Statistics of Radiation Events

Mind Map

Learning Guide


Visuals for



Objectives and Learning Activities

  • Using a piece of paper and a pen, make dots that represent the random nature of x-ray photons exposing a surface like in an image.  This is an example of how visual noise in an image is formed.
  • Think of some common events that might occur randomly with time (telephone calls, rain, etc). This is an example of how radiation events, such as the emission of radiation from a radioactive source occurs.
  • Let's think of a radioactive source that is emitting an average of 100 photons each second.  Describe the actual number of photons that you would expect to be emitted in each one-second interval over a 10-second period. There is no way to know the actual number in each but use your knowledge of the statistical distribution to produce reasonable estimates.

  • Now, draw a simple graph showing the general distribution of how many times you would expect to have the different number of photons in many one-second intervals.  This is to demonstrate the frequency that the different numbers of photons, like 98, 86, 100, 55, etc would be expected to occur.
  • Describe the general characteristics of a Gaussian statistical  distribution and how the standard deviation (SD) applies to it.  Think of some things in medicine and biology that probably follow a Gaussian distribution. 
  • If we are counting radiation photons from a radioactive source to measure its activity, it appears that we will get a different number each time we count (measure) because of the normal statistical distribution.  Let's assume that for our example being used here, the average or mean of 100 photons per second is an indication of the true activity.  Calculate the errors (% of true value) if you observe each of the following  for several one-second measurements: 95 counts, 80 counts, 75 counts.
    That was easy, but the problem in the real world is if we make just one measurement (lets say we get 85 counts) we cannot calculate the error because we do not know what the mean values is, that would take many measurements to determine.
  • If we make just one measurement of radioactivity by counting emitted photons we do not know what the actual error is.  However, we can develop some knowledge of the range of possible errors and the probability that our one measurement and the associated error is within a specific range.  Recognizing that the SD actually describes a range of measured values some questions to answer are:
    1. What is the probability (% chance) that our one measurement value was within one (1) SD of the true value, or mean value if we made many measurements?
    2. What range of measurement values, expressed in SDs, would we expect our one measured value to be included in 95% of the time?
    3. What range of measurement values, expressed in SDs, would we expect our one measured value to be included in most (over 99%) of the time?
  • Describe the general relationship that is being observed here between error values and the probability of errors falling within certain ranges.
  • Describe the Poisson distribution characteristics applied to radiation events that relate the value of the SD to the mean value of many measurements if they were to be made.
  • Calculate (actually it is an estimation)  the value of the SD both in number of counted photons and as a percentage of the number for the following:
    Number of Photons      SD (Number)        SD (%)
           100                               ?                     ?
          3600                              ?                     ?
      1,000,000                           ?                    ?
    Now describe the observed relationship between the number of photons in a measurement and the range in size of the expected error.
  • Determine the number of photons that must be collected in a measurement to have an error of not more than 1% at a 95% confidence level.
  • Consider a situation where on digital image is to be subtracted from another, as in DSA.  Here we will consider one pixel in the images.  The SD of the number of photons captured by a pixel is a general indication of the expected noise in the image.
    Calculate the SD (noise) for each of the following:
         Image     Photons/Pixel     SD (%)
            A             1600                ?
            B             1000                ?
          A-B             600                ?
    Describe your observation on the effect of image subtraction on noise.