R/XPSCustomBaseline.r
In GSperanza/RxpsG_2.3-1: Processing Tool for X-ray Photoelectron Spectroscopy Data
Defines functions
Tougaard4P
Tougaard3P
Tougaard2P
LPShirley
Shirley3P
Shirley2P
Shirley0
baseSpline
Documented in
baseSpline
LPShirley
Shirley0
Shirley2P
Shirley3P
Tougaard2P
Tougaard3P
Tougaard4P
# definition of CUSTOM baseline functions
#====================================
# Spline background
#====================================
#' @title Spline Baseline
#' @description definition of the Spline Algorythms
#' Computes the Spline curve trough a set of splinePoints
#' provided by the user by mouse-clicking on the Core-Line spectrum
#' This function is called by the XPSAnalysisGUI
#' @param spectra coreline on which apply spline function
#' @param splinePoints set of points where the spline has to pass through
#' @param limits the abscissa range where the spline is defined
#' @export
#'
baseSpline <- function(spectra, splinePoints, limits) {
object <- list(y=spectra[1,]) #spectra contiene solo l'ordinata
npt <- length(object$y)
BGND<-spline(x=splinePoints$x, y=splinePoints$y, method="natural", n=npt)
if (limits$x[1] > limits$x[2]) {
BGND$y<-rev(BGND$y) #se ho scala in BE inverto la spline
}
baseline <- matrix(data=BGND$y, nrow=1)
#here a list following the baseline package format is returned
return(list(baseline = baseline, corrected = spectra - baseline, spectra=spectra))
}
#====================================
# Classic Shirley background
#====================================
#' @title Shirley0 Classic Shirley background
#' @description Shirley0 function prepresents the classic
#' algorithm to define the Shirley background below a given Core-Line
#' Shirley0(E) = S(E) is calculated iteratively, at step i:
#' S(E)i) = integral[S(E)i-1) J(E) dE ]
#' S(E)i), S(E)i-1) are the Shirley at step i and i-1
#' J(E) is the measured spectrum
#' This function is called by the XPSAnalysisGUI
#' @param object XPSSample CoreLine
#' @param limits limits of the XPSSample object
#' @return returns the Two_parameter Shirley background.
#' @export
#'
Shirley0 <- function(object, limits) { #Iterative Shirley following the Sherwood method
obj <- object@RegionToFit$y
LL <- length(object@RegionToFit$y)
if(LL == 0){
gmessage("WARNING: no data to generate the baseline", title="WARNING", icon="warning")
return()
}
if (object@Flags[1] == FALSE){ #KE scale
object@RegionToFit$x<-rev(object@RegionToFit$x)
}
Lim1 <- limits$y[1]
Lim2 <- limits$y[2]
spect <- object@RegionToFit$y-Lim2
LL <- length(obj)
Ymin <- min(limits$y)
BGND <- rep.int(Ymin, LL)
SumBGND <- sum(BGND)
SumRTF <- sum(obj)
RangeY <- diff(range(limits$y))
maxit <-50
err <- 1e-6
if (diff(limits$y) > 0) {
for (nloop in seq_len(LL)) {
for (idx in rev(seq_len(LL))) {
BGND[LL - idx + 1] <- ((RangeY/(SumRTF-sum(BGND)))*(sum(obj[LL:idx])-sum(BGND[LL:idx])))+Ymin
}
if ( abs( (sum(BGND)-SumBGND)/SumBGND ) < err ) { break }
SumBGND <- abs(sum(BGND))
}
} else {
for (nloop in seq_len(LL)) {
for (idx in seq_len(LL)) {
BGND[idx] <- ((RangeY/(SumRTF-sum(BGND)))*(sum(obj[idx:LL])-sum(BGND[idx:LL])))+Ymin
}
if ( abs( (sum(BGND)-SumBGND)/SumBGND ) < err ) { break }
SumBGND <- abs(sum(BGND))
}
}
return(BGND)
}
#============================================
# 2 Parameter CrossSection Shirley background
#============================================
# Shirley2P, 2 parameter Shirley background derived from J. Vegh, Surface Science 563, (2004), 183
# This background is based on Aproximated Shirley Cross section function defined by
# SC = Integral[ K(E'-E) dE]
# The energy loss (background) is then defined by
#
# Shirley(E) = Integral[ K(E'-E) * J(E)dE' ] J(E) = acquired spectrum
#
# K is the universal cross section function see S. Tougaard, Surf. Sci. 216 (1989) 343.
# which may be expressed by a two paramenter function:
# K(T) = BsT/(Cs + T^2) where T=E'-E
#
# Shirley(E) = Integral[ BsT/(Cs + T^2) * J(E)dT ]
#
#' @title Shirley2P a two parameter Shirley function
#' @description Shirley2P is a Shirley backgroung generated
#' using the two parameter Bs, Cs. Shirley(E) = S(E)is evaluated iteratively.
#' S(E) = Integral[ K(E'-E) * J(E)dE' ]
#' J(E) is the acquired spectrum
#' K(E'-E) describes the energy loss E-E' and is described by: B*(E-E')/[C + (E-E')^2]
#' see J. Vegh, Surface Science 563 (2004) 183,
#' J. Vegh J.Electr.Spect.Rel.Phen. 151 (2006) 159
#' This function is called by the XPSAnalysisGUI
#' @param object XPSSample CoreLine
#' @param limits limits of the XPSSample object
#' @return returns the Two_parameter Shirley background.
#' @export
#'
Shirley2P <- function(object, limits){
LL <- length(object@RegionToFit$x)
#KE scale: reverse vectors to make the routine compatible with BE scale
if (object@Flags[1] == FALSE){ #KE scale
object@RegionToFit$x <- rev(object@RegionToFit$x)
}
Lim1 <- limits$y[1]
Lim2 <- limits$y[2]
spect <- object@RegionToFit$y - Lim2
Cs <- 750
shirley2P <- vector(mode="numeric", length=LL)
lK <- vector(mode="numeric", length=LL)
# Evaluation of the Shirley Cross Section lK() the Bs parameter
tmp <- 0
dE <- (object@RegionToFit$x[2] - object@RegionToFit$x[1]) # Estep
for (ii in 1:LL){
deltaE <- (ii-1)*dE
num <- dE #dE
denom <- (Cs+deltaE^2) #(Cs+[E'-E]^2)
lK[ii] <- num/denom #dE/{Cs+[E'-E]^2) the Shirley Cross Section/B
tmp <- tmp+lK[ii]*spect[ii] #j(E')dE/{Cs+[E'-E]^2}
}
Bs <- (Lim1-Lim2)/tmp
#--- Computation shirley2P background: OK for both KE and BE scale
for (ii in 1:LL){
shirley2P[ii] <- Bs*sum(lK[1:(LL-ii+1)]*spect[ii:LL])
}
shirley2P <- shirley2P+Lim2 #add the Low-Energy-Side value of the spectrum
return(shirley2P)
}
#============================================
# 3 Parameter CrossSection Shirley background
#============================================
# 3 parameter Shirley background derived from J. Vegh J.Electr.Spect.Rel.Phen. 151 (2006) 159
# This background is based on Aproximated Shirley Cross section function defined by
# SC = Integral( L(E)* K(E'-E) )
# The energy loss (background) is then defined by
#
# Shirley(E) = Integral( L(E)*K(E'-E) * J(E)dE'
# J(E) = acquired spectrum
# K(E'-E) is the universal cross section function (see S. Tougaard, Surf. Sci. 216 (1989) 343)
#
# which may be expressed by a two paramenter function plus an exponential decay:
#
# Shirley3p = Integral[ BsT/(Cs + T^2)*(1-exp(-Ds*T)) * J(E)dT ] where T=E'-E
#
#' @title Shirley3P three parameter Shirley background
#' @description Shirley3p is described by three parameters
#' Bs=30eV^2, Cs=750eV^2, Ds=0.75
#' which are needed to describe the
#' Universal Cross Section function described by: B*T/(C + T^2)
#' and an exponential decay L(E)= (1-exp(-Ds*T))
#' where T = E'-E = energy loss
#' The Shirley3P background is then described by
#' Shirley(E) = Integral[ L(E)*K(E'-E) * J(E)dE' ]
#' J(E) = acquired spectrum
#' see J. Vegh J.Electr.Spect.Rel.Phen. 151 (2006) 159
#' This function is called by the XPSAnalysisGUI
#' @param object XPSSample object
#' @param Wgt XPSSample object
#' @param limits limits of the XPSSample object
#' @return returns the 3-parameter Shirley background.
#' @export
#'
Shirley3P <- function(object, Wgt, limits){
LL <- length(object@RegionToFit$x)
#KE scale: reverse vectors to make the routine compatible with BE scale
if (object@Flags[1] == FALSE){
object@RegionToFit$x<-rev(object@RegionToFit$x)
}
Lim1 <- limits$y[1]
Lim2 <- limits$y[2]
spect <- object@RegionToFit$y-Lim2
Cs <- 2500
shirley3P <- vector(mode="numeric", length=LL)
lK <- vector(mode="numeric", length=LL)
# Evaluation of the Shirley Cross Section lK() the Bs parameter
tmp <- 0
dE <-(object@RegionToFit$x[2] - object@RegionToFit$x[1]) # Estep
for (ii in 1:LL){
deltaE <- (ii-1)*dE
num <- 1-exp(-Wgt*abs(deltaE)) #(1-exp(-Ds*T)*dE
denom <- (Cs+deltaE^2) #(Cs+[E'-E]^2)
lK[ii] <- dE*num/denom #(1-exp(-Ds*T)*dE/(Cs+[E'-E]^2) the Shirley Cross Section/B
tmp <- tmp+lK[ii]*spect[ii] #j(E')dE/{Cs+[E'-E]^2}
}
Bs <- (Lim1-Lim2)/tmp
#--- Computation shirley3P background: OK for both KE and BE scale
for (ii in 1:LL){
shirley3P[ii] <- Bs*sum(lK[1:(LL-ii+1)]*spect[ii:LL])
}
shirley3P <- shirley3P+Lim2 #add the Low-Energy-Side value of the spectrum
return(shirley3P)
}
#====================================
# Polynomial+Shirley background
#====================================
#
#' @title LPShirley combination of a Shirley and linear Baselines
#' @description LPShirley generates a Baseline which is defined by
#' LinearPolynomial * Shirley Baseline see Practical Surface Analysis Briggs and Seah Wiley Ed.
#' Applies in all the cases where the Shirley background crosses the spectrum
#' causing the Shirley algorith to diverge.
#' In LPShirley firstly a linear background subtraction is performed to recognize
#' presence of multiple peaks. Then a Modified Bishop polynom weakens the Shirley cross section
#' Bishop polynom: PP[ii]<-1-m*ii*abs(dX) dX = energy step, m=coeff manually selected
#' in LPShirley the classical Shirley expression is multiplied by PP:
#' S(E)i) = Shirley(E) = Integral[ S(E)i-1)* PP(E)* J(E)dE' ]
#' S(E)i), S(E)i-1) are the Shirley at step i and i-1
#' J(E) = acquired spectrum
#' This function is called by XPSAnalysisGUI
#' @param object CoreLine where to apply LPshirley function
#' @param mm coefficient of the linear BKG component
#' @param limits limits of the XPSSample CoreLine
#' @return returns the LPShirley background
#'
LPShirley <- function(object, mm, limits) {
LL <- length(object@RegionToFit$y)
objX <- object@RegionToFit$x
objY <- object@RegionToFit$y
if (object@Flags[1] == FALSE){ #KE scale
objX <- rev(objX)
}
Lim1 <- limits$y[1]
Lim2 <- limits$y[2]
# objY<-objY-Lim2
MinLy <- min(limits$y)
MaxLy <- max(limits$y)
dX <- abs(objX[1]-objX[2]) #energy step
BGND <- rep.int(MinLy, LL)
SumBGND <- sum(BGND)
SumRTF <- sum(objY)
RangeY <- diff(range(limits$y))
maxit <- 50
err <- 1e-6
dY <- (limits$y[2]-limits$y[1])/LL
LinBkg <- vector(mode="numeric", length=LL)
for (ii in 1:LL){ #generating a linear Bkg under the RegionToFit
LinBkg[ii] <- limits$y[1]+(ii-1)*dY
}
object@Baseline$x <- objX
object@Baseline$y <- LinBkg
#LinBKg subtraction
objY_L <- objY-LinBkg
maxY_L <- max(objY_L)
#search for multiple peaks: no derivative used because noise causes uncontrollable derivative oscillation
#are there multiple peaks (spin orbit splitting, oxidized components...)
idx <- which(objY_L > maxY_L/2) #regions where peaks are > maxY_L/2
Lidx <- length(idx)
#idx contains the indexes of the spectral points where the intensity I > maxY/2
#in presence of spin orbit splitting there are two regions satisfying this condition
#in presence of oxidized components the spin orbit leads to 4 peaks:
#two for the pure element two for the oxidized element.
#In general more than one peak could be present => more than one region where I > maxY/2
#How to identify the number of these regions?
#idx2[ii] = idx[ii]-idx[ii-1]
#if idx[1]==0 this difference > 1 in correspondence of the beginning of each region:
#
idx[1] <- 0 #idx== 0 225 226 ... 344 345 655 656 657 ... 943 944 1164 1165 1166 ...
idx2 <- idx[2:Lidx]-idx[1:Lidx-1] #idx2== 225 1 1 1 ... 1 1 310 1 1 1 ... 1 1 220 1 1 1 ....
# ----------REG1--------- ++++++++++++REG2++++++++++ ----------REG3--------- ...
# 255-0=255 655-345==310 1164-944=220
Regs <- which(idx2>1)
Nr <- length(Regs)
#now working on the original non subtracted data
#position of the last peak if BE scale, of the first peak if KE scale
PeakMax <- max(objY[idx[Regs[Nr]+1]:LL]) #max of the last region
posPeak <- which(objY==PeakMax)
#Is there any flat region at the edge of the coreline?
tailTresh <- (max(objY)-MinLy)/50+MinLy #define a treshold on the basis of peak and edge intensities
for (Tpos in LL:1){ #Tpos = beginning of the flat region
if(objY[Tpos] > tailTresh) { break }
}
PP <- vector(mode="numeric", length=LL)
for (ii in 1:posPeak) {
PP[ii] <- 1-mm*ii*abs(dX) #Bishop weakening polynom see Practical Surface Analysis Briggs and Seah Wiley Ed.
}
#Bishop polynom modified to better describe the flat region at high BE (lowKE)
#PP decreases linearly until the max of peak at higher BE (lower KE) then linearly
#increases till PP==1 the value assumed in the flat region at the end (beginning) of the
#core line. PP==1 means background == non weakened classical Shirley
dPP <- (1-PP[posPeak])/abs(Tpos-posPeak)
for (ii in (posPeak+1):Tpos) {
PP[ii] <- PP[posPeak]+dPP*(ii-posPeak)
}
PP[Tpos:LL] <- 1
# PP <- baseline(objY, method="modpolyfit", t=objX, degree = 3, tol = 0.01, rep = 100)
# PP <- as.vector(polyBkg@baseline)
# PP <- 1-mm*polyBkg
for (nloop in seq_len(maxit)) {
for (ii in 1:LL) {
BGND[ii] <- ((RangeY/(SumRTF-sum(BGND)))*(sum(objY[ii:LL]*PP[ii:LL])-sum(BGND[ii:LL])))+MinLy
}
if ( abs( (sum(BGND)-SumBGND)/SumBGND ) < err ) { break }
SumBGND <- abs(sum(BGND))
}
## reverse y-baseline in case of reverse bgnd
# if ( limits$y[which.max(limits$x)] < limits$y[which.min(limits$x)] ) {
# baseline <- matrix(data=rev(BGND), nrow=1) }
# else { baseline <- matrix(data=BGND, nrow=1) }
baseline <- matrix(data=BGND, nrow=1)
MinBGND <- min(c(BGND[1], BGND[LL]))
BGND <- (limits$y[1]-limits$y[2])/(BGND[1]-BGND[LL]) * (BGND-MinBGND)+MinLy #Adjust BGND on the limits$y values
return(BGND)
}
#====================================
# 2 Parameter Tougaard background
#====================================
# 2 parameter Tougaard background for metallic like samples
# This background is based on the Universal Cross section function defined by
# UC = Integral( L(E)* K(E'-E) )
# The energy loss (background) is then defined by
#
# Tougaard(E) = Integral[ L(E)*K(E'-E) * J(E)dE' ] J(E) = acquired spectrum
#
# which may be expressed by a two paramenter function:
#
# Tougaard2p = Integral( BT/(C + T^2)^2 * J(E)dT where T=E'-E
#
#' @title Tougaard2P two parameter Togaard Baseline
#' @description Tougaard2P two parameter B and C are used to define
#' the Tougaard Baseline:
#' Tougaard(E) = L * Integral[ K(E'-E) * J(E)dE' ]
#' J(E) = acquired spectrum
#' K(E'-E) = Universal Cross Section described by: B*T/(C + T^2)^2 T=E'-E
#' see S. Tougaard, Surf. Sci. (1989), 216, 343; S. Tougaard, Sol. Stat. Comm.(1987), 61(9), 547
#' L = l/(1-lcos a) l=mean free path, a = take-off angle
#' This function is called by XPSAnalysisGUI
#' @param object XPSSample CoreLine
#' @param limits limits of the XPSSample CoreLine
#' @return returns the 2parameter Tougaard background.
#' @export
#'
Tougaard2P <- function(object, limits){
LL <- length(object@RegionToFit$x)
if (object@Flags[1] == FALSE){ #KE scale
object@RegionToFit$x <- rev(object@RegionToFit$x)
}
avg1 <- limits$y[1]
avg2 <- sum(object@RegionToFit$y[(LL-4):LL])/5
object@RegionToFit$y <- object@RegionToFit$y-avg2
C <- 1643
tougaard <- vector(mode="numeric", length=LL)
lK <- vector(mode="numeric", length=LL)
# Evaluation of the Universal Cross Section lK() and the B parameter
tmp <- 0
dE <- (object@RegionToFit$x[2] - object@RegionToFit$x[1]) # Estep
for (ii in 1:LL){
deltaE <- (ii-1)*dE
num <- deltaE*dE #(E'-E)*dE
denom <- (C+deltaE^2)^2 #(C+[E'-E]^2}^2
lK[ii] <- num/denom #(E'-E)/{C+[E'-E]^2}^2 the uniiversal Cross Section/B
tmp <- tmp+lK[ii]*object@RegionToFit$y[ii] #j(E')(E'-E)/{C+[E'-E]^2}^2
}
B <- (avg1-avg2)/tmp
#--- Computation Tougaard background: OK for both KE and BE scale
for (ii in 1:LL){
tougaard[ii] <- B*sum(lK[1:(LL-ii+1)]*object@RegionToFit$y[ii:LL])
}
tougaard<-tougaard+avg2 #add the Low-Energy-Side value of the spectrum
return(tougaard)
}
#====================================
# 3 Parameter Tougaard background
#====================================
# 3 parameter Tougaard background for non metallic matter such as polymers
# This background is based on the Universal Cross section function defined by
# UC = Integral( L(E)* K(E'-E) )
# The energy loss (background) is then defined by
#
# Tougaard(E) = L * Integral[ K(E'-E) * J(E)dE' ]
# J(E) = acquired spectrum
# L = l/(1-1cos a) l inelastic mean free path a=take-off angle
#
# which may be expressed by a three paramenter B, C, D function:
#
# Tougaard3p = Integral( BT/[(C + T^2)^2 + D*T^2] * J(E)dT where T=E'-E
#
#' @title Tougaard3P three parameter Togaard Baseline
#' @description Tougaard3P is the three parameter Tougaard Baseline
# defined using three B, C and D parameters
#' Tougaard3p = Integral[ BT/[(C + T^2)^2 + D*T^2] * J(T)dT ]
#' J(T) = the measured spectrum
#' B*T/[(C + T^2)^2 + D*T^2] = Modified Universal Cross Section
#' T=energy loss = E'-E
#' see S. Hajati, Surf. Sci. (2006), 600, 3015
#' This function is called by XPSAnalysisGUI
#' @param object XPSSample CoreLine
#' @param limits limits of the XPSSample CoreLine
#' @return returns the 3parameter Tougaard background.
#' @export
Tougaard3P <- function(object, limits){
LL <- length(object@RegionToFit$x)
if (object@Flags[1] == FALSE){ #KE scale
object@RegionToFit$x <- rev(object@RegionToFit$x)
}
avg1 <- limits$y[1]
avg2 <- sum(object@RegionToFit$y[(LL-4):LL])/5
object@RegionToFit$y<-object@RegionToFit$y-avg2
C <- 551
D <- 436
tougaard <- vector(mode="numeric", length=LL)
lK <- vector(mode="numeric", length=LL)
# Evaluation of the Universal Cross Section lK() and the B parameter
tmp <- 0
dE <- (object@RegionToFit$x[2] - object@RegionToFit$x[1]) # Estep
for (ii in 1:LL){
deltaE <- (ii-1)*dE
num <- deltaE*dE #(E'-E)*dE
denom <- (C+deltaE^2)^2 + D*deltaE^2 #(C+[E'-E]^2}^2 + D(E'-E)^2
lK[ii] <- num/denom #(E'-E)/{C+[E'-E]^2}^2 the modified uniiversal Cross Section L(E)*K(E,T) T=E'-E
tmp <- tmp+lK[ii]*object@RegionToFit$y[ii] #j(E')(E'-E)/{C+[E'-E]^2}^2
}
B <- (avg1-avg2)/tmp
#--- Computation Tougaard background: OK for both KE and BE scale
for (ii in 1:LL){
tougaard[ii] <- B*sum(lK[1:(LL-ii+1)]*object@RegionToFit$y[ii:LL])
}
tougaard <- tougaard+avg2 #add the Low-Energy-Side value of the spectrum
return(tougaard)
}
#====================================
# 4 Parameter Tougaard background
#====================================
# 4 parameter Tougaard background for non metallic homogeneous matter such as polymers
# This background is based on the Universal Cross section function defined by
# UC = Integral( L(E)* K(E'-E) )
# The energy loss (background) is then defined by
#
# Tougaard(E) = Integral( L(E)*K(E'-E) * J(E)dE' J(E) = acquired spectrum
#
# which may be expressed by a three paramenter B, C, C', D function:
#
# Tougaard4p = Integral( BT/[(C + C'*T^2)^2 + D*T^2] * J(E)dT where T=E'-E
#
#' @title Tougaard4P four parameters Tougaard Baseline
#' @description Tougaard4P is a Tougaard Baseline defined usinf
#' the four parameters B, C, C' and D
#' Tougaard4p = Integral{ BT/[(C + C'*T^2)^2 + D*T^2] * J(E)dT }
#' J(T) = the measured spectrum
#' B*T/[(C + C'*T^2)^2 + D*T^2] = Modified Universal Cross Section
#' T=energy loss = E'-E
#' see R. Hesse et al., Surf. Interface Anal. (2011), 43, 1514
#' This function is called by XPSAnalysisGUI
#' @param object XPSSample CoreLine
#' @param C1 numeric is a parameter value
#' @param limits limits of the XPSSample CoreLine
#' @return Return the 4parameter Tougaard background.
#' @export
Tougaard4P <- function(object, C1, limits){
LL <- length(object@RegionToFit$x)
if (object@Flags[1] == FALSE){ #KE scale
object@RegionToFit$x <- rev(object@RegionToFit$x)
}
avg1 <- limits$y[1]
avg2 <- limits$y[2] #sum(object@RegionToFit$y[(LL-4):LL])/5
object@RegionToFit$y <- object@RegionToFit$y-avg2
C <- 551
D <- 436
tougaard <- vector(mode="numeric", length=LL)
lK <- vector(mode="numeric", length=LL)
# Evaluation of the Universal Cross Section lK() and the B parameter
tmp <- 0
dE <- (object@RegionToFit$x[2] - object@RegionToFit$x[1]) # Estep
for (ii in 1:LL){
deltaE <- (ii-1)*dE
num <- deltaE*dE #(E'-E)*dE
denom <- (C+C1*deltaE^2)^2 + D*deltaE^2 #(C+[E'-E]^2}^2 + D(E'-E)^2
lK[ii] <- num/denom #(E'-E)/{C+[E'-E]^2}^2 the modified universal Cross Section L(E)*K(E,T) T=E'-E
tmp <- tmp+lK[ii]*object@RegionToFit$y[ii] #j(E')(E'-E)/{C+[E'-E]^2}^2
}
B <- (avg1-avg2)/tmp
#--- Computation Tougaard background: OK for both KE and BE scale
for (ii in 1:LL){
tougaard[ii] <- B*sum(lK[1:(LL-ii+1)]*object@RegionToFit$y[ii:LL])
}
tougaard <- tougaard+avg2 #add the Low-Energy-Side value of the spectrum
return(tougaard)
}
GSperanza/RxpsG_2.3-1 documentation built on Feb. 11, 2024, 5:09 p.m.
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Defines functions Tougaard4P Tougaard3P Tougaard2P LPShirley Shirley3P Shirley2P Shirley0 baseSpline
Documented in baseSpline LPShirley Shirley0 Shirley2P Shirley3P Tougaard2P Tougaard3P Tougaard4P
# definition of CUSTOM baseline functions
#====================================
# Spline background
#====================================
#' @title Spline Baseline
#' @description definition of the Spline Algorythms
#' Computes the Spline curve trough a set of splinePoints
#' provided by the user by mouse-clicking on the Core-Line spectrum
#' This function is called by the XPSAnalysisGUI
#' @param spectra coreline on which apply spline function
#' @param splinePoints set of points where the spline has to pass through
#' @param limits the abscissa range where the spline is defined
#' @export
#'
baseSpline <- function(spectra, splinePoints, limits) {
object <- list(y=spectra[1,]) #spectra contiene solo l'ordinata
npt <- length(object$y)
BGND<-spline(x=splinePoints$x, y=splinePoints$y, method="natural", n=npt)
if (limits$x[1] > limits$x[2]) {
BGND$y<-rev(BGND$y) #se ho scala in BE inverto la spline
}
baseline <- matrix(data=BGND$y, nrow=1)
#here a list following the baseline package format is returned
return(list(baseline = baseline, corrected = spectra - baseline, spectra=spectra))
}
#====================================
# Classic Shirley background
#====================================
#' @title Shirley0 Classic Shirley background
#' @description Shirley0 function prepresents the classic
#' algorithm to define the Shirley background below a given Core-Line
#' Shirley0(E) = S(E) is calculated iteratively, at step i:
#' S(E)i) = integral[S(E)i-1) J(E) dE ]
#' S(E)i), S(E)i-1) are the Shirley at step i and i-1
#' J(E) is the measured spectrum
#' This function is called by the XPSAnalysisGUI
#' @param object XPSSample CoreLine
#' @param limits limits of the XPSSample object
#' @return returns the Two_parameter Shirley background.
#' @export
#'
Shirley0 <- function(object, limits) { #Iterative Shirley following the Sherwood method
obj <- object@RegionToFit$y
LL <- length(object@RegionToFit$y)
if(LL == 0){
gmessage("WARNING: no data to generate the baseline", title="WARNING", icon="warning")
return()
}
if (object@Flags[1] == FALSE){ #KE scale
object@RegionToFit$x<-rev(object@RegionToFit$x)
}
Lim1 <- limits$y[1]
Lim2 <- limits$y[2]
spect <- object@RegionToFit$y-Lim2
LL <- length(obj)
Ymin <- min(limits$y)
BGND <- rep.int(Ymin, LL)
SumBGND <- sum(BGND)
SumRTF <- sum(obj)
RangeY <- diff(range(limits$y))
maxit <-50
err <- 1e-6
if (diff(limits$y) > 0) {
for (nloop in seq_len(LL)) {
for (idx in rev(seq_len(LL))) {
BGND[LL - idx + 1] <- ((RangeY/(SumRTF-sum(BGND)))*(sum(obj[LL:idx])-sum(BGND[LL:idx])))+Ymin
}
if ( abs( (sum(BGND)-SumBGND)/SumBGND ) < err ) { break }
SumBGND <- abs(sum(BGND))
}
} else {
for (nloop in seq_len(LL)) {
for (idx in seq_len(LL)) {
BGND[idx] <- ((RangeY/(SumRTF-sum(BGND)))*(sum(obj[idx:LL])-sum(BGND[idx:LL])))+Ymin
}
if ( abs( (sum(BGND)-SumBGND)/SumBGND ) < err ) { break }
SumBGND <- abs(sum(BGND))
}
}
return(BGND)
}
#============================================
# 2 Parameter CrossSection Shirley background
#============================================
# Shirley2P, 2 parameter Shirley background derived from J. Vegh, Surface Science 563, (2004), 183
# This background is based on Aproximated Shirley Cross section function defined by
# SC = Integral[ K(E'-E) dE]
# The energy loss (background) is then defined by
#
# Shirley(E) = Integral[ K(E'-E) * J(E)dE' ] J(E) = acquired spectrum
#
# K is the universal cross section function see S. Tougaard, Surf. Sci. 216 (1989) 343.
# which may be expressed by a two paramenter function:
# K(T) = BsT/(Cs + T^2) where T=E'-E
#
# Shirley(E) = Integral[ BsT/(Cs + T^2) * J(E)dT ]
#
#' @title Shirley2P a two parameter Shirley function
#' @description Shirley2P is a Shirley backgroung generated
#' using the two parameter Bs, Cs. Shirley(E) = S(E)is evaluated iteratively.
#' S(E) = Integral[ K(E'-E) * J(E)dE' ]
#' J(E) is the acquired spectrum
#' K(E'-E) describes the energy loss E-E' and is described by: B*(E-E')/[C + (E-E')^2]
#' see J. Vegh, Surface Science 563 (2004) 183,
#' J. Vegh J.Electr.Spect.Rel.Phen. 151 (2006) 159
#' This function is called by the XPSAnalysisGUI
#' @param object XPSSample CoreLine
#' @param limits limits of the XPSSample object
#' @return returns the Two_parameter Shirley background.
#' @export
#'
Shirley2P <- function(object, limits){
LL <- length(object@RegionToFit$x)
#KE scale: reverse vectors to make the routine compatible with BE scale
if (object@Flags[1] == FALSE){ #KE scale
object@RegionToFit$x <- rev(object@RegionToFit$x)
}
Lim1 <- limits$y[1]
Lim2 <- limits$y[2]
spect <- object@RegionToFit$y - Lim2
Cs <- 750
shirley2P <- vector(mode="numeric", length=LL)
lK <- vector(mode="numeric", length=LL)
# Evaluation of the Shirley Cross Section lK() the Bs parameter
tmp <- 0
dE <- (object@RegionToFit$x[2] - object@RegionToFit$x[1]) # Estep
for (ii in 1:LL){
deltaE <- (ii-1)*dE
num <- dE #dE
denom <- (Cs+deltaE^2) #(Cs+[E'-E]^2)
lK[ii] <- num/denom #dE/{Cs+[E'-E]^2) the Shirley Cross Section/B
tmp <- tmp+lK[ii]*spect[ii] #j(E')dE/{Cs+[E'-E]^2}
}
Bs <- (Lim1-Lim2)/tmp
#--- Computation shirley2P background: OK for both KE and BE scale
for (ii in 1:LL){
shirley2P[ii] <- Bs*sum(lK[1:(LL-ii+1)]*spect[ii:LL])
}
shirley2P <- shirley2P+Lim2 #add the Low-Energy-Side value of the spectrum
return(shirley2P)
}
#============================================
# 3 Parameter CrossSection Shirley background
#============================================
# 3 parameter Shirley background derived from J. Vegh J.Electr.Spect.Rel.Phen. 151 (2006) 159
# This background is based on Aproximated Shirley Cross section function defined by
# SC = Integral( L(E)* K(E'-E) )
# The energy loss (background) is then defined by
#
# Shirley(E) = Integral( L(E)*K(E'-E) * J(E)dE'
# J(E) = acquired spectrum
# K(E'-E) is the universal cross section function (see S. Tougaard, Surf. Sci. 216 (1989) 343)
#
# which may be expressed by a two paramenter function plus an exponential decay:
#
# Shirley3p = Integral[ BsT/(Cs + T^2)*(1-exp(-Ds*T)) * J(E)dT ] where T=E'-E
#
#' @title Shirley3P three parameter Shirley background
#' @description Shirley3p is described by three parameters
#' Bs=30eV^2, Cs=750eV^2, Ds=0.75
#' which are needed to describe the
#' Universal Cross Section function described by: B*T/(C + T^2)
#' and an exponential decay L(E)= (1-exp(-Ds*T))
#' where T = E'-E = energy loss
#' The Shirley3P background is then described by
#' Shirley(E) = Integral[ L(E)*K(E'-E) * J(E)dE' ]
#' J(E) = acquired spectrum
#' see J. Vegh J.Electr.Spect.Rel.Phen. 151 (2006) 159
#' This function is called by the XPSAnalysisGUI
#' @param object XPSSample object
#' @param Wgt XPSSample object
#' @param limits limits of the XPSSample object
#' @return returns the 3-parameter Shirley background.
#' @export
#'
Shirley3P <- function(object, Wgt, limits){
LL <- length(object@RegionToFit$x)
#KE scale: reverse vectors to make the routine compatible with BE scale
if (object@Flags[1] == FALSE){
object@RegionToFit$x<-rev(object@RegionToFit$x)
}
Lim1 <- limits$y[1]
Lim2 <- limits$y[2]
spect <- object@RegionToFit$y-Lim2
Cs <- 2500
shirley3P <- vector(mode="numeric", length=LL)
lK <- vector(mode="numeric", length=LL)
# Evaluation of the Shirley Cross Section lK() the Bs parameter
tmp <- 0
dE <-(object@RegionToFit$x[2] - object@RegionToFit$x[1]) # Estep
for (ii in 1:LL){
deltaE <- (ii-1)*dE
num <- 1-exp(-Wgt*abs(deltaE)) #(1-exp(-Ds*T)*dE
denom <- (Cs+deltaE^2) #(Cs+[E'-E]^2)
lK[ii] <- dE*num/denom #(1-exp(-Ds*T)*dE/(Cs+[E'-E]^2) the Shirley Cross Section/B
tmp <- tmp+lK[ii]*spect[ii] #j(E')dE/{Cs+[E'-E]^2}
}
Bs <- (Lim1-Lim2)/tmp
#--- Computation shirley3P background: OK for both KE and BE scale
for (ii in 1:LL){
shirley3P[ii] <- Bs*sum(lK[1:(LL-ii+1)]*spect[ii:LL])
}
shirley3P <- shirley3P+Lim2 #add the Low-Energy-Side value of the spectrum
return(shirley3P)
}
#====================================
# Polynomial+Shirley background
#====================================
#
#' @title LPShirley combination of a Shirley and linear Baselines
#' @description LPShirley generates a Baseline which is defined by
#' LinearPolynomial * Shirley Baseline see Practical Surface Analysis Briggs and Seah Wiley Ed.
#' Applies in all the cases where the Shirley background crosses the spectrum
#' causing the Shirley algorith to diverge.
#' In LPShirley firstly a linear background subtraction is performed to recognize
#' presence of multiple peaks. Then a Modified Bishop polynom weakens the Shirley cross section
#' Bishop polynom: PP[ii]<-1-m*ii*abs(dX) dX = energy step, m=coeff manually selected
#' in LPShirley the classical Shirley expression is multiplied by PP:
#' S(E)i) = Shirley(E) = Integral[ S(E)i-1)* PP(E)* J(E)dE' ]
#' S(E)i), S(E)i-1) are the Shirley at step i and i-1
#' J(E) = acquired spectrum
#' This function is called by XPSAnalysisGUI
#' @param object CoreLine where to apply LPshirley function
#' @param mm coefficient of the linear BKG component
#' @param limits limits of the XPSSample CoreLine
#' @return returns the LPShirley background
#'
LPShirley <- function(object, mm, limits) {
LL <- length(object@RegionToFit$y)
objX <- object@RegionToFit$x
objY <- object@RegionToFit$y
if (object@Flags[1] == FALSE){ #KE scale
objX <- rev(objX)
}
Lim1 <- limits$y[1]
Lim2 <- limits$y[2]
# objY<-objY-Lim2
MinLy <- min(limits$y)
MaxLy <- max(limits$y)
dX <- abs(objX[1]-objX[2]) #energy step
BGND <- rep.int(MinLy, LL)
SumBGND <- sum(BGND)
SumRTF <- sum(objY)
RangeY <- diff(range(limits$y))
maxit <- 50
err <- 1e-6
dY <- (limits$y[2]-limits$y[1])/LL
LinBkg <- vector(mode="numeric", length=LL)
for (ii in 1:LL){ #generating a linear Bkg under the RegionToFit
LinBkg[ii] <- limits$y[1]+(ii-1)*dY
}
object@Baseline$x <- objX
object@Baseline$y <- LinBkg
#LinBKg subtraction
objY_L <- objY-LinBkg
maxY_L <- max(objY_L)
#search for multiple peaks: no derivative used because noise causes uncontrollable derivative oscillation
#are there multiple peaks (spin orbit splitting, oxidized components...)
idx <- which(objY_L > maxY_L/2) #regions where peaks are > maxY_L/2
Lidx <- length(idx)
#idx contains the indexes of the spectral points where the intensity I > maxY/2
#in presence of spin orbit splitting there are two regions satisfying this condition
#in presence of oxidized components the spin orbit leads to 4 peaks:
#two for the pure element two for the oxidized element.
#In general more than one peak could be present => more than one region where I > maxY/2
#How to identify the number of these regions?
#idx2[ii] = idx[ii]-idx[ii-1]
#if idx[1]==0 this difference > 1 in correspondence of the beginning of each region:
#
idx[1] <- 0 #idx== 0 225 226 ... 344 345 655 656 657 ... 943 944 1164 1165 1166 ...
idx2 <- idx[2:Lidx]-idx[1:Lidx-1] #idx2== 225 1 1 1 ... 1 1 310 1 1 1 ... 1 1 220 1 1 1 ....
# ----------REG1--------- ++++++++++++REG2++++++++++ ----------REG3--------- ...
# 255-0=255 655-345==310 1164-944=220
Regs <- which(idx2>1)
Nr <- length(Regs)
#now working on the original non subtracted data
#position of the last peak if BE scale, of the first peak if KE scale
PeakMax <- max(objY[idx[Regs[Nr]+1]:LL]) #max of the last region
posPeak <- which(objY==PeakMax)
#Is there any flat region at the edge of the coreline?
tailTresh <- (max(objY)-MinLy)/50+MinLy #define a treshold on the basis of peak and edge intensities
for (Tpos in LL:1){ #Tpos = beginning of the flat region
if(objY[Tpos] > tailTresh) { break }
}
PP <- vector(mode="numeric", length=LL)
for (ii in 1:posPeak) {
PP[ii] <- 1-mm*ii*abs(dX) #Bishop weakening polynom see Practical Surface Analysis Briggs and Seah Wiley Ed.
}
#Bishop polynom modified to better describe the flat region at high BE (lowKE)
#PP decreases linearly until the max of peak at higher BE (lower KE) then linearly
#increases till PP==1 the value assumed in the flat region at the end (beginning) of the
#core line. PP==1 means background == non weakened classical Shirley
dPP <- (1-PP[posPeak])/abs(Tpos-posPeak)
for (ii in (posPeak+1):Tpos) {
PP[ii] <- PP[posPeak]+dPP*(ii-posPeak)
}
PP[Tpos:LL] <- 1
# PP <- baseline(objY, method="modpolyfit", t=objX, degree = 3, tol = 0.01, rep = 100)
# PP <- as.vector(polyBkg@baseline)
# PP <- 1-mm*polyBkg
for (nloop in seq_len(maxit)) {
for (ii in 1:LL) {
BGND[ii] <- ((RangeY/(SumRTF-sum(BGND)))*(sum(objY[ii:LL]*PP[ii:LL])-sum(BGND[ii:LL])))+MinLy
}
if ( abs( (sum(BGND)-SumBGND)/SumBGND ) < err ) { break }
SumBGND <- abs(sum(BGND))
}
## reverse y-baseline in case of reverse bgnd
# if ( limits$y[which.max(limits$x)] < limits$y[which.min(limits$x)] ) {
# baseline <- matrix(data=rev(BGND), nrow=1) }
# else { baseline <- matrix(data=BGND, nrow=1) }
baseline <- matrix(data=BGND, nrow=1)
MinBGND <- min(c(BGND[1], BGND[LL]))
BGND <- (limits$y[1]-limits$y[2])/(BGND[1]-BGND[LL]) * (BGND-MinBGND)+MinLy #Adjust BGND on the limits$y values
return(BGND)
}
#====================================
# 2 Parameter Tougaard background
#====================================
# 2 parameter Tougaard background for metallic like samples
# This background is based on the Universal Cross section function defined by
# UC = Integral( L(E)* K(E'-E) )
# The energy loss (background) is then defined by
#
# Tougaard(E) = Integral[ L(E)*K(E'-E) * J(E)dE' ] J(E) = acquired spectrum
#
# which may be expressed by a two paramenter function:
#
# Tougaard2p = Integral( BT/(C + T^2)^2 * J(E)dT where T=E'-E
#
#' @title Tougaard2P two parameter Togaard Baseline
#' @description Tougaard2P two parameter B and C are used to define
#' the Tougaard Baseline:
#' Tougaard(E) = L * Integral[ K(E'-E) * J(E)dE' ]
#' J(E) = acquired spectrum
#' K(E'-E) = Universal Cross Section described by: B*T/(C + T^2)^2 T=E'-E
#' see S. Tougaard, Surf. Sci. (1989), 216, 343; S. Tougaard, Sol. Stat. Comm.(1987), 61(9), 547
#' L = l/(1-lcos a) l=mean free path, a = take-off angle
#' This function is called by XPSAnalysisGUI
#' @param object XPSSample CoreLine
#' @param limits limits of the XPSSample CoreLine
#' @return returns the 2parameter Tougaard background.
#' @export
#'
Tougaard2P <- function(object, limits){
LL <- length(object@RegionToFit$x)
if (object@Flags[1] == FALSE){ #KE scale
object@RegionToFit$x <- rev(object@RegionToFit$x)
}
avg1 <- limits$y[1]
avg2 <- sum(object@RegionToFit$y[(LL-4):LL])/5
object@RegionToFit$y <- object@RegionToFit$y-avg2
C <- 1643
tougaard <- vector(mode="numeric", length=LL)
lK <- vector(mode="numeric", length=LL)
# Evaluation of the Universal Cross Section lK() and the B parameter
tmp <- 0
dE <- (object@RegionToFit$x[2] - object@RegionToFit$x[1]) # Estep
for (ii in 1:LL){
deltaE <- (ii-1)*dE
num <- deltaE*dE #(E'-E)*dE
denom <- (C+deltaE^2)^2 #(C+[E'-E]^2}^2
lK[ii] <- num/denom #(E'-E)/{C+[E'-E]^2}^2 the uniiversal Cross Section/B
tmp <- tmp+lK[ii]*object@RegionToFit$y[ii] #j(E')(E'-E)/{C+[E'-E]^2}^2
}
B <- (avg1-avg2)/tmp
#--- Computation Tougaard background: OK for both KE and BE scale
for (ii in 1:LL){
tougaard[ii] <- B*sum(lK[1:(LL-ii+1)]*object@RegionToFit$y[ii:LL])
}
tougaard<-tougaard+avg2 #add the Low-Energy-Side value of the spectrum
return(tougaard)
}
#====================================
# 3 Parameter Tougaard background
#====================================
# 3 parameter Tougaard background for non metallic matter such as polymers
# This background is based on the Universal Cross section function defined by
# UC = Integral( L(E)* K(E'-E) )
# The energy loss (background) is then defined by
#
# Tougaard(E) = L * Integral[ K(E'-E) * J(E)dE' ]
# J(E) = acquired spectrum
# L = l/(1-1cos a) l inelastic mean free path a=take-off angle
#
# which may be expressed by a three paramenter B, C, D function:
#
# Tougaard3p = Integral( BT/[(C + T^2)^2 + D*T^2] * J(E)dT where T=E'-E
#
#' @title Tougaard3P three parameter Togaard Baseline
#' @description Tougaard3P is the three parameter Tougaard Baseline
# defined using three B, C and D parameters
#' Tougaard3p = Integral[ BT/[(C + T^2)^2 + D*T^2] * J(T)dT ]
#' J(T) = the measured spectrum
#' B*T/[(C + T^2)^2 + D*T^2] = Modified Universal Cross Section
#' T=energy loss = E'-E
#' see S. Hajati, Surf. Sci. (2006), 600, 3015
#' This function is called by XPSAnalysisGUI
#' @param object XPSSample CoreLine
#' @param limits limits of the XPSSample CoreLine
#' @return returns the 3parameter Tougaard background.
#' @export
Tougaard3P <- function(object, limits){
LL <- length(object@RegionToFit$x)
if (object@Flags[1] == FALSE){ #KE scale
object@RegionToFit$x <- rev(object@RegionToFit$x)
}
avg1 <- limits$y[1]
avg2 <- sum(object@RegionToFit$y[(LL-4):LL])/5
object@RegionToFit$y<-object@RegionToFit$y-avg2
C <- 551
D <- 436
tougaard <- vector(mode="numeric", length=LL)
lK <- vector(mode="numeric", length=LL)
# Evaluation of the Universal Cross Section lK() and the B parameter
tmp <- 0
dE <- (object@RegionToFit$x[2] - object@RegionToFit$x[1]) # Estep
for (ii in 1:LL){
deltaE <- (ii-1)*dE
num <- deltaE*dE #(E'-E)*dE
denom <- (C+deltaE^2)^2 + D*deltaE^2 #(C+[E'-E]^2}^2 + D(E'-E)^2
lK[ii] <- num/denom #(E'-E)/{C+[E'-E]^2}^2 the modified uniiversal Cross Section L(E)*K(E,T) T=E'-E
tmp <- tmp+lK[ii]*object@RegionToFit$y[ii] #j(E')(E'-E)/{C+[E'-E]^2}^2
}
B <- (avg1-avg2)/tmp
#--- Computation Tougaard background: OK for both KE and BE scale
for (ii in 1:LL){
tougaard[ii] <- B*sum(lK[1:(LL-ii+1)]*object@RegionToFit$y[ii:LL])
}
tougaard <- tougaard+avg2 #add the Low-Energy-Side value of the spectrum
return(tougaard)
}
#====================================
# 4 Parameter Tougaard background
#====================================
# 4 parameter Tougaard background for non metallic homogeneous matter such as polymers
# This background is based on the Universal Cross section function defined by
# UC = Integral( L(E)* K(E'-E) )
# The energy loss (background) is then defined by
#
# Tougaard(E) = Integral( L(E)*K(E'-E) * J(E)dE' J(E) = acquired spectrum
#
# which may be expressed by a three paramenter B, C, C', D function:
#
# Tougaard4p = Integral( BT/[(C + C'*T^2)^2 + D*T^2] * J(E)dT where T=E'-E
#
#' @title Tougaard4P four parameters Tougaard Baseline
#' @description Tougaard4P is a Tougaard Baseline defined usinf
#' the four parameters B, C, C' and D
#' Tougaard4p = Integral{ BT/[(C + C'*T^2)^2 + D*T^2] * J(E)dT }
#' J(T) = the measured spectrum
#' B*T/[(C + C'*T^2)^2 + D*T^2] = Modified Universal Cross Section
#' T=energy loss = E'-E
#' see R. Hesse et al., Surf. Interface Anal. (2011), 43, 1514
#' This function is called by XPSAnalysisGUI
#' @param object XPSSample CoreLine
#' @param C1 numeric is a parameter value
#' @param limits limits of the XPSSample CoreLine
#' @return Return the 4parameter Tougaard background.
#' @export
Tougaard4P <- function(object, C1, limits){
LL <- length(object@RegionToFit$x)
if (object@Flags[1] == FALSE){ #KE scale
object@RegionToFit$x <- rev(object@RegionToFit$x)
}
avg1 <- limits$y[1]
avg2 <- limits$y[2] #sum(object@RegionToFit$y[(LL-4):LL])/5
object@RegionToFit$y <- object@RegionToFit$y-avg2
C <- 551
D <- 436
tougaard <- vector(mode="numeric", length=LL)
lK <- vector(mode="numeric", length=LL)
# Evaluation of the Universal Cross Section lK() and the B parameter
tmp <- 0
dE <- (object@RegionToFit$x[2] - object@RegionToFit$x[1]) # Estep
for (ii in 1:LL){
deltaE <- (ii-1)*dE
num <- deltaE*dE #(E'-E)*dE
denom <- (C+C1*deltaE^2)^2 + D*deltaE^2 #(C+[E'-E]^2}^2 + D(E'-E)^2
lK[ii] <- num/denom #(E'-E)/{C+[E'-E]^2}^2 the modified universal Cross Section L(E)*K(E,T) T=E'-E
tmp <- tmp+lK[ii]*object@RegionToFit$y[ii] #j(E')(E'-E)/{C+[E'-E]^2}^2
}
B <- (avg1-avg2)/tmp
#--- Computation Tougaard background: OK for both KE and BE scale
for (ii in 1:LL){
tougaard[ii] <- B*sum(lK[1:(LL-ii+1)]*object@RegionToFit$y[ii:LL])
}
tougaard <- tougaard+avg2 #add the Low-Energy-Side value of the spectrum
return(tougaard)
}
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