The optimum distribution of counting times for determining integrated intensities with a diffractometer

For a given total counting time in a diffractometer experiment the variance (or square of the standard deviation) of the estimated integrated intensity of a reflexion is least when the counting time at each point is proportional to the square root of the intensity at that point. If the ratio of the peak to background intensity does not exceed 10 and data points are equidistant, a constant counting time at each point gives a variance not more than 1.4 times the minimum possible value. For greater peak/background ratios a further improvement in variance is achieved. The effect of subtracting off the background intensity is equivalent to regarding the line as extended, at background intensity, over a further range equal to the range over which measurements are made. Full advantage of the optimum choice can be obtained by computer control of the diffractometer, and then less time is required for collection of data of the same accuracy.