Bokeh

Usually, the chief concern of lens designers is the best possible image quality of the plane of sharp focus. The rendering of out-of-focus (OOF) image parts does not enjoy a large weight in the overall design compromise of a normal photographic lens. However, the OOF blur characteristics mattered to certain Japanese photographers who introduced the term "bokeh" to the photographic society to describe the aesthetic quality of the blur. In the absence of a single English word with the same meaning, there seems no reason not to adopt the Japanese term. The internet abounds with lens qualifications like "good bokeh" and "bad bokeh" but strictly speaking this use of the word should be discouraged. Owing to the subjective implications of some unquantifiable aesthetic value, it would be more appropriate to speak of pleasant or unpleasant bokeh, respectively.

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. This blur disk is characterized by

A size.
A shape.
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 circular, in which case the designations "circle of confusion" or "blur disk" are misnomers. Nonetheless, for convenience the word disk will be freely used to mean a patch of arbitrary shape. Although the size and the shape of the disk are unmistakable blur characteristics, they do not touch the essence of bokeh as the Japanese intended the word. The distribution of light across the disk does [1]. However, the distinction is not always clear and what follows is intended as an overview of a variety of factors that influence the rendering of OOF image parts. Explanations of the underlying mechanisms will be brief and the reader is referred to other pages for elaborateness.

Amount of blur

It is well known that the amount of background or foreground blur is controlled, among other things, by the F-number. Fig. 1 shows a picture taken at a small and at a large aperture. The larger aperture comes with a more blurred background, but 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. In this case, the Japanese would probably speak of a neutral bokeh.

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 (OOFH's) assume the shape of the lens aperture. At reduced apertures the shape of the blur disk is the same as that of the diaphragm opening. For instance, a six-sided diaphragm leads to hexagonal blur patches. Generally, the better an aperture approximates a round opening, the more pleasing the blur. However, when a lens is used at a large aperture, obliquely incident light is confronted with a narrower aperture than normally incident light. Consequently, the blur disk narrows 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 OOFH's scattered across the frame, the cat's eye effect yields the impression of a rotational background motion (Fig. 2).

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.

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, and, once spherical aberration passes in review, the essence of bokeh is touched. 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, since the main concern of the average user is that the subject is rendered with high fidelity. However, aberrations that are well controlled in the plane of best focus are not necessarily well behaved in OOF foregrounds or backgrounds.

The transverse chromatic aberration (lateral color) often leads to noticeable color fringing around OOFH's. 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 OOF 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 grass and croci in the foreground for that matter, is aberrated.

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.

Yet another aberration presents itself in Fig. 5. 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 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 OOFH's 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 a viewer is not pleased by this type of bokeh.

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 OOFH's 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 a 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. A lens obeying Gaussian optics, i.e., untroubled by aberrations, would have yielded "grayscale" images with similar blur characteristics at either side of the best focus. Notice that the negative distances in Fig. 7 would correspond to the background blur of a three-dimensional scene. The behavior of the lens must therefore be ascribed to overcorrected spherical aberration.

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

Concluding remarks

Admittedly, the strikingness of the phenomena in Fig. 5 and Fig. 7 is due to the deployment of a lens in a regime for which it was not designed. However, Fig. 4 and Fig. 6 illustrate that noticeable departures from a Gaussian bokeh may occur with normal lens uses as well. While the chief concern of lens designers is usually the best possible image quality of 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 [2]. 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 [3]. The illustrations in the last reference suggest that axial color responds to these adjustments too.

The strength of residual aberrations, as well as the amount of vignetting and the size of the blur disk, depend on the subject distance and F-number. As a result, the aesthetic quality of the blur depends on several settings. It is not uncommon for a lens to receive mixed bokeh reports. The foreground blur and the background blur must be considered separately, because they can have different characters. Another important aspect that influences the reproducibility of bokeh assessments is the nature of the OOF image parts. Low-contrast tableaux are less likely to surprise the viewer than scenes with specular highlights or otherwise high contrasts. Finally, in many cases there will be nothing special at all to the blur characteristics. A neutral bokeh is more common than double contours or its smooth counterpart.

© PA van Walree 2004-2007

References

[1]	Harold M. Merklinger, "A technical view of bokeh," Photo Techniques, May/June 1997.
[2]	Sidney F. Ray, Applied photographic optics, 3rd ed., Focal Press, 2002, p. 88.
[3]	http://www.stacken.kth.se/~maxz/defocuscontrol/