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Based on the the third-order aberration theory of plane-symmetric optical systems, this paper studies the effect on aberrations of the second-order accuracy of aperture-ray coordinates and the extrinsic aberrations of this kind of optical system; their calculation expressions are derived. The resultant aberration expressions are then applied to calculate the aberrations of two design examples of soft X-ray and vacuum ultraviolet (XUV) optical systems; images are compared with ray-tracing results using SHADOW software to validate the aberration expressions. The study shows that the accuracy of the aberration expressions is satisfactory.

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Portable Document Format (PDF) file https://doi.org/10.1107/S1600577519007823/ve5105sup1.pdf
Modification aberration coefficients due to the second-order accuracy of aperture ray and extrinsic aberration coefficients


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