CHAPTER 4. CALIBRATION AND STATISTICAL ANALYSIS OF TIME-SERIES MEASUREMENTSChapter 4 summarizes the calibration and statistical methods used to access the X-ray images. Section 4.1 outlines the calibrations used to correct for beam hardening and penumbra effects that are common in tube source X-rays. Due to the beam hardening effects, it will be shown that the attenuation coefficient for the broadband X-ray is a complex function related to energy level and wavelength, which is difficult to determine. Section 4.2 provides a general attenuation coefficient estimated from a liquid stream that may be used in white beam imaging.The estimated attenuation coefficient matches the theoretical attenuation coefficient of water.Section 4.3 shows the influence of sampling method on the image data sets. The influence of sampling period and sampling frequency of the spray are discussed. 4.1 Calibration of Beam Hardening Effect and Penumbra Effect * Section 4.1 is a conference paper submitted for 14th Triennial International Conference on Liquid Atomization and Spray Systems (ICLASS 2018).