Precision and Accuracy of Wavelength Measurements

Resolving power and light-gathering power are not the only criteria by which a wavelength-dispersing instrument should be judged. A very important question is the attainable preoision and accuracy of absolute wavelength measurements. 

To measure a physical quantity always means to compare it with a reference standard. This comparison involves statistical and systematic errors. Measuring the same quantity n times will yield values X. which scatter around 

The attainable precision for such a set of measurements is determined by statistical errors and is mainly limited by the signal-to-noise ratio for a single measurement and by the number n of measurements (i.e., by the total measuring time). The precision can be characterized by the standard deviation (see for instance [4.44]) 

The adopted mean value X, averaged over many measured values X j, is claimed to have a certain aoouraoy, which is a measure of the reliability of this value, expressed by its probable deviation AX from the unknown true value X. A stated accuracy of %/TK means a certain confidence that the true value X is within X AX. Since the accuracy is determined not only by statistical errors but particularly by systematic errors of apparatus and measuring procedure, it is always lower than the precision. It is also influenced by the precision with which the reference standard can be measured and by the accuracy of its comparison with the value X. Although the attainable accuracy depends on the experimental efforts and expenditures, the skillfulness, imagination, and critical judgement of the experimentalist always have a major influence on the finally achieved and stated accuracy. 

We shall characterize precision and accuracy by the ratios a/X, AX/X, respectively. Note that often both quantities are inversely defined as being inversely proportional to a or Although the latter definition has the advantage that a high precision or a high accuracy means a small uncertainty in accordance with the common meaning of both expressions, we 

We shall characterize precision and accuracy by the relative uncertainties of the measured quantity X, expressed by the ratios 

Also in absorption spectroscopy with a tunable laser the accuracy of line positions is limited by the nonuniform scan speed dA/dt of the laser (Sect.5.6). One has to record reference wavelength marks simultaneously with the spectrum in order to correct for the nonuniformities of dA/dt. 

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Let us now briefly examine the attainable precision and accuracy of wavelength measurements with the different instruments discussed above. 

The possibility of choosing a particular wavelength, rather than taking the output of one of the standard laboratory X-ray tubes, provides opportunities for special types of experiment beyond the scope of this discussion. Among the possible advantages are the avoidance or reduction of some systematic errors such as X-ray absorption or extinction, which may severely affect measured intensities and hence the precision and accuracy of crystal structures, and the exploitation of effects such as anomalous scattering for the determination of absolute configuration of chiral structures, as described in Section 2A.2.1. 

Definition and Uses of Standards. In the context of this paper, the term "standard" denotes a well-characterized material for which a physical parameter or concentration of chemical constituent has been determined with a known precision and accuracy. These standards can be used to check or determine (a) instrumental parameters such as wavelength accuracy, detection-system spectral responsivity, and stability (b) the instrument response to specific fluorescent species and (c) the accuracy of measurements made by specific Instruments or measurement procedures (assess whether the analytical measurement process is in statistical control and whether it exhibits bias). Once the luminescence instrumentation has been calibrated, it can be used to measure the luminescence characteristics of chemical systems, including corrected excitation and emission spectra, quantum yields, decay times, emission anisotropies, energy transfer, and, with appropriate standards, the concentrations of chemical constituents in complex S2unples. 

The accuracy of wavelength determination depends on the knowledge of the absolute laser wavelength and its specific Zeeman shift and on the measurement of the magnetic field strength H. All three parameters can be determined with high precision... 

For instrument with effective bandpass of 2 nm or less Wavelength dependent (kmax and Xmm are measured) Careful preparation is required for precision and accuracy... 

Accuracy and linearity of the measured values of the reflectance p can be verified by measuring materials with known absolute reflectances of less than 100%. Examples of spectra of two such reference standards measured versus a 100% standard are shown in Figure 9. The reflectance of the two different standards is specified depending on the wavelength, as follows 48.5% at 250 nm, 46.8 at 350 nm (minimum), and 56.6% at 2500 nm 18.7% at 250 nm, 17.2% at 400 nm (minimum), and 26.3% at 2500 nm. It is evident from Figure 9 that the measured reflectance values do not correspond exactly to the specification. Furthermore, repeated measurements indicate less than perfect reproducibility. Analysis of the spectra in Figure 9 shows accuracy and precision of the measurements to be 2-5%. The deviations from the specified values could be caused by imperfect reference materials or could point towards a problem with the measurement apparatus (Thiede and Melsheimer, 2002). 

This system employs a simultaneous film thickness measurement method, which incorporates a two-dimensional CCD camera detector , a variable wavelength light source, and an analyzer for the captured image data. With this configuration the system can, not only measure test pattern film thickness but also be used for a variety of visual wafer checks and film data inspections for Cu and other metal films during metal CMP. Moreover, we now have evidence that the system may even be able to handle moving wafers. With such potential, this system could evolve into a true In-Situ Monitor which measures film thickness inside the CMP unit itself with the same precision and accuracy. 

Wavelength repeatability is a measure of the precision of wavelength measured. The bandwidth refers to the width of an emission band (from the monochromator) at half peak height. This value, normally provided by the manufacturer is accepted. Using a mercury vapor lamp one can also check the spectral width. A number of well defined emission lines at 243.7, 364.9, 404.5, 435.8, 546.1, 576.9, and 579 nm can be used to check spectral bandwidth. However, the accuracy of the absorbance measured is dependent on the ratio of spectral bandwidth to the normal bandwidth (NEW) of the absorbing species. Most active pharmaceutical compounds have a normal bandwidth of approximately... 

Quantitative analysis can be carried out by measuring the intensity of fluorescence at the wavelength characteristic of the element being determined. The method has wide application to most of the elements in the periodic table, both metals and nonmetals and many types of sample matrices. It is comparable in precision and accuracy to most atomic spectroscopic instrumental techniques. The sensitivity limits are of the order of... 

The qualification of a Raman spectrometer is described in USP chapter < 1120>. In particular, the tests for the operational and performance qualification of a Raman spectrometer are described x-axis precision, photometric precision, laser power precision and accuracy. The x-axis of the Raman spectrometer is the Raman shift measured in wavenumbers. Before the Raman shift can be determined, both the laser wavelength and spectrophotometer calibration must be determined. The precision of the Raman shift can then be measured using an American Society for Testing and Materials (ASTM) Raman standard material [20]. A commonly used Raman standard material is acetaminophen. The peak position of the known reference peaks can be determined visually, but is better done with a peak location algorithm. The USP chapter on Raman specifies that the peak location should not vary more than... 

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