We present an interferometry setup and the detailed fringe analysis method for intense short pulse (SP) laser experiments. The interferometry scheme was refined through multiple campaigns to investigate the effects of pre-plasmas on energetic electrons at the Jupiter Laser Facility at Lawrence Livermore National Laboratory. The interferometer used a frequency doubled ($\unicode[STIX]{x1D706}=0.527~\unicode[STIX]{x03BC}\text{m}$) 0.5 ps long optical probe beam to measure the pre-plasma density, an invaluable parameter to better understand how varying pre-plasma conditions affect the characteristics of the energetic electrons. The hardware of the diagnostic, data analysis and example data are presented. The diagnostic setup and the analysis procedure can be employed for any other SP laser experiments and interferograms, respectively.