
Hyper Focal Distances are in metres

You can copy the table, laminate it and keep it in your camera bag so that you can have it handy, if you use a DSLR with APC sized sensor.
While setting your camera at HFD is very useful when photographing landscapes, another useful application is candid photography. Here, presetting the focus to HFD will allow you to concentrate on the subject and quickly take a picture – something which is very much needed in candid photography.
You need to be aware of some issues regarding DOF when using digital point and shoot (P&S) and bridge cameras.  In these cameras, due to the very small size of sensors, the focal length of the lenses is very small. This in turn causes the magnification to reduce drastically causing a corresponding increase in DOF.
Also, at these short focal lengths, even moderately small apertures will result in the physical diaphragm opening to be very small. Such a setup is prone to diffraction. Hence it is common to limit the minimum aperture in these cameras to f/8 or so. For comparison, SLR and DSLR lenses can generally stop down to f/22 and large format lenses can stop down to f/64.
Remember however that even at f/8 the DOF will be quite high as mentioned earlier.  You can remember a thumb rule to get an idea what the DOF will be with relation to a 35mm camera. First determine the cropping factor with reference to the 35mm film format.  As an example, a camera with 2/3” sensor will have an approximate cropping factor of 4.
Then, at a focal length of 7mm and an aperture of f4.0 on such a camera, you will get approximately the same DOF of a 28mm (7mm X 4) lens on a 35mm camera but at an aperture 4 times smaller or f/16. This corresponds to a huge DOF though the lens is stopped down only to f/4.
This can be seen mathematically also. One valid assumption here is that circle of confusion is also smaller allowing for smaller sensor size and hence larger magnification while printing. Using apertures smaller on such a short focal length will result in definite diffraction.
In general with digital P&S and bridge cameras, too much DOF is a problem. It is very difficult to get blurred backgrounds unless you are photographing very close to the subject with a corresponding increase in magnification.

How to control DOF:
You now have a good understanding of DOF. To recap it is a complex blend of many factors – the primary ones being the aperture and magnification. These two are essentially optical issues.
In digital photography there is one more variable available to you when you want to change DOF. This you can do this by changing the ISO value. Of course, remember that ISO has no direct control over DOF. Consider the example below:
Assume that you are in a situation where you don’t have a tripod and the available light gives you let us say a shutter speed of 1/30 sec and an aperture of f/4. However, you need an aperture of f/11 for sufficient DOF and for that you need to reduce the shutter speed to ¼ of a sec which would be too slow to hand hold. In such cases, you can increase the ISO from say 100 to 800 and get f/11. The penalty you will need to pay will come in the form of increased noise (grainy image) at high ISO.
The following table could come in handy when you want to control DOF.

 

To decrease DOF	Use larger apertures (use smaller f/ numbers). You will need to use faster shutter speeds to maintain proper exposure. Increase magnification by –  moving closer to the subject and / or increasing the focal length Use lower ISO values which will allow you to use larger apertures
To increase DOF	Use small apertures (higher f/ numbers). You will have to use slower shutter speeds which may necessitate the use of a camera support like tripod. Decrease magnification by moving away from the subject and / or decreasing focal length. Use higher ISO values which will allow you to use smaller  apertures