## Depth of Field

A demonstration tool for calculating depth of field is provided: Depth of field calculator

For details of the mathematics, see: Depth of field derivation

When the subject distance is much less than the hyperfocal distance and the magnification is small (i.e. not macro), an approximation to depth of field is given by:

Where N is f/number, c is acceptable circle of confusion, f is focal length and s is distance to subject.

**Effect of f/number.** From the expression above, we can see that the effect of f/number (N) is straightforward. DOF is proportional to the f/number set on the lens – doubling the f/number doubles the DOF.

**Effect of Focal Length.** The expression above indicates that DOF is inversely proportional to the square of the focal length, i.e. doubling focal length reduces the DOF by a factor of four.

But what happens if we adjust both focal length and distance to subject? If we take a given camera (thus defining c) and set up a head and shoulders shot, we can maintain the same magnification across a variety of focal lengths simply by changing the distance such that (s/f) remains constant. The DOF then depends only on f/number (N). This gives rise to the common observation that for a fixed composition, the DOF is independent of the focal length. While this is something of a half-truth, it is a point worth noting.

**Effect of Sensor Size.** To understand the effect of sensor size, we have to consider the **“acceptable circle of confusion”** (c) in the expressions above. Consider photographing a single, very small point of light. If we focus exactly on that point, the image created on the sensor will also be a tiny point. If we then focus slightly in front or behind the point of light, the image on the sensor will be a small, blurred circle. The question is, at what amount of out-of-focus will we start to notice the blurring..? The “acceptable circle of confusion” is defined as the largest blurred circle on the sensor that, when viewed in normal conditions in the final print, will still be perceived as a point. Normal conditions is sometimes defined as viewing an 8″ by 10″ print at 25 centimetres, i.e. hand held.

If we start with the (physically small) image on the sensor and create an 8″ by 10″ print, the amount of magnification involved depends on the relative size of the sensor and the print. If the sensor were 1″ wide, the image would be magnified 10 times to fill a 10″ print. If our small point of light was slightly out-of-focus and was recorded as a small blurred circle on the sensor, the blurred circle will be 10 times bigger on the print. But will we actually see it as a point or as a blurred circle?

Starting with the print, let's assume that the smallest circle we can identify as a circle is about 1/125″ - anything smaller will be seen simply as a dot. With a 10-times magnification between sensor and print, this circle would be just 1/1250″ on the 1″ sensor. So the acceptable circle of confusion for the 1″ sensor would be 1/1250″ or 0.02 mm.

Now switch to a camera with a 2″ sensor. The magnification between sensor and print is now just 5-times - and a circle of 1/125″ on the print will correspond to a circle of 1/5th of that size on the sensor - i.e. 1/625″ or 0.04 mm. So the acceptable circle of confusion for the 2″ sensor is twice that for the 1″ sensor.

The acceptable circle of confusion is therefore proportional to the size of the sensor. Examples of acceptable circle of confusion for common sensors sizes are:

- ♣ 0.029mm for 35mm sensor
- ♣ 0.018mm for APS-C Canon
- ♣ 0.015mm for Four Thirds

Note from the expressions above for DOF that if we set up a studio shot with a given subject distance (s), focal length (f) and f/number (N), the DOF is proportional to the acceptable circle of confusion (c) and therefore proportional to the sensor size. A larger sensor gives a larger DOF.

However, consider setting up a full-frame 35mm camera and a Four-Thirds camera side by side, with the same f/number, and choosing lenses to get the same field of view, perhaps a head-and-shoulders shot. If we choose a standard 50mm lens on the full frame camera, we would need a 25mm lens on the Four-Thirds camera to reproduce the same field of view on its smaller sensor. The effect of the smaller sensor on the Four-Thirds camera would be to halve the DOF. But the focal length used on the Four-Thirds camera has also been halved - and halving the focal length should increase the DOF by a factor of four. The effect of focal length wins and the overall effect is a doubling of the DOF for the Four-Thirds camera.

It is frequently said that a characteristic of cameras with small sensors is that they have large DOF. This again is a half-truth. The direct effect of reducing the size of sensor is to reduce the DOF. However, as described above, cameras with small sensors are generally used with lenses of short(er) focal lengths which, for a given composition, increases the DOF.

For a discussion of equivalence of different sensor formats, see: Equivalence