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Using Collins Formula with Scaling Factor to Analysis the Propagation Properties in Laser Focus System Design

A Collins formula method with a scaling factor between the target-and source-plane has been proposed for the laser propagation in the optical system design, which can be used to evaluate the laser optical system performance and the tolerance analysis. The laser propagation in the optical systems can be calculated by the Collins integral formula, and an angular spectrum method has been derived by coordinate substitution. A scaling factor m is introduced to make the choice of the observation-plane more flexibility and the calculation more accurate. The laser optical system has been designed, and its tolerance analysis is conducted by the Angular-Spectrum method. The evaluating criterion is the laser spot radius in the far field, which is defined by 86.5% power in bucket (PIB). The radius of the laser spot in 90m between 0.8mm and 1.4mm with the expectation of 0.92mm is calculated by the tolerance analysis, and the experimental result is 1.01mm. In the distance of 47m, the radius is between 0.42mm and 0.73mm with the expectation of 0.48mm calculated by the tolerance analysis, the experimental result is 0.46mm. The experiment agrees the result of the tolerance analysis well. The focal shift for laser propagation in the optical systems is validated. The experiment results confirm the calculation and it proved the use of the method in laser focus optical system design.