tgcd: Thermoluminescence glow curve deconvolution (tgcd)
In tgcd: Thermoluminescence Glow Curve Deconvolution
tgcd R Documentation
Thermoluminescence glow curve deconvolution (tgcd)
Description
Thermoluminescence glow curve deconvolution according to various first-order, second-order, general-order, and mixed-order empirical expressions.
Usage
tgcd(Sigdata, npeak, model = "g1", subBG = FALSE, pickp = "d2",
pickb = "d0", nstart = 60, kkf = 0.03, mdt = NULL, mwt = NULL,
mr = NULL, edit.inis = TRUE, inisPAR = NULL, inisBG = NULL,
hr = NULL, hwd = NULL, pod = NULL, plot = TRUE, outfile = NULL)
Arguments
Sigdata
matrix(required): a 2-column matrix, temperature values (in unit K) and thermoluminescence signal values are
stored in the first and second column, respectively
npeak
integer(required): number of glow peaks, the allowed maximum number of glow peaks is set equal to 13
model
character(with default): model used for glow curve deconvolution, "f1", "f2", and "f3" for first-order models, "s1",
"s2" for second-order models, "g1", "g2", "g3" for general-order models, "wo" and "lw" for the Wright Omega and the Lambert W functions,
"m1", "m2", and "m3" for the mixed-order models (see Details)
subBG
logical(with default): whether the user want to subtract the background during the deconvolution
pickp
character(with default): mode used for initialization of kinetic parameters if inisPAR=NULL,
"d0" and "d01" prompt the user to click with a mouse on the original and log-scale glow curves respectively to locate each glow peak,
"d1", "d2", "d3", and "d4" prompt the user to click with a mouse on the first-, second-, third-,
and fourth-derivative of the glow curve respectively to locate each glow peak
pickb
character(with default): mode used for initialization of background parameters if inisBG=NULL,
"d0" and "d01" prompt the user to click with a mouse on the original and log-scale glow curves respectively to initilize the background parameters
nstart
integer(with default): number of trials performed in a "trial-and-error" protocol, the upper limit is set equal to 10000
kkf
numeric(with default): factor controlling the range of values from which random starting parameters will be generated during
the "trial-and-error" protocol, 0<kkf<1. For example, if kkf=0.03 then kinetic parameters will be generated uniformly between
(1.0-kkf)*inisPAR and (1.0+kkf)*inisPAR and background parameters will be generated uniformly between
(1.0-kkf)*inisBG and (1.0+kkf)*inisBG
mdt
numeric(optional): allowed minimum distance between Tm values of glow peaks.
A larger mdt prevents the appearance of strongly overlapping peaks
mwt
numeric(optional): allowed maximum total half-width of deconvoluted glow peaks.
A smaller mwt prevents the appearance of glow peaks with large total half-width
mr
numeric(optional): allowed minimum resolution of glow peaks.
A larger mr prevents the appearance of strongly overlapping peaks
edit.inis
logical(with default): whether the user want to further modify, constrain, or fix
the initialized kinetic (and/or background) parameters through an automatically generated Dialog Table
inisPAR
matrix(optional): a matrix (3 or 4 columns) used for storing initial
kenetic parameters Im, E, Tm, b (or R, a) (see Examples)
inisBG
vector(optional): a 3-element vector containing initial background parameters
A, B, and C used for background subtraction (see Examples)
hr
numeric(optional): linear heating rate used for calculating the frequency factor
hwd
integer(with default): half width (length) of the segement used for Savitzky-Golay smoothing
pod
integer(with default): order of the polynomial used for Savitzky-Golay smoothing
plot
logical(with default): draw a plot according to the fitting result or not
outfile
character(optional): if specified, fitted signal values for each glow peak will be written to
a file named "outfile" in CSV format and saved to the current work directory
Details
Function tgcd is used for deconvolving thermoluminescence glow curves according to various kinetic models.
In the text below, I(T) is the thermoluminescence intensity as function of temperature T, E the activation energyin ev, k the Boltzmann constant in eV/k,
T the temperature in K with constant heating rate K/s, T_m the temperature at maximum thermoluminescence intensity in K,
I_m the maximum intensity, b is an extra parameter (the kinetic order) in application of a general-order model,
R is an extra parameter in application of the Lambert W (Wright Omega) function,
and \alpha is an extra parameter in application of the mixed-order models.
First-order glow peaks appear if the recombination probability (A_m) is greater than that of re-trapping (A_n) during excitation.
The three parameters describing a glow peak are: I_m, E, and T_m.
Three empirical expressions describing first-order glow peaks are available in function tgcd:
<1>The first type of first-order empirical expression (model="f1") is (Bos et al., 1993a)
I(T)=I_mexp(\frac{E}{kT_m}-\frac{E}{kT})exp[\frac{E}{kT_m}\alpha(\frac{E}{kT_m})-(\frac{T}{T_m})\alpha(\frac{E}{kT})exp(\frac{E}{kT_m}-\frac{E}{kT})]
where \alpha(x) is a quotient of 4th-order polynomials of the form
\alpha(x)=\frac{a_0+a_1x+a_2x^2+a_3x^3+x^4}{b_0+b_1x+b_2x^2+b_3x^3+x^4}
a_0=0.267773734, a_1=8.6347608925, a_2=8.059016973, a_3=8.5733287401,
b_0=3.9584969228, b_1=21.0996530827, b_2=25.6329561486, b_3=9.5733223454
<2>The second type of first-order empirical expression (model="f2") is (Kitis et al., 1998)
I(T)=I_mexp[1+\frac{E}{kT}\frac{T-T_m}{T_m}-\frac{T^2}{T_m^2}exp(\frac{E}{kT}\frac{T-T_m}{T_m})(1-\frac{2kT}{E})-\frac{2kT_m}{E}]
<3>The third type of first-order function fits a weibull function (model="f3") (Pagonis et al., 2001)
I(T)=2.713I_m(\frac{T-T_m}{b}+0.996)^{15}exp[-(\frac{T-T_m}{b}+0.996)^{16}]
where b=\sqrt{\frac{242.036T_m^3k^2}{(E+T_mk)^2-7T_m^2k^2}}
Second-order glow peaks appear if the re-trapping probability is comparable with or greater than that of recombination during excitation.
The three parameters describing a glow peak are the same as those of first-orders.
Two empirical expressions describing second-order glow peaks are available in function tgcd:
<4>The first type of second-order empirical expression (model="s1") is (Kitis et al., 1998)
I(T)=4I_mexp(\frac{E}{kT}\frac{T-T_m}{T_m})[\frac{T^2}{T_m^2}(1-\frac{2kT}{E})exp(\frac{E}{kT}\frac{T-T_m}{T_m})+1+\frac{2kT_m}{E}]^{-2}
<5>The second type of second-order function fit a logistic asymmetric function (model="s2") (Pagonis and Kitis, 2001)
I(T)=5.2973I_m[1+exp(-(\frac{T-T_m}{a_2}+0.38542))]^{-2.4702}exp[-(\frac{T-T_m}{a_2}+0.38542)]
where a_2=\sqrt{\frac{1.189T_m^4k^2}{E^2+4ET_mk}}
General-order glow peaks are produced in intermediate cases (neither of first-order, nor of second-order).
The four parameters describing a glow peak are: I_m, E, T_m, and b.
Three empirical expressions describing general-order glow peaks are available in function tgcd:
<6>The first type of general-order empirical expression (model="g1") is (Kitis et al., 1998)
I(T)=I_mb^{\frac{b}{b-1}}exp(\frac{E}{kT}\frac{T-T_m}{T_m})[(b-1)(1-\frac{2kT}{E})\frac{T^2}{T_m^2}exp(\frac{E}{kT}\frac{T-T_m}{T_m})+1+\frac{2kT_m(b-1)}{E}]^{-\frac{b}{b-1}}
<7>The second type of general-order empirical expression (model="g2") is (Gomez-Ros and Kitis, 2002)
I(T)=I_mexp(\frac{E}{kT_m}-\frac{E}{kT})[1+\frac{b-1}{b}\frac{E}{kT_m}(\frac{T}{T_m}exp(\frac{E}{kT_m}-\frac{E}{kT})F(\frac{E}{kT})-F(\frac{E}{kT_m}))]^{-\frac{b}{b-1}}
where F(x) is a rational approximation function of the form
F(x)=1-\frac{a_0+a_1x+x^2}{b_0+b_1x+x^2}
a_0=0.250621, a_1=2.334733, b_0=1.681534, b_1=3.330657
<8>The third type of general-order empirical expression (model="g3") is (Gomez-Ros and Kitis, 2002)
I(T)=I_mexp(\frac{E}{kT_m^2}(T-T_m))[\frac{1}{b}+\frac{b-1}{b}exp(\frac{E}{kT_m^2}(T-T_m))]^{-\frac{b}{b-1}}
One trap-one recombination (OTOR) model based semi-analytical expressions have also been applied to fit glow peaks,
by using either the Lambert W function (Kitis and Vlachos, 2013; Sadek et al., 2015; Kitis et al., 2016) or
the Wright Omega function (Singh and Gartia, 2013; 2014; 2015).
The four parameters describing a glow peak are: I_m, E, T_m, and R=\frac{A_n}{A_m}
(where A_n and A_m represent the retrapping and recombination probabilities, respectively).
Two analytical expressions describing the OTOR model are available in function tgcd:
<9>The semi-analytical expression derived using the Wright Omega function (R=\frac{A_n}{A_m}<1) can be described as (model="wo")
I(T)=I_mexp(-\frac{E}{kT}\frac{T_m-T}{T_m})\frac{\omega(Z_m)+[\omega(Z_m)]^2}{\omega(Z)+[\omega(Z)]^2}
where Z_m=\frac{R}{1-R}-log(\frac{1-R}{R})+\frac{Eexp(\frac{E}{kT_m})}{kT_m^2(1-1.05R^{1.26})}F(T_m,E),
and Z=\frac{R}{1-R}-log(\frac{1-R}{R})+\frac{Eexp(\frac{E}{kT_m})}{kT_m^2(1-1.05R^{1.26})}F(T,E),
<10.1>The semi-analytical expression derived using the Lambert W function for R=\frac{A_n}{A_m}<1 can be described as (model="lw")
I(T)=I_mexp(-\frac{E}{kT}\frac{T_m-T}{T_m})\frac{W(exp(Z_m))+[W(exp(Z_m))]^2}{W(exp(Z))+[W(exp(Z))]^2}
where Z_m=\frac{R}{1-R}-log(\frac{1-R}{R})+\frac{Eexp(\frac{E}{kT_m})}{kT_m^2(1-1.05R^{1.26})}F(T_m,E),
and Z=\frac{R}{1-R}-log(\frac{1-R}{R})+\frac{Eexp(\frac{E}{kT_m})}{kT_m^2(1-1.05R^{1.26})}F(T,E),
<10.2>The semi-analytical expression derived using the Lambert W function for R=\frac{A_n}{A_m}>1 can be described as (model="lw")
I(T)=I_mexp(-\frac{E}{kT}\frac{T_m-T}{T_m})\frac{W(-1,-exp(-Z_m))+[W(-1,-exp(-Z_m))]^2}{W(-1,-exp(-Z))+[W(-1,-exp(-Z))]^2}
where Z_m=|\frac{R}{1-R}|+log(|\frac{1-R}{R}|)+\frac{Eexp(\frac{E}{kT_m})}{kT_m^2(2.963-3.24R^{-0.74})}F(T_m,E),
and Z=|\frac{R}{1-R}|+log(|\frac{1-R}{R}|)+\frac{Eexp(\frac{E}{kT_m})}{kT_m^2(2.963-3.24R^{-0.74})}F(T,E)
F(T_m,E) and F(T,E) are described as follows
F(T_m,E)=T_mexp(-\frac{E}{kT_m})+\frac{E}{k}Ei(-\frac{E}{kT_m}),
F(T,E)=Texp(-\frac{E}{kT})+\frac{E}{k}Ei(-\frac{E}{kT})
where \omega(x) and Ei(x) are the wright Omega function and the exponential integral function for variable x, respectively.
W(x) and W(-1,x) are the principal and the second branches of the Lambert W function, respectively.
The Fortran 90 subroutine used for evaluating the Wright Omega function is transformed from the Matlab code provided by Andrew Horchler (https://github.com/horchler/wrightOmegaq).
The Fortran 90 subroutine (original Fortran 77 version by William Cody) used for evaluating the Lambert W function written by John Burkardt is available at
https://people.sc.fsu.edu/~jburkardt/f_src/toms743/toms743.f90.
The Fortran 90 subroutine used for evaluating the exponential integral function is written by John Burkardt (original Fortran 77 version by William Cody)
(https://people.sc.fsu.edu/~jburkardt/f_src/toms715/toms715.f90).
Mixed-order kinetic models introduce an extra parameter \alpha=\frac{n_0}{n_0+M} where n_0 is the initial filled concentration of the active traps and M
is the trap concentration of the thermally disconnected deep traps (Sunta et al., 2002). The four parameters describing a glow peak are: I_m, E, T_m, and \alpha.
Three empirical expressions describing mixed-order glow peaks are available in function tgcd:
<11>The first type of mixed-order empirical expression (model="m1") is (Kitis and Gomez-Ros, 2000)
I(T)=\frac{I_m[exp(\frac{1-\frac{2kT_m}{E}}{R_m})-\alpha]^2exp(\frac{E}{kT}\frac{T-T_m}{T_m})exp[\frac{T^2}{T_m^2R_m}exp(\frac{E}{kT}\frac{T-T_m}{T_m})
(1-\frac{2kT}{E})]}{exp(\frac{1-\frac{2kT_m}{E}}{R_m})[exp[\frac{T^2}{T_m^2R_m}exp(\frac{E}{kT}\frac{T-T_m}{T_m})(1-\frac{2kT}{E})]-\alpha]^2}
where R_m=\frac{A_m+\alpha}{A_m-\alpha} and A_m=exp(\frac{A_m-\alpha}{A_m+\alpha}(1-\frac{2kT_m}{E}))
<12>The second type of mixed-order empirical expression (model="m2") is (Gomez-Ros and Kitis, 2002)
I(T)=\frac{4I_mR_m^2exp(\frac{E}{kT_m}-\frac{E}{kT})exp[R_m\frac{E}{kT_m}(\frac{T}{T_m}exp(\frac{E}{kT_m}-\frac{E}{kT})F(\frac{E}{kT})-F(\frac{E}{kT_m}))]}
{(1+R_m)[exp[R_m\frac{E}{kT_m}(\frac{T}{T_m}exp(\frac{E}{kT_m}-\frac{E}{kT})F(\frac{E}{kT})-F(\frac{E}{kT_m}))]-(1-R_m)]^2}
where R_m=(1-\alpha)(1+0.2922\alpha-0.2783\alpha^2)
F(x)=1-\frac{a_0+a_1x+x^2}{b_0+b_1x+x^2}
a_0=0.250621, a_1=2.334733, b_0=1.681534, b_1=3.330657
<13>The third type of mixed-order empirical expression (model="m3") is (Vejnovic et al., 2008)
I(T)=\frac{I_m\alpha(2-l)^2exp[\frac{T^2}{T_m^2}(\frac{2}{l}-1)exp(\frac{E}{kT_m}\frac{T-T_m}{T_m})(1-\frac{2kT}{E})]exp(\frac{E}{kT_m}\frac{T-T_m}{T_m})}{
(l-1)[exp[\frac{T^2}{T_m^2}(\frac{2}{l}-1)exp(\frac{E}{kT_m}\frac{T-T_m}{T_m})(1-\frac{2kT}{E})]-\alpha]^2}
where \alpha=(l-1)exp[\frac{2-l}{l}(1-\frac{2kT_m}{E})]
The background will be subtracted using the following expression if subBG=TRUE (Horowitz and Yossian, 1995; Kitis et al., 2012)
I(T)=A+Bexp(\frac{T}{C})
where A, B, and C are positive parameters to be optimized.
The procedure minimizes the objective:
fcn=\sum_{i=1}^n |y_i^o-y_i^f|, i=1,...,n
where y_i^o and y_i^f denote the i-th observed and fitted signal value, respectively,
and n indicates the number of data points.
The Levenberg-Marquardt algorithm (More, 1978) (minpack: https://netlib.org/minpack/, original Fortran 77 version by Jorge More, Burton Garbow, Kenneth Hillstrom.
Fortran 90 version by John Burkardt https://people.sc.fsu.edu/~jburkardt/f_src/minpack/minpack.f90) was modified so as to supports constraints and fixes of parameters.
A "trial-and-error" protocol with starting values generated uniformly around the given starting parameters inisPAR and inisBG is performed
repeatedly to search the optimal parameters that give a minimum Figure Of Merit (FOM) value (Balian and Eddy, 1977).
Kinetic parameters can be initialized by the user through argument inisPAR or by clicking with a mouse on
the plot of the thermoluminescence glow curve showing peak maxima if inisPAR=NULL.
Background parameters can be initialized by the user through argument inisBG or by clicking with a mouse on
the plot of the thermoluminescence glow curve to select 4 data points if inisBG=NULL.
Parameters can be interactively constrained and fixed by modifying the following elements in a automatically
generated Dialog Table if edit.inis=TRUE:
(1) INTENS[min,max,ini,fix]: lower and upper bounds, starting and fixing values of I_m
(2) ENERGY[min,max,ini,fix]: lower and upper bounds, starting and fixing values of E
(3) TEMPER[min,max,ini,fix]: lower and upper bounds, starting and fixing values of T_m
(4) bValue[min,max,ini,fix]: lower and upper bounds, starting and fixing values of b in the general-order model
(5) rValue[min,max,ini,fix]: lower and upper bounds, starting and fixing values of R in the OTOR model
(6) aValue[min,max,ini,fix]: lower and upper bounds, starting and fixing values of \alpha in the mixed-order model
(7) BG[min,max,ini,fix]: lower and upper bounds, starting and fixing values of background parameters A, B, and C
Value
Return an invisible list containing the following elements:
comp.sig
calculated signal values for each glow peak
residuals
calculated residual values
pars
optimized parameters stored in a matrix
BGpars
optimized background parameters, it returns NULL if subBG=FALSE
ff
calculated frequency factors, it returns NULL if hr=NULL
sp
parameters used for describing the shape of a glow peak, see function simPeak for details
resolution
resolutions of optimized glow peaks calculated after Kitis and Pagonis (2019), it returns NULL if npeak=1
SSR
Squared Sum of Residuals
RCS
Reduced Chi-Square value
R2
squared "pearson" correlation between observed and fitted signals
FOM
Figure Of Merit value calculated after Balian and Eddy (1977)
Note
Function tgcd analyzes only thermoluminescence glow curves recorded with linear heating function (LHF) profile.
The model to be optimized should not be underdetermined. This means that the number of data points (n_d) should exceed the number of parameters (n_2).
If it is not NULL the argument inisPAR, the procedure used for initializing kinetic parameters by clicking with a mouse will not be triggered.
Similarly, if it is not NULL the argment inisBG, the procedure used for initializing background parameters by clicking with a mouse will not be triggered.
The user is advocated to use mwt, mdt, and mr to specify the allowed maximum total half-width,
the allowed minimum distance, and the allowed minimum resolution respectively to resolve seriously overlapped glow peaks during the trial-and-error protocol.
Adrie J.J. Bos is appreciated for providing the reference glow curves of the GLOCANIN project to test this routine.
Amr M. Sadek is thanked for providing the Matlab code implementing the Lambert W (Wright Omega) function for reference.
George Kitis is appreciated for giving some useful suggestions to improve the program and providing many experimentally measured thermoluminescence glow curves to check the routine.
References
Balian HG, Eddy NW, 1977. Figure-of-merit (FOM), an improved criterion over the normalized chi-squared test for assessing goodness-of-fit of gamma-ray spectral peaks.
Nuclear and Instruments Methods, 145: 389-395.
Bos AJJ, Piters TM, Gomez-Ros JM, Delgado A, 1993a. An intercomparison of glow curve analysis computer programs.
IRI-CIEMAT Report, 131-93-005.
Gomez-Ros JM, Kitis G, 2002. Computerised glow curve deconvolution using general and mixed order kinetics.
Radiation Protection Dosimetry, 101(1-4): 47-52.
Horowitz YS, Yossian D, 1995. Computerized glow curve deconvolution: application to thermoluminescence dosimetry.
Radiation Protection Dosimetry, 60: 1-114.
Kitis G, Carinou E, Askounis P, 2012. Glow-curve de-convolution analysis of TL glow-curve from constant temperature hot gas TLD readers.
Radiation Measurements, 47: 258-265.
Kitis G, Gomes-Ros JM, 2000. Thermoluminescence glow-curve deconvolution functions for mixed order of kinetics and continuous trap distribution.
Nuclear Instruments and Methods in Physics Research A, 440: 224-231.
Kitis G, Gomes-Ros JM, Tuyn JWN, 1998. Thermoluminescence glow curve deconvolution functions for first, second and general orders of kinetics.
Journal of Physics D: Applied Physics, 31(19): 2636-2641.
Kitis G, Pagonis V, 2019. On the resolution of overlapping peaks in complex thermoluminescence glow curves.
Nuclear Instruments and Methods in Physics Research, A, 913: 78-84.
Kitis G, Polymeris GS, Pagonis V, 2019. Stimulated luminescence emission: From phenomenological models to master analytical equations.
Applied Radiation and Isotopes, 153: 108797.
Kitis G, Polymeris GS, Sfampa IK, Prokic M, Meric N, Pagonis V, 2016. Prompt isothermal decay of thermoluminescence in MgB4O7:Dy, Na and LiB4O7:Cu, In dosimeters.
Radiation Measurements, 84: 15-25.
Kitis G, Vlachos ND, 2013. General semi-analytical expressions for TL, OSL and other luminescence stimulation modes derived from the OTOR model using the Lambert W-function.
Radiation Measurements, 48: 47-54.
More JJ, 1978. "The Levenberg-Marquardt algorithm: implementation and theory," in Lecture Notes in Mathematics: Numerical Analysis, Springer-Verlag: Berlin. 105-116.
Pagonis V, Mian SM, Kitis G, 2001. Fit of first order thermoluminescence glow peaks using the weibull distribution function.
Radiation Protection Dosimetry, 93(1): 11-17.
Pagonis V, Kitis G, 2001. Fit of second order thermoluminescence glow peaks using the logistic distribution function.
Radiation Protection Dosimetry, 95(3): 225-229.
Sadek AM, Eissa HM, Basha AM, Carinou E, Askounis P, Kitis G, 2015. The deconvolution of thermoluminescence glow-curves using general expressions
derived from the one trap-one recombination (OTOR) level model. Applied Radiation and Isotopes, 95: 214-221.
Singh LL, Gartia RK, 2013. Theoretical derivation of a simplified form of the OTOR/GOT differential equation.
Radiation Measurements, 59: 160-164.
Singh LL, Gartia RK, 2014. Glow-curve deconvolution of thermoluminescence curves in the simplified OTOR equation using the Hybrid Genetic Algorithm.
Nuclear Instruments and Methods in Physics Research B, 319: 39-43.
Singh LL, Gartia RK, 2015. Derivation of a simplified OSL OTOR equation using Wright Omega function and its application.
Nuclear Instruments and Methods in Physics Research B, 346: 45-52.
Sunta CM, Ayta WEF, Chubaci JFD, Watanabe S, 2002. General order and mixed order of thermoluminescence glow curves-a comparison.
Radiation Measurements, 35: 47-57.
Vejnovic Z, Pavlovic MB, Davidovi M, 2008. Thermoluminescence glow curve deconvolution function for the mixed-order kinetics.
Radiation Measurements, 43: 1325-1330.
Further reading
Afouxenidis D, Polymeris GS, Tsirliganis NC, Kitis G., 2011. Computerised curve deconvolution of TL/OSL curves using a popular spreadsheet program.
Radiation Protection Dosimetry, 1-8.
Bos AJJ, Piters TM, Gomez Ros JM, Delgado A, 1993b. An intercomparison of glow curve analysis computer programs: I. Synthetic glow curves.
Radiation Protection Dosimetry, 47(1-4), 473-477.
Chung KS, Choe HS, Lee JI, Kim JL, Chang SY, 2005. A computer program for the deconvolution of thermoluminescence glow curves.
Radiation Protection Dosimetry, 115(1-4): 345-349.
Delgado A, Gomez-Ros JM, 2001. Computerised glow curve analysis: a tool for routine thermoluminescence dosimetry.
Radiation Protection Dosimetry, 96(1-3): 127-132.
El-Hafez AI, Yasin MN, Sadek AM, 2011. GCAFIT-A new tool for glow curve analysis in thermoluminescence nanodosimetry.
Nuclear Instruments and Methods in Physics Research A, 637: 158-163.
Espinosa G, Castano VM, 1991. Automated derivative analysis of thermoluminescence glow curves.
Applied Radiation and Isotopes, 42(4): 377-381.
Harvey JA, Rodrigues ML, Kearfott JK, 2011. A computerized glow curve analysis (GCA) method for WinREMS thermoluminescent dosimeter data using MATLAB.
Applied Radiation and Isotopes, 69(9):1282-1286.
Horowitz YS, Moscovitch M, 2012. Highlights and pitfalls of 20 years of application of computerised glow curve ananlysis to thermoluminescence research and dosimetry.
Radiation Protection Dosimetry, 1-22.
Horowitz Y, Delgado A, Pradhan AS, Yoder RC, 2002. Topics under debate: the use of computerised glow curve analysis will optimise personal thermoluminescence dosimetry.
Radiation Protection Dosimetry, 102(3): 269-277.
Karmakar M, Bhattacharyya S, Sarkar A, Mazumdar PS, Singh SD, 2017. Analysis of thermoluminescence glow curves using derivatives of different orders.
Radiation Protection Dosimetry, 1-10.
Kiisk V, 2013. Deconvolution and simulation of thermoluminescence glow curves with Mathcad.
Radiation Protection Dosimetry, 156(3): 261-267.
Pagonis V, Kitis G, Furetta C, 2006. Numerical and practical exercises in thermoluminescence.
Springer Science & Business Media.
Puchalska M, Bilski P, 2006. GlowFit-a new tool for thermoluminescence glow-curve deconvolution.
Radiation Measurements, 41(6): 659-664.
Sadek AM, 2013. Test of the accuracy of the computerized glow curve deconvolution algorithm for the analysis of thermoluminescence glow curves.
Nuclear Instruments and Methods in Physics Research A, 712: 56-61.
Sadek AM, Kitis G., 2018. Impact of non-fulfillment of the super position principle on the analysis of thermoluminescence glow-curve.
Radiation Measurements, 116: 14-23.
Singh TB, Rey L, Gartia RK, 2011. Applications of PeakFit software in thermoluminescence studies.
Indian Journal of Pure & Applied Physics, 49: 297-302.
Sunta CM, 2015. Unraveling thermoluminescence. Springer India.
See Also
simPeak; simqOTOR; savgol
Examples
# Load the data.
data(Refglow)
data(Kitis)
# (1) Deconvolution of a glow curve using 4 peaks (no background subtraction) with
# the Wright Omega function using specified initial kinetic parameters.
knPars <-
cbind(c(400, 550, 850, 1600), # Im
c(1.4, 1.5, 1.6, 2), # E
c(420, 460, 480, 510), # Tm
c(0.1, 0.1, 0.1, 0.1)) # R
dd1 <- tgcd(Refglow$x002, npeak=4, model="wo",
inisPAR=knPars, nstart=10, edit.inis=FALSE)
head(dd1$comp.sig)
dd1$pars
dd1$sp
dd1$FOM
# (2) Deconvolution of a glow curve using 5 peaks (with background subtraction) with
# a mixed-order model using user-supplied intial kinetic and background parameters.
knPars <-
cbind(c(46829.06, 187942.43, 121876.22, 110390.55, 67978.33), #Im
c(1.17, 1.14, 1.57, 0.77, 1.31), # E
c(369.86, 400.69, 428.51, 482.41, 537.28), # Tm
c(0.75, 0.81, 0.92, 0.001, 0.29)) # a
bgPars <- c(1, 10, 100) # A, B, C.
dd2 <- tgcd(Kitis$x009, npeak=5, model="m1", subBG=TRUE,
inisPAR=knPars, inisBG=bgPars, nstart=10, edit.inis=FALSE)
dd2$residual
dd2$SSR
dd2$R2
dd2$BGpars
tgcd documentation built on Sept. 8, 2023, 6:10 p.m.
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| tgcd | R Documentation |
Thermoluminescence glow curve deconvolution (tgcd)
Description
Thermoluminescence glow curve deconvolution according to various first-order, second-order, general-order, and mixed-order empirical expressions.
Usage
tgcd(Sigdata, npeak, model = "g1", subBG = FALSE, pickp = "d2",
pickb = "d0", nstart = 60, kkf = 0.03, mdt = NULL, mwt = NULL,
mr = NULL, edit.inis = TRUE, inisPAR = NULL, inisBG = NULL,
hr = NULL, hwd = NULL, pod = NULL, plot = TRUE, outfile = NULL)
Arguments
Sigdata |
matrix(required): a |
npeak |
integer(required): number of glow peaks, the allowed maximum number of glow peaks is set equal to 13 |
model |
character(with default): model used for glow curve deconvolution, |
subBG |
logical(with default): whether the user want to subtract the background during the deconvolution |
pickp |
character(with default): mode used for initialization of kinetic parameters if |
pickb |
character(with default): mode used for initialization of background parameters if |
nstart |
integer(with default): number of trials performed in a "trial-and-error" protocol, the upper limit is set equal to 10000 |
kkf |
numeric(with default): factor controlling the range of values from which random starting parameters will be generated during
the "trial-and-error" protocol, |
mdt |
numeric(optional): allowed minimum distance between |
mwt |
numeric(optional): allowed maximum total half-width of deconvoluted glow peaks.
A smaller |
mr |
numeric(optional): allowed minimum resolution of glow peaks.
A larger |
edit.inis |
logical(with default): whether the user want to further modify, constrain, or fix the initialized kinetic (and/or background) parameters through an automatically generated Dialog Table |
inisPAR |
matrix(optional): a matrix ( |
inisBG |
vector(optional): a 3-element vector containing initial background parameters
|
hr |
numeric(optional): linear heating rate used for calculating the frequency factor |
hwd |
integer(with default): half width (length) of the segement used for Savitzky-Golay smoothing |
pod |
integer(with default): order of the polynomial used for Savitzky-Golay smoothing |
plot |
logical(with default): draw a plot according to the fitting result or not |
outfile |
character(optional): if specified, fitted signal values for each glow peak will be written to
a file named |
Details
Function tgcd is used for deconvolving thermoluminescence glow curves according to various kinetic models.
In the text below, I(T) is the thermoluminescence intensity as function of temperature T, E the activation energyin ev, k the Boltzmann constant in eV/k,
T the temperature in K with constant heating rate K/s, T_m the temperature at maximum thermoluminescence intensity in K,
I_m the maximum intensity, b is an extra parameter (the kinetic order) in application of a general-order model,
R is an extra parameter in application of the Lambert W (Wright Omega) function,
and \alpha is an extra parameter in application of the mixed-order models.
First-order glow peaks appear if the recombination probability (A_m) is greater than that of re-trapping (A_n) during excitation.
The three parameters describing a glow peak are: I_m, E, and T_m.
Three empirical expressions describing first-order glow peaks are available in function tgcd:
<1>The first type of first-order empirical expression (model="f1") is (Bos et al., 1993a)
I(T)=I_mexp(\frac{E}{kT_m}-\frac{E}{kT})exp[\frac{E}{kT_m}\alpha(\frac{E}{kT_m})-(\frac{T}{T_m})\alpha(\frac{E}{kT})exp(\frac{E}{kT_m}-\frac{E}{kT})]
where \alpha(x) is a quotient of 4th-order polynomials of the form
\alpha(x)=\frac{a_0+a_1x+a_2x^2+a_3x^3+x^4}{b_0+b_1x+b_2x^2+b_3x^3+x^4}
a_0=0.267773734, a_1=8.6347608925, a_2=8.059016973, a_3=8.5733287401,
b_0=3.9584969228, b_1=21.0996530827, b_2=25.6329561486, b_3=9.5733223454
<2>The second type of first-order empirical expression (model="f2") is (Kitis et al., 1998)
I(T)=I_mexp[1+\frac{E}{kT}\frac{T-T_m}{T_m}-\frac{T^2}{T_m^2}exp(\frac{E}{kT}\frac{T-T_m}{T_m})(1-\frac{2kT}{E})-\frac{2kT_m}{E}]
<3>The third type of first-order function fits a weibull function (model="f3") (Pagonis et al., 2001)
I(T)=2.713I_m(\frac{T-T_m}{b}+0.996)^{15}exp[-(\frac{T-T_m}{b}+0.996)^{16}]
where b=\sqrt{\frac{242.036T_m^3k^2}{(E+T_mk)^2-7T_m^2k^2}}
Second-order glow peaks appear if the re-trapping probability is comparable with or greater than that of recombination during excitation.
The three parameters describing a glow peak are the same as those of first-orders.
Two empirical expressions describing second-order glow peaks are available in function tgcd:
<4>The first type of second-order empirical expression (model="s1") is (Kitis et al., 1998)
I(T)=4I_mexp(\frac{E}{kT}\frac{T-T_m}{T_m})[\frac{T^2}{T_m^2}(1-\frac{2kT}{E})exp(\frac{E}{kT}\frac{T-T_m}{T_m})+1+\frac{2kT_m}{E}]^{-2}
<5>The second type of second-order function fit a logistic asymmetric function (model="s2") (Pagonis and Kitis, 2001)
I(T)=5.2973I_m[1+exp(-(\frac{T-T_m}{a_2}+0.38542))]^{-2.4702}exp[-(\frac{T-T_m}{a_2}+0.38542)]
where a_2=\sqrt{\frac{1.189T_m^4k^2}{E^2+4ET_mk}}
General-order glow peaks are produced in intermediate cases (neither of first-order, nor of second-order).
The four parameters describing a glow peak are: I_m, E, T_m, and b.
Three empirical expressions describing general-order glow peaks are available in function tgcd:
<6>The first type of general-order empirical expression (model="g1") is (Kitis et al., 1998)
I(T)=I_mb^{\frac{b}{b-1}}exp(\frac{E}{kT}\frac{T-T_m}{T_m})[(b-1)(1-\frac{2kT}{E})\frac{T^2}{T_m^2}exp(\frac{E}{kT}\frac{T-T_m}{T_m})+1+\frac{2kT_m(b-1)}{E}]^{-\frac{b}{b-1}}
<7>The second type of general-order empirical expression (model="g2") is (Gomez-Ros and Kitis, 2002)
I(T)=I_mexp(\frac{E}{kT_m}-\frac{E}{kT})[1+\frac{b-1}{b}\frac{E}{kT_m}(\frac{T}{T_m}exp(\frac{E}{kT_m}-\frac{E}{kT})F(\frac{E}{kT})-F(\frac{E}{kT_m}))]^{-\frac{b}{b-1}}
where F(x) is a rational approximation function of the form
F(x)=1-\frac{a_0+a_1x+x^2}{b_0+b_1x+x^2}
a_0=0.250621, a_1=2.334733, b_0=1.681534, b_1=3.330657
<8>The third type of general-order empirical expression (model="g3") is (Gomez-Ros and Kitis, 2002)
I(T)=I_mexp(\frac{E}{kT_m^2}(T-T_m))[\frac{1}{b}+\frac{b-1}{b}exp(\frac{E}{kT_m^2}(T-T_m))]^{-\frac{b}{b-1}}
One trap-one recombination (OTOR) model based semi-analytical expressions have also been applied to fit glow peaks,
by using either the Lambert W function (Kitis and Vlachos, 2013; Sadek et al., 2015; Kitis et al., 2016) or
the Wright Omega function (Singh and Gartia, 2013; 2014; 2015).
The four parameters describing a glow peak are: I_m, E, T_m, and R=\frac{A_n}{A_m}
(where A_n and A_m represent the retrapping and recombination probabilities, respectively).
Two analytical expressions describing the OTOR model are available in function tgcd:
<9>The semi-analytical expression derived using the Wright Omega function (R=\frac{A_n}{A_m}<1) can be described as (model="wo")
I(T)=I_mexp(-\frac{E}{kT}\frac{T_m-T}{T_m})\frac{\omega(Z_m)+[\omega(Z_m)]^2}{\omega(Z)+[\omega(Z)]^2}
where Z_m=\frac{R}{1-R}-log(\frac{1-R}{R})+\frac{Eexp(\frac{E}{kT_m})}{kT_m^2(1-1.05R^{1.26})}F(T_m,E),
and Z=\frac{R}{1-R}-log(\frac{1-R}{R})+\frac{Eexp(\frac{E}{kT_m})}{kT_m^2(1-1.05R^{1.26})}F(T,E),
<10.1>The semi-analytical expression derived using the Lambert W function for R=\frac{A_n}{A_m}<1 can be described as (model="lw")
I(T)=I_mexp(-\frac{E}{kT}\frac{T_m-T}{T_m})\frac{W(exp(Z_m))+[W(exp(Z_m))]^2}{W(exp(Z))+[W(exp(Z))]^2}
where Z_m=\frac{R}{1-R}-log(\frac{1-R}{R})+\frac{Eexp(\frac{E}{kT_m})}{kT_m^2(1-1.05R^{1.26})}F(T_m,E),
and Z=\frac{R}{1-R}-log(\frac{1-R}{R})+\frac{Eexp(\frac{E}{kT_m})}{kT_m^2(1-1.05R^{1.26})}F(T,E),
<10.2>The semi-analytical expression derived using the Lambert W function for R=\frac{A_n}{A_m}>1 can be described as (model="lw")
I(T)=I_mexp(-\frac{E}{kT}\frac{T_m-T}{T_m})\frac{W(-1,-exp(-Z_m))+[W(-1,-exp(-Z_m))]^2}{W(-1,-exp(-Z))+[W(-1,-exp(-Z))]^2}
where Z_m=|\frac{R}{1-R}|+log(|\frac{1-R}{R}|)+\frac{Eexp(\frac{E}{kT_m})}{kT_m^2(2.963-3.24R^{-0.74})}F(T_m,E),
and Z=|\frac{R}{1-R}|+log(|\frac{1-R}{R}|)+\frac{Eexp(\frac{E}{kT_m})}{kT_m^2(2.963-3.24R^{-0.74})}F(T,E)
F(T_m,E) and F(T,E) are described as follows
F(T_m,E)=T_mexp(-\frac{E}{kT_m})+\frac{E}{k}Ei(-\frac{E}{kT_m}),
F(T,E)=Texp(-\frac{E}{kT})+\frac{E}{k}Ei(-\frac{E}{kT})
where \omega(x) and Ei(x) are the wright Omega function and the exponential integral function for variable x, respectively.
W(x) and W(-1,x) are the principal and the second branches of the Lambert W function, respectively.
The Fortran 90 subroutine used for evaluating the Wright Omega function is transformed from the Matlab code provided by Andrew Horchler (https://github.com/horchler/wrightOmegaq).
The Fortran 90 subroutine (original Fortran 77 version by William Cody) used for evaluating the Lambert W function written by John Burkardt is available at
https://people.sc.fsu.edu/~jburkardt/f_src/toms743/toms743.f90.
The Fortran 90 subroutine used for evaluating the exponential integral function is written by John Burkardt (original Fortran 77 version by William Cody)
(https://people.sc.fsu.edu/~jburkardt/f_src/toms715/toms715.f90).
Mixed-order kinetic models introduce an extra parameter \alpha=\frac{n_0}{n_0+M} where n_0 is the initial filled concentration of the active traps and M
is the trap concentration of the thermally disconnected deep traps (Sunta et al., 2002). The four parameters describing a glow peak are: I_m, E, T_m, and \alpha.
Three empirical expressions describing mixed-order glow peaks are available in function tgcd:
<11>The first type of mixed-order empirical expression (model="m1") is (Kitis and Gomez-Ros, 2000)
I(T)=\frac{I_m[exp(\frac{1-\frac{2kT_m}{E}}{R_m})-\alpha]^2exp(\frac{E}{kT}\frac{T-T_m}{T_m})exp[\frac{T^2}{T_m^2R_m}exp(\frac{E}{kT}\frac{T-T_m}{T_m})
(1-\frac{2kT}{E})]}{exp(\frac{1-\frac{2kT_m}{E}}{R_m})[exp[\frac{T^2}{T_m^2R_m}exp(\frac{E}{kT}\frac{T-T_m}{T_m})(1-\frac{2kT}{E})]-\alpha]^2}
where R_m=\frac{A_m+\alpha}{A_m-\alpha} and A_m=exp(\frac{A_m-\alpha}{A_m+\alpha}(1-\frac{2kT_m}{E}))
<12>The second type of mixed-order empirical expression (model="m2") is (Gomez-Ros and Kitis, 2002)
I(T)=\frac{4I_mR_m^2exp(\frac{E}{kT_m}-\frac{E}{kT})exp[R_m\frac{E}{kT_m}(\frac{T}{T_m}exp(\frac{E}{kT_m}-\frac{E}{kT})F(\frac{E}{kT})-F(\frac{E}{kT_m}))]}
{(1+R_m)[exp[R_m\frac{E}{kT_m}(\frac{T}{T_m}exp(\frac{E}{kT_m}-\frac{E}{kT})F(\frac{E}{kT})-F(\frac{E}{kT_m}))]-(1-R_m)]^2}
where R_m=(1-\alpha)(1+0.2922\alpha-0.2783\alpha^2)
F(x)=1-\frac{a_0+a_1x+x^2}{b_0+b_1x+x^2}
a_0=0.250621, a_1=2.334733, b_0=1.681534, b_1=3.330657
<13>The third type of mixed-order empirical expression (model="m3") is (Vejnovic et al., 2008)
I(T)=\frac{I_m\alpha(2-l)^2exp[\frac{T^2}{T_m^2}(\frac{2}{l}-1)exp(\frac{E}{kT_m}\frac{T-T_m}{T_m})(1-\frac{2kT}{E})]exp(\frac{E}{kT_m}\frac{T-T_m}{T_m})}{
(l-1)[exp[\frac{T^2}{T_m^2}(\frac{2}{l}-1)exp(\frac{E}{kT_m}\frac{T-T_m}{T_m})(1-\frac{2kT}{E})]-\alpha]^2}
where \alpha=(l-1)exp[\frac{2-l}{l}(1-\frac{2kT_m}{E})]
The background will be subtracted using the following expression if subBG=TRUE (Horowitz and Yossian, 1995; Kitis et al., 2012)
I(T)=A+Bexp(\frac{T}{C})
where A, B, and C are positive parameters to be optimized.
The procedure minimizes the objective:
fcn=\sum_{i=1}^n |y_i^o-y_i^f|, i=1,...,n
where y_i^o and y_i^f denote the i-th observed and fitted signal value, respectively,
and n indicates the number of data points.
The Levenberg-Marquardt algorithm (More, 1978) (minpack: https://netlib.org/minpack/, original Fortran 77 version by Jorge More, Burton Garbow, Kenneth Hillstrom.
Fortran 90 version by John Burkardt https://people.sc.fsu.edu/~jburkardt/f_src/minpack/minpack.f90) was modified so as to supports constraints and fixes of parameters.
A "trial-and-error" protocol with starting values generated uniformly around the given starting parameters inisPAR and inisBG is performed
repeatedly to search the optimal parameters that give a minimum Figure Of Merit (FOM) value (Balian and Eddy, 1977).
Kinetic parameters can be initialized by the user through argument inisPAR or by clicking with a mouse on
the plot of the thermoluminescence glow curve showing peak maxima if inisPAR=NULL.
Background parameters can be initialized by the user through argument inisBG or by clicking with a mouse on
the plot of the thermoluminescence glow curve to select 4 data points if inisBG=NULL.
Parameters can be interactively constrained and fixed by modifying the following elements in a automatically
generated Dialog Table if edit.inis=TRUE:
(1) INTENS[min,max,ini,fix]: lower and upper bounds, starting and fixing values of I_m
(2) ENERGY[min,max,ini,fix]: lower and upper bounds, starting and fixing values of E
(3) TEMPER[min,max,ini,fix]: lower and upper bounds, starting and fixing values of T_m
(4) bValue[min,max,ini,fix]: lower and upper bounds, starting and fixing values of b in the general-order model
(5) rValue[min,max,ini,fix]: lower and upper bounds, starting and fixing values of R in the OTOR model
(6) aValue[min,max,ini,fix]: lower and upper bounds, starting and fixing values of \alpha in the mixed-order model
(7) BG[min,max,ini,fix]: lower and upper bounds, starting and fixing values of background parameters A, B, and C
Value
Return an invisible list containing the following elements:
comp.sig |
calculated signal values for each glow peak |
residuals |
calculated residual values |
pars |
optimized parameters stored in a matrix |
BGpars |
optimized background parameters, it returns |
ff |
calculated frequency factors, it returns |
sp |
parameters used for describing the shape of a glow peak, see function simPeak for details |
resolution |
resolutions of optimized glow peaks calculated after Kitis and Pagonis (2019), it returns |
SSR |
Squared Sum of Residuals |
RCS |
Reduced Chi-Square value |
R2 |
squared "pearson" correlation between observed and fitted signals |
FOM |
Figure Of Merit value calculated after Balian and Eddy (1977) |
Note
Function tgcd analyzes only thermoluminescence glow curves recorded with linear heating function (LHF) profile.
The model to be optimized should not be underdetermined. This means that the number of data points (n_d) should exceed the number of parameters (n_2).
If it is not NULL the argument inisPAR, the procedure used for initializing kinetic parameters by clicking with a mouse will not be triggered.
Similarly, if it is not NULL the argment inisBG, the procedure used for initializing background parameters by clicking with a mouse will not be triggered.
The user is advocated to use mwt, mdt, and mr to specify the allowed maximum total half-width,
the allowed minimum distance, and the allowed minimum resolution respectively to resolve seriously overlapped glow peaks during the trial-and-error protocol.
Adrie J.J. Bos is appreciated for providing the reference glow curves of the GLOCANIN project to test this routine.
Amr M. Sadek is thanked for providing the Matlab code implementing the Lambert W (Wright Omega) function for reference.
George Kitis is appreciated for giving some useful suggestions to improve the program and providing many experimentally measured thermoluminescence glow curves to check the routine.
References
Balian HG, Eddy NW, 1977. Figure-of-merit (FOM), an improved criterion over the normalized chi-squared test for assessing goodness-of-fit of gamma-ray spectral peaks. Nuclear and Instruments Methods, 145: 389-395.
Bos AJJ, Piters TM, Gomez-Ros JM, Delgado A, 1993a. An intercomparison of glow curve analysis computer programs. IRI-CIEMAT Report, 131-93-005.
Gomez-Ros JM, Kitis G, 2002. Computerised glow curve deconvolution using general and mixed order kinetics. Radiation Protection Dosimetry, 101(1-4): 47-52.
Horowitz YS, Yossian D, 1995. Computerized glow curve deconvolution: application to thermoluminescence dosimetry. Radiation Protection Dosimetry, 60: 1-114.
Kitis G, Carinou E, Askounis P, 2012. Glow-curve de-convolution analysis of TL glow-curve from constant temperature hot gas TLD readers. Radiation Measurements, 47: 258-265.
Kitis G, Gomes-Ros JM, 2000. Thermoluminescence glow-curve deconvolution functions for mixed order of kinetics and continuous trap distribution. Nuclear Instruments and Methods in Physics Research A, 440: 224-231.
Kitis G, Gomes-Ros JM, Tuyn JWN, 1998. Thermoluminescence glow curve deconvolution functions for first, second and general orders of kinetics. Journal of Physics D: Applied Physics, 31(19): 2636-2641.
Kitis G, Pagonis V, 2019. On the resolution of overlapping peaks in complex thermoluminescence glow curves. Nuclear Instruments and Methods in Physics Research, A, 913: 78-84.
Kitis G, Polymeris GS, Pagonis V, 2019. Stimulated luminescence emission: From phenomenological models to master analytical equations. Applied Radiation and Isotopes, 153: 108797.
Kitis G, Polymeris GS, Sfampa IK, Prokic M, Meric N, Pagonis V, 2016. Prompt isothermal decay of thermoluminescence in MgB4O7:Dy, Na and LiB4O7:Cu, In dosimeters. Radiation Measurements, 84: 15-25.
Kitis G, Vlachos ND, 2013. General semi-analytical expressions for TL, OSL and other luminescence stimulation modes derived from the OTOR model using the Lambert W-function. Radiation Measurements, 48: 47-54.
More JJ, 1978. "The Levenberg-Marquardt algorithm: implementation and theory," in Lecture Notes in Mathematics: Numerical Analysis, Springer-Verlag: Berlin. 105-116.
Pagonis V, Mian SM, Kitis G, 2001. Fit of first order thermoluminescence glow peaks using the weibull distribution function. Radiation Protection Dosimetry, 93(1): 11-17.
Pagonis V, Kitis G, 2001. Fit of second order thermoluminescence glow peaks using the logistic distribution function. Radiation Protection Dosimetry, 95(3): 225-229.
Sadek AM, Eissa HM, Basha AM, Carinou E, Askounis P, Kitis G, 2015. The deconvolution of thermoluminescence glow-curves using general expressions derived from the one trap-one recombination (OTOR) level model. Applied Radiation and Isotopes, 95: 214-221.
Singh LL, Gartia RK, 2013. Theoretical derivation of a simplified form of the OTOR/GOT differential equation. Radiation Measurements, 59: 160-164.
Singh LL, Gartia RK, 2014. Glow-curve deconvolution of thermoluminescence curves in the simplified OTOR equation using the Hybrid Genetic Algorithm. Nuclear Instruments and Methods in Physics Research B, 319: 39-43.
Singh LL, Gartia RK, 2015. Derivation of a simplified OSL OTOR equation using Wright Omega function and its application. Nuclear Instruments and Methods in Physics Research B, 346: 45-52.
Sunta CM, Ayta WEF, Chubaci JFD, Watanabe S, 2002. General order and mixed order of thermoluminescence glow curves-a comparison. Radiation Measurements, 35: 47-57.
Vejnovic Z, Pavlovic MB, Davidovi M, 2008. Thermoluminescence glow curve deconvolution function for the mixed-order kinetics. Radiation Measurements, 43: 1325-1330.
Further reading
Afouxenidis D, Polymeris GS, Tsirliganis NC, Kitis G., 2011. Computerised curve deconvolution of TL/OSL curves using a popular spreadsheet program. Radiation Protection Dosimetry, 1-8.
Bos AJJ, Piters TM, Gomez Ros JM, Delgado A, 1993b. An intercomparison of glow curve analysis computer programs: I. Synthetic glow curves. Radiation Protection Dosimetry, 47(1-4), 473-477.
Chung KS, Choe HS, Lee JI, Kim JL, Chang SY, 2005. A computer program for the deconvolution of thermoluminescence glow curves. Radiation Protection Dosimetry, 115(1-4): 345-349.
Delgado A, Gomez-Ros JM, 2001. Computerised glow curve analysis: a tool for routine thermoluminescence dosimetry. Radiation Protection Dosimetry, 96(1-3): 127-132.
El-Hafez AI, Yasin MN, Sadek AM, 2011. GCAFIT-A new tool for glow curve analysis in thermoluminescence nanodosimetry. Nuclear Instruments and Methods in Physics Research A, 637: 158-163.
Espinosa G, Castano VM, 1991. Automated derivative analysis of thermoluminescence glow curves. Applied Radiation and Isotopes, 42(4): 377-381.
Harvey JA, Rodrigues ML, Kearfott JK, 2011. A computerized glow curve analysis (GCA) method for WinREMS thermoluminescent dosimeter data using MATLAB. Applied Radiation and Isotopes, 69(9):1282-1286.
Horowitz YS, Moscovitch M, 2012. Highlights and pitfalls of 20 years of application of computerised glow curve ananlysis to thermoluminescence research and dosimetry. Radiation Protection Dosimetry, 1-22.
Horowitz Y, Delgado A, Pradhan AS, Yoder RC, 2002. Topics under debate: the use of computerised glow curve analysis will optimise personal thermoluminescence dosimetry. Radiation Protection Dosimetry, 102(3): 269-277.
Karmakar M, Bhattacharyya S, Sarkar A, Mazumdar PS, Singh SD, 2017. Analysis of thermoluminescence glow curves using derivatives of different orders. Radiation Protection Dosimetry, 1-10.
Kiisk V, 2013. Deconvolution and simulation of thermoluminescence glow curves with Mathcad. Radiation Protection Dosimetry, 156(3): 261-267.
Pagonis V, Kitis G, Furetta C, 2006. Numerical and practical exercises in thermoluminescence. Springer Science & Business Media.
Puchalska M, Bilski P, 2006. GlowFit-a new tool for thermoluminescence glow-curve deconvolution. Radiation Measurements, 41(6): 659-664.
Sadek AM, 2013. Test of the accuracy of the computerized glow curve deconvolution algorithm for the analysis of thermoluminescence glow curves. Nuclear Instruments and Methods in Physics Research A, 712: 56-61.
Sadek AM, Kitis G., 2018. Impact of non-fulfillment of the super position principle on the analysis of thermoluminescence glow-curve. Radiation Measurements, 116: 14-23.
Singh TB, Rey L, Gartia RK, 2011. Applications of PeakFit software in thermoluminescence studies. Indian Journal of Pure & Applied Physics, 49: 297-302.
Sunta CM, 2015. Unraveling thermoluminescence. Springer India.
See Also
simPeak; simqOTOR; savgol
Examples
# Load the data.
data(Refglow)
data(Kitis)
# (1) Deconvolution of a glow curve using 4 peaks (no background subtraction) with
# the Wright Omega function using specified initial kinetic parameters.
knPars <-
cbind(c(400, 550, 850, 1600), # Im
c(1.4, 1.5, 1.6, 2), # E
c(420, 460, 480, 510), # Tm
c(0.1, 0.1, 0.1, 0.1)) # R
dd1 <- tgcd(Refglow$x002, npeak=4, model="wo",
inisPAR=knPars, nstart=10, edit.inis=FALSE)
head(dd1$comp.sig)
dd1$pars
dd1$sp
dd1$FOM
# (2) Deconvolution of a glow curve using 5 peaks (with background subtraction) with
# a mixed-order model using user-supplied intial kinetic and background parameters.
knPars <-
cbind(c(46829.06, 187942.43, 121876.22, 110390.55, 67978.33), #Im
c(1.17, 1.14, 1.57, 0.77, 1.31), # E
c(369.86, 400.69, 428.51, 482.41, 537.28), # Tm
c(0.75, 0.81, 0.92, 0.001, 0.29)) # a
bgPars <- c(1, 10, 100) # A, B, C.
dd2 <- tgcd(Kitis$x009, npeak=5, model="m1", subBG=TRUE,
inisPAR=knPars, inisBG=bgPars, nstart=10, edit.inis=FALSE)
dd2$residual
dd2$SSR
dd2$R2
dd2$BGpars
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