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Abstract
A confocal fluorescence microscope is a serial rather than parallel image-acquisition device: the object is illuminated point by point and the generated fluorescence, imaged onto the detection pinhole, is measured sequentially for each illuminated point. In such an instrument, the image acquisition is discrete rather than continuous. The image is built up in discrete spatial steps, the fluorescence is sampled in discrete steps that correlate to a particular spatial position, and the image is displayed in some discrete manner as pixels of a certain intensity in the image. However, the object itself is continuous in all practical senses and will show structure at every level of detail. So the question arises: In how many steps does the object need to be sampled to form an image to faithfully represent reality? Naturally, extremely fine sampling in an almost infinite number of steps will provide a faithful image, but it will take infinitely long and provide an infinite amount of data. Too few steps, on the other hand, may result in a loss of information, or worse, in artifacts introduced into the image. The issue of the best strategy for discrete sampling of a continuous signal is relevant to a great number of practical problems. For instance, digital sound recording, as for CD players, for example, requires digitization of continuous signals (the sound waves) without losing the information required for high-quality reproduction. But oversampling should be avoided to minimize the disk space required to digitize a particular song. Film and TV are other instruments that work with discrete steps—the frames in the film and the refresh rate of the screen—that appear continuous to the viewer when reproduced at sufficient speed. They also show the artifacts that arise from undersampling: stagecoach wheels that appear to rotate in the wrong direction as a consequence of a frame rate lower than the rotation rate of the wheels, causing undersampling of the motion. This phenomenon of artifacts that result from undersampling is known as aliasing.
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CHAPTER 4
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