Stitching Fresnel lens are designed for the application in the micro-focus X-ray, but splicing errors between sub-apertures will affect optical performance of the entire mirror. The offset error tolerance of different degrees of freedom between the sub-apertures are analyzed theoretically according to the wave-front aberration theory and with the Rayleigh criterion as evaluation criteria, and then validate the correctness of the theory using simulation software of ZEMAX. The results show that Z-axis piston error tolerance and translation error tolerance of XY axis increases with the increasing F-number of stitching Fresnel lens, and tilt error tolerance of XY axis decreases with increasing diameter. The results provide a theoretical basis and guidance for the design, detection and alignment of stitching Fresnel lens.
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