MICADO, a near-infrared imager for the Extremely Large Telescope, is being designed to deliver diffraction limited imaging and 50 microarcsecond (μas) astrometric accuracy. MICADO employs an atmospheric dispersion corrector (ADC) to keep the chromatic elongation of the point spread function (PSF) under control. We must understand the dispersion and residuals after correction to reach the optimum performance. Therefore, we identified several sources of chromatic dispersion that need to be considered for the MICADO ADC. First, we compared common models of atmospheric dispersion to investigate whether these models remain suitable for MICADO. We showed that the differential dispersion between common atmospheric models and integration over the full atmosphere is less than 10 μas for most observations in H band. We then performed an error propagation analysis to understand the uncertainty in the atmospheric dispersion as a function of atmospheric conditions. In addition, we investigated the impact of photometric colour on the astrometric performance. While the differential refraction between stars within the same field of view can be significant, the inclusion of an ADC rendered this effect negligible. For MICADO specifically, we found that the current optomechanical design dominates the residual dispersion budget of 0.4 milliarcseconds (mas), with a contribution of 0.31 mas due to the positioning accuracy of the prisms and up to 0.15 mas due to a mismatch between the dispersive properties of the glass and the atmosphere. We found no showstoppers in the design of the MICADO ADC for achieving 50 μas relative astrometric accuracy.

中文翻译：

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量化 MICADO 近红外成像仪器的预期残余色散

MICADO 是一种用于超大望远镜的近红外成像仪，旨在提供衍射受限成像和 50 微弧秒 (μas) 的天体测量精度。MICADO 采用大气色散校正器 (ADC) 来控制点扩展函数 (PSF) 的色度伸长率。我们必须了解校正后的色散和残差，才能达到最佳性能。因此，我们确定了 MICADO ADC 需要考虑的几个色散来源。首先，我们比较了常见的大气扩散模型，以研究这些模型是否仍然适用于 MICADO。我们表明，对于 H 波段的大多数观测，常见大气模型和全大气积分之间的差异色散小于 10 μas。然后，我们进行了误差传播分析，以了解作为大气条件函数的大气扩散的不确定性。此外，我们研究了光度颜色对天体测量性能的影响。虽然同一视野内的恒星之间的不同折射可能很重要，但包含 ADC 使这种影响可以忽略不计。特别是对于 MICADO，我们发现当前的光机械设计主导了 0.4 毫弧秒 (mas) 的残余色散预算，由于棱镜的定位精度而贡献了 0.31 mas，由于色散特性之间的不匹配而贡献高达 0.15 mas玻璃和大气。我们在 MICADO ADC 的设计中没有发现可实现 50 μas 相对天体测量精度的阻碍因素。