Bokeh and DOF, part 1

Background blur, out of focus areas, lens blur, bokeh, whatever you choose to call it. It's the areas in the photo that are not in the plane of sharp focus. Because most of our pictures are of three dimensional objects, bokeh exists in every picture. Background blur helps convey a sense of three dimensionality from a flat picture. Sometimes it is nice to blur out distracting backgrounds, this technique is especially common for portrait shots.

So how does bokeh occur and what governs the blurriness of the bokeh? What is good/bad bokeh? For that, it's time to review your high school optics.

WARNING: Lots of ray diagrams ahead. Skip to "Bluriness and Depth of Field" if needed.

Whenever the film/sensor is not at the point of sharp focus, the rays that reach the film exist as a patch in the shape of the aperture (triangular in this diagram, hexagonal or round for most lenses) and it is these patches of light that make up the bokeh. Convince yourself that the larger the patch of light, the more defocused the image is. Once you've done that, it's time to talk about the 3 factors that affect the bluriness of bokeh, i.e. focal length, aperture and subject-background distance.

Effect of Focal length
The longer the focal length, the more blurry out-of-focus (OOF) objects become (given that the other two factors are kept the same).
Here we have two lenses, one of focal length 30mm and the other 80mm. The 80mm lens has more background blur than the 30mm lens. If we treat the red object (object giving out red rays) as the subject of interest, we would move the lens to place the image of the red object at the film plane. The bokeh of the green object is given by the unfocused green light that reaches the film plane (where the image of the red object is). It is seen that d2 is larger than d1. In other words, the unfocused light from the green object is more unfocused when it gets to the film plane. So the image of the green object is blurier when the 80mm lens is used.

Effect of Aperture
The larger the aperture, the more OOF objects become.
Using our hypothetical 80mm lens, we take a photo at full aperture, again focused at the red object. The spread of the green rays is then d3. If we stop down, the light that reaches the lens becomes "straighter" (closer to the centre). The effect is that the spread of the exiting rays is decreased (d4 Vs d3) and the green object appears less blurry. Taken to an extreme case, if we do away with the lens and use a pinhole, then everything would be equally sharp in the picture regardless of object distance.

Effects of Object Distance
This is perhaps the most puzzling part of OOF objects. Intuitive enough is the fact that the greater the seperation between the object and the background the more blurry the background. What is puzzling is that given the same distance between the subject and the background, the background is more blurred if the subject is closer to the lens.Given 3 objects (red, green and blue) equidistant from each other, their images after passing through our hypothetical 80mm lens are as shown above.

The first point that the further away the object the more blurred it becomes can be seen by comparing the spread of the green and blue rays at the plane of the red image. The spread of the further away object (blue) is much greater than the closer object (green). Intuitive. The further away from the point that the lens is focused at (i.e. the red object), the more defocused you are.

The second part that even if the objects are separated equally, the closer pair will yield a more blurred background can be illustrated by comparing d1 and d2. If we focus the lens on the green object, the spread of the blue rays in the image is d1. When we focus on the red object instead, the spread of the green rays is d2 which is larger than d1. This means that although the distance between red and green and green and blue are the same, because red and green are closer to the lens, green is more blurred. If we think of it in another way, this too becomes intuitive. Consider two people one 3m in front of the other. If you were 1 meter away, they would be 1 and 4m away from you, a 400% difference. If you were 1km away, they would be 1000 and 1004m away, which is just a 0.4% difference. Now it is intuitive that two objects differing by 0.4% yield similar images while objects differing by 400% should give vastly different images.


Bluriness and Depth of Field

In an ideal world with film of infinite resolution where we can view images with infinite magnification, the plane of sharp focus has no thickness and only objects at a specific distance, e.g. 3m and not 3.0000001m, will be in focus. In this world however, we do not view images with infinite magnificantion, even if we did, we would hit the resolution limit of the film/sensor where slightly out of focus and sharply focused images cannot be distinguished. Depth of field (DOF) is simply how much bluriness can "fly under the radar". If we cannot percieve it as blurred, it is sharp.

A large DOF means that the transition from sharp to perceptible bluriness is over a large object distance. Most, if not all, parts of the image are perceived as sharp. A shallow DOF is the opposite, the transition from sharp to blurred occurs over a short distance, only objects close to the plane of sharp focus are perceived as sharp.

The trick to shallow DOF? Use a long lens, use a larger aperture, get close to the subject and choose a background that is far away.