fit_OSLLifeTimes function

Fitting and Deconvolution of OSL Lifetime Components

fit_OSLLifeTimes(
  object,
  tp = 0,
  signal_range = NULL,
  n.components = NULL,
  method_control = list(),
  plot = TRUE,
  plot_simple = FALSE,
  verbose = TRUE,
  ...
)

Arguments

• object: RLum.Data.Curve , RLum.Analysis , data.frame or matrix (required ): Input object containing the data to be analysed. All objects can be provided also as list for an automated processing. Please note: NA values are automatically removed and the dataset should comprise at least 5 data points (possibly more if n.components is set to a value greater than 1)
• tp: numeric (with default): option to account for the stimulation pulse width. For off-time measurements the default value is 0. tp has the same unit as the measurement data, e.g., µs. Please set this parameter carefully, if it all, otherwise you may heavily bias your fit results.
• signal_range: numeric (optional): allows to set a channel range, by default all channels are used, e.g. signal_range = c(2,100) considers only channels 2 to 100 and signal_range = c(2) considers only channels from channel 2 onwards.
• n.components: numeric (optional): Fix the number of components. If set the algorithm will try to fit the number of predefined components. If nothing is set, the algorithm will try to find the best number of components.
• method_control: list (optional): Named to allow a more fine control of the fitting process. See details for allowed options.
• plot: logical (with default): Enable/disable the plot output.
• plot_simple: logical (with default): Enable/disable the reduced plot output. If TRUE, no residual plot is shown, however, plot output can be combined using the standard R layout options, such as par(mfrow = c(2,2)).
• verbose: logical (with default): Enable/disable output to the terminal.
• ...: parameters passed to plot.default to control the plot output, supported are: main, xlab, ylab, log, xlim, ylim, col, lty, legend.pos, legend.text. If the input object is of type RLum.Analysis this arguments can be provided as a list .

Returns

---

[ NUMERICAL OUTPUT ]

---

‘RLum.Results’ -object

slot: @data

Element	Type	Description
$data	matrix	the final fit matrix
$start_matrix	matrix	the start matrix used for the fitting
$total_counts	integer	Photon count sum
$fit	nls	the fit object returned by minpack.lm::nls.lm

slot: @info

The original function call

---

[ TERMINAL OUTPUT ]

---

Terminal output is only shown of the argument verbose = TRUE.

(1) Start parameter and component adaption

Trave of the parameter adaptation process

(2) Fitting results (sorted by ascending tau)

The fitting results sorted by ascending tau value. Please note that if you access the nls fitting object, the values are not sorted.

(3) Further information

• The photon count sum

• Durbin-Watson residual statistic to assess whether the residuals are correlated, ideally the residuals should be not correlated at all. Rough measures are:

  D = 0: the residuals are systematically correlated

  D = 2: the residuals are randomly distributed

  D = 4: the residuals are systematically anti-correlated

You should be suspicious if D differs largely from 2.

---

[ PLOT OUTPUT ]

---

A plot showing the original data and the fit so far possible. The lower plot shows the residuals of the fit.

Details

The function intends to provide an easy access to pulsed optically stimulated luminescence (POSL) data, in order determine signal lifetimes. The fitting is currently optimised to work with the off-time flank of POSL measurements only. For the signal deconvolution, a differential evolution optimisation is combined with nonlinear least-square fitting following the approach by Bluszcz & Adamiec (2006).

Component deconvolution algorithm

The component deconvolution consists of two steps:

(1) Adaptation phase

In the adaptation phase the function tries to figure out the optimal and statistically justified number of signal components following roughly the approach suggested by Bluszcz & Adamiec (2006). In contrast to their work, for the optimisation by differential evolution here the package 'DEoptim' is used.

The function to be optimized has the form:

$$\chi^2 = \sum(w * (n_i/c - \sum(A_i * exp(-x/(tau_i + t_p))))^2)$$

with $w = 1$ for unweighted regression analysis (method_control = list(weights = FALSE)) or $w = c^2/n_i$ for weighted regression analysis. The default values is TRUE.

$$F = (\Delta\chi^2 / 2) / (\chi^2/(N - 2*m - 2))$$

(2) Final fitting

‘method_control’

Parameter	Type	Description
p	numeric	controls the probability for the F statistic reference values. For a significance level of 5 % a value of 0.95 (the default) should be added, for 1 %, a value of 0.99 is sufficient: 1 > p > 0 (cf. stats::FDist )
seed	numeric	set the seed for the random number generator, provide a value here to get reproducible results
DEoptim.trace	logical	enable/disable the tracing of the differential evolution (cf. DEoptim::DEoptim.control )
DEoptim.itermax	logical	control the number of the allowed generations (cf. DEoptim::DEoptim.control )
weights	logical	enable/disable the weighting for the start parameter estimation and fitting (see equations above). The default values is TRUE
nlsLM.trace	logical	enable/disable trace mode for the nls fitting ( minpack.lm::nlsLM ), can be used to identify convergence problems, default is FALSE
nlsLM.upper	logical	enable/disable upper parameter boundary, default is TRUE
nlsLM.lower	logical	enable/disable lower parameter boundary, default is TRUE

Function version

0.1.5

Examples

##load example data
data(ExampleData.TR_OSL, envir = environment())

##fit lifetimes (short run)
fit_OSLLifeTimes(
 object = ExampleData.TR_OSL,
 n.components = 1)

##long example
## Not run:

fit_OSLLifeTimes(
object = ExampleData.TR_OSL)
## End(Not run)

How to cite

Kreutzer, S., Schmidt, C., 2025. fit_OSLLifeTimes(): Fitting and Deconvolution of OSL Lifetime Components. Function version 0.1.5. In: Kreutzer, S., Burow, C., Dietze, M., Fuchs, M.C., Schmidt, C., Fischer, M., Friedrich, J., Mercier, N., Philippe, A., Riedesel, S., Autzen, M., Mittelstrass, D., Gray, H.J., Galharret, J., Colombo, M., Steinbuch, L., Boer, A.d., 2025. Luminescence: Comprehensive Luminescence Dating Data Analysis. R package version 1.0.1. https://r-lum.github.io/Luminescence/

References

Bluszcz, A., Adamiec, G., 2006. Application of differential evolution to fitting OSL decay curves. Radiation Measurements 41, 886-891. tools:::Rd_expr_doi("10.1016/j.radmeas.2006.05.016")

Durbin, J., Watson, G.S., 1950. Testing for Serial Correlation in Least Squares Regression: I. Biometrika 37, 409-21. doi:10.2307/2332391

Further reading

Hughes, I., Hase, T., 2010. Measurements and Their Uncertainties. Oxford University Press.

Storn, R., Price, K., 1997. Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces. Journal of Global Optimization 11, 341–359.

See Also

minpack.lm::nls.lm , DEoptim::DEoptim

Author(s)

Sebastian Kreutzer, Geography & Earth Sciences, Aberystwyth University, Christoph Schmidt, University of Bayreuth (Germany) , RLum Developer Team