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.