A theory of measurement with applications to spectrometry

An analytic function operating on experimental data is optimized for making the most accurate measurement of a parameter of the expected data, under the conditions of non-stationary shot noise. The value of the parameter is obtained by equating the operation on experimental data with the same operation on the expected data which contains the parameter as an unknown value. If the operation is represented by a weighting function, the form of the optimum weighting function depends on the initial transformation of the experimental data by the measuring instrument. The optimum weighting function always contains the derivative of the expected signal with respect to the unknown parameter, divided by the time-dependent variance of the received signal. Weighting functions for the logarithmic output of a spectrophotometer are described. The superiority over least-squares curve-matching is shown. A method for determination of peak position by optimum slope measurement is derived. In general, the optimum weighting function is not a matched filter. The optimum result is the same for center-of-gravity measurements. The optimum parameter measurement is equivalent to a least-squares error minimization weighted by the inverse variance or mean-square noise level. This variance weighting is significant in photometric measurements limited by shot noise or other measurements described by Poisson statistics, such that the mean-square noise level varies with time. The form of the optimum filter, for non-white, non-stationary noise is derived.     

Real-time internal standardization with an axially-viewed inductively coupled plasma for optical emission spectrometry

An evaluation of precision improvements using real-time internal standardization with an axially-viewed inductively coupled plasma (ICP) is presented. New findings are presented with respect to the nature of the noise in the analytical signals from the axial ICP. It is observed that a high degree of correlation exists in the line signals from the axial ICP. Using the yttrium ion line at 371.030 nm as the internal standard, the analytical precision after the application of real-time internal standardization is maintained between 0.1 and 0.2% relative standard deviation (RSD) for ion lines. Precision improvement factors of 3 to 4 are obtained by comparison with the uncorrected results. With atomic lines, real-time internal standardization using the yttrium ion line is less effective, yielding precision values between 0.2 and 0.7% RSD. The precision improvement factors for atomic lines are between 1.5 and 3. Thus, real-time internal standardization provides significant improvements in the RSDs of the line signals. The limits of these improvements are explored and an equation is presented which yields the fundamental shot noise limit for precision. Shot noise limited precision is demonstrated. However, this is not possible for all elements using a single internal standard signal. The effectiveness of real-time internal standardization is shown to be dependent on the nature of the specific spectral line. With the axially-viewed ICP, the dominant phenomenon preventing the full benefit of internal standardization from being obtained is the amplitude of the noise in the line signals and not the degree of correlation between analyte and internal standard signals. A trend is observed for atomic transitions in which lower excitation energy is correlated with higher relative noise amplitudes. This finding is in contrast with previously published work on the radially-viewed ICP. An explanation of this result is proposed which takes into account the influence of vaporizing sample droplets in the observation volume.     

A technique for estimating contamination tolerance limits for stable isotope ratio determinations

A model of the interaction between the precision of an isotope ion signal measurement and the accuracy of an isotope ratio determination was developed and used to derive the equations required to calculate the maximum tolerable amount of contamination for stable isotope ratio determinations. Comparison of the calculated tolerance limits and the blank estimated amount of contaminant will establish whether or not a correction for the contribution of the contaminant to the gross signals will be required. The 1000:1 sample-to-contaminant concentration tolerance limit used in stable isotope ratio plasma mass spectrometry will, in some situations, underestimate the contamination error compared to the model calculations.Derivation of the limit equations required an empirically determined relation between the signal strength and the signal's relative standard deviation (signal noise function). A single hyperbolic signal noise function was used to describe the behaviour of isotope ion signals of Ni, Cu, Tl and Pb measured using a plasma source double focusing magnetic sector mass spectrometer. The derivation could be extended to accommodate different signal noise functions.     

Prediction of precision from signal and noise measurement in liquid chromatography: Mathematical relationship between integration domain and precision

Summary The precision of integration over noisy instrumental output for quantitative analysis is studied. A probability theory is developed to predict the relative standard deviation (RSD) of integration results over an integration domain from one-point integration (peak height measurement) to entire area integration in HPLC. Common integration modes of horizontal zero line and oblique zero line are taken into account, but no peak overlap is assumed. The question of the analytical superiority of peak height measurement or integration for quantitation is answered. In the HPLC apparatus used, the minimum RSD of measurements is found in the integration domain of ca. ±0.5 σ for analytes [peaks are approximated by the Gaussian signal of width, σ (standard deviation)]. The RSD of integration measurements is also shown to depend on the stochastic properties of background noise (uncorrelated noise and correlated 1/f type noise). The theoretical conclusion is verified by Monte Carlo simulation and HPLC experiments for some aromatic compounds. Second Part of series cited as Ref. [1].     

Limits in Enhancement Factor in Near-Brewster Angle Reflection Pump-Probe Two-Dimensional Infrared Spectroscopy

In this work, we simulated 2D infrared spectroscopy (IR) spectroscopy in both transmission geometry and Brewster-angle reflection geometry. Light dispersion and the leakage of s-polarized light are considered in simulating the enhancement factor of the reflection mode. Our simulation shows that the dispersion in reflection will only alter the 2D IR lineshape slightly and can be corrected. Leaking s-polarized light due to imperfectness of IR polarizers in the reflection geometry may limit the enhancement factor, but such limit is above what a typical experiment can reach. In the current experiment, the enhancement factor is mainly limited by the precision of incident angle, for which ordinary rotation stages are probably not adequate enough. Moreover, traditional energy ratio of pump and probe pulses, which is 9:1, may not be ideal and could be changed to 2:1 in the reflection geometry. Considering all the above factors, the enhancement on the order of 1000 is possible in the current experiment. Nevertheless, near-Brewster angle reflection will enhance both the signal and the noise caused by the signal itself, therefore this method only works if the noise is unrelated to the signal, particularly if the noise is caused by the fluctuation in the probe. It cannot improve the signal to noise ratio when the dominate noise is from the signal itself. The theoretical results here agree reasonably well with published experiment results and pave way for realizing even higher enhancement at nearer-Brewster angle.     

Prediction of measurement precision of apparatus using a chemometric tool in electrochemical detection of high-performance liquid chromatography

The relative standard deviation (RSD) of measurements in high-performance liquid chromatography with electrochemical detection (HPLC-ECD) was predicted by a chemometric tool based on the 1/f fluctuation model which is made up of white noise and a Markov process, called the Function of Mutual Information (FUMI) theory. FUMI theory can provide aprecise and reliable detection limit from a single measurement of noise and signal in HPLC-ECD. To obtain RSD (n = 5) for determination of (-)-epicatechin at five concentrations required 12.5 h, while the predicted RSD by FUMI theory required only 0.5 h (one measurement). Moreover, to trace the source of instrumental noise, power spectra of chromatographic baseline were used. Selection of a suitable apparatus in HPLC-ECD system, acquisition of RSD, and detection limits for determination of catechins by HPLC-ECD were simply and easily made by this chemometric tool within a very short time. The use of the FUMI theory for the prediction of measuring precision was more efficient and the optimization was less time-consuming to be suited for determination.     

Prediction of precision from signal and noise measurement in liquid chromatography: Mathematical relationship between integration domain and precision

Summary The precision of integration over noisy instrumental output for quantitative analysis is studied. A probability theory is developed to predict the relative standard deviation (RSD) of integration results over an integration domain from one-point integation (peak height measurement) to entire area integration in HPLC. Common integration modes of horizontal zero line and oblique zero line are taken into account, but no peak overlap is assumed. The question of the analytical superiority of peak height measurement or integration for quantitation is answered. In the HPLC apparatus used, the minimum RSD of measurements is found in the integration domain of ca. ±0.5 for analytes [peaks are approximated by the Gaussian signal of width, (standard deviation)]. The RSD of integration measurements is also shown to depend on the stochastic properties of back-ground noise (uncorrelated noise and correlated 1/f type noise). The theoretical conclusion is verified by Monte Carlo simulation and HPLC experiments for some aromatic compounds.Second Part of series cited as Ref. [1].     

田口方法在X射线荧光分析时曲线校正中的应用

根据田口玄一博士在测量工程学中提出的信噪比概念,计算了X荧光分析中某一标准曲线极限信噪比。当日常测试中系统的信噪比大于极限值时,不需要对曲线进行校正;当日常测试中系统的信噪比小于极限值时,应对曲线进行校正．以保证该测量系统工作的稳定性。     

Noise in atomic absorption flame spectrometry—a comparison between single beam and double beam instruments

Noise levels have been measured under a variety of conditions using comparable single and double beam instruments. At low absorbance, in the vicinity of the detection limit, the major types of noise are photon noise, flame transmission noise and lamp flicker noise. The precision at low absorbance is slightly better with single than double beam providing a blank correction is made before and after each sample measurement. At higher absorbances, analyte absorption noise is dominant and there is no difference in precision between single and double beam.     

Characterization of heteroscedastic measurement noise in the absence of replicates

A method is described for the characterization of measurement errors with non-uniform variance (heteroscedastic noise) in contiguous signal vectors (e.g., spectra, chromatograms) that does not require the use of replicated measurements. High-pass digital filters based on inverted Blackman windowed sinc smoothing coefficients are employed to provide point estimates of noise from measurement vectors. Filter parameters (number of points, cutoff frequency) are selected based on the amplitude spectrum of the signal in the Fourier domain. Following this, noise estimates from multiple signals are partitioned into bins based on a variable that correlates with the noise amplitude, such as measurement channel or signal intensity. The noise estimates in each bin are combined to estimate the standard deviation and, where appropriate, a functional model of the noise can be obtained to characterize instrumental errors (e.g., shot noise, proportional noise). The proposed method is demonstrated and evaluated with both simulated and experimental data sets, and results are compared with replicated measurements. Experimental data includes fluorescence spectra, ion chromatograms from liquid chromatography/mass spectrometry, and UV–vis absorbance spectra. The limitations and advantages of the new method compared to replicate analysis are presented.     

Studies of the mechanically generated noise in static mercury drop electrodes

The moving parts needed for the operation of a mechanized static mercury drop electrode were found to generate additional noise which affects measurement of the polarographic current. A Fourier transformation method was employed in analysis of experimental data giving information about the frequency, amplitude and decay characteristics of the noise. The dominant noise frequency was found to depend on the drop size. Drop formation at a potential where no electrolysis takes place combined with a waiting period long enough for the mechanical vibrations to decay improved the precision of the polarographic current measurement.     

Signal processing of transient atomic absorption signals

This article is an electronic publication in Spectrochimica Acta Electronica (SAE), the electronic section of Spectrochimica Acta Part B (SAB). The hard copy text is accompanied by a disk with a demonstration version of the simulation program, libraries of electronic and optical component blocks, simulation models, manual, and other files.Absorbance signals for electrothermal atomization atomic absorption spectroscopy (ETA-AAS) were generated digitally and the effect of various types and sources of noise upon the precision of the absorbance measurement was evaluated by numerical calculation. Peak area measurement, peak height measurement, and matched filtering were used for processing these signals. The performance of these three techniques in the presence of various types of noises and the sensitivity of each to small variation in the atomization conditions was calculated. It is demonstrated that significant improvement in signal-to-noise ratios can be realized by application of appropriate signal processing methods. The results also indicate that one of the principal causes for loss of precision could be the variation in the heating characteristics of the furnace.     

Bayesian Methods for Ion Selective Electrodes

With the increasing use of ion‐selective electrodes in environmental and health applications, it is important to know the precision of estimated concentrations. A Bayesian model for non‐linear calibration is introduced which provides estimates of measurement precision by incorporating uncertainty in calibration parameters and inherent random noise in emf response. The analysis of lead in 17 soil samples demonstrates that large gains in precision are possible when calibrations are extended to include multiple electrodes and standard addition data. The results highlight the need for improved calibration and routine use of standard addition as ion selective electrodes become increasingly popular for demanding, real world applications.     

A camera-based strain measurement technique for elastomer tensile testing: Simulation and practical application to understand the strain dependent accuracy characteristics

The present work investigates the precision characteristics of two optical strain measurement techniques applied to elastomers subjected to large deformations. The measurement approach is based on generating intensity profiles by using several horizontal image lines in the region of an optical marker to be detected. For detectability and accuracy reasons, these lines are combined using a rank (maximum) value filter and a moving average filter, while the calculation of the marker centers is carried out either geo- or gravimetrically. Based on simulated profiles, the first part of this work investigates the influence of method related parameters on the measurement precision obtained, expressed in terms of the root mean square error (rms). Further, it establishes model relations between most important image/profile parameters and rms. In the second part, experimental image data obtained during tensile testing of an elastomer sample is analyzed by i) applying the strain measurement technique, ii) determining experimental rms-values and iii) discussing them in comparison to values predicted by the rms-model of part one. It was found that, for the gravimetrical center calculation, rms strongly depends on the number of profile pixels which is caused by image noise. In the present approach, image noise was reduced by multiple image line fusion, which can be assumed to be in terms of computation effort more effective than averaging multiple images. The developed rms-models were found to represent the strain dependent decrease of accuracy efficiently up to high strains (e.g. 900%) under practical conditions. To obtain optimal measurement precision with the presented methods in practice, appropriate low marker detection threshold intensities of about 0.3g_s (g_s –signal intensity) and application of a single application cycle of the moving average filter were proved to yield optimal results. At high strains, the application of the rank filter in combination with a geometric center calculation results in best measurement precision, while the differences to the gravimetric method are less but its trend is comparable to the simulation.     

用分段训练的Elman递归神经网络滤除色谱数据中的噪声

分析了色谱信号噪声的分形特征,采用分段训练的Elman递归神经网络除噪.实验结果表明,此方法在滤除噪声时具有一般神经网络和中值滤波器所没有的优点,精度明显提高.     

Chemical measurements with optical fibers for process control

Several aspects of remote in situ spectrophotometric measurement by means of optical fibers are considered in the context of chemical process control. The technique makes it possible to measure a species in a particular oxidation state, such as plutonium(VI), sequentially, under the stringent conditions of automated analysis. For the control of several species in solution, measurements at discrete wavelengths on the sides of the absorption peaks serve to increase the dynamic range. Examples are given concerning the isotopic separation of uranium in the Chemex process. The chemical control of complex solutions containing numerous mutually interfering species requires a more elaborate spectral scan and real-time processing to determine the chemical kinetics. Photodiode array spectrophotometers are therefore ideal for analysing the uranium and plutonium solutions of the Purex process. Remote on-line control by ultraviolet monitoring exhibits limitations chiefly due to Rayleigh scattering in the optical fibers. The measurement of pH in acidic (0.8-3.2) and basic media (10-13) has also been attempted. Prior calibration, signal processing and optical spectra modeling are also discussed.     

Increasing the signal to noise ratio in amperometry and polarography using the controlled-growth mercury drop electrode

A new approach to current sampling in amperometric and polarographic measurement is described. This approach requires the application of a step-by-step mode of mercury drop generation. The advantages are: (1) in amperometric measurements an increase of the signal to noise ratio; (2) in polarographic measurements and computer aided experiments the noise level can be markedly reduced.     

食品安全速测设备光谱标定仪的研制

对没有光谱测量功能的分光光度计类测量设备的光谱分析问题进行系统研究,研制成可自校准并有效溯源的食品安全速测设备光谱标定仪,解决了设备光源标定问题,为食品安全速测设备的准确测量提供可靠技术保证。     

一种新的小波滤波方法在化学谱图信号滤噪中的应用

仪器分析测定中，噪声的存在往往影响分析的准确度和仪器的检出限。小波变换多分辨分析的特性使得它成为一种很好的滤噪方法。基于小波分解后信号与噪声的小波系数随尺度变化规律不同的特性，提出了一种新的滤波滤方法-空域相关法，即通过不同尺度上相关系数模值与小波系数模模值的比较，达到滤波滤的目的。本文提出的方法具有无需人为选定无需人为选定滤噪阈值和小波函数、方法简单、失真度小等优点，可以大在提高信号的信噪比。模拟数据和ICP-AES实验数据证明了该方法的有效性。     

Non-linear signal response functions and their effects on the statistical and noise cancellation properties of isotope ratio measurements by multi-collector plasma mass spectrometry

A nebulizer-centric response function model of the analytical inductively coupled argon plasma ion source was used to investigate the statistical frequency distributions and noise reduction factors of simultaneously measured flicker noise limited isotope ion signals and their ratios. The response function model was extended by assuming i) a single gaussian distributed random noise source (nebulizer gas pressure fluctuations) and ii) the isotope ion signal response is a parabolic function of the nebulizer gas pressure.Model calculations of ion signal and signal ratio histograms were obtained by applying the statistical method of translation to the non-linear response function model of the plasma. Histograms of Ni, Cu, Pr, Tl and Pb isotope ion signals measured using a multi-collector plasma mass spectrometer were, without exception, negative skew. Histograms of the corresponding isotope ratios of Ni, Cu, Tl and Pb were either positive or negative skew. There was a complete agreement between the measured and model calculated histogram skew properties.The nebulizer-centric response function model was also used to investigate the effect of non-linear response functions on the effectiveness of noise cancellation by signal division. An alternative noise correction procedure suitable for parabolic signal response functions was derived and applied to measurements of isotope ratios of Cu, Ni, Pb and Tl. The largest noise reduction factors were always obtained when the non-linearity of the response functions was taken into account by the isotope ratio calculation.Possible applications of the nebulizer-centric response function model to other types of analytical instrumentation, large amplitude signal noise sources (e.g., lasers, pumped nebulizers) and analytical error in isotope ratio measurements by multi-collector plasma mass spectrometry are discussed.