How depth of field (DOF) occurs in optics

In film and photography, depth of field is the distance between objects that appear acceptably sharp in an image. Creative professionals use depth of field as an aesthetic tool; making use of shallow or deep focus for various applications. Shallow focus allows subjects to be isolated from the background, while deep focus can be nearly infinite.

Understanding circles of confusion

There isn’t an abrupt change between focused objects and defocused objects. Depth of field is a range of focus that gradually loses focus the farther away an object is from either side of the focal plane. The gradual change in sharpness that’s not perceived by the eye or the camera’s resolution creates an acceptable range of sharpness, known as the depth of field (DOF).

In fact, camera lenses cannot focus all light rays perfectly. Even the most focused points of light are rendered as spots, rather than points. In optics, these are called circles of confusion; spots caused by cones of light from a lens not coming to perfect focus. The sharpest point, which falls closest to the focal plane, is called the circle of least confusion. From the circle of least confusion to the circle of maximum confusion is the acceptable range of sharpness we refer to as depth of field.

Circles of confusion

Once an image point falls beyond the circle of maximum confusion, it becomes defocused; which simply means it’s out of focus. Rather than a point, it is a blur spot. These blur spots have the same shape as the lens aperture. The look, shape and overall aesthetic quality of the blur is known as the bokeh. Bokeh occurs with all out-of-focus regions of an image, but single bokeh shapes are most visible with out-of-focus specular highlights or hard light sources (like Christmas tree lights).

How and why light points range in focus

There are a few factors which attribute to whether depth of field is shallow or deep, but the reason depth of field occurs at all is because of how a lens refocuses light to an image plane. It all starts with light rays emitting from a point.

A point light source emits light

Light rays bounce around and shoot out in all sorts of different directions. Using a lens, we can refocus cones of light in order to create a sharp and discernible image. If a point source falls perfectly within the focal plane, then the cone of light rays focus to a circle of least confusion on the image sensor or film plane.

For the sake of simplicity, we’ll render a lens (below) as one piece of glass. In reality, a photographic lens is an optical system constructed of multiple glass elements, mechanical elements and an aperture hole.

A lens refocuses light rays

When a point source falls shortly after or before the focal plane, it renders as a less discernible circle of confusion. Although greatly exaggerated, notice below how a cone of light rays from points outside the focal plane meet at circles, rather than points. Applying the concept of circles of confusion, we know that all point sources are rendered as circles rather than true points; from the circle of least confusion to the circle of maximum confusion. Beyond the circle of maximum confusion, points simply go out of focus.

Points that fall outside the focal plane

Why depth of field changes with aperture size

We know this much: we all want fast lenses. Why? Because the faster the lens, the less light needed for proper exposure and the shallower the depth of field. Requiring less light for proper exposure makes sense; the wider the hole, the more light is allowed to enter. But how is depth of field related to aperture size? Let’s look at the figure below.

Narrow vs. Wide aperture

The wider the cone of light rays passing through the aperture, the more dramatically the rays have to converge, creating greater size discrepancy between the circles of confusion, which leads to a shallower range of focus. However, as the aperture narrows, less rays of light are allowed in, focusing the cone tighter and creating a greater range of acceptably sharp circles of confusion.

Focal length has virtually no effect on DOF

Although increased focal length (telephoto) appears to create shallower depth of field, the actual range of focus remains virtually the same. There might be a subtle change in DOF, but the change is negligible. Depth of field appears shallower with telephoto lenses because they enlarge the background relative to the foreground. Since the blur (bokeh) is enlarged, the out of focus background appears even more out of focus.