Abstract In this paper, a highly accurate correction method for errors caused by spherical aberrations in long focal length measurements based on divergent light and Talbot interferometry is presented. Simulations and analysis indicate that spherical aberrations are key factors affecting the precision of moire fringe angles, which are ignored in most methods yet. Moire fringes are transformed into frequency domains, and a new method based on weighted averages is proposed to improve the precision of measurements. The modified measurement results of 13500 mm focal length lens reveal that the relative accuracy is better than 0.007%. Comparing the modified relative accuracy with that obtained in interferometry measurement, the proposed method is proved to be highly effective and reliable.

中文翻译：

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长焦距测量球差分析与校正

摘要 本文提出了一种基于发散光和Talbot干涉法的长焦距测量中球面像差引起的误差的高精度校正方法。仿真和分析表明，球面像差是影响莫尔条纹角精度的关键因素，目前大多数方法都忽略了这一点。将莫尔条纹转化为频域，提出了一种基于加权平均的新方法，以提高测量精度。13500mm焦距镜头修正后的测量结果表明相对精度优于0.007%。将修正后的相对精度与干涉测量中获得的相对精度进行比较，证明所提出的方法是高度有效和可靠的。