论随机噪声对光谱测量的影响

Theory study on the effect of random noise on spectrum

光谱分析在分析化学,特别是定量分析中有越来越多用途。光谱测量过程中不可避免地存在随机噪声,会影响光谱分析结果。目前光谱预处理技术主要研究减小噪声的方法,未从理论上研究噪声对光谱的影响。本文从理论上推导随机噪声对光谱的影响公式,旨为后续光谱分析中噪声的减小和抑制奠定理论基础。论文从光谱测量所得原始信号为理论信号与随机噪声之和入手,推导了测量光谱的表达式,并将该表达式代入吸光度公式,推导出吸光度与噪声的关系。通过期望与方差的定义,推导了吸光度的期望与方差表达式。结果表明,实测吸光度是对理论吸光度的有偏估计,且实测吸光度中的噪声功率不仅与测量过程中的随机噪声功率有关,还与理论光谱有关。最后通过对多次重复测量的红外光谱与紫外光谱的分析说明了理论分析的正确性。因此,为了更加准确地估计光谱参数,降低光谱分析的最低检测门限,提高光谱分析的科学性、系统性、适用性与可信性,应在此理论分析基础上深入研究光谱预处理技术,以便将随机噪声对光谱的影响降低到最低程度。

Spectrum analysis has been more and more applied in chemical analysis, especially in the quantitative analysis. Random noise always exists in the measurement process of spectrum, and it has impact on the results of spectrum analysis. At present, the spectrum preprocessing method is focusing on how to reduce noise. In this paper, we discuss the effect of random noise on spectrum theoretically, and derive the formula which represents the relationship between measured spectrum and random noise. The purpose of this work is to lay a theoretical foundation for reducing or restraining noise of spectrum. The derivation procedure is as follows. Firstly, we suppose that original signal is the sum of theory signal and random noise, and then derive the expression of measurement spectrum. Secondly, according to the definition of absorbance, we derive the relationship between absorbance and noise. Thirdly, according to the definition of expectation and variance, we derive the relationship between expectation and variance of absorbance. Results shows that the measurement spectrum is biased estimation result of theoretical spectrum, and the noise power of measurement spectrum is related not only to random noise in measurement process, but also to the theoretical spectrum. At last, experiment results verify the correctness of the theory. Therefore, in order to depress the detection threshold of spectrum analysis, and improve the reasonableness, systematicness, applicability, dependability of spectrum analysis, above-mentioned derivation deserves greatly attention and in-depth theoretical study.