Inadequate exposure is easy to diagnose. Simply look at the histogram. It is easy to determine the correct exposure. If the "mountain" of the histogram is pushed all the way up against the left side of the histogram box, the image is underexposed. A correctly exposed image's histogram is well separated from the left side of the histogram box, as seen in the mouse-over above of the 300 second image. Correctly exposing the image gets the faintest detail up out of the noise of the camera.
Above we can see the result of trying to stretch the inadequately exposed 30-second image to bring up the faint detail in the spiral arms of galaxy M81. The noise in the image overwhelms any faint detail present when the contrast is increased. Even stacking ten 30-second exposures to equal one 300 second exposure would not save this image. Remember, we do not want the sky to be black in our long-exposure deep-sky images. The faintest detail in an image is just above the sky background, and if the sky background is black, then the faintest detail will be lost in the noise.
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