Aperture and depth of field

The aperture is the adjustable opening inside the lens. It controls how much light passes, and it has a powerful side effect: it decides how much of the scene in front of and behind the point of focus looks sharp. A wide aperture can isolate a face against a soft, dissolving background; a small one can keep everything sharp from wildflowers at your feet to mountains on the horizon. This lesson explains the f-number scale and why it runs the way it does, depth of field and the factors that control it, how to calculate it and the hyperfocal distance, how sensor size enters through equivalence, the quality of out-of-focus areas, and the limit set by diffraction. VIS-101 introduced depth of field as a tool for creating depth in a composition; here it becomes a setting you control precisely.

The f-number

The size of the aperture is expressed as an f-number N, the focal length divided by the diameter of the opening (the entrance pupil):

So f/2 on a 50 mm lens means an opening 25 mm across, and f/8 means 6.25 mm. Because the f-number is a ratio, the same f-number lets through the same intensity of light on any lens, which is why exposure settings transfer between lenses and cameras. A larger f-number means a smaller opening: f/16 is a small aperture, f/1.4 a wide one. Photographers say "stopping down" for moving to a larger f-number and "opening up" for a smaller one.

The light admitted depends on the area of the opening, which is proportional to D², so it varies as 1/N². To halve the light (one stop), the area must halve, so the diameter must fall by √2 and the f-number must rise by √2 ≈ 1.414. That is why the standard full-stop sequence looks irregular:

Every second number doubles (1.4, 2.8, 5.6, 11, 22 and 2, 4, 8, 16), which makes the sequence easy to remember. Most cameras also set apertures in thirds of a stop, such as f/4.5 and f/5 between f/4 and f/5.6. The widest aperture a lens can reach is its maximum aperture, given in its name; a lens with a wide maximum aperture is called fast, because it allows faster shutter speeds in a given light.

Depth of field

A lens focuses perfectly at one distance only. A point on an object nearer or farther than that distance is imaged not as a point but as a small disc, the circle of confusion. If the disc is small enough, the eye cannot distinguish it from a point at normal viewing size, and the object looks sharp. Depth of field (DOF) is the range of distances, in front of and behind the focus point, within which the blur stays below that acceptable size. It is not a sharp boundary: sharpness falls off gradually on either side of the focused distance.

Depth of field depends on three things:

• Aperture: smaller apertures (larger f-numbers) give more depth of field, because the cone of light from each point is narrower.
• Focus distance: closer subjects give much less depth of field; it shrinks roughly with the square of the distance.
• Focal length and magnification: at the same distance, longer lenses give less depth of field. For the same framing of the subject, the effect of focal length on the depth of field around the subject is small; what changes is how blurred the distant background looks.

At ordinary distances, depth of field extends somewhat farther behind the focus point than in front of it, roughly one-third in front and two-thirds behind; at close-up distances it becomes nearly equal on both sides.

Calculating depth of field

Depth of field can be calculated from the focal length f, f-number N, focus distance s and the acceptable circle of confusion c. A common value of c for full frame is 0.03 mm (about 0.02 mm for APS-C and 0.015 mm for Micro Four Thirds), based on a typical print viewed at a normal distance; demanding work uses smaller values. First compute the hyperfocal distance H, then the near and far limits:

If s is at or beyond H, the far limit is infinity.

Tighter framing shrinks depth of field quickly. A head-and-shoulders portrait with an 85 mm lens at f/1.8 from 2.5 m has only about 9 cm of depth of field, less than the distance from the tip of the nose to the ears, which is why focusing precisely on the nearer eye matters so much (Lesson 7). In close-up work it is often only a few millimetres.

The hyperfocal distance

Focusing at the hyperfocal distance H makes everything from H/2 to infinity acceptably sharp, the greatest depth of field possible at that aperture. Landscape photographers use it to keep both a nearby foreground and the distant horizon sharp.

When even the smallest sensible aperture cannot give enough depth of field, as in close-up and product work or a landscape with flowers a few centimetres from the lens, photographers use focus stacking: several frames at different focus distances combined in software, taking the sharp parts of each.

Sensor size and equivalence

For the same framing, angle of view and f-number, a smaller sensor gives more depth of field, because it uses a shorter focal length and the acceptable circle of confusion scales with the sensor. To a good approximation, two cameras give the same framing and depth of field if their focal lengths and their f-numbers are both scaled by the crop factor. A 33 mm lens at f/1.8 on APS-C (crop 1.5) gives about the same picture as a 50 mm lens at f/2.7 on full frame: the depth of field in the example above becomes about 26 cm instead of 17 cm. Phones, with crop factors around 3 to 7 and apertures around f/1.8, have depth of field like f/6 to f/13 on full frame, which is why their "portrait mode" simulates background blur computationally by estimating depth and blurring the background in software, sometimes with errors around hair and glasses.

Equivalence concerns depth of field and framing only. The exposure for a given f-number, shutter speed and ISO is the same on every format.

Bokeh: the quality of blur

Bokeh (from a Japanese word for blur or haze) describes the character of the out-of-focus areas of an image. Lenses differ: some render blurred backgrounds smoothly and creamily, others with harsh edges, "busy" swirls or doubled lines. The shape of the aperture also shows in out-of-focus points of light, such as street lamps behind a portrait: lenses with many rounded aperture blades give circular highlights, while those with few straight blades give polygons when stopped down. The amount of background blur grows with focal length, aperture diameter, and the distance between subject and background relative to subject distance. To make a background melt away, open up, move closer to the subject, use a longer lens and move the subject away from the background.

Sharpness, the sweet spot and diffraction

Most lenses are slightly soft at their widest aperture because of optical aberrations, and become sharpest about two to three stops down, often around f/5.6 to f/8: the lens's sweet spot. Stopping down further increases depth of field but eventually reduces sharpness because of diffraction, the spreading of light as it passes through a small opening. The blur disc from diffraction has a diameter of about 2.44λN, where λ is the wavelength of light (about 0.55 µm for green):

• At f/8: 2.44 × 0.55 × 8 ≈ 11 µm.
• At f/16: about 21 µm.

When the diffraction disc grows to several times the pixel pitch (about 4 µm on a 24 MP APS-C sensor, 6 µm on a 24 MP full-frame sensor), fine detail softens across the whole image. This is why landscape photographers often work at f/8 to f/11 rather than f/22, and why very high-resolution cameras show diffraction softening sooner. Like most technical limits, it is a trade-off: a slightly soft image with the foreground in focus is usually better than a crisp one with a blurred foreground.

Cinema lenses are marked in T-stops rather than f-stops: a T-stop measures the light actually transmitted, accounting for losses in the glass, so that exposures match exactly between lenses. For still photography, the difference is small and f-numbers are used.