The well-known problem of fitting a straight line to data with uncertainties in both coordinates is revisited. An algorithm is developed which treats x- and y-data in a symmetrical way. The problem is reduced to a one-dimensional search for a minimum. Global convergence and stability are assured by determining the angle of the straight line with respect to the abscissa instead of the slope. As opposed to previous publications on the subject, the complete uncertainty matrix is calculated, i.e. variances and covariance of the fitting parameters. The algorithm is tested using Pearson's data with York's weights. Although the algorithm is implemented in MATLAB, implementation in a different programming language is straightforward using the formulae presented. An application example is given, a calibration line for dosimetry based on electron spin resonance of alanine is investigated.

In radiation therapy, the effect of ionizing radiation is quantified in terms of the absorbed dose to water. Dosimetry with alanine and readout via electron spin resonance (ESR) is a method which is used as a secondary standard by several national metrology institutions. The advantages of the method are the good water-equivalence of the probes, their small size and the very weak dependence of the response on the radiation quality for MV x-rays and high-energy electrons used in radiation therapy. For radiation therapy, a small uncertainty of the applied dose is required. The present publication describes the determination of the uncertainty budget for the alanine/ESR dosimetry system of the Physikalisch-Technische Bundesanstalt (PTB), which relies on the use of a reference sample. A method is also presented which allows a reduction of the influence of fading or other changes of the ESR amplitude of irradiated alanine probes with time. If certain conditions are met which are described in detail, a relative uncertainty of less than 0.5% can be reached for probes irradiated with (60)Co in the 5-25 Gy dose range, including the uncertainty of the primary standard. First results for dose values between 2 Gy and 10 Gy are presented as well. From the high accuracy achievable with alanine dosimetry, we conclude that this method has great potential to solve measurement problems for modern methods of radiation therapy such as intensity modulated radiation therapy (IMRT) or tomotherapy.

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The well-known problem of fitting a straight line to data with uncertainties in both coordinates is revisited. An algorithm which treats x- and y-data in a symmetrical way and which had been published previously is generalized to the case when there are correlations. Taking known correlations into account helps to reduce the uncertainties of the parameters of the fit which is of major importance in metrology. Although the algorithm is implemented in MATLAB, implementation in a different programming language is straightforward using the formulae presented. The effectiveness of the algorithm is demonstrated with simulated data as well as with experimental data. As application examples, measurements of the temperature coefficient for alanine dosimetry are used.