In this paper, we propose the fifth-order intrinsic aberration calculation method for soft x-ray and vacuum ultraviolet optical systems. First, the sixth-order intrinsic wave aberrations with the aperture-ray coordinates on the optical surface are derived based on the wave aberration method, and then applying the sixth-order mapping relationship of aperture-ray coordinates between the optical surface and the reference exit wavefront, the expressions with those on the reference exit wavefront can be obtained. Second, we derived the calculation expression for the fifth-order intrinsic aberration on the image plane. Finally, the fifth-order intrinsic aberration calculation expressions of the soft x-ray and vacuum ultraviolet optical system derived in this paper are applied to calculate the aberration distribution on the image plane of two design examples of this kind of optical system, and the calculation results are compared with the ray-tracing ones with Shadow software to validate the aberration expressions. The study shows that the accuracy of the aberration expressions is satisfactory.
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