Slaying Dragons #15 – The Aperture Effect

John Watkinson looks at the aperture effect and finds that it crops up in a surprising number of places.

One way of considering the aperture effect is that it is nature’s way of pointing out how non-ideal our efforts are. The ubiquity of the aperture effect underlines that next to nothing is ideal.

An aperture in common parlance is an opening or a hole; something having a dimension in space. In technology, the aperture may be in another dimension, such as time. A good place to start is the pin hole camera, or its predecessor, the camera oscura. If the pin hole is very small, the picture is sharp. As the hole is made larger, the picture gets brighter, but resolution is lost, so there has to be a compromise.

Moving forward a few centuries, we have video cameras based on discrete CCD or CMOS sensors. The image sensitive area is divided into pixels, each of which develops a charge proportional to the amount of light that falls on it. The more pixels there are, the better the resolution, but equally, less light falls on each pixel so the noise floor rises. Again there is a compromise. The best noise performance is where the sensor can accept light over its entire area, which means that the pixels essentially touch one another.

The problem then is that the pixels are not sampling according to Shannon. Shannon sampling of an image requires the samples to be of zero size, whereas in the video camera we have substituted a sample whose size is substantially the space between sampling sites. That space is the aperture. Essentially we have replaced a point sample, which is a delta function or a spike, with a rectangle. The size of the rectangle is the aperture. To see what happens, we take the …

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