Calibration equation

To determine the concentration of Pb + in the sample of blood, we replace Sstand in the calibration equation with Ssamp and solve for C ... 

Substituting the sample s initial rate into the calibration equation gives an aluminum concentration of 0.331 )J,M. 

Over the last seventeen year s the Analytical center at our Institute amassed the actual material on the application of XRF method to the quantitative determination of some major (Mg, Al, P, S, Cl, K, Ti, Mn, Fe) and trace (V, Cr, Co, Ni, Zn, Rb, Sr, Y, Zr, Nb, Mo, Ba, La, Ce, Pb, Th, U) element contents [1, 2]. This paper presents the specific features of developed techniques for the determination of 25 element contents in different types of rocks using new Biaiker Pioneer automated spectrometer connected to Intel Pentium IV. The special features of X-ray fluorescence analysis application to the determination of analyzed elements in various types of rocks are presented. The softwai e of this new X-ray spectrometer allows to choose optimal calibration equations and the coefficients for accounting for line overlaps by Equant program and to make a mathematic processing of the calibration ai ray of CRMs measured by the Loader program. 

These values, and the corresponding SLIs for these tasks (from Table 5.4), are substituted in the general equation (1). The resulting simultaneous equations can be used to calculate the constants A and B. These are substituted in the general equation (1) to produce the following calibration equation ... 

The broad-standard linear calibration curves for polystyrene in THF in Figure 1 and 4 are used to illustrate the K and a calculations as follows. The particular calibration curves are found to correspond to the following calibration equations ... 

In prachce, coefficients a and b (and c) must be determined for every couple of a stationary phase and a mobile phase (and sometime for a given class of compounds) using retenhon factors of reference compounds of known log Poet-Then this calibration equation can be used to determine log Poet of novel compounds. 

While it is certainly possible to replace the constant with the appropriate values for constituent parameters ( 2eVID2), it is much more practical to determine the value empirically. A common calibration equation for TOF mass spectrometry is slightly more complicated (with the addition of an offset m/z value, b) and is given by... 

To solve problems involving calibration equations using multivariate linear models, we need to be able to perform elementary operations on sets or systems of linear equations. So before using our newly discovered powers of matrix algebra, let us solve a problem using the algebra many of us learned very early in life. 

Even though the two-site model has shortcomings, it is excellent for fitting intensity quenching curves. Thus, it has excellent predictive and calibration properties, has a chemically sound basis, and (at least for inorganic complex sensors) is preferable to the less accurate power law calibration equation. 

In order to obtain the calibration curve of pesticide metobromuron, absorbances were measured at the corresponding as a function of concentration and the data were fitted to Lambert-Beer law by the method of least square analysis. The resulting correlation coefficient (R 1.0000) show that the fit to Lambert-Beer law is excellent. The obtained calibration equation was used to convert absorbances into concentrations in kinetic and equilibrium studies. 

Standardizing the coefficients of the model entails modifying the calibration equation. This procedure is applicable when the original equipment is replaced (situation 1 above). Forina et al. developed a two-step calibration procedure by which a calibration model is constructed for the master (F-X), its spectral response correlated with that of the slave X-X) and, finally, a global model correlating variable Y with both X and X is obtained. The process is optimized in terms of SEP and SEC for both instruments as it allows the number of PLS factors used to be changed. Smith et al. propose a very simple procedure to match two different spectral responses. 

In practice the regression coefficients a and b have to be determined for every couple of stationary and mobile phases, by measuring the log k values for a series of reference compounds with known log P values. The calibration equation obtained then allows the determination of log P of new compounds. 

Figure 2-7 A diagram for IR calibration (Equation 2-86). The data for each given H20t content is obtained by heating the sample to different temperatures to vary the species concentrations. For a perfect calibration, all the trends would lie on a single straight line. However, there is some scatter. Furthermore, the slope defined by data for one fixed H20t content does not equal that for another. Hence, the calibration results (8523 = 0.168 8452 = 0.166) shown in this diagram have a relative precision of only about 10%, whereas the relative precision of IR band intensity data is about 1%.

When generating calibration equations using samples of known composition, the independent variable is represented by the spectroscopic readings (i.e., log HR) at specific wavelengths, while the concentration of the analyte of interest, for example, determined by traditional laboratory techniques, is the dependent variable. 

Multiple regression programs also calculate auxiliary statistics, designed to help decide how well the calibration fits the data, and how well it can be expected to predict future samples. For example, two of these statistics are the standard error of calibration (SEC) and the multiple correlation coefficient (R). The SEC (also called standard error of estimate, or residual standard deviation) and the multiple correlation coefficient indicate how well the calibration equation fits the data. Their formulas are given in Table 3. 

The multiple correlation coefficient R is a dimensionless measure of how well the calibration fits the data. R can have values between -1 and +1, but in a calibration situation only positive values exist. A value close to zero indicates that the calibration fails to relate the spectra to the reference values. As the correlation coefficient increases, the spectra become better and better predictors of the reference values. Because the multiple correlation coefficient is dimensionless, it is a useful way of comparing data or results with different units, and that are difficult to compare in other ways. However, its value gives no indication of how well the calibration equation can be expected to perform on future samples. 

The purpose of a calibration line is to use it to estimate the concentration of an unknown sample when it is presented to the instrument. This is achieved by inverting the calibration equation to make x the subject. For an indication Jo,... 

When calibrating the method for the first time attention must be given to whether the calibration equation is properly followed... 

To perform quantitative analyses of food using NIR, it is necessary to initially establish a calibration equation which relates spectral data to objective chemical data. Multiple linear regression (MLR) analysis is typically used to make a calibration equation using a calibration sample set analyzed accurately by a conventional chemical method. The general calibration equation can be written as ... 

In the case of protein determination of flour for example, the following calibration equation can be obtained using log(l/R2180)(absorbance at 2180 nm), which is the key absorption band for the protein. 

In the same manner, calibration equations for quantitative analyses of moisture, fat, carbohydrates, sugar, etc. can be established. 

Iodine number as well as melting point is one of the most important factors for quality control of processed fats and oils. However, a time-consuming chemical analysis is generally used for determining iodine number which sometimes stops production. In order to overcome this problem, an on-line NIR sensor has been developed [10]. Transmittance spectra of many kinds of oils were measured in the wavelength region from 1100 nm to 2500 nm to make a calibration equation. 

FT-IR has been applied for determining the sucrose content of sugar cane juice [21]. In place of the more familiar transmission cell, an attenuated total reflectance (ATR) cell and clarified sugar cane juice were used to record FT-IR spectra from 800 to 1250 cm"1. In the spectra, significant wavenumbers (927.59, 997.02, 1054.87, 1116.51, and 1137.80 cm"1) have been identified for sucrose. The application of PCR has been proposed for the development of a calibration equation for sucrose content. PCR is basically a MLR applied to scores assessed by PCA. On the basis of FT-IR spectra and sucrose content, an accurate calibration equation could be obtained by the application of PCR. The root mean square difference between predicted FT-IR values and the actual values were 0.12 % (w/v) with a bias of -0.03 % (w/v). The accuracy of FT-IR for determining sugar cane sucrose is almost equal to that of NIR [25]. 

---