CW2pPMi: Transform a CW-OSL curve into a pPM-OSL curve via interpolation under parabolic modulation conditions

Description

Transforms a conventionally measured continuous-wave (CW) OSL-curve into a pseudo parabolic modulated (pPM) curve under parabolic modulation conditions using the interpolation procedure described by Bos & Wallinga (2012).

Usage

CW2pPMi(values, P)

Arguments

values

data.frame (required): measured curve data of type stimulation time (t) (values[,1]) and measured counts (cts) (values[,2])

vector (optional): stimulation period in seconds, if no value is given, the optimal value is estimated automatically (see details). Greater values of P produce more points in the rising tail of the curve.

Value

Returns a data.frame with three columns:
rl{
$x : time $y.t : transformed count values $x.t : transformed time values $method : used method for the production of the new data points }

Details

The complete procedure of the transformation is given in Bos & Wallinga (2012). The input data.frame consists of two columns: time (t) and count values (CW(t))

Nomenclature

P = stimulation time (s) 1/P = stimulation rate (1/s)

Internal transformation steps

(1) log(CW-OSL) values

(2) Calculate t' which is the transformed time:

$t^{'} = (1 / 3) * (1 / P^{2}) t^{3}$

(3) Interpolate CW(t'), i.e. use the log(CW(t)) to obtain the count values for the transformed time (t'). Values beyond min(t) and max(t) produce NA values.

(4) Select all values for t' < min(t), i.e. values beyond the time resolution of t. Select the first two values of the transformed data set which contain no NA values and use these values for a linear fit using lm.

(5) Extrapolate values for t' < min(t) based on the previously obtained fit parameters. The extrapolation is limited to two values. Other values at the beginning of the transformed curve are set to 0.

(6) Transform values using

$p L M (t) = t^{2} / P^{2} * C W (t^{'})$

(7) Combine all values and truncate all values for t' > max(t)

The number of values for t' < min(t) depends on the stimulation period P. To avoid the production of too many artificial data at the raising tail of the determined pPM curve, it is recommended to use the automatic estimation routine for P, i.e. provide no value for P.

References

Bos, A.J.J. & Wallinga, J., 2012. How to visualize quartz OSL signal components. Radiation Measurements, 47, 752-758.

Further

Bulur, E., 1996. An Alternative Technique For Optically Stimulated Luminescence (OSL) Experiment. Radiation Measurements, 26, 701-709.

Bulur, E., 2000. A simple transformation for converting CW-OSL curves to LM-OSL curves. Radiation Measurements, 32, 141-145.

Examples

Run this code

##(1)
##load CW-OSL curve data
data(ExampleData.CW_OSL_Curve)

##transform values
values.transformed<-CW2pPMi(ExampleData.CW_OSL_Curve)

##plot
plot(values.transformed$x,values.transformed$y.t, log = "x")

##(2) - produce Fig. 4 from Bos & Wallinga (2012)

##load data
data(ExampleData.CW_OSL_Curve)
values<-CW_Curve.BosWallinga2012

##open plot area
plot(NA, NA,
     xlim=c(0.001,10),
     ylim=c(0,8000),
     ylab="pseudo OSL (cts/0.01 s)",
     xlab="t [s]",
     log="x",
     main="Fig. 4 - Bos & Wallinga (2012)", 
     )

values.t<-CW2pLMi(values, P=1/20)
lines(values[1:length(values.t[,1]),1],CW2pLMi(values, P=1/20)[,2], col="red" ,lwd=1.3)
text(0.03,4500,"LM", col="red" ,cex=.8)

values.t<-CW2pHMi(values, delta=40)
lines(values[1:length(values.t[,1]),1],CW2pHMi(values, delta=40)[,2], col="black", lwd=1.3)
text(0.005,3000,"HM", cex=.8)
 
values.t<-CW2pPMi(values, P=1/10)
lines(values[1:length(values.t[,1]),1],CW2pPMi(values, P=1/10)[,2], col="blue", lwd=1.3)
text(0.5,6500,"PM", col="blue" ,cex=.8)

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