# 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). ```r convert_CW2pHMi(values, delta) 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. ## Returns The function returns the same data type as the input data type with the transformed curve values. ‘RLum.Data.Curve’ ||| |:--|:--| |`$CW2pHMi.x.t`|: transformed time values| |`$CW2pHMi.method`|: used method for the production of the new data points| ‘data.frame’ ||| |:--|:--| |`$x`|: time| |`$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 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`. ## 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 0.2.3 ## Examples ```r ##(1) - simple transformation ##load CW-OSL curve data data(ExampleData.CW_OSL_Curve, envir = environment()) ##transform values values.transformed <- convert_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 ##load BINfile #BINfileData<-readBIN2R("[path to BIN-file]") data(ExampleData.BINfileData, envir = environment()) ##grep first CW-OSL curve from ALQ 1 curve.ID<-CWOSL.SAR.Data@METADATA[CWOSL.SAR.Data@METADATA[,"LTYPE"]=="OSL" & CWOSL.SAR.Data@METADATA[,"POSITION"]==1 ,"ID"] curve.HIGH<-CWOSL.SAR.Data@METADATA[CWOSL.SAR.Data@METADATA[,"ID"]==curve.ID[1] ,"HIGH"] curve.NPOINTS<-CWOSL.SAR.Data@METADATA[CWOSL.SAR.Data@METADATA[,"ID"]==curve.ID[1] ,"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[1]])) ##transform values curve.transformed <- convert_CW2pHMi(curve) ##plot curve plot(curve.transformed$x, curve.transformed$y.t, log = "x") ##(3) - produce Fig. 4 from Bos & Wallinga (2012) ##load data 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 <- convert_CW2pLMi(values, P = 1/20) lines(values[1:length(values.t[, 1]), 1], values.t[, 2], col="red" ,lwd=1.3) text(0.03,4500,"LM", col="red" ,cex=.8) values.t <- convert_CW2pHMi(values, delta = 40) lines(values[1:length(values.t[, 1]), 1], values.t[, 2], col="black", lwd=1.3) text(0.005,3000,"HM", cex=.8) values.t <- convert_CW2pPMi(values, P = 1/10) lines(values[1:length(values.t[, 1]), 1], values.t[, 2], col="blue", lwd=1.3) text(0.5,6500,"PM", col="blue" ,cex=.8) ``` ## How to cite Kreutzer, S., 2025. convert_CW2pHMi(): Transform a CW-OSL curve into a pHM-OSL curve via interpolation under hyperbolic modulation conditions. Function version 0.2.3. 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 1.1.1. https://r-lum.github.io/Luminescence/ ## References Bos, A.J.J. & Wallinga, J., 2012. How to visualize quartz OSL signal components. Radiation Measurements, 47, 752-758. Further Reading 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. ## See Also convert_CW2pLM , convert_CW2pLMi , convert_CW2pPMi , fit_LMCurve , lm , RLum.Data.Curve ## Author(s) Sebastian Kreutzer, Institute of Geography, Heidelberg University (Germany) Based on comments and suggestions from: Adrie J.J. Bos, Delft University of Technology, The Netherlands , RLum Developer Team

convert_CW2pHMi function