"""ODMR fit models."""
import numpy as np
import scipy
import uncertainties.umath as um
from nvtools import unit
[docs]
class ModelLorentz1:
r"""
Lorentz model with 1 resonance.
.. math::
L(x) = 1 - \frac{C\alpha^2}{4(x - f_{\text{res}})^2 + \alpha^2}
"""
[docs]
@staticmethod
def f(x, c, alpha, f_res):
"""
Lorentz profile.
:param x: X data
:param c: contrast
:param alpha: FWHM linewidth
:param f_res: resonance frequency
"""
return 1 - (c * np.power(alpha, 2)) / (4 * np.power(x - f_res, 2) + np.power(alpha, 2))
[docs]
class ModelGauss1:
r"""
Gauss model with 1 resonance.
.. math::
G(x) = 1 - C \exp\left(4\ln\left(\frac{1}{2}\right)\frac{(x-f_{\text{res}})^2}{\alpha^2}\right)
"""
[docs]
@staticmethod
def f(x, c, alpha, f_res):
"""
Gauss profile.
:param x: X data
:param c: contrast
:param alpha: FWHM linewidth
:param f_res: resonance frequency
"""
return 1 - c * np.exp(4 * np.log(0.5) * np.power(x - f_res, 2) / np.power(alpha, 2))
[docs]
class ModelVoigt1:
r"""
Voigt model with 1 resonance.
.. math::
V(x) = \int G(x-\tau) L(x) \, d\tau
"""
[docs]
@staticmethod
def f(x, a, sigma, nu, f_res, c):
"""
Voigt profile with 1 resonance.
:param x: X data
:param a: area
:param sigma: Gauss width
:param nu: Lorentz width
:param f_res: resonance frequency
:param c: offset
"""
z = (x - f_res + 1j * nu) / (sigma * np.sqrt(2))
return c - a * np.real(scipy.special.wofz(z)) / (sigma * np.sqrt(2 * np.pi))
[docs]
@staticmethod
def voigt_parameters(area, sigma, nu, units=True):
r"""
Calculate useful parameters from Voigt fit parameters.
.. math::
\alpha_\text{L} &= 2\nu \\
\alpha_\text{G} &= 2\sigma\sqrt{2\log 2} \\
\alpha_\text{V} &= 0.5346\alpha_\text{L} + \sqrt{0.2166\alpha_\text{L}^2 + \alpha_\text{G}^2} \\
d &= \frac{\alpha_\text{L} - \alpha_\text{G}}{\alpha_\text{L} + \alpha_\text{G}} \\
C &= V(x=f_{\text{res}})
:param area: area under graph
:param sigma: Gauss linewidth
:param nu: Lorentz linewidth
:returns: alpha_l, alpha_g, alpha_v, d, contrast
"""
try:
area = area.to("MHz^2").magnitude
sigma = sigma.to("MHz").magnitude
nu = nu.to("MHz").magnitude
except AttributeError:
pass
alpha_l = 2 * nu
alpha_g = 2 * sigma * um.sqrt(2 * um.log(2))
alpha_v = 0.5346 * alpha_l + um.sqrt(0.2166 * alpha_l**2 + alpha_g**2)
d = (alpha_l - alpha_g) / (alpha_g + alpha_l)
try:
area_val = area.nominal_value
nu_val = nu.nominal_value
sigma_val = sigma.nominal_value
except AttributeError:
area_val = area
nu_val = nu
sigma_val = sigma
z0 = (1j * nu_val) / (sigma_val * np.sqrt(2))
contrast = area_val * np.real(scipy.special.wofz(z0)) / (sigma_val * np.sqrt(2 * np.pi))
if units:
return alpha_l * unit.MHz, alpha_g * unit.MHz, alpha_v * unit.MHz, d, contrast
else:
return alpha_l, alpha_g, alpha_v, d, contrast
[docs]
class ModelVoigt8:
r"""
Voigt model with 8 resonances.
.. math::
V(x) = c - \sum_{i=1}^8 V_i(x)
"""
[docs]
@staticmethod
def f(
x,
a1,
s1,
n1,
f1,
a2,
s2,
n2,
f2,
a3,
s3,
n3,
f3,
a4,
s4,
n4,
f4,
a5,
s5,
n5,
f5,
a6,
s6,
n6,
f6,
a7,
s7,
n7,
f7,
a8,
s8,
n8,
f8,
c,
):
"""Voigt profile for eight resonances."""
model_voigt_1 = ModelVoigt1()
return (
c
- model_voigt_1.f(x, -a1, s1, n1, f1, 0)
- model_voigt_1.f(x, -a2, s2, n2, f2, 0)
- model_voigt_1.f(x, -a3, s3, n3, f3, 0)
- model_voigt_1.f(x, -a4, s4, n4, f4, 0)
- model_voigt_1.f(x, -a5, s5, n5, f5, 0)
- model_voigt_1.f(x, -a6, s6, n6, f6, 0)
- model_voigt_1.f(x, -a7, s7, n7, f7, 0)
- model_voigt_1.f(x, -a8, s8, n8, f8, 0)
)
[docs]
@staticmethod
def voigt_parameters(area, sigma, nu, units=True):
"""Same as ModelVoigt1.voigt_parameters."""
return ModelVoigt1().voigt_parameters(area, sigma, nu, units)