The function analysis fading measurements and returns a fading rate including an error estimation. The function is not limited to standard fading measurements, as can be seen, e.g., Huntley and Lamothe 2001. Additionally, the density of recombination centres (rho') is estimated after Kars et al. 2008.

```
analyse_FadingMeasurement(object, structure = c("Lx", "Tx"),
signal.integral, background.integral, t_star = "half", n.MC = 100,
verbose = TRUE, plot = TRUE, plot.single = FALSE, ...)
```

object

'>RLum.Analysis (**required**):
input object with the measurement data. Alternatively, a list containing '>RLum.Analysis
objects or a data.frame with three columns
(x = LxTx, y = LxTx error, z = time since irradiation) can be provided.
Can also be a wide table, i.e. a data.frame with a number of colums divisible by 3
and where each triplet has the before mentioned column structure.

If data from multiple aliquots are provided please **see the details below** with regard to
Lx/Tx normalisation.

structure

character (*with default*):
sets the structure of the measurement data. Allowed are `'Lx'`

or `c('Lx','Tx')`

.
Other input is ignored

signal.integral

vector (**required**):
vector with the limits for the signal integral.
Not required if a `data.frame`

with LxTx values are provided.

background.integral

vector (**required**):
vector with the bounds for the background integral.
Not required if a `data.frame`

with LxTx values are provided.

t_star

character (*with default*):
method for calculating the time elasped since irradiaton. Options are:
`'half'`

, which is \(t_star := t_1 + (t_2 - t_1)/2\) (Auclair et al., 2003)
and `'end'`

, which takes the time between irradiation and the measurement step.
Default is `'half'`

n.MC

integer (*with default*):
number for Monte Carlo runs for the error estimation

verbose

logical (*with default*):
enables/disables verbose mode

plot

logical (*with default*):
enables/disables plot output

plot.single

logical (*with default*):
enables/disables single plot mode, i.e. one plot window per plot.
Alternatively a vector specifying the plot to be drawn, e.g.,
`plot.single = c(3,4)`

draws only the last two plots

...

(*optional*) further arguments that can be passed to internally used functions (see details)

An '>RLum.Results object is returned:

Slot: **@data**

OBJECT |
TYPE |
COMMENT |

`fading_results` |
`data.frame` |
results of the fading measurement in a table |

`fit` |
`lm` |
object returned by the used linear fitting function stats::lm |

`rho_prime` |
`data.frame` |
results of rho' estimation after Kars et al. 2008 |

`LxTx_table` |
`data.frame` |
Lx/Tx table, if curve data had been provided |

`irr.times` |
`integer` |
vector with the irradiation times in seconds |

Slot: **@info**

OBJECT |
`TYPE` |
`COMMENT` |

`call` |
`call` |
the original function call |

0.1.5 (2018-10-03 19:36:42)

Kreutzer, S., Burow, C. (2018). analyse_FadingMeasurement(): Analyse fading measurements and returns the fading rate per decade (g-value). Function version 0.1.5. 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

All provided output corresponds to the \(tc\) value obtained by this analysis. Additionally in the output object the g-value normalised to 2-days is provided. The output of this function can be passed to the function calc_FadingCorr.

**Fitting and error estimation**

For the fitting the function stats::lm is used without applying weights. For the error estimation all input values, except tc, as the precision can be consdiered as sufficiently high enough with regard to the underlying problem, are sampled assuming a normal distribution for each value with the value as the mean and the provided uncertainty as standard deviation.

**Density of recombination centres**

The density of recombination centres, expressed by the dimensionless variable rho', is estimated by fitting equation 5 in Kars et al. 2008 to the data. For the fitting the function stats::nls is used without applying weights. For the error estimation the same procedure as for the g-value is applied (see above).

**Multiple aliquots & Lx/Tx normalisation**

Be aware that this function will always normalise all Lx/Tx values by the Lx/Tx value of the
prompt measurement of the first aliquot. This implicitly assumes that there are no systematic
inter-aliquot variations in Lx/Tx values. If deemed necessary to normalise the Lx/Tx values
of each aliquot by its individual prompt measurement please do so **before** running
analyse_FadingMeasurement and provide the already normalised values for `object`

instead.

Auclair, M., Lamothe, M., Huot, S., 2003. Measurement of anomalous fading for feldpsar IRSL using SAR. Radiation Measurements 37, 487-492. doi:10.1016/S1350-4487(03)00018-0

Huntley, D.J., Lamothe, M., 2001. Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating. Canadian Journal of Earth Sciences 38, 1093-1106. doi:10.1139/cjes-38-7-1093

Kars, R.H., Wallinga, J., Cohen, K.M., 2008. A new approach towards anomalous fading correction for feldspar IRSL dating-tests on samples in field saturation. Radiation Measurements 43, 786-790. doi:10.1016/j.radmeas.2008.01.021

calc_OSLLxTxRatio, read_BIN2R, read_XSYG2R, extract_IrradiationTimes

# NOT RUN { ## load example data (sample UNIL/NB123, see ?ExampleData.Fading) data("ExampleData.Fading", envir = environment()) ##(1) get fading measurement data (here a three column data.frame) fading_data <- ExampleData.Fading$fading.data$IR50 ##(2) run analysis g_value <- analyse_FadingMeasurement( fading_data, plot = TRUE, verbose = TRUE, n.MC = 10) ##(3) this can be further used in the function ## to correct the age according to Huntley & Lamothe, 2001 results <- calc_FadingCorr( age.faded = c(100,2), g_value = g_value, n.MC = 10) # }