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Quality indexes based on water measurements for low and medium energy x-ray beams: A theoretical study with PENELOPE
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Image of FIG. 1.
FIG. 1.

Geometry of the PTW 30010 ionization chamber used in our simulations.

Image of FIG. 2.
FIG. 2.

as a function of various indexes . The linear fits are plotted with solid lines. The corresponding parameters, as given by Eq. (8) , are shown together with the value of χ2 per degree of freedom, χ2/. The values between parenthesis indicate the uncertainty of the parameter, with a coverage factor = 1, that is, 0.859(7) means 0.859 ± 0.007. The same coverage factor has been used to represent the and uncertainties of the fitted points.

Image of FIG. 3.
FIG. 3.

χ2 per degree of freedom obtained in the linear fits performed to vs . The arrow indicates the minimum value, that was obtained for . Also the proposal of Rosser (Ref. 8 ), , is marked with a cross. Solid dots, open dots, and solid triangles indicate those cases that satisfy the relation , with = 1, 2, and 3, respectively.

Image of FIG. 4.
FIG. 4.

Same as in Fig. 2 but for for which the minimum χ2/ was found. The gray area represents the uncertainty of the fit estimated according to the uncertainties of the fitting parameters. All uncertainties are given with a coverage factor = 1.

Image of FIG. 5.
FIG. 5.

Values of obtained for various PDD ratios, according to Eq. (8) and using the best fit parameters found in the set of linear fits described in the text. for ( , ) pairs (1.4,4), (1.4,5), (2,4), (2,5), and (3,5) are shown. The clear gray bars indicate the uncertainty range obtained with the experimentally measured PDDs (with a coverage factor = 1). Dots have been calculated with PDDs obtained in MC simulation of the corresponding beams. In this case, statistical uncertainties with the same coverage factor are included. The dark horizontal dark represents the value found with the simulated PDDs for the ratio with the minimum χ2/, .


Generic image for table

Characteristics of the x-ray beams used in this work. The values between parentheses in the column indicate the uncertainty with a coverage factor = 1, that is, 0.947(4) means 0.947 ± 0.004. The reference quality Q has taken to be 60Co.

Generic image for table

Characteristics of the experimental x-ray beams used to illustrate the method proposed in the present work. The anode angle was 22° in all cases.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Quality indexes based on water measurements for low and medium energy x-ray beams: A theoretical study with PENELOPE