## Wednesday, October 02, 2013

### Depth of field does not depend on the focal length of the lens

Many photographer believe that a wide angle (= short focal length) lens give more depth of field (DOF) than longer lenses. This is a misconception! For a given magnification the focal length of the lens does not effect the depth of field which is (almost) entirely determined by the aperture. The Wickipedia article on DOF gives the following formula to (approximately) calculate the DOF in close-up situations (i.e. where the distance to the subject is very much less that the hyperfocal distance):

$\mathrm {DOF} \approx 2 N c \, \frac {m + 1} {m^2} \$ where m is the magnification, N is the f-number and c is the circle of confusion.

For more information on circles of confusion see this Wickipedia article which gives a value of c = 0.018mm for the Canon APS-C sensor.

The following table and chart show the DOF in millimetres at various f-stops for reproduction ratios from quarter life size to twice life size calculated using this formula for the APS-C sensor:

I wanted to try and demonstrate this for talks I give on macro photography. What I came up with was to take a series of photos of a relatively small subject (an 18cm tall figure of an Uruk-hai from Lord of the Rings) using a series of different focal lengths, but moviing the camera so that the subject was kept at the same size in the viewfinder (hence maintaining the same reproduction ratio). Here is the setup:

The Uruk was placed, standing on a ruler, in the garden and a piece of string stretched from his middle across the garden. At each focal length, the camera was positioned with the lens aligned along the string to keep the same angle of view and then moved backwards and forwards until the Uruk was positioned in the same way in the viewfinder with his feet on the bottom of the frame and the top (active) focus point on his chest armour:

All the pictures were taken at f6.3. I used my Sigma 150-500mm to take pictures at 200, 300, 400 and 500mm, my 100mm macro and my 17-85mm zoom for 80, 50 and 35mm (I could not get close enough to achieve the same magnification and still focus at focal lengths below 35mm!).
 400mm (at 5.8m)

 200mm (at 3.2m)

 100mm (at 1.7m)

 50mm (at 90cm)

 35mm (at 74cm)
Examining these images closely, focus extends from about the 34/34.5 to the 37cm mark on the ruler. The part of the ruler that is in sharp focus does not change as far as I can tell when examining the originals at 100%. The block of wood used to angle the ruler is clearly out of focus in all the shots. However, what is very clearly shown is the effect of focal length in changing the working distance and perspective. The same subject magnification was achieved at 5.8m away using the 400mm as at 74cm with the 35mm focal length. But, using the 400mm, there is very little of the background in shot, whilst at the other extreme there is a wide sweep of the background wall.

The effect of the focal length of the lens on the working distance for macro shots can be seen in the following shots. Here is the Uruk's lovely face at a reproduction ratio of 1:1:

 1:1 shot of the Uruk-hai's face
And here are the 100mm macro and 65mm macro focused on his face at 1:1. Note the difference in working distance, how much closer you have to be using the 65mm (front of the lens just about touching his crossbow):
 100mm macro focused on the face at 1:1

 65mm macro focused on the face at 1:1