Usually, the chief concern of lens designers is a good image quality in the plane of sharp focus. The rendering of blurred image parts does not receive a large weight in the overall design compromise of a normal photographic lens. However, the blur characteristics mattered to certain Japanese photographers who used the word "boke" to describe the aesthetic quality of the blur. The term was introduced to a larger audience through an American photo magazine in 1997, and an "h" was added for the pronunciation: bokeh. In the absence of a single English word with the same meaning, there seems no reason not to adopt the Japanese term.

Characterization of the blur disk

Since any image is represented by a large number of images of points, we may attempt to understand the whole by considering the blurring of a single point. An unsharply imaged point is associated with a circle of confusion, or a blur disk. With increasing "bokeh-ness", this blur disk is characterized by

  1. A size.
  2. A shape.
  3. The light distribution across the disk.

The size of the disk determines the amount of blur. The shape of the blur patch does not need to be round, in which case the designations "circle of confusion" or "blur disk" are misnomers. Nonetheless, for convenience the word disk will be freely used in the present article to mean a patch of arbitrary shape. Although the size of the disk is an important blur characteristic, it does not touch the essence of bokeh as an unquantifiable and subjective descriptor of the "pleasingness" of the blur. The shape of the blur patch has some influence on the bokeh, but the key factor is the distribution of light across the disk [1]. However, the distinction is not always clear and what follows is an overview of a variety of factors that influence the rendering of blurred image parts.

Amount of blur

It is well known that the amount of background or foreground blur is controlled, among other things, by the F-number. Figure 1 shows a picture taken at a small and at a large aperture. The larger aperture comes with a more blurred background, and today there are people who will say that the right image has "more bokeh". This drifts away from the original meaning of the term. The question that needs to be answered to define the bokeh is not to what degree the background is blurred, but whether the blur is a pleasing one.

Effect of aperture on background blur Effect of aperture on background blur

Figure 1. Gromit captured at f/22 (left) and at f/4 (right).

Shape of the blur patch

It is also well known that out-of-focus highlights (OOFHs) assume the shape of the lens aperture. For instance, a six-sided diaphragm leads to hexagonal blur patches. However, when a lens is used at or near its maximum aperture, obliquely incident light is confronted with a narrower aperture than normally incident light. Consequently, the shape of the blur disk changes from the image center towards the corner. This is known as the cat's eye effect, a result of optical vignetting. When there are many OOFHs scattered across the frame, the cat's eye effect yields the impression of a rotational background motion (Fig. 2).

Optical vignetting

Figure 2. Optical vignetting creates a sense of rotational motion of the background around the street sign. Photograph by Edo Engel.

Fig. 3 is an additional illustration of the cat's eye effect. The picture was taken with an unusually large-aperture lens of F/1.2. In this photograph the highlights are clipped in a curious fashion. The cause of the clipping is, however, not due to the lens, but to the camera. Indeed, the mirror chamber of the SLR that Mike used is too small to support the speed of the lens. The light cone that emerges from the lens exit pupil is clipped by the camera before it reaches the sensor.

clipped cat's eyes

Figure 3. Picture taken with an 85/1.2 at full aperture. The cat's eyes are clipped by mechanical obstructions behind the lens. Photograph by Mike Nunan.

Lens aberrations

So far we have been concerned with the size and the shape of blur disks. By considering lens aberrations the blur characterization becomes more sophisticated. As mentioned before the lens designer's main concern is to deliver a lens with the best possible image quality for the given application and price tag. Typically, this image quality concerns the plane of best focus, so as to render the subject with high fidelity. However, aberrations that are well controlled in the plane of best focus are not necessarily well behaved in out-of-focus foregrounds or backgrounds.

Strictly speaking (chromatic) aberrations are defined only for the image plane. If the in-focus image is completely free of color artifacts, the lens has no chromatic aberration. The transverse chromatic aberration (lateral color) often leads to noticeable color fringing around OOFHs. More often than not the fringes are magenta at one side of the blur disk, and green at the other side, characteristic of an achromatic color correction scheme. The longitudinal chromatic aberration (axial color) can be equally conspicuous and may leave a fingerprint on the entire blur disk. Fig. 4 illustrates the occurrence of axial color in a magnified portion of the out-of-focus background. A close examination of the Egyptian geese on the original slide reveals a high quality of the in-focus image parts, but the blurred background highlights, nicely matching the colors of the grass and croci in the foreground, is aberrated.

Axial color

Figure 4. Axial color manifests itself in out-of-focus highlights.

Astigmatism and field curvature can have a marked impact on the shape and size of blur disks, respectively. Fig. 5 shows a target of regularly spaced white dots photographed at unit magnification with a 50-mm standard lens. The center of the target is deliberately out of focus, but the corners are unintentionally further out of focus because of a curved field. Moreover, the off-axis patches are subject to a peculiar elongation ascribed to astigmatism.


Figure 5. Field curvature and astigmatism give rise to changes in size and shape of the blur patches across the frame.

Figure 5 reveals yet another aberration. As it appears, the light distribution is not uniform across the blur disks. The dark core surrounded by a brighter margin is a sign of spherical aberration. This phenomenon mimics the donut-shaped OOFH delivered by mirror lenses and is the quintessence of the so-called "nisen-bokeh". For an isolated highlight there is only the donut, but in an extended image it may lead to double contours [1]. The photograph in Fig. 6, taken with a normal photographic lens, shows just that. There is a modest cluster of two or three OOFHs towards the top right corner that evidence the donut effect. The frames and wheels of the bicycles at the right are composed of an array of such donuts. Together, these donuts add up to the observed double contours and an overall harsh quality of the background blur. Many viewers are not pleased by this type of bokeh.

Spherical aberration

Figure 6. A cropped image that shows the double-line effect (nisen-bokeh) in the blurred background due to overcorrected spherical aberration. Photograph by Jiawei Ye.

From the discussion on the spherical aberration page it emerges that a lens that yields donut-like OOFHs at one side of the object in focus, yields a different OOFH at the other side. That OOFH has a bright core surrounded by a faint halo, and its influence on a compound image is markedly different. A lens with undercorrected spherical aberration is associated with a smooth background blur and a harsh foreground blur; the situation is reversed for a lens with overcorrected spherical aberration. As an illustration of both types of bokeh, Fig. 7 exhibits a series of blurred crosses. It concerns the center cross of this target photographed at unit magnification with an 85/1.4 lens for the 35-mm format. The camera and lens are separated by bellows, which allows for a direct survey of the image space by movement of the camera. The camera (and thus the sensor) was moved in 1-mm increments from 4 mm behind (–4), to 4 mm in front (+4) of the best focus (0). The changing face of the cross thoughout the series is quite dramatic as spherical aberration and axial color operate in tandem. The color effects are due to axial color, whereas the harsh contours at negative separations, and the much smoother blur at positive separations, must be ascribed to spherical aberration. Notice that the negative distances in Fig. 7 would correspond to the background blur of a three-dimensional scene. This is a lens with overcorrected spherical aberration.

Through focus blur changes

Figure 7. Through-focus blur changes of a cross affected by both axial color and spherical aberration.

Onion rings and dust

The appearance of ring patterns in blur disks is sometimes referred to as "onion-ring bokeh". Such rings are not due to lens aberrations, but to aspherical elements or diffraction. They may be observed with defocused highlights, but it is generally difficult to predict their occurrence. Two necessary conditions are that the highlights are small enough, and far enough out of focus. In the case of diffraction, the characteristics of the light source also play a role.

Certain types of aspherical elements can cause onion rings because of their production process. The turning process used to manufacture the mould results in a somewhat uneven lens surface, which may leave a fingerprint on blur disks [2]. An example is shown in Fig. 8. With diffraction on the other hand, the cause is light bending around edges and obstacles, which may result in interference patterns. Figure 9 gives an example for diffraction at the lens aperture.

Onion rings due to aspherical element

Figure 8. Onion rings due to an aspherical element in the lens design. Top: image center. Bottom: off axis. Left: full aperture. Right: lens closed down by two stops.

Diffraction bokeh

Figure 9. Bokeh with diffraction structures that conform to the pentagonal shape of the aperture. (Photographer unknown.)

The following clues give an indication of whether onion rings are due to aspherical elements or diffraction. Aspherical surfaces tend to yield somewhat irregular rings; a spiral pattern is a particularly strong aspherics clue. In the image center, and at full aperture, the pattern is more pronounced toward the center of the blur disk. For off-axis points, the center of the pattern does not coincide with that of the blur disk. If the lens aperture is reduced, the pattern does not change (but less is shown). On the other hand, diffraction patterns follow the shape of the lens aperture and tend to be more pronounced toward the margins of the blur disk. The interference patterns in Fig. 9 are not ring-like, but follow the pentagonal shape of the diaphragm opening. Diffraction patterns can change shape as the lens aperture is varied.

Unfortunately, the analysis is not always that straightforward. Since the lens of Fig. 10 lacks aspherical elements, it is tempting to point to diffraction as the cause of the onion rings. However, the f/2.8 image shows that the rings are perfectly circular and do not adopt the smooth 9-sided shape of the aperture. Residual unevennes of lens surfaces cannot be ruled out as the cause, as there exist different manufacturing methods for spherical elements. It is not impossible for a spherical element to carry a fingerprint of its production process. Another possible cause is interference between neighboring surfaces in cemented groups, similar to Newton's rings. Interference effects in optical systems can be complex and difficult to understand, and the origin of the rings in Fig. 10 is uncertain.

Onion rings and dust

Figure 10. Strongly defocused images of a tiny light source, produced with an F/2 macro lens without aspherical elements. A: F/2.0, before cleaning. B: F/2.0, after cleaning. C: F/2.8, before cleaning. (Zeiss material.)

The blur disks in Fig. 10 are not only characterized by concentric rings, but also by numerous dots and other structures. These are dust particles and fibers on and in the lens. Blur disk B shows that a lot of this dirt disappears from the blur disk after cleaning of the lens. Note that some dust spots are also visible in Fig. 8. The bright rings around the dust spots are most likely due to diffraction.

Concluding remarks

The size and shape of the blur disk, the amount of optical vignetting, the strength of residual lens aberrations, and the visibility of onion rings and dust, depend on many factors and settings. As a result, the aesthetic quality of the blur depends on many parameters. It is not uncommon for a lens to receive mixed bokeh reports, and since bokeh is subjective, even from people looking at the same image. A factor that is often overlooked is the nature of the background (or foreground) itself. The background blur in a photographic image is always the convolution of the point spread function of the lens, with the background scene. The bokeh appreciation may change considerably if a background is changed, with all else equal. Low-contrast tableaux are less likely to surprise the viewer than scenes with specular highlights or otherwise high contrasts. If there are periodic structures in the scene, more actual blur may even result in less perceived blur. This is illustrated by this figure on spurious resolution. Bokeh is not a property of the lens alone.

While the chief concern of lens designers is usually the image quality in the plane of best focus, there are known exceptions. Certain portrait lenses, such as the Rodenstock Imagon lens, deliberately allow undercorrected spherical aberration in the image to provide a pleasing character suited to some forms of portraiture and advertizing photography [3]. Nikon offer a couple of lenses with adjustable floating elements that control the spherical aberration to influence the blur character of OOF foregrounds or backgrounds [4]. The illustrations in the last reference suggest that axial color responds to these adjustments too.

© Paul van Walree 2004–2016


[1]   Harold M. Merklinger, "A technical view of bokeh," Photo Techniques, May/June 1997.
[2]   H. H. Nasse, Depth of field and bokeh, Carl Zeiss Camera Lens Division, (2010).
[3]   Sidney F. Ray, Applied photographic optics, 3rd ed., Focal Press, 2002, p. 88.