Fit

ODMR

ODMR fitting tools.

import nvtools as nv

fitter = nv.ODMRFitter()

# assume you have some ODMR spectrum
mw_frequency = np.array(...)
odmr = np.array(...)

# tries to automatically guess the starting parameters for the fit
fit_results = fitter.fit_odmr_full(mw_frequency, odmr)
# if that does not work, try inputting the frequencies manually:
fit_results = fitter.fit_odmr_full(mw_frequency, odmr, p0_frequency=[<list of eight values>])

# fit_results contains all kinds of useful values
print(fit_results.frequency)                                 # resonance frequency
print(fit_results.contrast)                                  # ODMR contrast
print(fit_results.linewidth)                                 # ODMR linewidth
print(fit_results.r_squared)                                 # R^2 value of the fit
print(fit_results.sensitivity(photon_rate=1e6 * unit.Hz))    # CW ODMR sensitivity

plt.figure()
plt.plot(mw_frequency, odmr)
plt.plot(mw_frequency, fit_results.fit_func)     # plot fit function
plt.show()

class nvtools.fit.odmr.ODMRFitResult(mw_frequency: list, odmr: list, popt: list, pcov: list, perr: list, model: Callable, frequency: float | list[float], contrast: float | list[float], linewidth: float | list[float])[source]

ODMR fit results.

contrast: float | list[float]

property fit_func: Fit function values.

frequency: float | list[float]

linewidth: float | list[float]

model: Callable

mw_frequency: list

odmr: list

pcov: list

perr: list

popt: list

property r_squared: R^2 value of fit.

$R^2 = 1 - \frac{SS_\text{res}}{SS_\text{tot}}$

sensitivity(photon_rate: float) → float[source]

Calculate CW ODMR sensitivity.

Parameters:: photon_rate (float) – Photon rate I_0

$\eta = \frac{1}{\text{max}\frac{\partial V(f)}{\partial f}} \frac{1}{\gamma_\text{NV}} \frac{1}{\sqrt{I_0}}$

class nvtools.fit.odmr.ODMRFitter[source]

ODMR fitter.

static fit_odmr_full(mw_frequency, odmr, p0_frequency=None, units=True)[source]

Fit ODMR with eight resonances.

Parameters:

mw_frequency – MW frequency
odmr – ODMR
p0_frequency (list | None) – estimates for resonance frequencies

Raises:

RuntimeError when peaks can not be found

static fit_odmr_single(mw_frequency, odmr)[source]

Fit ODMR with one resonance.

Parameters:

mw_frequency – MW frequency
odmr – ODMR

ODMR Model

ODMR fit models.

class nvtools.fit.odmr_model.ModelGauss1[source]

Gauss model with 1 resonance.

$G(x) = 1 - C \exp\left(4\ln\left(\frac{1}{2}\right)\frac{(x-f_{\text{res}})^2}{\alpha^2}\right)$

static f(x, c, alpha, f_res)[source]

Gauss profile.

Parameters:

x – X data
c – contrast
alpha – FWHM linewidth
f_res – resonance frequency

class nvtools.fit.odmr_model.ModelLorentz1[source]

Lorentz model with 1 resonance.

$L(x) = 1 - \frac{C\alpha^2}{4(x - f_{\text{res}})^2 + \alpha^2}$

static f(x, c, alpha, f_res)[source]

Lorentz profile.

Parameters:

x – X data
c – contrast
alpha – FWHM linewidth
f_res – resonance frequency

class nvtools.fit.odmr_model.ModelVoigt1[source]

Voigt model with 1 resonance.

$V(x) = \int G(x-\tau) L(x) \, d\tau$

static f(x, a, sigma, nu, f_res, c)[source]

Voigt profile with 1 resonance.

Parameters:

x – X data
a – area
sigma – Gauss width
nu – Lorentz width
f_res – resonance frequency
c – offset

static voigt_parameters(area, sigma, nu, units=True)[source]

Calculate useful parameters from Voigt fit parameters.

$\alpha_\text{L} &= 2\nu \\ \alpha_\text{G} &= 2\sigma\sqrt{2\log 2} \\ \alpha_\text{V} &= 0.5346\alpha_\text{L} + \sqrt{0.2166\alpha_\text{L}^2 + \alpha_\text{G}^2} \\ d &= \frac{\alpha_\text{L} - \alpha_\text{G}}{\alpha_\text{L} + \alpha_\text{G}} \\ C &= V(x=f_{\text{res}})$

Parameters:

area – area under graph
sigma – Gauss linewidth
nu – Lorentz linewidth

Returns:

alpha_l, alpha_g, alpha_v, d, contrast

class nvtools.fit.odmr_model.ModelVoigt8[source]

Voigt model with 8 resonances.

$V(x) = c - \sum_{i=1}^8 V_i(x)$

static 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)[source]: Voigt profile for eight resonances.

static voigt_parameters(area, sigma, nu, units=True)[source]: Same as ModelVoigt1.voigt_parameters.