Bokeh

In some areas of photography and especially in portraiture, we want to create a look where a sharp main subject stands out from a non-focused, blurred background. Basically, this 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, scale, or other relevant context of the scene. The way the lens renders the out of focus areas is known as 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, creamy or even swirly; 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 may result in vastly different opinions. Technically, there are several factors contriburing to the bokeh including 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, duplicated structures or onion rings around highlights. Some of these are attributed to imperfections in lens making, as for some aspheric lenses [Etchells 2014].

However, the bokeh also 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.

Night shot of Mandalay Hill with the lens focused at infinity. 45 mm | f/1.8The same scene, with the lens focused at less than 1 m. Distant lights are rendered as bokeh circles. 45 mm | f/1.8

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 circlesbokeh spheres or bokeh balls. For simplicity, we consider light sources at infinity.

According to equation (D6b), the diameter b of the bokeh circle of a highlight  somewhere behind the object plane is given by

hfar = h f / (f + A b) (B1)

where f is the focal length, h is the image distance of the main object in focus, hfar is the image distance of the highlight, and A is the f-stop. Solving for b, we get

b = f (h – hfar) / (A hfar) (B2)

If the light is near the main object, 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

b = (h – f) / A (B3)

With the lens equation, we can substitute the image distance h by the object distance g and get

b = f2 / (A (g – f)) (B4)

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 size of your sensor.

Approximation

If the object is reasonably far away, i.e. d is much bigger than f, we can approximate (gf) by d and get

b f2 / (A d) (B5)

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 focusing distance. For large bokeh circles, use a long lens, open the aperture and get as close to your subject as possible.