This report was automatically created at 2021-02-16 09:07:18 by the function RLum.OSL_global_fitting() of the R package OSLdecomposition (21.2.15). Visit luminescence.de to learn more.

Results

Step 1 of a component-resolved dose calculation is the identification of the components occurring in the data set. Constant signal component decay rates \(\lambda\) over all measurements were assumed and one global average CW-OSL curve was calculated. A series of multi-exponential decay model fittings with an increasing number of components \(K\) was performed. The resulting CW-OSL models can be compared by their photoionisation cross sections \(\sigma\) and their fitting quality to select the optimum set of signal components.

OSL plots

Global average


Figure 1.1: Red line: Global average curve built from the arithmetic mean of the individual curves.
Grey points: Data points of all measurements.

K = 1


Figure 1.2: Fit model with K = 1 signal components
Upper left: CW-OSL plot of global average curve and fitting model.
Upper right: pseudoLM-OSL transformed plot
Lower left: Residual curve between fitting and global average curve
Lower right: Estimated type of quartz OSL component (colored), photoionisation cross sections \(\sigma\), decay rates \(\lambda\) and signal intensity \(n\).

K = 2


Figure 1.3: Fit model with K = 2 signal components
Upper left: CW-OSL plot of global average curve and fitting model.
Upper right: pseudoLM-OSL transformed plot
Lower left: Residual curve between fitting and global average curve
Lower right: Estimated type of quartz OSL component (colored), photoionisation cross sections \(\sigma\), decay rates \(\lambda\) and signal intensity \(n\).

K = 3


Figure 1.4: Fit model with K = 3 signal components
Upper left: CW-OSL plot of global average curve and fitting model.
Upper right: pseudoLM-OSL transformed plot
Lower left: Residual curve between fitting and global average curve
Lower right: Estimated type of quartz OSL component (colored), photoionisation cross sections \(\sigma\), decay rates \(\lambda\) and signal intensity \(n\).

K = 4


Figure 1.5: Fit model with K = 4 signal components
Upper left: CW-OSL plot of global average curve and fitting model.
Upper right: pseudoLM-OSL transformed plot
Lower left: Residual curve between fitting and global average curve
Lower right: Estimated type of quartz OSL component (colored), photoionisation cross sections \(\sigma\), decay rates \(\lambda\) and signal intensity \(n\).

Photoionisation cross sections

Under the assumption that the provided optical stimulation parameters (\(\lambda_{stim}=\) 470 \(\mathrm{nm}, \Phi_{stim}=\) 35 \(\mathrm{\frac{mW}{cm^2}}\)) are correct, the found decay rates were translated into photoionisation cross section values and set into relation with quartz OSL literature values:


Figure 2: Photoionisation cross section comparison assuming a stimulation light intensity of 35 mW/cm² and a stimulation light wavelength of 470 nm.

Systematic shifts in the photoionisation cross sections are likely when compared to literature values. These are caused by false estimates of the effective stimulation intensity. To manually correct for these shifts, apply the following rules when setting RLum.OSL_global_fitting(stimulation_intensity = ?):

  • Increase stimulation intensity to shift the cross sections towards lower absolute values
  • Decrease stimulation intensity to shift the cross sections towards higher absolute values

Fitting quality

Selecting a fitting model with the physically correct number of components \(K\) is not trivial. According to Bailey et al. (1997), Mittelstraß (2019) and others, most quartz samples are sufficiently described by three CW-OSL components. Thus, the \(K = 3\) fitting is chosen as default model. However, a fourth components might contribute a significant signal. Likewise, a measurement may contain just two components. An indication provides an \(F\)-test as suggested by Bluszcz & Adamiec (2006). The test criterion \(F_K\) measures the improvement in the fitting quality by an additional component, see section F-test for details. An \(F_K\) below the preset value of Fthreshold = 150 indicates that the last added component did not improve the model significantly.


Table 2: Decay rates and fitting quality parameters as function of component number \(K\).
\(RSS\): Residual square sum. \(F_K\): Measure of fitting improvement.
Green stripe: Default CW-OSL model for quartz. Blue stripe: F-test selected model.
\(K\) \(\lambda_1\) \((s^{-1})\) \(\lambda_2\) \((s^{-1})\) \(\lambda_3\) \((s^{-1})\) \(\lambda_4\) \((s^{-1})\) \(RSS\) \(F_K\)
1 1.369 1.011e+07 Inf
2 1.519 0.05269 2.883e+05 3340
3 1.651 0.5231 0.009421 2.863e+04 879.6
4 11.07 1.779 0.6933 0.01487 1220 2156




Methods

Basics

The data analysis approach assumes that all CW-OSL signal curves in a data set can be sufficently described by a sum of exponential decays with first order kinetics:

\[I(t) = \sum_{i=1}^K n_ie^{-\lambda_it}\]

Here, \(I(t)\) is the CW-OSL signal, \(K\) is the number of signal components. Each component is defined by its intensity \(n\) and its decay rate \(\lambda\).

To achieve component-seperated dose information, the data analysis process is divided into multiple steps:

Step 1 workflow

This report covers the Step 1 analysis, which can be outlined as following:

Detailed explanations on step 1.1 and step 1.2 can be found in Mittelstraß (2019). Practical advice can be found in the R documentations ?sum_OSLcurves and ?fit_OSLcurve.

Step 1.2 is based on the ideas of Bluszcz & Adamiec (2006). The decay parameter are evaluated through differential evolution (see Price et al. 2006), performed by the function DEoptim from the package DEoptim (Ardia et al. 2020). The function DEoptim deploys the function decompose_OSLcurve (see Step2) for the calculation of the signal intensities. An Levenberg-Marquardt fitting refines the resulting parameter and is performed by the function nlsLM from the package minpack.lm (Elzhov et al. 2016).

Photoionisation cross sections

The signal decay rate \(\lambda_{k}\) of each component is translated into the photoionisation cross section \(\sigma_{k}\) of the associated defect state by:

\[\sigma_{k}=\lambda_{k} {hc \over \Phi_{stim}\lambda_{stim}}\] Here, \(h\) is the Planck constant, \(c\) is the speed of light, \(\Phi_{stim}\) is the stimulation light intensity and \(\lambda_{stim}\) is the stimulation light wavelength. If this wavelength is about ~ 470 nm and the measured sample material is quartz, then the resulting photoionisation cross sections can be compared with literature values, see figure 2. For the automatic assignement of component names, an approximated 2-\(\sigma\) bandwidth of the average literature value was used, see ?fit_OSLcurve for the exact definition.

Important note: The stimulation light intensity, displayed by OSL/TL reader control software, might differ from the effective stimulation light intensity. Degrading of stimulation light sources and filters as well as a dirty chamber window can significantly decrease the light output. In addition, the light flux in the bulk material depends on the reflectance and transmittance of the sample, its fixation and the sample carrier. Systematic shifts in the photoionisation cross section values are therefore likely.

F-test

Bluszcz & Adamiec (2006) proposed the use of an F-test to compare CW-OSL models by their fitting quality. The test criterion \(F_K\) measures the improvement caused by an additional component. It compares the residual square sum (RSS) of the \(K-1\) model with the new \(K\) model:

\[F_K = \frac{(RSS_{K-1} - RSS_K)/2}{RSS_K(N - 2K)} \]

Here, \(N\) is the number data points (channels) of the global average curve and \(K\) is the number of OSL components in the fitting model. If \(F_K\) falls below a preset threshold value (here, \(F_{threshold}\) = 150), the new fitting model with one additional component is apparently not significantly better than the K - 1 model. Mittelstraß (2019) showed that reasonable values for \(F_{threshold}\) are in the range of: \(50 < F_{threshold} < 300\). Parametrized for the current analysis is \(F_{threshold}\) = 150.

However, CW-OSL components with non-first-order kinetics, variations in the decay rates and too long measurement duration can lead to the detection of imaginary signal components, as Mittelstraß (2019) discussed in more detail. Therefore, the F-test outcome should be taken with care as over-fitting is still likely.

General remarks

This report was automatically generated by functions of the R package OSLdecomposition written and maintained by Dirk Mittelstraß (). This package is preferably used together with the R package Luminescence (link) by Kreutzer et al. (2012). For the dynamic creation of this HTML report, the R packages knitr and rmarkdown are used, see Xie (2015) and Xie et al. (2018). All diagrams are drawn with ggplot2 (Wickham 2016).

The data analysis method covered with this report was developed for CW-OSL SAR protocol measured quartz samples, see Murray and Wintle (2000). It might be also useful for the analysis of Al2O3 or feldspar samples measured with SAR-like protocols. You can use, share and publish this report and the containing results at will. But we demand to refer to the R package OSLdecomposition including its version number (21.2.15) if you publish the results in a peer-reviewed journal. Please include the following reference to your publication:

Mittelstraß, D., 2019. Decomposition of weak optically stimulated luminescence signals and its application in retrospective dosimetry at quartz, Master thesis, TU Dresden, Dresden.
https://iktp.tu-dresden.de/IKTP/pub/19/Dirk_Mittelstrass_Master.pdf
(reference will be replaced as soon as peer-reviewed publication is accepted)

We allow and encourage you to add the HTML file of this report to the electronical supplement of your publication.

References

Ardia, D., Mullen, K.M., Peterson, B.G., Ulrich, J., 2020. DEoptim: Differential Evolution in R.
https://CRAN.R-project.org/package=DEoptim

Bailey, R. M., Smith, B. W. and Rhodes, E. J., 1997. Partial bleaching and the decay form characteristics of quartz OSL, Radiation Measurements, 27(2), 123–136.
https://doi.org/10.1016/S1350-4487(96)00157-6

Bluszcz, A., Adamiec, G., 2006. Application of differential evolution to fitting OSL decay curves. Radiation Measurements 41, 886–891.
https://doi.org/10.1016/j.radmeas.2006.05.016

Durcan, J.A., Duller, G.A.T., 2011. The fast ratio: A rapid measure for testing the dominance of the fast component in the initial OSL signal from quartz. Radiation Measurements 46, 1065–1072.
https://doi.org/10.1016/j.radmeas.2011.07.016

Elzhov, T.V., Mullen, K.M., Spiess, A.-N., Bolker, B., 2016. minpack.lm: R Interface to the Levenberg-Marquardt Nonlinear Least-Squares Algorithm Found in MINPACK, Plus Support for Bounds.
https://CRAN.R-project.org/package=minpack.lm

Jain, M., Murray, A.S., Bøtter-Jensen, L., 2003. Characterisation of blue-light stimulated luminescence components in different quartz samples: implications for dose measurement. Radiation Measurements 37, 441–449.
https://doi.org/10.1016/S1350-4487(03)00052-0

Kreutzer, S., Schmidt, C., Fuchs, M.C., Dietze, M., Fuchs, M., 2012. Introducing an R package for luminescence dating analysis. Ancient TL 30.
http://ancienttl.org/ATL_30-1_2012/ATL_30-1_Kreutzer_p1-8.pdf

Mittelstraß D., Schmidt C., Beyer J., and Straessner A., 2019. Automated identification and separation of quartz CW-OSL signal components with R. talk presented at the Central European Conference on Luminescence and Trapped-Charge dating: DLED 2019, Bingen, Germany
http://luminescence.de/OSLdecomp_talk.pdf

Murray, A. S. and Wintle, A. G., 2000. Luminescence dating of quartz using an improved single-aliquot regenerative-dose protocol. Radiation Measurements 32
https://doi.org/10.1016/S1350-4487(99)00253-X

Price, K.V., Storn, R.M., Lampinen, J.A., 2006. Differential Evolution - A Practical Approach to Global Optimization, Natural Computing. Springer-Verlag.

Singarayer, J.S., Bailey, R.M., 2003. Further investigations of the quartz optically stimulated luminescence components using linear modulation. Radiation Measurements, Proceedings of the 10th international Conference on Luminescence and Electron-Spin Resonance Dating (LED 2002) 37, 451–458.
https://doi.org/10.1016/S1350-4487(03)00062-3

Wickham, H., 2016. ggplot2: elegant graphics for data analysis, Second edition. ed, Use R! Springer, Cham.
https://ggplot2.tidyverse.org/

Xie, Y., 2015. Dynamic documents with R and Knitr, Second edition. ed. CRC Press/Taylor & Francis, Boca Raton.
https://yihui.org/knitr/

Xie, Y., Allaire, J.J., Grolemund, G., 2018. R Markdown: the definitive guide. Taylor & Francis, CRC Press, Boca Raton.
https://bookdown.org/yihui/rmarkdown/

Script parameters
Settings
Analyzed data set data_set
Analyzed record type OSL
Maximum allowed components Kmax = 4
Threshold F-value Fthreshold = 150
Photoionisation cross section parameter
Stimulation wavelength 470 nm
Stimulation intensity 35 mW/cm²
Global curve properties
No. of input measurements 384
No. of input aliquots 24
Channel time \(\delta\)t = 0.1 s
Channels N = 200
Global curve length t = N\(\delta\)t = 20 s



Last major change in the script code: 2021-02-15 by D. Mittelstraß

Session info:

R version 4.0.3 (2020-10-10) Platform: i386-w64-mingw32/i386 (32-bit) Running under: Windows 10 x64 (build 19041)

Matrix products: default

attached base packages: [1] stats graphics grDevices utils datasets methods base

other attached packages: [1] scales_1.1.1 gridExtra_2.3 ggplot2_3.3.3
[4] knitr_1.31 kableExtra_1.3.1 Luminescence_0.9.10
[7] magrittr_2.0.1 OSLdecomposition_21-02-15

loaded via a namespace (and not attached): [1] Rcpp_1.0.6 lattice_0.20-41 tidyr_1.1.2 digest_0.6.27
[5] cellranger_1.1.0 R6_2.5.0 backports_1.2.1 evaluate_0.14
[9] httr_1.4.2 highr_0.8 pillar_1.4.7 rlang_0.4.10
[13] readxl_1.3.1 curl_4.3 rstudioapi_0.13 data.table_1.13.6 [17] car_3.0-10 raster_3.4-5 rmarkdown_2.6 labeling_0.4.2
[21] webshot_0.5.2 stringr_1.4.0 foreign_0.8-80 munsell_0.5.0
[25] broom_0.7.3 compiler_4.0.3 xfun_0.20 pkgconfig_2.0.3
[29] htmltools_0.5.1.1 tidyselect_1.1.0 tibble_3.0.5 rio_0.5.16
[33] codetools_0.2-16 viridisLite_0.3.0 crayon_1.3.4 dplyr_1.0.3
[37] withr_2.4.1 ggpubr_0.4.0 grid_4.0.3 DEoptim_2.2-5
[41] gtable_0.3.0 lifecycle_0.2.0 zip_2.1.1 carData_3.0-4
[45] stringi_1.5.3 farver_2.0.3 ggsignif_0.6.0 sp_1.4-5
[49] xml2_1.3.2 ellipsis_0.3.1 generics_0.1.0 vctrs_0.3.6
[53] cowplot_1.1.1 openxlsx_4.2.3 tools_4.0.3 forcats_0.5.0
[57] glue_1.4.2 purrr_0.3.4 hms_1.0.0 abind_1.4-5
[61] parallel_4.0.3 yaml_2.2.1 colorspace_2.0-0 rstatix_0.6.0
[65] rvest_0.3.6 minpack.lm_1.2-1 haven_2.3.1