Depth of field

Object-field calculation methods

Traditional depth-of-field formulas can be hard to use in practice. As an alternative, the same effective calculation can be done without regard to the focal length and f-number. Moritz von Rohr and later Merklinger observe that the effective absolute aperture diameter can be used for similar formula in certain circumstances.

Moreover, traditional depth-of-field formulas assume equal acceptable circles of confusion for near and far objects. Merklinger suggested that distant objects often need to be much sharper to be clearly recognizable, whereas closer objects, being larger on the film, do not need to be so sharp. The loss of detail in distant objects may be particularly noticeable with extreme enlargements. Achieving this additional sharpness in distant objects usually requires focusing beyond the hyperfocal distance, sometimes almost at infinity. For example, if photographing a cityscape with a traffic bollard in the foreground, this approach, termed the object field method by Merklinger, would recommend focusing very close to infinity, and stopping down to make the bollard sharp enough. With this approach, foreground objects cannot always be made perfectly sharp, but the loss of sharpness in near objects may be acceptable if recognizability of distant objects is paramount.

Other authors such as Ansel Adams have taken the opposite position, maintaining that slight unsharpness in foreground objects is usually more disturbing than slight unsharpness in distant parts of a scene.

Overcoming DOF limitations

Some methods and equipment allow altering the apparent DOF, and some even allow the DOF to be determined after the image is made. These are based or supported by computational imaging processes. For example, focus stacking combines multiple images focused on different planes, resulting in an image with a greater (or less, if so desired) apparent depth of field than any of the individual source images. Similarly, in order to reconstruct the 3-dimensional shape of an object, a depth map can be generated from multiple photographs with different depths of field. Xiong and Shafer concluded, in part, "... the improvements on precisions of focus ranging and defocus ranging can lead to efficient shape recovery methods."

Another approach is focus sweep. The focal plane is swept across the entire relevant range during a single exposure. This creates a blurred image, but with a convolution kernel that is nearly independent of object depth, so that the blur is almost entirely removed after computational deconvolution. This has the added benefit of dramatically reducing motion blur.

Light Scanning Photomacrography (LSP) is another technique used to overcome depth of field limitations in macro and micro photography. This method allows for high-magnification imaging with exceptional depth of field. LSP involves scanning a thin light plane across the subject that is mounted on a moving stage perpendicular to the light plane. This ensures the entire subject remains in sharp focus from the nearest to the farthest details, providing comprehensive depth of field in a single image. Initially developed in the 1960s and further refined in the 1980s and 1990s, LSP was particularly valuable in scientific and biomedical photography before digital focus stacking became prevalent.

Other technologies use a combination of lens design and post-processing: Wavefront coding is a method by which controlled aberrations are added to the optical system so that the focus and depth of field can be improved later in the process.

The lens design can be changed even more: in colour apodization the lens is modified such that each colour channel has a different lens aperture. For example, the red channel may be f/2.4, green may be f/2.4, whilst the blue channel may be f/5.6. Therefore, the blue channel will have a greater depth of field than the other colours. The image processing identifies blurred regions in the red and green channels and in these regions copies the sharper edge data from the blue channel. The result is an image that combines the best features from the different f-numbers.

At the extreme, a plenoptic camera captures 4D light field information about a scene, so the focus and depth of field can be altered after the photo is taken.

Diffraction and DOF

Diffraction causes images to lose sharpness at high f-numbers (i.e., narrow aperture stop opening sizes), and hence limits the potential depth of field. (This effect is not considered in the above formula giving approximate DOF values.) In general photography this is rarely an issue; because large f-numbers typically require long exposure times to acquire acceptable image brightness, motion blur may cause greater loss of sharpness than the loss from diffraction. However, diffraction is a greater issue in close-up photography, and the overall image sharpness can be degraded as photographers are trying to maximize depth of field with very small apertures.

Hansma and Peterson have discussed determining the combined effects of defocus and diffraction using a root-square combination of the individual blur spots. Hansma's approach determines the f-number that will give the maximum possible sharpness; Peterson's approach determines the minimum f-number that will give the desired sharpness in the final image and yields a maximum depth of field for which the desired sharpness can be achieved. In combination, the two methods can be regarded as giving a maximum and minimum f-number for a given situation, with the photographer free to choose any value within the range, as conditions (e.g., potential motion blur) permit. Gibson gives a similar discussion, additionally considering blurring effects of camera lens aberrations, enlarging lens diffraction and aberrations, the negative emulsion, and the printing paper. Couzin gave a formula essentially the same as Hansma's for optimal f-number, but did not discuss its derivation.

Hopkins, Stokseth, and Williams and Becklund have discussed the combined effects using the modulation transfer function.

DOF scales

Many lenses include scales that indicate the DOF for a given focus distance and f-number; the 35 mm lens in the image is typical. That lens includes distance scales in feet and meters; when a marked distance is set opposite the large white index mark, the focus is set to that distance. The DOF scale below the distance scales includes markings on either side of the index that correspond to f-numbers. When the lens is set to a given f-number, the DOF extends between the distances that align with the f-number markings.

Photographers can use the lens scales to work backwards from the desired depth of field to find the necessary focus distance and aperture. For the 35 mm lens shown, if it were desired for the DOF to extend from 1 m to 2 m, focus would be set so that index mark was centered between the marks for those distances, and the aperture would be set to f/11.

On a view camera, the focus and f-number can be obtained by measuring the depth of field and performing simple calculations. Some view cameras include DOF calculators that indicate focus and f-number without the need for any calculations by the photographer.

Hyperfocal distance

In optics and photography, hyperfocal distance is a distance from a lens beyond which all objects can be brought into an "acceptable" focus. As the hyperfocal distance is the focus distance giving the maximum depth of field, it is the most desirable distance to set the focus of a fixed-focus camera. The hyperfocal distance is entirely dependent upon what level of sharpness is considered to be acceptable.

The hyperfocal distance has a property called "consecutive depths of field", where a lens focused at an object whose distance from the lens is at the hyperfocal distance H will hold a depth of field from H/2 to infinity, if the lens is focused to H/2, the depth of field will be from H/3 to H; if the lens is then focused to H/3, the depth of field will be from H/4 to H/2, etc.

Thomas Sutton and George Dawson first wrote about hyperfocal distance (or "focal range") in 1867. Louis Derr in 1906 may have been the first to derive a formula for hyperfocal distance. Rudolf Kingslake wrote in 1951 about the two methods of measuring hyperfocal distance.

Some cameras have their hyperfocal distance marked on the focus dial. For example, on the Minox LX focusing dial there is a red dot between 2 m and infinity; when the lens is set at the red dot, that is, focused at the hyperfocal distance, the depth of field stretches from 2 m to infinity. Some lenses have markings indicating the hyperfocal range for specific f-stops, also called a depth-of-field scale.

Near:far distribution

The DOF beyond the subject is always greater than the DOF in front of the subject. When the subject is at the hyperfocal distance or beyond, the far DOF is infinite, so the ratio is 1:∞; as the subject distance decreases, near:far DOF ratio increases, approaching unity at high magnification. For large apertures at typical portrait distances, the ratio is still close to 1:1.

DOF formulae

This section covers some additional formulas for evaluating depth of field; however they are all subject to significant simplifying assumptions: for example, they assume the paraxial approximation of Gaussian optics. They are suitable for practical photography, lens designers would use significantly more complex ones.

Focus and f-number from DOF limits

For given near and far DOF limits D_N and D_F, the required f-number is smallest when focus is set to

$${\displaystyle s=\frac{2D_{\mathrm{N}}{D}_{\mathrm{F}}}{D_{\mathrm{N}}+D_{\mathrm{F}}},}$$

the harmonic mean of the near and far distances. In practice, this is equivalent to the arithmetic mean for shallow depths of field. Sometimes, view camera users refer to the difference v_N − v_F as the focus spread.

Foreground and background blur

If a subject is at distance s and the foreground or background is at distance D, let the distance between the subject and the foreground or background be indicated by

$${\displaystyle x_{\mathrm{d}}=|D-s|.}$$

The blur disk diameter b of a detail at distance x_d from the subject can be expressed as a function of the subject magnification m_s, focal length f, f-number N, or alternatively the aperture d, according to

$${\displaystyle b=\frac{f{m}_{\mathrm{s}}}{N}\frac{x_{\mathrm{d}}}{s\pm x_{\mathrm{d}}}=d{m}_{\mathrm{s}}\frac{x_{\mathrm{d}}}{D}.}$$

The minus sign applies to a foreground object, and the plus sign applies to a background object.

The blur increases with the distance from the subject; when b is less than the circle of confusion, the detail is within the depth of field.