probe.probe - Instrument probe

BaseProbe
NeutronProbe	Neutron probe.
PolarizedNeutronProbe	Polarized neutron probe
PolarizedNeutronQProbe	alias of PolarizedQProbe
PolarizedQProbe
Probe	Defines the incident beam used to study the material.
ProbeSet
QProbe	A pure Q, R probe
Qmeasurement_union	Determine the unique Q, dQ across all datasets.
XrayProbe	X-Ray probe.
make_probe	Return a reflectometry measurement object of the given resolution.
spin_asymmetry	Compute spin asymmetry for R++, R--.

Experimental probe.

The experimental probe describes the incoming beam for the experiment. Scattering properties of the sample are dependent on the type and energy of the radiation.

See Data Representation for details.

class refl1d.probe.probe.BaseProbe

Bases: object

Q: NDArray

Q_c(substrate=None, surface=None)

R: NDArray

property Ro

apply_beam(calc_Q, calc_R, resolution=True, interpolation=0)

Apply factors such as beam intensity, background, backabsorption, resolution to the data.

resolution is True if the resolution function should be applied to the reflectivity.

interpolation is the number of Q points to show between the nominal Q points of the probe. Use this to draw a smooth theory line between the data points. The resolution dQ is interpolated between the resolution of the surrounding Q points.

If an amplitude signal is provided, \(r\) will be scaled by \(\surd I + i \surd B / |r|\), which when squared will equal \(I |r|^2 + B\). The resolution function will be applied directly to the amplitude. Unlike intensity and background, the resulting \(|G \ast r|^2 \ne G \ast |r|^2\) for convolution operator \(\ast\), but it should be close.

back_absorption: Parameter

back_reflectivity: bool = False

background: Parameter

property calc_Q

Define in derived classes

dQ: Sequence | NDArray | None = None

dR: Sequence | NDArray | None = None

fresnel(substrate=None, surface=None)

Returns a Fresnel reflectivity calculator given the surface and and substrate. The calculated reflectivity includes The Fresnel reflectivity for the probe reflecting from a block of material with the given substrate.

Returns F = R(probe.Q), where R is magnitude squared reflectivity.

intensity: Parameter

label(prefix=None, gloss='', suffix='')

log10_to_linear()

Convert data from log to linear.

Older reflectometry reduction code stored reflectivity in log base 10 format. Call probe.log10_to_linear() after loading this data to convert it to linear for subsequent display and fitting.

name: str | None = None

plot(view=None, **kwargs)

Plot theory against data.

Need substrate/surface for Fresnel-normalized reflectivity

plot_Q4(**kwargs)

Plot the Q**4 reflectivity associated with the probe.

Note that Q**4 reflectivity has the intensity and background applied so that hydrogenated samples display more cleanly. The formula to reproduce the graph is:

\[R' = R / ( (100*Q)^{-4} I + B) \Delta R' = \Delta R / ( (100*Q)^{-4} I + B )\]

where \(B\) is the background.

plot_fft(theory=None, suffix='', label=None, substrate=None, surface=None, **kwargs)

FFT analysis of reflectivity signal.

plot_fresnel(substrate=None, surface=None, **kwargs)

Plot the Fresnel-normalized reflectivity associated with the probe.

Note that the Fresnel reflectivity has the intensity and background applied before normalizing so that hydrogenated samples display more cleanly. The formula to reproduce the graph is:

\[R' = R / (F(Q) I + B) \Delta R' = \Delta R / (F(Q) I + B)\]

where \(I\) is the intensity and \(B\) is the background.

plot_linear(**kwargs)

Plot the data associated with probe.

plot_log(**kwargs)

Plot the data associated with probe.

plot_logfresnel(*args, **kw)

Plot the log Fresnel-normalized reflectivity associated with the probe.

plot_residuals(theory=None, suffix='', label=None, plot_shift=None, **kwargs)

plot_resolution(suffix='', label=None, **kwargs)

plot_shift = 0

residuals_shift = 0

resolution: Literal['normal', 'uniform'] = 'uniform'

resolution_guard()

Make sure each measured \(Q\) point has at least 5 calculated \(Q\) points contributing to it in the range \([-3\Delta Q, 3\Delta Q]\).

Not Implemented

restore_data()

Restore the original data after resynth.

resynth_data()

Generate new data according to the model R’ ~ N(R, dR).

The resynthesis step is a precursor to refitting the data, as is required for certain types of monte carlo error analysis. The first time it is run it will save the original R into Ro. If you reset R in the probe you will also need to reset Ro so that it is used for subsequent resynth analysis.

save(filename, theory, substrate=None, surface=None)

Save the data and theory to a file.

show_resolution = True

simulate_data(theory, noise=2.0)

Set the data for the probe to R + eps with eps ~ normal(dR^2).

theory is (Q, R),

If the percent noise is provided, set dR to R*noise/100 before simulating. noise defaults to 2% if no dR is present.

Note that measured data estimates uncertainty from the number of counts. This means that points above the true value will have larger uncertainty than points below the true value. This bias is not captured in the simulated data.

view = 'log'

class refl1d.probe.probe.NeutronProbe(T=None, dT=0, L=None, dL=0, data=None, intensity=1, background=0, back_absorption=1, theta_offset=0, sample_broadening=0, back_reflectivity=False, name: str | None = None, filename=None, dQo=None, resolution: Literal['normal', 'uniform'] = 'normal', oversampling=None, oversampling_seed=1)

Bases: Probe

Neutron probe.

By providing a scattering factor calculator for X-ray scattering, model components can be defined by mass density and chemical composition.

Aguide = 270.0

L: NDArray

property Q

Q_c(substrate=None, surface=None)

R: Any | None = None

property Ro

T: NDArray

static alignment_uncertainty(w, I, d=0)

Compute alignment uncertainty.

Parameters:

wfloat | degrees

Rocking curve full width at half max.

Ifloat | counts

Rocking curve integrated intensity.

d = 0: float | degrees

Motor step size

Returns:

dthetafloat | degrees

uncertainty in alignment angle

apply_beam(calc_Q, calc_R, resolution=True, interpolation=0)

Apply factors such as beam intensity, background, backabsorption, resolution to the data.

resolution is True if the resolution function should be applied to the reflectivity.

interpolation is the number of Q points to show between the nominal Q points of the probe. Use this to draw a smooth theory line between the data points. The resolution dQ is interpolated between the resolution of the surrounding Q points.

If an amplitude signal is provided, \(r\) will be scaled by \(\surd I + i \surd B / |r|\), which when squared will equal \(I |r|^2 + B\). The resolution function will be applied directly to the amplitude. Unlike intensity and background, the resulting \(|G \ast r|^2 \ne G \ast |r|^2\) for convolution operator \(\ast\), but it should be close.

back_absorption: Parameter

back_reflectivity: bool = False

background: Parameter

property calc_Q

Define in derived classes

critical_edge(substrate=None, surface=None, n=51, delta=0.25)

Oversample points near the critical edge.

The critical edge is defined by the difference in scattering potential for the substrate and surface materials, or the reverse if back_reflectivity is true.

n is the number of \(Q\) points to compute near the critical edge.

delta is the relative uncertainty in the material density, which defines the range of values which are calculated.

Note: critical_edge() will remove the extra Q calculation points introduced by oversample().

The \(n\) points \(Q_i\) are evenly distributed around the critical edge in \(Q_c \pm \delta Q_c\) by varying angle \(\theta\) for a fixed wavelength \(< \lambda >\), the average of all wavelengths in the probe.

Specifically:

\[\begin{split}Q_c^2 &= 16 \pi (\rho - \rho_\text{incident}) \\ Q_i &= Q_c - \delta_i Q_c (i - (n-1)/2) \qquad \text{for} \; i \in 0 \ldots n-1 \\ \lambda_i &= < \lambda > \\ \theta_i &= \sin^{-1}(Q_i \lambda_i / 4 \pi)\end{split}\]

If \(Q_c\) is imaginary, then \(-|Q_c|\) is used instead, so this routine can be used for reflectivity signals which scan from back reflectivity to front reflectivity. For completeness, the angle \(\theta = 0\) is added as well.

dL: Any | None = 0

property dQ

dQo: Sequence | 'NDArray' | None = None

dR: Any | None = 0

dT: Any | None = 0

filename: str | None = None

fresnel(substrate=None, surface=None)

Returns a Fresnel reflectivity calculator given the surface and and substrate. The calculated reflectivity includes The Fresnel reflectivity for the probe reflecting from a block of material with the given substrate.

Returns F = R(probe.Q), where R is magnitude squared reflectivity.

classmethod from_dict(**kw)

intensity: Parameter

label(prefix=None, gloss='', suffix='')

log10_to_linear()

Convert data from log to linear.

Older reflectometry reduction code stored reflectivity in log base 10 format. Call probe.log10_to_linear() after loading this data to convert it to linear for subsequent display and fitting.

name: str | None = None

oversample(n=20, seed=1)

Generate an over-sampling of Q to avoid aliasing effects.

Oversampling is needed for thick layers, in which the underlying reflectivity oscillates so rapidly in Q that a single measurement has contributions from multiple Kissig fringes.

Sampling will be done using a pseudo-random generator so that accidental structure in the function does not contribute to the aliasing. The generator will usually be initialized with a fixed seed so that the point selection will not change from run to run, but a seed of None will choose a different set of points each time oversample is called.

The value n is the number of points that should contribute to each Q value when computing the resolution. These will be distributed about the nominal measurement value, but varying in both angle and energy according to the resolution function. This will yield more points near the measurement and fewer farther away. The measurement point itself will not be used to avoid accidental bias from uniform Q steps. Depending on the problem, a value of n between 20 and 100 should lead to stable values for the convolved reflectivity.

Note: oversample() will remove the extra Q calculation points introduced by critical_edge().

oversampling: int | None = None

oversampling_seed: int = 1

parameters()

plot(view=None, **kwargs)

Plot theory against data.

Need substrate/surface for Fresnel-normalized reflectivity

plot_Q4(**kwargs)

Plot the Q**4 reflectivity associated with the probe.

Note that Q**4 reflectivity has the intensity and background applied so that hydrogenated samples display more cleanly. The formula to reproduce the graph is:

\[R' = R / ( (100*Q)^{-4} I + B) \Delta R' = \Delta R / ( (100*Q)^{-4} I + B )\]

where \(B\) is the background.

plot_fft(theory=None, suffix='', label=None, substrate=None, surface=None, **kwargs)

FFT analysis of reflectivity signal.

plot_fresnel(substrate=None, surface=None, **kwargs)

Plot the Fresnel-normalized reflectivity associated with the probe.

Note that the Fresnel reflectivity has the intensity and background applied before normalizing so that hydrogenated samples display more cleanly. The formula to reproduce the graph is:

\[R' = R / (F(Q) I + B) \Delta R' = \Delta R / (F(Q) I + B)\]

where \(I\) is the intensity and \(B\) is the background.

plot_linear(**kwargs)

Plot the data associated with probe.

plot_log(**kwargs)

Plot the data associated with probe.

plot_logfresnel(*args, **kw)

Plot the log Fresnel-normalized reflectivity associated with the probe.

plot_residuals(theory=None, suffix='', label=None, plot_shift=None, **kwargs)

plot_resolution(suffix='', label=None, **kwargs)

plot_shift = 0

polarized = False

radiation: Literal['neutron', 'xray'] = 'neutron'

residuals_shift = 0

resolution: Literal['normal', 'uniform'] = 'uniform'

resolution_guard()

Make sure each measured \(Q\) point has at least 5 calculated \(Q\) points contributing to it in the range \([-3\Delta Q, 3\Delta Q]\).

Not Implemented

restore_data()

Restore the original data after resynth.

resynth_data()

Generate new data according to the model R’ ~ N(R, dR).

The resynthesis step is a precursor to refitting the data, as is required for certain types of monte carlo error analysis. The first time it is run it will save the original R into Ro. If you reset R in the probe you will also need to reset Ro so that it is used for subsequent resynth analysis.

sample_broadening: Parameter

save(filename, theory, substrate=None, surface=None)

Save the data and theory to a file.

scattering_factors(material, density)

Returns the scattering factors associated with the material given the range of wavelengths/energies used in the probe.

show_resolution = True

simulate_data(theory, noise=2.0)

Set the data for the probe to R + eps with eps ~ normal(dR^2).

theory is (Q, R),

If the percent noise is provided, set dR to R*noise/100 before simulating. noise defaults to 2% if no dR is present.

Note that measured data estimates uncertainty from the number of counts. This means that points above the true value will have larger uncertainty than points below the true value. This bias is not captured in the simulated data.

subsample(dQ)

Select points at most every dQ.

Use this to speed up computation early in the fitting process.

This changes the data object, and is not reversible.

The current algorithm is not picking the “best” Q value, just the nearest, so if you have nearby Q points with different quality statistics (as happens in overlapped regions from spallation source measurements at different angles), then it may choose badly. Simple solutions based on the smallest relative error dR/R will be biased toward peaks, and smallest absolute error dR will be biased toward valleys.

theta_offset: Parameter

to_dict()

Return a dictionary representation of the parameters

view = 'log'

write_data(filename, columns=('Q', 'R', 'dR'), header=None)

Save the data to a file.

header is a string with trailing n containing the file header. columns is a list of column names from Q, dQ, R, dR, L, dL, T, dT.

The default is to write Q, R, dR data.

class refl1d.probe.probe.PolarizedNeutronProbe(xs: Tuple | None = None, mm: NeutronProbe | Literal[None] = None, mp: NeutronProbe | Literal[None] = None, pm: NeutronProbe | Literal[None] = None, pp: NeutronProbe | Literal[None] = None, name=None, Aguide=270.0, H=0, oversampling=None, oversampling_seed=1)

Bases: object

Polarized neutron probe

xs (4 x NeutronProbe) is a sequence pp, pm, mp and mm.

Aguide (degrees) is the angle of the applied field relative to the plane of the sample, with angle 270º in the plane of the sample.

H (tesla) is the magnitude of the applied field

Aguide: Parameter

H: Parameter

apply_beam(Q, R, resolution=True, interpolation=0)

Apply factors such as beam intensity, background, backabsorption, and footprint to the data.

property calc_Q

fresnel(*args, **kw)

Returns a Fresnel reflectivity calculator given the surface and and substrate. The calculated reflectivity includes The Fresnel reflectivity for the probe reflecting from a block of material with the given substrate.

Returns F = R(probe.Q), where R is magnitude squared reflectivity.

mm: NeutronProbe | Literal[None] = None

mp: NeutronProbe | Literal[None] = None

name: str

oversample(n=20, seed=1)

Generate an over-sampling of Q to avoid aliasing effects.

Oversampling is needed for thick layers, in which the underlying reflectivity oscillates so rapidly in Q that a single measurement has contributions from multiple Kissig fringes.

Sampling will be done using a pseudo-random generator so that accidental structure in the function does not contribute to the aliasing. The generator will usually be initialized with a fixed seed so that the point selection will not change from run to run, but a seed of None will choose a different set of points each time oversample is called.

The value n is the number of points that should contribute to each Q value when computing the resolution. These will be distributed about the nominal measurement value, but varying in both angle and energy according to the resolution function. This will yield more points near the measurement and fewer farther away. The measurement point itself will not be used to avoid accidental bias from uniform Q steps. Depending on the problem, a value of n between 20 and 100 should lead to stable values for the convolved reflectivity.

Note: oversample() will remove the extra Q calculation points introduced by critical_edge().

oversampling: int | None = None

oversampling_seed: int = 1

parameters()

plot(view=None, **kwargs)

Plot theory against data.

Need substrate/surface for Fresnel-normalized reflectivity

plot_Q4(**kwargs)

plot_SA(theory=None, label=None, plot_shift=None, **kwargs)

plot_fresnel(**kwargs)

plot_linear(**kwargs)

plot_log(**kwargs)

plot_logfresnel(**kwargs)

plot_residuals(**kwargs)

plot_resolution(**kwargs)

pm: NeutronProbe | Literal[None] = None

polarized = True

pp: NeutronProbe | Literal[None] = None

restore_data()

Restore the original data after resynth.

resynth_data()

Generate new data according to the model R’ ~ N(R, dR).

The resynthesis step is a precursor to refitting the data, as is required for certain types of monte carlo error analysis. The first time it is run it will save the original R into Ro. If you reset R in the probe you will also need to reset Ro so that it is used for subsequent resynth analysis.

save(filename, theory, substrate=None, surface=None)

Save the data and theory to a file.

scattering_factors(material, density)

Returns the scattering factors associated with the material given the range of wavelengths/energies used in the probe.

select_corresponding(theory)

Select theory points corresponding to the measured data.

Since we have evaluated theory at every Q, it is safe to interpolate measured Q into theory, since it will land on a node, not in an interval.

shared_beam(intensity=1, background=0, back_absorption=1, theta_offset=0, sample_broadening=0)

Share beam parameters across all four cross sections.

New parameters are created for intensity, background, theta_offset, sample_broadening and back_absorption and assigned to the all cross sections. These can be replaced with an explicit parameter in an individual cross section if that parameter is independent.

show_resolution = None

simulate_data(theory, noise=2.0)

Set the data for the probe to R + eps with eps ~ normal(dR^2).

theory is (Q, R),

If the percent noise is provided, set dR to R*noise/100 before simulating. noise defaults to 2% if no dR is present.

Note that measured data estimates uncertainty from the number of counts. This means that points above the true value will have larger uncertainty than points below the true value. This bias is not captured in the simulated data.

substrate = None

surface = None

view = None

property xs: List[NeutronProbe | None]

refl1d.probe.probe.PolarizedNeutronQProbe

alias of PolarizedQProbe

class refl1d.probe.probe.PolarizedQProbe(xs: Tuple | None = None, mm: refl1d.probe.probe.NeutronProbe | Literal[None] = None, mp: refl1d.probe.probe.NeutronProbe | Literal[None] = None, pm: refl1d.probe.probe.NeutronProbe | Literal[None] = None, pp: refl1d.probe.probe.NeutronProbe | Literal[None] = None, name=None, Aguide=270.0, H=0, oversampling: int | None = None, oversampling_seed: int = 1)

Bases: PolarizedNeutronProbe

Aguide: Parameter

H: Parameter

apply_beam(Q, R, resolution=True, interpolation=0)

Apply factors such as beam intensity, background, backabsorption, and footprint to the data.

property calc_Q

fresnel(*args, **kw)

Returns a Fresnel reflectivity calculator given the surface and and substrate. The calculated reflectivity includes The Fresnel reflectivity for the probe reflecting from a block of material with the given substrate.

Returns F = R(probe.Q), where R is magnitude squared reflectivity.

mm: NeutronProbe | Literal[None] = None

mp: NeutronProbe | Literal[None] = None

name: str

oversample(n=20, seed=1)

Generate an over-sampling of Q to avoid aliasing effects.

Oversampling is needed for thick layers, in which the underlying reflectivity oscillates so rapidly in Q that a single measurement has contributions from multiple Kissig fringes.

Sampling will be done using a pseudo-random generator so that accidental structure in the function does not contribute to the aliasing. The generator will usually be initialized with a fixed seed so that the point selection will not change from run to run, but a seed of None will choose a different set of points each time oversample is called.

The value n is the number of points that should contribute to each Q value when computing the resolution. These will be distributed about the nominal measurement value, but varying in both angle and energy according to the resolution function. This will yield more points near the measurement and fewer farther away. The measurement point itself will not be used to avoid accidental bias from uniform Q steps. Depending on the problem, a value of n between 20 and 100 should lead to stable values for the convolved reflectivity.

Note: oversample() will remove the extra Q calculation points introduced by critical_edge().

oversampling: int | None = None

oversampling_seed: int = 1

parameters()

plot(view=None, **kwargs)

Plot theory against data.

Need substrate/surface for Fresnel-normalized reflectivity

plot_Q4(**kwargs)

plot_SA(theory=None, label=None, plot_shift=None, **kwargs)

plot_fresnel(**kwargs)

plot_linear(**kwargs)

plot_log(**kwargs)

plot_logfresnel(**kwargs)

plot_residuals(**kwargs)

plot_resolution(**kwargs)

pm: NeutronProbe | Literal[None] = None

polarized = True

pp: NeutronProbe | Literal[None] = None

restore_data()

Restore the original data after resynth.

resynth_data()

Generate new data according to the model R’ ~ N(R, dR).

The resynthesis step is a precursor to refitting the data, as is required for certain types of monte carlo error analysis. The first time it is run it will save the original R into Ro. If you reset R in the probe you will also need to reset Ro so that it is used for subsequent resynth analysis.

save(filename, theory, substrate=None, surface=None)

Save the data and theory to a file.

scattering_factors(material, density)

Returns the scattering factors associated with the material given the range of wavelengths/energies used in the probe.

select_corresponding(theory)

Select theory points corresponding to the measured data.

Since we have evaluated theory at every Q, it is safe to interpolate measured Q into theory, since it will land on a node, not in an interval.

shared_beam(intensity=1, background=0, back_absorption=1, theta_offset=0, sample_broadening=0)

Share beam parameters across all four cross sections.

New parameters are created for intensity, background, theta_offset, sample_broadening and back_absorption and assigned to the all cross sections. These can be replaced with an explicit parameter in an individual cross section if that parameter is independent.

show_resolution = None

simulate_data(theory, noise=2.0)

Set the data for the probe to R + eps with eps ~ normal(dR^2).

theory is (Q, R),

If the percent noise is provided, set dR to R*noise/100 before simulating. noise defaults to 2% if no dR is present.

Note that measured data estimates uncertainty from the number of counts. This means that points above the true value will have larger uncertainty than points below the true value. This bias is not captured in the simulated data.

substrate = None

surface = None

view = None

property xs: List[NeutronProbe | None]

class refl1d.probe.probe.Probe(T=None, dT=0, L=None, dL=0, data=None, intensity=1, background=0, back_absorption=1, theta_offset=0, sample_broadening=0, back_reflectivity=False, name: str | None = None, filename=None, dQo=None, resolution: Literal['normal', 'uniform'] = 'normal', oversampling=None, oversampling_seed=1)

Bases: BaseProbe

Defines the incident beam used to study the material.

For calculation purposes, probe needs to return the values \(Q_\text{calc}\) at which the model is evaluated. This is normally going to be the measured points only, but for some systems, such as those with very thick layers, oversampling is needed to avoid aliasing effects.

A measurement point consists of incident angle, angular resolution, incident wavelength, FWHM wavelength resolution, reflectivity and uncertainty in reflectivity.

A probe is a set of points, defined by vectors for point attribute. For convenience, the attribute can be initialized with a scalar if it is constant throughout the measurement, but will be set to a vector in the probe. The attributes are initialized as follows:

Tfloat or [float] | degrees

Incident angle

dTfloat or [float] | degrees

FWHM angular divergence

Lfloat or [float] | Å

Incident wavelength

dLfloat or [float] | Å

FWHM wavelength dispersion

data([float], [float])

R, dR reflectivity measurement and uncertainty

dQ[float] or None | Å^-1

1-$sigma$ Q resolution when it cannot be computed directly from angular divergence and wavelength dispersion.

resolution‘normal’ or ‘uniform’

Distribution function for Q resolution.

Measurement properties:

intensityfloat or Parameter

Beam intensity

backgroundfloat or Parameter

Constant background

back_absorptionfloat or Parameter

Absorption through the substrate relative to beam intensity. A value of 1.0 means complete transmission; a value of 0.0 means complete absorption.

theta_offsetfloat or Parameter

Offset of the sample from perfect alignment

sample_broadeningfloat or Parameter

Additional FWHM angular divergence from sample curvature. Scale 1-\(\sigma\) rms by \(2 \surd(2 \ln 2) \approx 2.35\) to convert to FWHM.

back_reflectivityTrue or False

True if the beam enters through the substrate

Measurement properties are fittable parameters. theta_offset in particular should be set using probe.theta_offset.dev(dT), with dT equal to the FWHM uncertainty in the peak position for the rocking curve, as measured in radians. Changes to theta_offset will then be penalized in the cost function for the fit as if it were another measurement. Use alignment_uncertainty() to compute dT from the shape of the rocking curve.

Sample broadening adjusts the existing Q resolution rather than recalculating it. This allows it the resolution to describe more complicated effects than a simple gaussian distribution of wavelength and angle will allow. The calculation uses the mean wavelength, angle and angular divergence. See resolution.dQ_broadening() for details.

intensity and back_absorption are generally not needed — scaling the reflected signal by an appropriate intensity measurement will correct for both of these during reduction. background may be needed, particularly for samples with significant hydrogen content due to its large isotropic incoherent scattering cross section.

Aguide = 270.0

L: NDArray

property Q

Q_c(substrate=None, surface=None)

R: Any | None = None

property Ro

T: NDArray

static alignment_uncertainty(w, I, d=0)

Compute alignment uncertainty.

Parameters:

wfloat | degrees

Rocking curve full width at half max.

Ifloat | counts

Rocking curve integrated intensity.

d = 0: float | degrees

Motor step size

Returns:

dthetafloat | degrees

uncertainty in alignment angle

apply_beam(calc_Q, calc_R, resolution=True, interpolation=0)

Apply factors such as beam intensity, background, backabsorption, resolution to the data.

resolution is True if the resolution function should be applied to the reflectivity.

interpolation is the number of Q points to show between the nominal Q points of the probe. Use this to draw a smooth theory line between the data points. The resolution dQ is interpolated between the resolution of the surrounding Q points.

If an amplitude signal is provided, \(r\) will be scaled by \(\surd I + i \surd B / |r|\), which when squared will equal \(I |r|^2 + B\). The resolution function will be applied directly to the amplitude. Unlike intensity and background, the resulting \(|G \ast r|^2 \ne G \ast |r|^2\) for convolution operator \(\ast\), but it should be close.

back_absorption: Parameter

back_reflectivity: bool = False

background: Parameter

property calc_Q

Define in derived classes

critical_edge(substrate=None, surface=None, n=51, delta=0.25)

Oversample points near the critical edge.

The critical edge is defined by the difference in scattering potential for the substrate and surface materials, or the reverse if back_reflectivity is true.

n is the number of \(Q\) points to compute near the critical edge.

delta is the relative uncertainty in the material density, which defines the range of values which are calculated.

Note: critical_edge() will remove the extra Q calculation points introduced by oversample().

The \(n\) points \(Q_i\) are evenly distributed around the critical edge in \(Q_c \pm \delta Q_c\) by varying angle \(\theta\) for a fixed wavelength \(< \lambda >\), the average of all wavelengths in the probe.

Specifically:

\[\begin{split}Q_c^2 &= 16 \pi (\rho - \rho_\text{incident}) \\ Q_i &= Q_c - \delta_i Q_c (i - (n-1)/2) \qquad \text{for} \; i \in 0 \ldots n-1 \\ \lambda_i &= < \lambda > \\ \theta_i &= \sin^{-1}(Q_i \lambda_i / 4 \pi)\end{split}\]

If \(Q_c\) is imaginary, then \(-|Q_c|\) is used instead, so this routine can be used for reflectivity signals which scan from back reflectivity to front reflectivity. For completeness, the angle \(\theta = 0\) is added as well.

dL: Any | None = 0

property dQ

dQo: Sequence | NDArray | None = None

dR: Any | None = 0

dT: Any | None = 0

filename: str | None = None

fresnel(substrate=None, surface=None)

Returns a Fresnel reflectivity calculator given the surface and and substrate. The calculated reflectivity includes The Fresnel reflectivity for the probe reflecting from a block of material with the given substrate.

Returns F = R(probe.Q), where R is magnitude squared reflectivity.

classmethod from_dict(**kw)

intensity: Parameter

label(prefix=None, gloss='', suffix='')

log10_to_linear()

Convert data from log to linear.

Older reflectometry reduction code stored reflectivity in log base 10 format. Call probe.log10_to_linear() after loading this data to convert it to linear for subsequent display and fitting.

name: str | None = None

oversample(n=20, seed=1)

Generate an over-sampling of Q to avoid aliasing effects.

Oversampling is needed for thick layers, in which the underlying reflectivity oscillates so rapidly in Q that a single measurement has contributions from multiple Kissig fringes.

Sampling will be done using a pseudo-random generator so that accidental structure in the function does not contribute to the aliasing. The generator will usually be initialized with a fixed seed so that the point selection will not change from run to run, but a seed of None will choose a different set of points each time oversample is called.

The value n is the number of points that should contribute to each Q value when computing the resolution. These will be distributed about the nominal measurement value, but varying in both angle and energy according to the resolution function. This will yield more points near the measurement and fewer farther away. The measurement point itself will not be used to avoid accidental bias from uniform Q steps. Depending on the problem, a value of n between 20 and 100 should lead to stable values for the convolved reflectivity.

Note: oversample() will remove the extra Q calculation points introduced by critical_edge().

oversampling: int | None = None

oversampling_seed: int = 1

parameters()

plot(view=None, **kwargs)

Plot theory against data.

Need substrate/surface for Fresnel-normalized reflectivity

plot_Q4(**kwargs)

Plot the Q**4 reflectivity associated with the probe.

Note that Q**4 reflectivity has the intensity and background applied so that hydrogenated samples display more cleanly. The formula to reproduce the graph is:

\[R' = R / ( (100*Q)^{-4} I + B) \Delta R' = \Delta R / ( (100*Q)^{-4} I + B )\]

where \(B\) is the background.

plot_fft(theory=None, suffix='', label=None, substrate=None, surface=None, **kwargs)

FFT analysis of reflectivity signal.

plot_fresnel(substrate=None, surface=None, **kwargs)

Plot the Fresnel-normalized reflectivity associated with the probe.

Note that the Fresnel reflectivity has the intensity and background applied before normalizing so that hydrogenated samples display more cleanly. The formula to reproduce the graph is:

\[R' = R / (F(Q) I + B) \Delta R' = \Delta R / (F(Q) I + B)\]

where \(I\) is the intensity and \(B\) is the background.

plot_linear(**kwargs)

Plot the data associated with probe.

plot_log(**kwargs)

Plot the data associated with probe.

plot_logfresnel(*args, **kw)

Plot the log Fresnel-normalized reflectivity associated with the probe.

plot_residuals(theory=None, suffix='', label=None, plot_shift=None, **kwargs)

plot_resolution(suffix='', label=None, **kwargs)

plot_shift = 0

polarized = False

radiation: Literal['neutron', 'xray'] = 'xray'

residuals_shift = 0

resolution: Literal['normal', 'uniform'] = 'uniform'

resolution_guard()

Make sure each measured \(Q\) point has at least 5 calculated \(Q\) points contributing to it in the range \([-3\Delta Q, 3\Delta Q]\).

Not Implemented

restore_data()

Restore the original data after resynth.

resynth_data()

Generate new data according to the model R’ ~ N(R, dR).

The resynthesis step is a precursor to refitting the data, as is required for certain types of monte carlo error analysis. The first time it is run it will save the original R into Ro. If you reset R in the probe you will also need to reset Ro so that it is used for subsequent resynth analysis.

sample_broadening: Parameter

save(filename, theory, substrate=None, surface=None)

Save the data and theory to a file.

scattering_factors(material, density)

Returns the scattering factors associated with the material given the range of wavelengths/energies used in the probe.

show_resolution = True

simulate_data(theory, noise=2.0)

Set the data for the probe to R + eps with eps ~ normal(dR^2).

theory is (Q, R),

If the percent noise is provided, set dR to R*noise/100 before simulating. noise defaults to 2% if no dR is present.

Note that measured data estimates uncertainty from the number of counts. This means that points above the true value will have larger uncertainty than points below the true value. This bias is not captured in the simulated data.

subsample(dQ)

Select points at most every dQ.

Use this to speed up computation early in the fitting process.

This changes the data object, and is not reversible.

The current algorithm is not picking the “best” Q value, just the nearest, so if you have nearby Q points with different quality statistics (as happens in overlapped regions from spallation source measurements at different angles), then it may choose badly. Simple solutions based on the smallest relative error dR/R will be biased toward peaks, and smallest absolute error dR will be biased toward valleys.

theta_offset: Parameter

to_dict()

Return a dictionary representation of the parameters

view = 'log'

write_data(filename, columns=('Q', 'R', 'dR'), header=None)

Save the data to a file.

header is a string with trailing n containing the file header. columns is a list of column names from Q, dQ, R, dR, L, dL, T, dT.

The default is to write Q, R, dR data.

class refl1d.probe.probe.ProbeSet(probes, name=None)

Bases: object

property Q

apply_beam(calc_Q, calc_R, interpolation=0, **kw)

property calc_Q

property dQ

fresnel(*args, **kw)

Returns a Fresnel reflectivity calculator given the surface and and substrate. The calculated reflectivity includes The Fresnel reflectivity for the probe reflecting from a block of material with the given substrate.

Returns F = R(probe.Q), where R is magnitude squared reflectivity.

name: str | None

oversample(**kw)

Generate an over-sampling of Q to avoid aliasing effects.

Oversampling is needed for thick layers, in which the underlying reflectivity oscillates so rapidly in Q that a single measurement has contributions from multiple Kissig fringes.

Sampling will be done using a pseudo-random generator so that accidental structure in the function does not contribute to the aliasing. The generator will usually be initialized with a fixed seed so that the point selection will not change from run to run, but a seed of None will choose a different set of points each time oversample is called.

The value n is the number of points that should contribute to each Q value when computing the resolution. These will be distributed about the nominal measurement value, but varying in both angle and energy according to the resolution function. This will yield more points near the measurement and fewer farther away. The measurement point itself will not be used to avoid accidental bias from uniform Q steps. Depending on the problem, a value of n between 20 and 100 should lead to stable values for the convolved reflectivity.

Note: oversample() will remove the extra Q calculation points introduced by critical_edge().

parameters()

parts(theory)

plot(theory=None, **kw)

Plot theory against data.

Need substrate/surface for Fresnel-normalized reflectivity

plot_Q4(theory=None, **kw)

Plot the Q**4 reflectivity associated with the probe.

Note that Q**4 reflectivity has the intensity and background applied so that hydrogenated samples display more cleanly. The formula to reproduce the graph is:

\[R' = R / ( (100*Q)^{-4} I + B) \Delta R' = \Delta R / ( (100*Q)^{-4} I + B )\]

where \(B\) is the background.

plot_fresnel(theory=None, **kw)

Plot the Fresnel-normalized reflectivity associated with the probe.

Note that the Fresnel reflectivity has the intensity and background applied before normalizing so that hydrogenated samples display more cleanly. The formula to reproduce the graph is:

\[R' = R / (F(Q) I + B) \Delta R' = \Delta R / (F(Q) I + B)\]

where \(I\) is the intensity and \(B\) is the background.

plot_linear(theory=None, **kw)

Plot the data associated with probe.

plot_log(theory=None, **kw)

Plot the data associated with probe.

plot_logfresnel(theory=None, **kw)

Plot the log Fresnel-normalized reflectivity associated with the probe.

plot_residuals(theory=None, **kw)

plot_resolution(**kw)

polarized = False

probes: Sequence[Probe]

restore_data()

Restore the original data after resynth.

resynth_data()

Generate new data according to the model R’ ~ N(R, dR).

The resynthesis step is a precursor to refitting the data, as is required for certain types of monte carlo error analysis. The first time it is run it will save the original R into Ro. If you reset R in the probe you will also need to reset Ro so that it is used for subsequent resynth analysis.

save(filename, theory, substrate=None, surface=None)

Save the data and theory to a file.

scattering_factors(material, density)

Returns the scattering factors associated with the material given the range of wavelengths/energies used in the probe.

shared_beam(intensity=1, background=0, back_absorption=1, theta_offset=0, sample_broadening=0)

Share beam parameters across all segments.

New parameters are created for intensity, background, theta_offset, sample_broadening and back_absorption and assigned to the all segments. These can be replaced with an explicit parameter in an individual segment if that parameter is independent.

simulate_data(theory, noise=2.0)

Set the data for the probe to R + eps with eps ~ normal(dR^2).

theory is (Q, R),

If the percent noise is provided, set dR to R*noise/100 before simulating. noise defaults to 2% if no dR is present.

Note that measured data estimates uncertainty from the number of counts. This means that points above the true value will have larger uncertainty than points below the true value. This bias is not captured in the simulated data.

stitch(same_Q=0.001, same_dQ=0.001)

Stitch together multiple datasets into a single dataset.

Points within tol of each other and with the same resolution are combined by interpolating them to a common \(Q\) value then averaged using Gaussian error propagation.

Returns:

probe | Probe Combined data set.

Algorithm:

To interpolate a set of points to a common value, first find the common \(Q\) value:

\[\hat Q = \sum{Q_k} / n\]

Then for each dataset \(k\), find the interval \([i, i+1]\) containing the value \(Q\), and use it to compute interpolated value for \(R\):

\[\begin{split}w &= (\hat Q - Q_i)/(Q_{i+1} - Q_i) \\ \hat R &= w R_{i+1} + (1-w) R_{i+1} \\ \hat \sigma_{R} &= \sqrt{ w^2 \sigma^2_{R_i} + (1-w)^2 \sigma^2_{R_{i+1}} } / n\end{split}\]

Average the resulting \(R\) using Gaussian error propagation:

\[\begin{split}\hat R &= \sum{\hat R_k}/n \\ \hat \sigma_R &= \sqrt{\sum \hat \sigma_{R_k}^2}/n\end{split}\]

to_dict()

Return a dictionary representation of the parameters

property unique_L

class refl1d.probe.probe.QProbe(Q, dQ, R=None, dR=None, data=None, name=None, filename=None, intensity=1, background=0, back_absorption=1, back_reflectivity=False, resolution: Literal['normal', 'uniform'] = 'normal')

Bases: BaseProbe

A pure Q, R probe

This probe with no possibility of tricks such as looking up the scattering length density based on wavelength, or adjusting for alignment errors.

Q: NDArray

Q_c(substrate=None, surface=None)

R: NDArray

property Ro

apply_beam(calc_Q, calc_R, resolution=True, interpolation=0)

Apply factors such as beam intensity, background, backabsorption, resolution to the data.

resolution is True if the resolution function should be applied to the reflectivity.

interpolation is the number of Q points to show between the nominal Q points of the probe. Use this to draw a smooth theory line between the data points. The resolution dQ is interpolated between the resolution of the surrounding Q points.

If an amplitude signal is provided, \(r\) will be scaled by \(\surd I + i \surd B / |r|\), which when squared will equal \(I |r|^2 + B\). The resolution function will be applied directly to the amplitude. Unlike intensity and background, the resulting \(|G \ast r|^2 \ne G \ast |r|^2\) for convolution operator \(\ast\), but it should be close.

back_absorption: Parameter

back_reflectivity: bool = False

background: Parameter

property calc_Q

Define in derived classes

critical_edge(substrate=None, surface=None, n=51, delta=0.25)

Oversample points near the critical edge.

The critical edge is defined by the difference in scattering potential for the substrate and surface materials, or the reverse if back_reflectivity is true.

n is the number of \(Q\) points to compute near the critical edge.

delta is the relative uncertainty in the material density, which defines the range of values which are calculated.

Note: critical_edge() will remove the extra Q calculation points introduced by oversample().

The \(n\) points \(Q_i\) are evenly distributed around the critical edge in \(Q_c \pm \delta Q_c\) by varying angle \(\theta\) for a fixed wavelength \(< \lambda >\), the average of all wavelengths in the probe.

Specifically:

\[\begin{split}Q_c^2 &= 16 \pi (\rho - \rho_\text{incident}) \\ Q_i &= Q_c - \delta_i Q_c (i - (n-1)/2) \qquad \text{for} \; i \in 0 \ldots n-1 \\ \lambda_i &= < \lambda > \\ \theta_i &= \sin^{-1}(Q_i \lambda_i / 4 \pi)\end{split}\]

If \(Q_c\) is imaginary, then \(-|Q_c|\) is used instead, so this routine can be used for reflectivity signals which scan from back reflectivity to front reflectivity. For completeness, the angle \(\theta = 0\) is added as well.

dQ: NDArray = None

dR: NDArray = None

filename: str | None

fresnel(substrate=None, surface=None)

Returns a Fresnel reflectivity calculator given the surface and and substrate. The calculated reflectivity includes The Fresnel reflectivity for the probe reflecting from a block of material with the given substrate.

Returns F = R(probe.Q), where R is magnitude squared reflectivity.

intensity: Parameter

label(prefix=None, gloss='', suffix='')

log10_to_linear()

Convert data from log to linear.

Older reflectometry reduction code stored reflectivity in log base 10 format. Call probe.log10_to_linear() after loading this data to convert it to linear for subsequent display and fitting.

name: str | None = None

oversample(n=20, seed=1)

Generate an over-sampling of Q to avoid aliasing effects.

Oversampling is needed for thick layers, in which the underlying reflectivity oscillates so rapidly in Q that a single measurement has contributions from multiple Kissig fringes.

Sampling will be done using a pseudo-random generator so that accidental structure in the function does not contribute to the aliasing. The generator will usually be initialized with a fixed seed so that the point selection will not change from run to run, but a seed of None will choose a different set of points each time oversample is called.

The value n is the number of points that should contribute to each Q value when computing the resolution. These will be distributed about the nominal measurement value, but varying in both angle and energy according to the resolution function. This will yield more points near the measurement and fewer farther away. The measurement point itself will not be used to avoid accidental bias from uniform Q steps. Depending on the problem, a value of n between 20 and 100 should lead to stable values for the convolved reflectivity.

Note: oversample() will remove the extra Q calculation points introduced by critical_edge().

parameters()

plot(view=None, **kwargs)

Plot theory against data.

Need substrate/surface for Fresnel-normalized reflectivity

plot_Q4(**kwargs)

Plot the Q**4 reflectivity associated with the probe.

Note that Q**4 reflectivity has the intensity and background applied so that hydrogenated samples display more cleanly. The formula to reproduce the graph is:

\[R' = R / ( (100*Q)^{-4} I + B) \Delta R' = \Delta R / ( (100*Q)^{-4} I + B )\]

where \(B\) is the background.

plot_fft(theory=None, suffix='', label=None, substrate=None, surface=None, **kwargs)

FFT analysis of reflectivity signal.

plot_fresnel(substrate=None, surface=None, **kwargs)

Plot the Fresnel-normalized reflectivity associated with the probe.

Note that the Fresnel reflectivity has the intensity and background applied before normalizing so that hydrogenated samples display more cleanly. The formula to reproduce the graph is:

\[R' = R / (F(Q) I + B) \Delta R' = \Delta R / (F(Q) I + B)\]

where \(I\) is the intensity and \(B\) is the background.

plot_linear(**kwargs)

Plot the data associated with probe.

plot_log(**kwargs)

Plot the data associated with probe.

plot_logfresnel(*args, **kw)

Plot the log Fresnel-normalized reflectivity associated with the probe.

plot_residuals(theory=None, suffix='', label=None, plot_shift=None, **kwargs)

plot_resolution(suffix='', label=None, **kwargs)

plot_shift = 0

polarized = False

residuals_shift = 0

resolution: Literal['normal', 'uniform'] = 'uniform'

resolution_guard()

Make sure each measured \(Q\) point has at least 5 calculated \(Q\) points contributing to it in the range \([-3\Delta Q, 3\Delta Q]\).

Not Implemented

restore_data()

Restore the original data after resynth.

resynth_data()

Generate new data according to the model R’ ~ N(R, dR).

The resynthesis step is a precursor to refitting the data, as is required for certain types of monte carlo error analysis. The first time it is run it will save the original R into Ro. If you reset R in the probe you will also need to reset Ro so that it is used for subsequent resynth analysis.

save(filename, theory, substrate=None, surface=None)

Save the data and theory to a file.

scattering_factors(material, density)

Returns the scattering factors associated with the material given the range of wavelengths/energies used in the probe.

show_resolution = True

simulate_data(theory, noise=2.0)

Set the data for the probe to R + eps with eps ~ normal(dR^2).

theory is (Q, R),

If the percent noise is provided, set dR to R*noise/100 before simulating. noise defaults to 2% if no dR is present.

Note that measured data estimates uncertainty from the number of counts. This means that points above the true value will have larger uncertainty than points below the true value. This bias is not captured in the simulated data.

view = 'log'

refl1d.probe.probe.Qmeasurement_union(xs)

Determine the unique Q, dQ across all datasets.

class refl1d.probe.probe.XrayProbe(T=None, dT=0, L=None, dL=0, data=None, intensity=1, background=0, back_absorption=1, theta_offset=0, sample_broadening=0, back_reflectivity=False, name: str | None = None, filename=None, dQo=None, resolution: Literal['normal', 'uniform'] = 'normal', oversampling=None, oversampling_seed=1)

Bases: Probe

X-Ray probe.

By providing a scattering factor calculator for X-ray scattering, model components can be defined by mass density and chemical composition.

Aguide = 270.0

L: NDArray

property Q

Q_c(substrate=None, surface=None)

R: Any | None = None

property Ro

T: NDArray

static alignment_uncertainty(w, I, d=0)

Compute alignment uncertainty.

Parameters:

wfloat | degrees

Rocking curve full width at half max.

Ifloat | counts

Rocking curve integrated intensity.

d = 0: float | degrees

Motor step size

Returns:

dthetafloat | degrees

uncertainty in alignment angle

apply_beam(calc_Q, calc_R, resolution=True, interpolation=0)

Apply factors such as beam intensity, background, backabsorption, resolution to the data.

resolution is True if the resolution function should be applied to the reflectivity.

interpolation is the number of Q points to show between the nominal Q points of the probe. Use this to draw a smooth theory line between the data points. The resolution dQ is interpolated between the resolution of the surrounding Q points.

If an amplitude signal is provided, \(r\) will be scaled by \(\surd I + i \surd B / |r|\), which when squared will equal \(I |r|^2 + B\). The resolution function will be applied directly to the amplitude. Unlike intensity and background, the resulting \(|G \ast r|^2 \ne G \ast |r|^2\) for convolution operator \(\ast\), but it should be close.

back_absorption: Parameter

back_reflectivity: bool = False

background: Parameter

property calc_Q

Define in derived classes

critical_edge(substrate=None, surface=None, n=51, delta=0.25)

Oversample points near the critical edge.

The critical edge is defined by the difference in scattering potential for the substrate and surface materials, or the reverse if back_reflectivity is true.

n is the number of \(Q\) points to compute near the critical edge.

delta is the relative uncertainty in the material density, which defines the range of values which are calculated.

Note: critical_edge() will remove the extra Q calculation points introduced by oversample().

The \(n\) points \(Q_i\) are evenly distributed around the critical edge in \(Q_c \pm \delta Q_c\) by varying angle \(\theta\) for a fixed wavelength \(< \lambda >\), the average of all wavelengths in the probe.

Specifically:

\[\begin{split}Q_c^2 &= 16 \pi (\rho - \rho_\text{incident}) \\ Q_i &= Q_c - \delta_i Q_c (i - (n-1)/2) \qquad \text{for} \; i \in 0 \ldots n-1 \\ \lambda_i &= < \lambda > \\ \theta_i &= \sin^{-1}(Q_i \lambda_i / 4 \pi)\end{split}\]

If \(Q_c\) is imaginary, then \(-|Q_c|\) is used instead, so this routine can be used for reflectivity signals which scan from back reflectivity to front reflectivity. For completeness, the angle \(\theta = 0\) is added as well.

dL: Any | None = 0

property dQ

dQo: Sequence | 'NDArray' | None = None

dR: Any | None = 0

dT: Any | None = 0

filename: str | None = None

fresnel(substrate=None, surface=None)

Returns a Fresnel reflectivity calculator given the surface and and substrate. The calculated reflectivity includes The Fresnel reflectivity for the probe reflecting from a block of material with the given substrate.

Returns F = R(probe.Q), where R is magnitude squared reflectivity.

classmethod from_dict(**kw)

intensity: Parameter

label(prefix=None, gloss='', suffix='')

log10_to_linear()

Convert data from log to linear.

Older reflectometry reduction code stored reflectivity in log base 10 format. Call probe.log10_to_linear() after loading this data to convert it to linear for subsequent display and fitting.

name: str | None = None

oversample(n=20, seed=1)

Generate an over-sampling of Q to avoid aliasing effects.

Oversampling is needed for thick layers, in which the underlying reflectivity oscillates so rapidly in Q that a single measurement has contributions from multiple Kissig fringes.

Sampling will be done using a pseudo-random generator so that accidental structure in the function does not contribute to the aliasing. The generator will usually be initialized with a fixed seed so that the point selection will not change from run to run, but a seed of None will choose a different set of points each time oversample is called.

The value n is the number of points that should contribute to each Q value when computing the resolution. These will be distributed about the nominal measurement value, but varying in both angle and energy according to the resolution function. This will yield more points near the measurement and fewer farther away. The measurement point itself will not be used to avoid accidental bias from uniform Q steps. Depending on the problem, a value of n between 20 and 100 should lead to stable values for the convolved reflectivity.

Note: oversample() will remove the extra Q calculation points introduced by critical_edge().

oversampling: int | None = None

oversampling_seed: int = 1

parameters()

plot(view=None, **kwargs)

Plot theory against data.

Need substrate/surface for Fresnel-normalized reflectivity

plot_Q4(**kwargs)

Plot the Q**4 reflectivity associated with the probe.

Note that Q**4 reflectivity has the intensity and background applied so that hydrogenated samples display more cleanly. The formula to reproduce the graph is:

\[R' = R / ( (100*Q)^{-4} I + B) \Delta R' = \Delta R / ( (100*Q)^{-4} I + B )\]

where \(B\) is the background.

plot_fft(theory=None, suffix='', label=None, substrate=None, surface=None, **kwargs)

FFT analysis of reflectivity signal.

plot_fresnel(substrate=None, surface=None, **kwargs)

Plot the Fresnel-normalized reflectivity associated with the probe.

Note that the Fresnel reflectivity has the intensity and background applied before normalizing so that hydrogenated samples display more cleanly. The formula to reproduce the graph is:

\[R' = R / (F(Q) I + B) \Delta R' = \Delta R / (F(Q) I + B)\]

where \(I\) is the intensity and \(B\) is the background.

plot_linear(**kwargs)

Plot the data associated with probe.

plot_log(**kwargs)

Plot the data associated with probe.

plot_logfresnel(*args, **kw)

Plot the log Fresnel-normalized reflectivity associated with the probe.

plot_residuals(theory=None, suffix='', label=None, plot_shift=None, **kwargs)

plot_resolution(suffix='', label=None, **kwargs)

plot_shift = 0

polarized = False

radiation: Literal['neutron', 'xray'] = 'xray'

residuals_shift = 0

resolution: Literal['normal', 'uniform'] = 'uniform'

resolution_guard()

Make sure each measured \(Q\) point has at least 5 calculated \(Q\) points contributing to it in the range \([-3\Delta Q, 3\Delta Q]\).

Not Implemented

restore_data()

Restore the original data after resynth.

resynth_data()

Generate new data according to the model R’ ~ N(R, dR).

The resynthesis step is a precursor to refitting the data, as is required for certain types of monte carlo error analysis. The first time it is run it will save the original R into Ro. If you reset R in the probe you will also need to reset Ro so that it is used for subsequent resynth analysis.

sample_broadening: Parameter

save(filename, theory, substrate=None, surface=None)

Save the data and theory to a file.

scattering_factors(material, density)

Returns the scattering factors associated with the material given the range of wavelengths/energies used in the probe.

show_resolution = True

simulate_data(theory, noise=2.0)

Set the data for the probe to R + eps with eps ~ normal(dR^2).

theory is (Q, R),

If the percent noise is provided, set dR to R*noise/100 before simulating. noise defaults to 2% if no dR is present.

Note that measured data estimates uncertainty from the number of counts. This means that points above the true value will have larger uncertainty than points below the true value. This bias is not captured in the simulated data.

subsample(dQ)

Select points at most every dQ.

Use this to speed up computation early in the fitting process.

This changes the data object, and is not reversible.

The current algorithm is not picking the “best” Q value, just the nearest, so if you have nearby Q points with different quality statistics (as happens in overlapped regions from spallation source measurements at different angles), then it may choose badly. Simple solutions based on the smallest relative error dR/R will be biased toward peaks, and smallest absolute error dR will be biased toward valleys.

theta_offset: Parameter

to_dict()

Return a dictionary representation of the parameters

view = 'log'

write_data(filename, columns=('Q', 'R', 'dR'), header=None)

Save the data to a file.

header is a string with trailing n containing the file header. columns is a list of column names from Q, dQ, R, dR, L, dL, T, dT.

The default is to write Q, R, dR data.

refl1d.probe.probe.make_probe(**kw)

Return a reflectometry measurement object of the given resolution.

refl1d.probe.probe.spin_asymmetry(Qp, Rp, dRp, Qm, Rm, dRm)

Compute spin asymmetry for R++, R–.

Parameters:

Qp, Rp, dRpvector

Measured ++ cross section and uncertainty.

Qm, Rm, dRmvector

Measured – cross section and uncertainty.

If dRp, dRm are None then the returned uncertainty will also be None.

Returns:

Q, SA, dSAvector

Computed spin asymmetry and uncertainty.

Algorithm:

Spin asymmetry, \(S_A\), is:

\[S_A = \frac{R_{++} - R_{--}}{R_{++} + R_{--}}\]

Uncertainty \(\Delta S_A\) follows from propagation of error:

\[\Delta S_A^2 = \frac{4(R_{++}^2\Delta R_{--}^2+R_{--}^2\Delta R_{++})} {(R_{++} + R_{--})^4}\]