In some areas of photography and especially in portraiture, we often want to create a look where a sharp main subject stands out from a non-focused, blurred background (and/or foreground). This obviously requires a shallow depth of field, but the appearance of the background is also important for the overall impression of the image. It should not be distracting, but it should not be uniform and boring either. Ideally, it conveys some of the atmosphere, location, size, or other relevant context of the scene. The way the lens renders the out of focus areas is called the bokeh (from the Japanese 暈け boke which means blur, not related to the French bouquet).
When is a bokeh good or bad? A good bokeh is often described as smooth, soft or dreamy; a bad bokeh as nervous, busy or harsh. However, whether you find a bokeh smooth or boring or another one nervous or energetic is highly subjective, and creating a bokeh that matches your main subject is part of the art of photography.
Technically, there are both qualitative and quantitative aspects of the bokeh. Qualitative aspects involve the scene, the lighting, and the lens. Some lenses have a reputation for creating a beautiful bokeh, while others are known for introducing unwanted patterns such as hard edges, outlines, or onion rings around highlights. Some of these are attributed to imperfections in lens making, as for some aspheric lenses.
On the quantitative side, the bokeh depends on the degree of blurring, which we can calculate using the formulas developed for the depth of field. For this, we will have a look at out of focus highlights.
12.1 Size of bokeh circles
Point light sources in out of focus areas have the interesting property that they appear as bright circles. These are known as bokeh circle, bokeh sphere, bokeh blob or bokeh ball. For simplicity, we assume the light sources are at infinity.
According to equation (D6b), the diameter b of the bokeh circle of a highlight somewhere beyond the subject plane is given by
|h f / (f + A b)
where f is the focal length of the lens, h is the image distance of the main subject in focus, hfar is the image distance of the highlight, and A is the f-stop used. Solving for b, we get
|f (h – hfar) / (A hfar)
If the light is near the main subject, the size of the bokeh circle thus becomes very small. On the other hand, for the light source at infinity, hfar becomes equal to f and the equation is simplified to
|(h – f) / A
With the lens equation, we can substitute the image distance h by the subject distance g and get
|f2 / (A (g – f))
Note that b is the diameter of the bokeh circle on the sensor; so how large it will appear on your final image also depends on the sensor size.
If the subject is reasonably far away, i.e. d is much bigger than f, we can approximate (g – f) by d and get
|f2 / (A d)
In other words, the size of the bokeh circles of distant highlights grows quadratically with the focal length, and inversely proportional to f-stop and focus distance. For large bokeh circles, use a long lens, a wide aperture and get as close to your subject as possible.