Question

我最近正在处理光发射数据，并希望通过将费米函数与高斯的卷积拟合到实际数据来估计仪器分辨率。目前，我忽略了我也必须纳入背景知识。我尝试根据在Link1

中找到的内容来尝试平息

不幸的是，我现在被困住了，请您帮忙。我提供了一个小例子，我模拟的数据（通过肉眼判断）实际上是背景缺失的真实数据expet的良好表示：

import array as ar
import math
from math import e, sqrt, pi
import pylab as plt
from numpy import array, linspace, arange, zeros, ceil, amax, amin, argmax, argmin, abs
from numpy import polyfit, polyval, seterr, trunc, mean
from numpy.linalg import norm
from scipy.interpolate import interp1d
import scipy.optimize
import numpy as np
import matplotlib.pyplot as plt

kb = 8.6173e-5 # Boltzmann k in eV/K


def f(e,scale,T=300,muf=0):
    return scale*(1.0 / (np.exp((-e - muf)/(kb*T)) + 1)) # -e due to binding energy scale

def gaussian(x, mu, sig,scale):
    return scale*(np.exp(-np.power(-x - mu, 2.) / (2 * np.power(sig, 2.))))  # -x due to binding energy scale




Points=10000 # If i change the points the "modelt data" doesn not look good anymore?
espan = np.linspace(-10, 10, Points)


# simulate the fermi edge data such that is close to the read real data
# note that it actually is a convoluiton of a fermi and a gaussian function.
Sim_data = np.random.normal((8.07+np.convolve(f(espan,scale=1.05), gaussian(espan, mu=0, sig=0.3,scale=1.05),mode="same")),10)

# min max norm not ( not used for now )
# Sim_data_norm = ((Sim_data - Sim_data.min()) / (Sim_data.max() - Sim_data.min()))


# convolution
# I know the actual data was meassured at T=300K so i preset this value in the fermi function
# The position of the fermi function and the gaussian should be 0 so mu and muf are set to 0
# i guess x_values would have to be replaced for the x axis of my real data later?
def Gaus_fermi_convolution(size,sigC,scaleC,xC=espan):
    return size* np.convolve(gaussian(x=xC,sig=sigC,scale=scaleC,mu=0), f(e=espan,scale=scaleC,T=300,muf=0), mode="same") 

# try to fit
lowerBounds = [0.0, 0.0,0.0] # A, B, C ,D lower bounds
upperBounds = [440.0, 0.6,440.0] # A, B, C, D upper bounds

popt, pcov = scipy.optimize.curve_fit(Gaus_fermi_convolution, espan, Sim_data,bounds=[lowerBounds, upperBounds])
Opt_size,Opt_sigC,Opt_scaleC = popt

# Print out the coefficients determined by the optimization
print(Opt_size,Opt_sigC,Opt_scaleC)

# Plotting 
plt.plot(espan,Sim_data)
#The result is clearly wrong
plt.plot(espan,Gaus_fermi_convolution(size=Opt_size,sigC=Opt_sigC,scaleC=Opt_scaleC,xC=espan))

plt.xlim([2, -2])
plt.xlabel( r'$Binding \: Energy  \: [eV]$')
plt.ylabel(r'$Intensity\: [arb. u.] $')
plt.show()

用Python将Fermi函数与高斯函数的卷积拟合到实际数据

0 个答案: