Performances of a far-ultraviolet (FUV) imaging spectrometer in an advanced design are presented with a toroidal uniform-line-space (TULS) grating. It provides high spatial resolution and spectral resolution for a broadband and a wide field of view. A particular analysis for the grating aberrations, including all the high-order coefficients neglected by previous existing designs, was generated for indicating their significance. The analysis indicates that these high-order off-axis aberrations would have a remarkable influence on the design results. The transcendental equations composed of these aberration coefficients do not have analytic solutions in algebra. To solve the problem, the past designs always do some simplified calculation which only suits a narrow field of view and waveband. Thus, the optimization of the genetic algorithm is introduced to propose reasonable ranges of optical parameters. Then ZEMAX software is used to obtain the final optical system from these ranges. By comparing different design results of the same example, our advanced TULS design performs better than conventional TULS design and spherical varied-line-space grating design, and as well as the toroidal varied-line-space design. It is demonstrated that aberrations are minimized when the TULS design is operated by our method. The advanced design is low-cost, easy to fabricate, and more suitable for FUV observations.
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