# CW2pHMi

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##### Transform a CW-OSL curve into a pHM-OSL curve via interpolation under hyperbolic modulation conditions

This function transforms a conventionally measured continuous-wave (CW) OSL-curve to a pseudo hyperbolic modulated (pHM) curve under hyperbolic modulation conditions using the interpolation procedure described by Bos & Wallinga (2012).

Keywords
manip
##### Usage
CW2pHMi(values, delta)
##### Arguments
values

'>RLum.Data.Curve or data.frame (required): '>RLum.Data.Curve or data.frame with measured curve data of type stimulation time (t) (values[,1]) and measured counts (cts) (values[,2]).

delta

vector (optional): stimulation rate parameter, if no value is given, the optimal value is estimated automatically (see details). Smaller values of delta produce more points in the rising tail of the curve.

##### Details

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

Internal transformation steps

(1) log(CW-OSL) values

(2) Calculate t' which is the transformed time: $$t' = t-(1/\delta)*log(1+\delta*t)$$

(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.

(6) Transform values using $$pHM(t) = (\delta*t/(1+\delta*t))*c*CW(t')$$ $$c = (1+\delta*P)/\delta*P$$ $$P = length(stimulation~period)$$

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

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

##### Value

The function returns the same data type as the input data type with the transformed curve values.

RLum.Data.Curve

 $CW2pHMi.x.t : transformed time values data.frame  $x : time $y.t : transformed count values $x.t : transformed time values

##### Note

According to Bos & Wallinga (2012), the number of extrapolated points should be limited to avoid artificial intensity data. If delta is provided manually and more than two points are extrapolated, a warning message is returned.

The function approx may produce some Inf and NaN data. The function tries to manually interpolate these values by calculating the mean using the adjacent channels. If two invalid values are succeeding, the values are removed and no further interpolation is attempted. In every case a warning message is shown.

##### Function version

0.2.2 (2018-01-21 17:22:38)

##### How to cite

Kreutzer, S. (2018). CW2pHMi(): Transform a CW-OSL curve into a pHM-OSL curve via interpolation under hyperbolic modulation conditions. Function version 0.2.2. In: Kreutzer, S., Burow, C., Dietze, M., Fuchs, M.C., Schmidt, C., Fischer, M., Friedrich, J. (2018). Luminescence: Comprehensive Luminescence Dating Data Analysis. R package version 0.8.6. https://CRAN.R-project.org/package=Luminescence

##### References

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

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.

CW2pLM, CW2pLMi, CW2pPMi, fit_LMCurve, lm, '>RLum.Data.Curve

• CW2pHMi
##### Examples
# NOT RUN {
##(1) - simple transformation

data(ExampleData.CW_OSL_Curve, envir = environment())

##transform values
values.transformed<-CW2pHMi(ExampleData.CW_OSL_Curve)

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

##(2) - load CW-OSL curve from BIN-file and plot transformed values

data(ExampleData.BINfileData, envir = environment())

##grep first CW-OSL curve from ALQ 1
,"ID"]

,"HIGH"]

,"NPOINTS"]

##combine curve to data set

curve<-data.frame(x = seq(curve.HIGH/curve.NPOINTS,curve.HIGH,
by = curve.HIGH/curve.NPOINTS),
y=unlist(CWOSL.SAR.Data@DATA[curve.ID]))

##transform values

curve.transformed <- CW2pHMi(curve)

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

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

data(ExampleData.CW_OSL_Curve, envir = environment())
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)

# }

Documentation reproduced from package Luminescence, version 0.8.6, License: GPL-3

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