Examples of Poisson noise and extraction of information
These animations show the impact of statistical Poisson noise on data acquisition. The first animation (plus the small selected region in the second animation) are more quantitative and demonstrate the impact of noise on photographic images (the 16-bit tif image of the River Limmat at the Lake of Zurich comes courtesy of Nyah Willmott). Essentially identical statistics determine images recorded with x-ray photon counting detectors.
The third animations tracks the statistics of a simple 1-dimensional plot of a small Gaussian peak sitting on a large constant background signal, fitting each accumulated data to a least-squares fit involving four fitting parameters - the background intensity (25), the peak position (250), the peak intensity (2), and the peak width (SD = 16). As one can see, the fitting routine obtains accurate estimates of these parameters long before one might call the signal “clean”.