Measurement platform must exhibit a stereoscopic space distribution in diagnostic systems for petawatt lasers to meet the requirement of a periodically poled lithium niobate (PPLN) crystal for light polarization in singlepulse contrast measuring instrument. A mathematical model of a 4D linear matrix is proposed to achieve rapid and accurate beam alignment in picosecond measurement platform. In the petawatt experiments, the alignment algorithm ensures that the near-field and far-field accuracy is less than 0.16 mm and 0.17 mrad, respectively. The motor is adjusted less than three times, and the corresponding elapsed time is in 2 min. The mathematical model meets measurement requirements for alignment accuracy and time. The pulse contrast of the petawatt lasers is obtained from the model. The pulse acquisition probability of the contrast measuring instrument reaches 90% from 10%, to guarantee that the experimental result of pulse contrast can meet the general requirement (more than 106).