Depth of Field & Image Resolution

In my article on Printing and Image Resolution I define image resolution in terms of pixels and the amount of detail that can be reproduced at a particular print size. However,  concepts such as 'resolution' and 'sharpness' in an image are also important at an earlier stage in the photographic process, i.e. when a camera is used to record an image on film or digital sensor array. Most photographers appreciate the value of a sharp picture, the more experienced even exploiting a combination of sharp subject matter against a defocused background. It is in this context that an understanding of the basic principles concerning Depth of Field (DoF) is of value to the photographer. This is illustrated in the image to the right, which was taken at f/13 with a focal length of 135 mm. Of course, colour and tonal values are also important in helping to separate subject from background. The similar image, below, despite stopping down to f/16, shows just how narrow the DoF is, the flower head on the left being slightly nearer to the camera.		Isolating the subject: Lens 24-135 mm, Focal Length 135 mm

The following diagram graphically illustrates how depth of field provides an acceptable range of focus in front of (Near) and behind (Far) the camera lens' best point of focus. The transition from acceptably sharp image detail to out of focus blur, however, is gradual and not as abrupt as the diagram might seem to suggest. Learning how to control DoF is part of the art of photography, enabling the photographer, either to extend the range of focus (DoF), or to decrease it and thereby differentiate subject matter from background.

There are a number of basic factors affecting DoF, which may serve as useful "rules of thumb" for the photographer:

• As can be seen in the diagram, the Far range of focus is greater than the Near range of focus.

• A large aperture, such as f2.8 narrows depth of field, whereas a smaller aperture, such as f16, increases it.

• Close-up photography also narrows depth of field. Depth of field increases with greater distance between camera and subject.

• A wide-angle lens (i.e. a lens with a short focal length) achieves a greater depth of field than a telephoto lens.

I am grateful to my friend Dr Ken Raine for the following technical contribution, which  examines, in more detail, some of the concepts appertaining to DoF, and may be of particular interest to those seeking a deeper understanding of the physics involved. Ken, now retired, was an optics specialist at the National Physical Laboratory, Teddington, London.

Depth of Field: An Introduction
When a camera lens, or any lens, is set to best focus for some object distance then at other distances, near and far, the image is out of focus. The amount of defocus that can be tolerated depends on the imaging quality of the eye, final print size and distance at which it is viewed, the original focus setting and the perceptual tolerance to loss of focus.

Like any lens or imaging system, the eye has a limited ability to resolve detail. If no visual defects are present the ultimate limit of resolution is set by the wavelength of light and the ratio of the diameter of the iris to the size of the eye. To overcome this limitation and see more detail we have invented telescopes and microscopes.

Under best lighting conditions the eye’s ability to resolve detail is at its best at a viewing distance of around 250 mm and is estimated to be an angle of about 1 minute of arc. This corresponds to about 0.1 mm at a distance of 250 mm. In a strict technical sense this means that two pinpoint objects or lines could just be seen as separate images. An animation that shows two star images approaching and passing inside the resolution limit, commonly referred to as the Rayleigh limit of resolution, can be seen by selecting Animation. At separations just less than the Rayleigh limit we cannot see the two objects clearly but rather as one ‘blurred’ together.' This does not mean that smaller objects cannot be seen. For example, every star you see in the sky has a size smaller than the limit of resolution of the naked eye. So they are seen as stars, i.e. pinpoints of light and not disks, but with varying brightness depending on their intrinsic brightness, size and range.

Similarly lines on a print that are thinner than 0.1 mm can be seen but if two lines are closer together than 0.1 mm will be seen as one line. The limit to the detail we can see is frequently referred to as the Rayleigh limit of resolution or the diffraction limited resolution.

This limit of resolution therefore gives us a value on which to base an estimate of the tolerance to defocus in an image formed by the camera lens. The ray diagram, figure 1, shows how the tolerance to defocus translates into a distances either side of the best focus for a lens at its lowest ‘f’ number (aperture). The length of the blue tolerance line is related to the limit of resolution and print enlargement, and represents the diameter of what is usually referred to as the Circle of least Confusion. Light rays passing through the lens must pass through, or touch, the blue tolerance line to be considered in focus. The distance values can be evaluated using a general lens equation.

The camera lens too, like the eye, has its limit of resolution. Fortunately this limit is seldom approached and can usually be ignored in the calculations that use the simple geometric approach shown in the figure.

It is worth keeping in mind that when viewing images it has been found that people will tolerate more ‘out of focus’ than we might expect using the Rayleigh criterion and an equivalent resolution of 2 min of arc can be used. Also at viewing distances away from 250 mm and under non ideal lighting the optical performance of the eye is reduced and will be further reduced if the person does not have good or well corrected vision.

Therefore values for the depth of field should always be taken as a guide, despite the underlying physics and apparent accuracy of the calculations made from the lens equation.

The effect of reducing the f-number (aperture) is shown in figures 2 and 3, which show only the depth of field in the near distance. Now rays, shown in red, from a closer object can intercept the end of the blue tolerance line and it is also in focus. In figure 2 the blue and green rays are shown, as they were in figure 1, for comparison, but are now dashed where they are blocked by the iris and no longer pass through the lens.

The full effect of increasing the f-number is shown in figure 3, where it can be seen that the green rays from our earlier depth of field limit now pass inside the blue tolerance line and are well in focus.

 and where c is given by c₀/M where c₀ is the diameter of the circle of confusion for the eye viewing at a distance of 250mm and has a commonly accepted value of 0.15mm, which is twice the limit of resolution of the eye, and M is given by the ratio of the area of the print to the area of the image on the film or CCD array and is usually approximated by forming ratios of the image widths.