Analysis of the Relationship Between Spectral and Color Uncertainty

O. Kupko
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Abstract

An approach is proposed for an approximate estimate of the relation between the uncertainties of spectral and color measurements. The approach is based on replacing the entire diversity of the spectra with simple models: a constant over all wavelengths, a pronounced peak, a sharp decrease and a sharp increase. The Monte-Carlo method was used for calculations. Small distortions were introduced to the model spectra at each wavelength, the standard deviation of these distortions was calculated, after which the chromaticity coordinates were calculated in the system (x, y, Y). The value of Y, as related to light measurements, was not further analyzed. The standard deviation of the distances between the chromaticity coordinates of the initial spectrum and the chromaticity coordinates of the distorted spectra in space (x, y) was used as a measure of the uncertainty of color measurements. The ratio of these standard devia­tions was considered to be a link between the uncertainties of the spectral and color measurements. The influence of the uncertainties of the spectral measurements, the effect of the spectral width of the model spectra in the form of a peak, a sharp decrease and a sharp increase on the axis of the wavelengths were analyzed. The ran­ges of the corresponding values are chosen taking into account the valid documents and the most common spectra. The influence of a stan­dard illuminator selected was considered: all calculations were carried out for both type A and D65 sources. The results of the calculations are provided in the form of graphs, which allow one to approximately determine the required level of accuracy of the spectral equipment before the measurements, in order to provide the necessary uncertainty of chromaticity measurements. The analysis of the results obtained.
光谱不确定度与颜色不确定度的关系分析
提出了一种近似估计光谱和颜色测量不确定性之间关系的方法。该方法基于用简单的模型取代光谱的整个多样性:在所有波长上都是常数,峰值明显,急剧下降和急剧增加。计算采用蒙特卡罗方法。在每个波长下,将小失真引入到模型光谱中,计算这些失真的标准偏差,然后计算系统(x,y,y)中的色度坐标。与光测量相关的Y值没有进一步分析。初始光谱的色度坐标和空间(x,y)中失真光谱的色度座标之间的距离的标准偏差被用作颜色测量的不确定度的测量。这些标准偏差的比率被认为是光谱和颜色测量的不确定性之间的联系。分析了光谱测量的不确定性、峰值形式的模型光谱的光谱宽度、波长轴上的急剧减少和急剧增加的影响。相应值的范围是在考虑有效文件和最常见光谱的情况下选择的。考虑了所选标准照明器的影响:所有计算均针对a型和D65型光源进行。计算结果以图表的形式提供,其允许在测量之前近似地确定光谱设备的所需精度水平,以便提供色度测量的必要不确定性。对获得的结果进行分析。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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