Using the gradient histogram to analyze the continuous phase plate

•Using geometrical method the far-field distribution of a phase plate is calculated.•The relationship between the histogram and the angular spectrum is explained.•The analytical expression of gradient histogram is deduced.•The application of this method in the statistical theory of focal spot is discussed.

The geometrical optical method has been used to discuss the far-field distribution characteristics of a continuous phase plate. The gradient histogram of the plate’s surface has been calculated. It has been proved that the gradient histogram can be used to show the angular spectrum of a phase plate. The gradient histogram can simplify the analysis process of the angular spectrum and describe the focal spot morphology more intuitively.