What kind of physical process lead to sigma_new prop to (I_o)^x, x>1?
E.g. x = 2
The standard uncertainties associated to diffracted intensities should always be based on counting statistics. For example, if you employ a point scintillation counter as a detector, you will measure random events occurring at definite average frequencies (i.e. visible photons emitted by the sensitive material upon X-ray absorption, that have a certain - usually low - probability to excite the photomultiplier tube). Therefore, in this case measured data are Poisson-distrubuted around an average expected value (number of successes in the excitation process). The least-biased estimate for the standard uncertainty is then sigma=sqrt(), 'sqrt' being the square root of . Therefore, it is true that the higher the intensity, the higher is the variance and this implies in principle no contadictions , as it depends on the properties of the second central moment of the Poisson distribution.
Hope this answers your question.
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