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Interference fringe density is an important parameter to be precisely measured and regulated for patterning varied-line-spacing gratings with scanning beam interference lithography. The impacts of the interference fringe density error on grating parameters and exposure performance must be fully analyzed in theory to guide system design and varied-line-spacing grating fabrication. In this paper, a mathematical model of the total exposure dose for varied-line-spacing grating fabrication with scanning beam interference lithography is established. Based on the model, the calculation methods of grating parameters and exposure contrast are presented. The impacts of the fringe density error on grating parameters and exposure performance are analyzed. According to the requirements of grating application and manufacturing process, the error threshold and susceptible parameters are determined. The improvement effect from the step size of stage on error threshold is discussed. The results of a typical grating show that the interference fringe density error leads to the grating performance and exposure contrast degradation. With the fringe density relative error of 0.001, the relative errors of the grating groove density coefficients can be controlled in the order of 10-8 and 10-6, respectively. The ghost line intensity and exposure contrast have higher requirements on fringe density error. Under the same conditions, to obtain a ghost line intensity smaller than 1×10-3 and an exposure contrast better than 0.9, the error threshold should be smaller than 1.7×10-4 and 7×10-4, respectively. A smaller step size of stage can significantly improve the ghost line intensity, and the fringe density error threshold can be relaxed at the expense of production efficiency. The error threshold calculation and error relaxation methods provide a theoretical basis for system design.
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