Depth-of-field and sensor size

 

 

 

 

 

 

With a smaller sensor, you get greater depth-of-field, true or false.

On various Internet photography forums, there’s been a lot of discussion about the idea that a smaller image sensor provides greater depth-of-field, why this is so, or if it is even true. Cause and effect are often confused on this topic.

The statement “With a slower shutter speed, you get more depth-of-field” is just as silly as “With a smaller sensor you get more depth-of-field”. And yet, there is a kernal of truth in both statements, you actually get more depth of field. But in both instances the real reason is not named.

With slower shutter speeds you usually have a smaller aperture, and a small aperture gives you the additional depth of field. Every serious photographer knows this. However, the reason for increased depth of field with a smaller sensor in not so readily apparent. That’s what I’ll try to explain in this article.

A smaller sensor has a smaller field of view, so you get less in the picture than with the same lens  on a full frame camera. To put it another way, to get the same image on that smaller sensor that  you’d get on a full sized sensor, you would need to move away from your subject. So you would  automatically have a different reproduction ratio. We’ll discuss reproduction ratio in a minute.

DEPTH OF FIELD IS ONLY DETERMINED BY THE REPRODUCTION RATIO IN COMBINATION WITH THE CHOSEN APERTURE.

The smaller your reproduction ratio, the greater your depth of field at a certain aperture. You can also turn that around, and say that a smaller aperture setting at a certain reproduction ratio, the greater your depth of field.

Now let’s define reproduction ratio. It is the relationship between the size of the object as it gets projected on your sensor to the actual size of an object. Literally the ratio at which it gets reproduced. If an object is 1 centimeter on your sensor, and in reality it is 10 centimeters, then the reproduction ratio in 1:10 (or to put it into decimals, 0.1). If your sensor image is 1 cm and in reality the object is 2 cm, the the reproduction ratio is 1:2 (or 0.5) etc.

It doesn’t matter what size your sensor is, 1 cm. on a full frame sensor is also 1 cm. on an APS-C sensor. To get the same picture with a small sensor as you would on a full frame sensor, the reproduction ratio will be smaller, and therefore the depth of field will be greater. I’ll explain this with the following example: A full frame sensor is 24 x 36 mm, and an APS-C sensor is 15 x 22 mm. Suppose you want to photograph a tree that is 3 meters high, so that it fills the frame. On a full frame camera the image on the sensor would be 24 mm.

This gives you a reproduction ratio of 0.008 (24 mm./3000 mm. = 0.008). If you want to photograph this same tree on an APS-C camera, you’d need to increase your distance from the tree, 1.6 times the distance actually.

On an APS-C camera the frame-filling image on the sensor will give you a reproduction ratio of 0.005 (15 mm/3000 mm = 0.0625). So you can see that the APS-C sensor has a smaller reproduction ratio (0.0625) which is what gives you a greater depth of field. It has nothing to do with the sensor size. With a compact camera, because of it’s even smaller sensor size, the change in reproduction ratio is even more extreme.

Above, I wrote that depth of field in only dependant on reproduction ratio and aperture. This means that the lens focal length doesn’t play a role either. Many people think that a wide angle lens has more depth of field than a telephoto lens, but this isn’t true either. To prove this, I photographed a matchbox at exactly the same angle, with a 50mm lens and with a 180mm lens. The reproduction ratio was exactly 1:3 for both shots, and the aperture was f/3.5 for both. The shot with the 50mm lens was obviously much closer to the subject than with the 180mm lens to get the same enlargement. I used the live-view zoom function on the camera to do the critical focus (See This Month – January 2012), exactly in the middle of the matchbox.

The photos at the top of the page were both shot at f/3.5, and the two at the bottom of the page were shot at f/16. You can see that the focus fall-off in the same between the left and right side photos in both cases. So you see that it has absolutley nothing to do with focal length, only reproduction ratio and aperture.

The focal length does have a significant effect on the perspective, as you can see. The first impression is that the matchbox on the right is larger, but the box fold above the strike area is exactly the same size. The far side of the box does get bigger because of the changed perspective. Also, the bumps on the Lego panel change dramatically, as do their the vanishing point.

In summary, you can see that for macro photography, you can just as easily use a Canon EOS 7D with a 100mm f/2.8 IS USM lens as a Canon EOS 5D mkIII or the new Canon EOS 6D with a 180mm f/3.5 Macro USM lens.

In the field, using a 180mm lens on a full frame camera is about the same as using a 100mm lens on an APS-C camera. The camera-to-subject distance for those shy dragonflies will be about the same with either setup. With an APS-C sensor you have a slight advantage that the reproduction ratio will be smaller, so you get a little more depth of field. On the flip side, the full sized sensor offers beautiful soft backgrounds (larger reproduction ratio = less depth of field). And of course the greatest advantage of a larger sensor is the higher image quality.