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.

Digital Processing

Finally we come to the part where purists will cringe at, digital post processing. In fact, such cringing is unrooted. We have been tweaking our film in the darkroom for as long as film has been around. We know that time, temperature, developer, dilution and agitation all affect the response curve of the negative; colour negatives are colour balanced during printing; and we have even applied more aggressive techniques such as dodging and burning or spilt contrast printing without feeling that we manipulated the negative. I think I have made my case.

Before this we have been dealing with image files coming directly from the camera, converted to JPEGs by the camera firmware and displayed on your computer monitor without user intervention. Somewhat akin to shooting slide film, where you have control only on the exposure but not the processing. Not being an expert of the digital darkroom, I shall only briefly talk about what I see as limitations of digital manipulation.

Above is a set of 3 images, exposure bracketted to +/-EV = +2, 0 and -2 respectively. I have tried to turn the over- and uderexposed into the "well exposed" image using Adobe Photoshop. The scene has around 4 zones. From my placing of the white paper as zone VI, the zones range from V to VIII. From my earlier experiments, I know that my setup (camera + monitor) has 9 useful zones. Therefore in the +2 picture, some of the highlights would be blown out becuase what was zone VIII would now be zone X, i.e. completely white. In the -2 picture, the darkest parts would lie in zone III. Theoretically, you can "rescue" a region as long as it is not completely black or white and therefore the -2 image should be easier to rescue that the +2 image which really pushes the dynamic range of the camera. This is reflected in the processed images where some areas in the overexposed image are white and lack any detail despite my efforts. Extreme pulling of these areas give only patches of grey but not detail, whereas pushing of the underexposed image yields more and more shadow detail.

Reality, on the other hand, says another story. As with film, "pushing" (lightening a dark image) gives noise and grain, the extent was and still is proportional to the ISO used and the amount of pushing. Also note that the 3 types of sensors, red, green and blue, have different sensitivities (notwithstanding the additional fact that there are twice as many green sensors on a CCD than red or blue) which means that pushed images inevitably have shifted colours which may or may not be completely correctable. Also worth noting is that pushed shots tend to be flat unless you tweak the curves to add contrast.

What is more important than the technical intracacies is the feel of the image. It is not the purpose of this blog to tell you what looks good and what doesn't; that is for you to decide. The 3 images were taken on a rainy day. I tried to be honest and preserve the feeling of overcast difused lighting in the normal exposure, in the post processed shots, the pulled shot looks like it was taken under directional lighting while the pushed shot looks more like the "normal" exposure. I could have faked directional sunlight with that shot on a rainy day if it was my purpose.

One last thing about adding digital light is to know how much digital light you can add without getting unusable grainy images with strange colour casts. This matters a lot when you are forced to underexpose, e.g. to avoid camera shake in low light conditions. Knowing for example that you can safely move zone III to zone V gives you a standard to judge how much underexposure you can use. But remember that "pushability" relates to the actual exposure time (longer digital exposures have significantly more noise while this is not as significant for film), the ISO used and perhaps most importantly, what you use to process the image and the image format. RAW files are much more tolerant to post processing. With memory devices becoming cheaper by the day, shoot RAW always.