Depth of Field – How Does It Really Work?

Depth of field is one of the least well-used aspects of photographic control. Yet it really is very simple to get your head around.

Depth of field

A camera lens will actually only focus one single, flat (if it is a good lens) plane perfectly. As you move away from the plane of sharp focus, objects become gradually more blurred. In practice we can tolerate a small amount of blur (called a circle of confusion, from the blurred circle of light you get if you focus a point source of light, like a star). How much blur we can tolerate is determined by how much we will blow up the image in printing or projection. Common values for this circle of confusion range from 0.025mm to 0.033 mm. The reason larger format images appear to have larger depth of fields is because you do not need to magnify them as much to get a resulting print size.

Depth of field

Aperture F number (or the f stop) is calculated by dividing lens focal length (fl) by the diameter of the aperture (a) (F number = f.l. / a). What this means is that for a given F number, a telephoto lens (long focal length) will have a larger aperture diameter (if you like, size of the front element of the lens reflects this) than will a wide angle lens. That’s why an f2.8 28mm lens is not as physically wide as an f2.8 400mm lens. For depth of field, it is actually the lens aperture diameter and not the focal length that matters, but you can see from the above how we can effectively think in terms of focal length because of the relationship between F number, aperture and focal length.

The basic lens equation is 1/subject distance + 1/focal plane distance = 1/focal length. The focal length (fl) is the distance from the lens that a subject at infinity will be brought to focus. Subject distance (s) is the distance from the lens to the subject we have focused on and focal plane distance (fpd) is the distance from the lens to the film or sensor plane in the camera. The above equation explains why a lens extends as you focus on closer subjects (fpd must get larger to compensate for s getting smaller, since fl remains constant). It also explains why adding extension tubes or a bellows to a lens allows it to focus on closer subjects (it increases fpd or focal plane distance).

A point of light is not, in practice, brought to a single point on the film plane, but to a tiny (hopefully) circle. The size of this tiny circle of blur (circle of confusion) is defined by the diffraction characteristics of the lens (and its aperture) and by the quality of the optical corrections in the lens. In many cases it is not, in fact, a perfect circle, due to the actual shape of the aperture and to any aberrations in the lens. As an object moves out of focus, this circle of confusion gets larger. One aside here – some lenses are marketed as having great out of focus blur, by having a carefully designed aperture iris that is as close to a perfect circle as the engineers can make it. It offers more pleasing out of focus images.

Depth of field

Images appear to us to be sharp when this circle of confusion is smaller than we can resolve with our eyes. This explains why an image can look sharp from a distance but becomes blurred as we get closer to it, we are finally close enough for our eyes to resolve the circle of confusion. Thus there is no such thing as a completely sharp image. The closest we can get is a photograph of a completely flat object, like a map or painting. Even here, there will be a fundamental level of sharpness caused by the lens characteristics.

When you focus on a subject at distance s, an object closer to the camera (sn) will be brought to a focus further from the lens (behind the film plane). This means that at the film plane the circle of confusion will be larger. A subject further from the camera (sf) will come to a focus in front of the film plane. This also means that at the film plane the circle of confusion will be larger. The size of the circle of confusion turns out to be directly related to the physical aperture of the lens and how far the subject is away from what we have focused on. What this means is that to maintain a certain maximum circle of confusion size (effectively how sharp we want the image to look), as we increase the lens aperture (or the lens focal length) we get less distance off the focal point in acceptable focus.

Circle of confusion is depth of field

So what all the above translates into is the following:
*    For a given lens, you get a greater depth of field as you stop down to smaller apertures (go from f2.8 to f11, say)
*    At a given aperture number, say f2.8, a telephoto lens will give you less depth of field than a wide angle lens, because the physical lens aperture will be larger for the longer focal length lens. This is provided you keep the lens to subject distance the same
*    The actual size of the depth of field decreases as the camera gets closer to the subject it is focused on (it can be 10 feet or 3m at a distance and only inches or centimeters up close)

Depth of field of a 50mm lens
Shot with a 50mm lens

Depth of field with 100mm lens
Shot from the same distance with a 100mm lens

Depth of field of 100mm lens
Shot with a 100mm lens from twice the distance

All the above also explains why compact digitals seem to have a much greater depth of field than digital SLRs. For a given effective focal length (say 50mm in 35mm camera terms), a camera with a smaller sensor will use a smaller focal length to achieve this than a camera with a larger sensor. Given the smaller focal length, at a given F number, the smaller sensor camera will use a smaller aperture, giving a larger effective depth of field. This is why many complain of not being able to use the same shallow depth of field techniques that we are used to using with 35mm cameras for things like portraiture.

For those who want a more mathematical discussion, see Norman Koren’s excellent article.

2 thoughts on “Depth of Field – How Does It Really Work?”

  1. Sir,
    Can you please tell me that where the image plane(or sensor) will be placed relative to camera lens,because as per thin-lens equation sharpest image need not be formed on focal plane but at a distance governed by:-
    1/f=(1/obj.distance)+(1/image distance)
    where image distance=f means sensor is at focal plane.

    Also at one point you mentioned,increasing aperture reduces the focal length,but how focal length of a lens can be changed(being an intrinsic property)?

    I think i am not clear with what you’re referring by ‘focal length’,but i suspect that it is image distance in thin lens formula.

    1. I suggest a re-read. Remember with digital cameras there is the real, optical focal length and then there is the effective focal length that takes into account the sensor size.

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