[Python] Cosine with a Gaussian envelope fit failing in python using scipy.optimize.curve_fit

I'm trying to fit data that resembles a cosine function with a decaying Gaussian envelope using python, and in particular scipy.optimize.curve_fit. However, it seems like my code is not varying the parameters enough.

For example, in this data, the center of the interferogram is slightly negative (around -0.1), but even when I provide a guess that is very close, the optimized parameters are clearly off. The horizontal offset just stays very close to my initial guess even if it is clearly not an optimal point. I checked that by manually varying the horizontal offset and calculating the coefficient of determination and the values offered by curve_fit are not the most optimal.

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from scipy.optimize import curve_fit

id_ = '0'

filename = '250516_FF_01_coincidences_'+id_+'mm.txt'


def FF_function(x,l,s,A,xoff):
d = x - xoff
return A*np.cos(2*np.pi/l*d)*np.exp(-0.5*(d/s)**2)+A #

data = pd.read_csv(filename, sep=' ',header= None).to_numpy()

# data = data.astype(dtype=np.float32)

fig = plt.subplots(figsize=(10,5))
ax = plt.subplot(111)

ax.plot(data[:,0],data[:,1],alpha = 0.3)

guess = [4.40673558e-02, 2.63973377e-01, 1.63702697e+02, -0.2]

xx=np.linspace(min(data[:,0]),max(data[:,0]),1000)
# ax.plot(xx,FF_function(xx,*guess)

popt,cov = curve_fit(FF_function,data[:,0],data[:,1],p0 = guess)
ax.plot(xx,FF_function(xx,*popt), color ='C0',alpha = 0.5)

SSE = np.sum(np.square(data[:,1]-FF_function(data[:,0], *popt)))
SST = np.sum(np.square(data[:,1]-np.mean(data[:,1])))
r2 = 1 - SSE/SST
print(r2)


print(popt)

#
ax.set_xlabel('Displacement (mm)')
ax.set_ylabel('Coincidences')


Example

I can try doing a manual minimization of the determination coefficient, but I'm curious about what is going wrong in my fit.

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