Calibration problems

The camera model has a high number of parameters with a high correlation between several parameters. Therefore, the calibration problem is a difficult nonlinear optimization problem with the well known problems of instable behaviour and local minima. In out work, an approach to separate the calibration of the distortion parameters and the calibration of the projection parameters is used to solve this problem. 

Shortly after this time, it was discovered that Bridgman s static high-pressure scale was in error due to calibration problems, and the shock-induced 13 GPa transition became the new calibration standard. 

Calibration problems, single wavelength equivalent to point measurement in areas with long view paths (50-100 km) limited applications to date still under development... 

The radical concentration, when coupled with information on the rate of polymerization, allows k (and k,) to be calculated. The EPR methods have been applied to various polymerizations including those of B, DMA, MMA,361 566 S 67 368 and VAc.369 Values for kp are not always in complete agreement with those obtained by other methods (e.g. PLP, SIP) and this may reflect a calibration problem. Problems may also arise because of the heterogeneity of the polymerization reaction mixture,365 and insufficient sensitivity for the radical concentrations in low conversion polymerizations 63 or very low molecular weights. Some data must be treated with caution. However, the difficulties are now generally recognized and are being resolved. 60... 

T. Naes and E. Risvik (Editors), Multivariate Analysis of Data in Sensory Science, Data Handling in Science and Technology Series. Elsevier, Amsterdam, 1996 P.K. Hopke and X.-H. Song, The chemical mass balance as a multivariate calibration problem. Chemom. Intell. Lab. Assist., 37 (1997) 5-14. 

So, overall the chemometrics bridge between the lands of the overly simplistic and severely complex is well under construction one may find at least a single lane open by which to pass. So why another series Well, it is still our labor of love to deal with specific issues that plague ourselves and our colleagues involved in the practice of multivariate qualitative and quantitative spectroscopic calibration. Having collectively worked with hundreds of instrument users over 25 combined years of calibration problems, we are compelled, like bees loaded with pollen, to disseminate the problems, answers, and questions brought about by these experiences. Then what would a series named Chemometrics in Spectroscopy hope to cover which is of interest to the readers of Spectroscopy ... 

In their day, Principal Components and Partial Least Squares were each considered almost as the magic answer to all calibration problems . It took a long time for the realization to dawn that they contain no magic and are subject to most of the... 

Of the three general methods, the last seems to be the most practical. Theoretically, with high enough concentrations of hydrocarbons, the first method, the headspace analysis, should be both the most accurate and the easiest to calibrate. Operationally, it leaves much to be desired both because of the problems of sensitivity and those of the accommodation of the larger molecules in water. The second method, vacuum degassing, requires much more equipment than the third method and requires that large amounts of water vapor be removed before the sample is injected into the gas chromatograph. The last method is so much less complicated that even with its calibration problems it has been adopted almost universally. 

Thanks are due David Kurtz for providing the Fenvalerate data and stimulating my interest in the detection-calibration problem. Helpful discussions with John Mandel concerning the Fenvalerate data set are also gratefully acknowledged. 

The calibration problem in chromatography and spectroscopy has been resolved over the years with varying success by a wide variety of methods. Calibration graphs have been drawn by hand, by instruments, and by commonly used statistical methods. Each method can be quite accurate when properly used. However, only a few papers, for example ( 1,2,15,16,26 ), show the sophisticated use of a chemometric method that contains high precision regression with total assessment of error. 

In the calibration problem two related quantities, X and Y, are investigated where Y, the response variable, is relatively easy to measure while X, the amount or concentration variable, is relatively difficult to measure in terms of cost or effort Furthermore, the measurement error for X is small compared with that of Y The experimenter observes a calibration set of N pairs of values (x, y ), i l,...,N, of the quantities X and Y, x being the known standard amount or concentration values and y the chromatographic response from the known standard The calibration graph is determined from this set of calibration samples using regression techniques Additional values of the dependent variable Y, say y., j l,, M, where M is arbitrary, are also observed whose corresponding X values, x. are the unknown quantities of interest The statistical literature on the calibration problem considers the estimation of these unknown values, x, from the observed and the... 

Use of Cubic Spline Functions in Solving Calibration Problems... 

Non-linear concentration/response relationships are as common in pesticide residue analysis as in analytical chemistry in general. Although linear approximations have traditionally been helpful the complexity of physical phenomena is a prime reason that the limits of usefulness of such an approximation are frequently exceeded. In fact, it should be regarded the rule rather than the exception that calibration problems cannot be handled satisfactorily by linear relationships particularly as the dynamic range of analytical methods is fully exploited. This is true of principles as diverse as atomic absorption spectrometry (U. X-ray fluorescence spectrometry ( ), radio-immunoassays (3), electron capture detection (4) and many more. 

The first applications in calibration problems appear to have been in the field of competitive protein binding assays. Marschner (19) have introduced the concept of smoothing... 

WEGSCHEIDER Cubic Spline Functions and Calibration Problems 173... 

One of the opportunities that researchers rarely have is to be in a position of a direct comparison of methods used by several researchers that use the same data. Three of the fenvalerate "unknown" Datasets described and used elsewhere in this volume have been used as primary datasets by 3 research groups in the solution of the calibration problem. Two aspects of the calibration problem, namely, the accuracy of the calibration graph and the description of statistical error as shown by the estimated amount interval are examined here in comparing each of the calibration methods. 

And he continues, The confidence bandwidth of a calibration problem does not adequately describe the solution of unknowns, but it could give information about the status of the analytical instrument, such as a gas chromatograph. It could tell how efficient it was running on a particular day. For the solution of unknowns, one needs, in addition to the confidence bandwidth, information about the response bandwidth which provides the more important portion of the error estimations in a calibration situation. ... 

An outlier can be defined as any observation that does not fit a pattern . In a typical PAT calibration problem, one can encounter three different types of outliers ... 

M. Sjostrom, S. Wold, W. Lindberg, J.A. Persson and H. Martens, A multivariate calibration problem in analytical chemistry solved by partial least squares models in latent variables. Anal. Chim. Acta, 150, 61-70 (1983). 

The PLS approach to multivariate linear regression modeling is relatively new and not yet fully investigated from a theoretical point of view. The results with calibrating complex samples in food analysis 122,123) j y jnfj-ared reflectance spectroscopy, suggest that PLS could solve the general calibration problem in analytical chemistry. 

Wold, S., Martens, H., Wold, H. The multivariate calibration problem in chemistry solved by the PLS method. Lecture notes in mathematics . Springer Verlag, Heidelberg, in press... 

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