An important problem encountered in photon counting is that the answer arrived at includes an uncertainty corresponding to the square root of the total number of photons counted. Therefore, the fractional error in the number of photons detected is 1//N where N is the total number of photons detected. If an astronomer counts 100 photons, the uncertainty is 10%, if 10,000, the uncertainty is 1%. Unfortunately, the detection of photons from astronomical objects is complicated by the fact that the sky is a source of photons as well. In the case of an idealized astronomical observation, one can imagine looking at an astronomical object with a typical optical detection system and trying to make an observation with 1% accuracy. Because the detector cannot avoid looking at both the sky and the object, it collects and counts the photons from both. However, when the object is very much brighter than the sky, the photons from the sky make a negligible contribution to the total signal, and we get 1% accuracy just as soon as we have detected 10,000 photons from the source. In such a case, the brightness of the source determines how long the observation will take. If, however, the number of photons received from the sky is comparable to or greater than the number from the object under study, then the brightness of a nearby portion of sky must be determined and subtracted from the observation of the object. However, sky photons can only be measured at best to an accuracy of 1//N~ just as photons are from the object. For example, if the sky is nine times brighter than the object and our detector counts 10,000 photons from the sky and object together, which gave us 1% accuracy before, our accuracy for measurement of the object would only be 10%. In this case, the observation is said to be "sky 1imited"--in order to get a 1% measurement of our source, the detector must have detected 1,000,000 photons. This value represents 100,000 photons from the source or ten times as many as was required to get a 1% measurement without the sky. Therefore, even if the sources in our two examples were the same brightness, the addition of the bright sky would increase by a factor of ten the amount of observing time required for the same accuracy measurement.
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