# Reproducibility of radiant energy measurements inside light scattering liquids

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3 Reproducibility of radiant energy measurements inside light scattering liquids Results He-Ne laser The results obtained for the wavelength nm for the test R1 are represented at the graphs of Figures 3 and 4. The data sequence for test R2 is shown at the graph of Figure 5, in which it is possible to see a change at the data for all distances, because of the same reasons of test R1. At Table 1 are the values for average, standard deviation and coeffi cient of variation for each test. The results for the measurements of laser incident energy are shown at Figure 6. The energy is relative to the average of the measurements of each position (position 1 and 2). There are no irregularities at the data, showing that the laser output is stable. Results for average, standard deviation, coeffi cient of variation and sample size are shown at Table 1. Figure 5. Graph with data for test R2, red laser. The graph shows data in chronological order for each distance from the fi ber to the center of the cuvette Energy (nj) ,85 59,90 59,95 60,00 60,05 60,10 60,15 60,20 Integration time (s) Figure 3. Graph with data for test R1, red laser. The graph shows integration time dispersion data, measured with manual chronometer. Energy (nj) Data number Figure 4. Graph with data for test R1, red laser. The graph shows data in chronological order. The arrows correspond to the change of measure series. Figure 6. Graph with data for laser incident energy, red laser. The energy is relative to the average of the measurements of each position. Table 1. Average, standard deviation and coeffi cient of variation of the radiant energy for each test (R1 and R2) realized with red laser and data for laser incident energy at positions 1 and 2 (lines Pos 1 and Pos 2, respectively). Test/ distance Average (nj) Standard deviation (nj) Coeffi cient of variation (%) Sample size R R2/4 mm R2/5 mm R2/6 mm Pos Pos Revista Brasileira de Física Médica.2011;5(1):

4 Magalhães AC, Yoshimura EM Infrared laser The data obtained for test R1, in chronological order, are shown at the graph of Figure 7. It is possible to note, at graph of Figure 7, that data oscillate a lot, without any clear change, neither tendencies. For test R2, the results are shown at the graph of Figure 8, in which is possible to note that there is a big change at energy for all distances after the seventh measurement. The reason for this alteration is a variation of the incident laser energy, which is changed by a factor of 2.6. After this big change, other variations with this magnitude did not occur. Table 2. Average, standard deviation and coeffi cient of variation of the radiant energy for each test (R1 and R2) realized with infrared laser and data for laser incident energy at positions 0, 1 and 2 (lines Pos 0, Pos 1 and Pos 2, respectively). Test/ distance Average (nj) Standard deviation (nj) Coeffi cient of variation (%) Sample Size R R2/4 mm R2/5 mm R2/6 mm Pos Pos Pos The results for the measurements of laser incident energy are shown at Figure 9. The energy is relative to the average of the measurements of each position (position 0, 1 and 2). There are no irregularities at the data, what means that there are not big variations of incident energy and there is not any important effect of the aperture and the mask. Results for average, standard deviation, coeffi cient of variation and sample size are shown at Table 2. Figure 7. Graph with data for test R1, infrared laser. The graph shows data in chronological order. Figure 9. Graph with data for laser incident energy, infrared laser. The energy is relative to the average of the measurements of each position. Figure 8. Graph with data for test R2, infrared laser. The graph shows data in chronological order for each distance measured. At Table 2 are the values for average, standard deviation and coeffi cient of variation for each test. Probably, the low standard deviation obtained for test R2, at distance of 4 mm, occurred because three series of measurements at this position were lost. Conclusions Through the analysis of the data, it was concluded that there are no tendencies related to the integration time, what is seen at integration time dispersion graphs. Therefore, it is possible to say that this source of error is considered when the energy analysis is done. There is an uncertainty associated to the optical fi - ber and cuvette positioning, shown by the standard 60 Revista Brasileira de Física Médica.2011;5(1):57-62.

5 Reproducibility of radiant energy measurements inside light scattering liquids deviation obtained for each group. As they have similar magnitudes, varying roughly between 2 and 8%, we will adopt 7% as a value of the uncertainty associated with the data collection. It is equivalent to the largest standard deviation found for the series data. A large portion of the radiant energy data variation is due to the laser stability, as the coefficients of variation of the incident energy are similar to the standard deviation of the reproducibility experiments. Acknowledgment The authors thank the personnel of the Optical Laboratory of Institute of Physics, where the measurements were done. References 1. Pogue BW, Patterson MS. Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry. J Biomed Opt. 2006;11(4): Revista Brasileira de Física Médica.2011;5(1):

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