No digital image sensor is perfect. Typically, a few pixels are dead (black) all the time, and in long exposures, many others are "hot," meaning they act as if light is reaching them when it isn't. As a result, the whole picture is covered with tiny, brightly colored specks.
Beginning with the 2004 generation of DSLRs, hot pixels are much less of a problem than with earlier digital cameras. For non-critical work, you can often ignore them.
The cure for hot pixels is dark-frame subtraction. Take an exposure just like your astronomical image, but with the lens cap on, with the same exposure time and other camera settings, then subtract the second exposure from the first one. Voila - the hot pixels are gone.
For more about dark-frame subtraction, see p. 183. It generally requires raw image files, not JPEGs.
Many newer DSLRs can do dark-frame subtraction for you. It's called "longexposure noise reduction." On Nikons, this is an obvious menu setting; on Canons, it is deep within the Custom Function menu.
Noise reduction is very handy but time-consuming; in a long astronomical session, you don't really want every 5-minute exposure to be followed by a 5-minute dark frame. Instead, usual practice is to take a few dark frames separately, and then, on your computer, average them (to get rid of random fluctuation) and subtract them from all the exposures of the same length and ISO setting taken on the same evening.
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Compared to film cameras, digital cameras are easy to use, fun and extremely versatile. Every day there’s more features being designed. Whether you have the cheapest model or a high end model, digital cameras can do an endless number of things. Let’s look at how to get the most out of your digital camera.