mlreflect.data_generation package

Submodules

mlreflect.data_generation.data_generator module

class mlreflect.data_generation.data_generator.ReflectivityGenerator(q_values: numpy.ndarray, sample: mlreflect.data_generation.multilayer.MultilayerStructure, random_seed: Optional[int] = None)

Bases: object

Generation of simulated reflectivity data and labels for neural network training.

Parameters

• q_values – An array-like object (list, tuple, ndarray, etc.) that contains the q-values in units of 1/Å at which the reflected intensity will be simulated.

• sample – MultilayerStructure object where the sample layers and their names and parameter ranges are defined.

• random_seed – Random seed for numpy.random.seed which affects the generation of the random labels (default None means random seed).

generate_random_labels(number_of_samples: int, distribution_type: str = 'bolstered', bolster_fraction: float = 0.15, bolster_width: float = 0.1) → pandas.core.frame.DataFrame

Generates random labels in the parameter ranges defined by the sample and returns them as pandas DataFrame.

Parameters

• number_of_samples – Number of label sets that will be generated.

• distribution_type – Can be 'bolstered' (default) or 'uniform'.

• bolster_fraction – Fraction of simulated samples that will be redistributed to the sides of the distribution.

• bolster_width – Width of the Gaussian distribution of the redistributed samples.

Returns

Pandas DataFrame with the randomly generated labels.

Return type

labels

make_sld_profile(thickness: numpy.ndarray, sld: numpy.ndarray, roughness: numpy.ndarray, sld_substrate: float, sld_ambient: float) → Tuple[numpy.ndarray, numpy.ndarray]

Generate scattering length density profile in units 1/Å^-2 * 10^-6 with height in units Å.

Parameters

• thickness – ndarray of layer thicknesses in units Å from bottom to top. For no layers (only substrate) provide empty tuple (,).

• sld – ndarray of layer scattering length densities in units 1/Å^-2 * 10^-6 from bottom to top. For no layers (only substrate) provide empty tuple (,).

• roughness – ndarray of RMS interface roughnesses in units Å from bottom to top. At least one has to be given.

• sld_substrate – Scattering length density of the used substrate in units 1/Å^-2 * 10^-6.

• sld_ambient – Scattering length density of the ambient medium in units 1/Å^-2 * 10^-6.

Returns

Tuple of ndarrays of sample height in units Å and the scattering length density profile in units 1/Å^-2 * 10^-6.

Return type

height, sld_profile

static separate_labels_by_category(labels: pandas.core.frame.DataFrame) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

simulate_reflectivity(labels: pandas.core.frame.DataFrame, q_noise_spread: float = 0, engine: str = 'refl1d', progress_bar=True) → numpy.ndarray

Simulates reflectivity curves for the given labels and returns them as ndarray.

Parameters

• labels – Must a pandas DataFrame with each column representing one label. The label order from left to right must be “thickness”, “roughness” and “scattering length density” with layers from bottom to top. Example for 2 layers: ['thickness_layer1', 'thickness_layer2', 'roughness_layer1', 'roughness_layer2', 'sld_layer1', 'sld_layer2']

• q_noise_spread – Standard deviation of the normal distribution of scaling factors (centered at 1) that are applied to each q-value during reflectivity simulation.

• engine – 'refl1d' (default): Uses C++-based simulation from the refl1d package. 'builtin': Uses the built-in python-based simulation (slower).

• progress_bar – If True, a tqdm progress bar will be displayed.

• labels – Must a pandas DataFrame with each column representing one label.

Returns

Simulated reflectivity curves.

Return type

reflectivity_curves

simulate_sld_profiles(labels: pandas.core.frame.DataFrame, progress_bar=True) → List[numpy.ndarray]

Simulates real scattering length density profiles for the given labels and returns them as ndarray.

Parameters

• labels – Must be pandas DataFrame with each column representing one label. The label order from left to right must be “thickness”, “roughness” and “scattering length density” with layers from bottom to top. Example for 2 layers: ['thickness_layer1', 'thickness_layer2', 'roughness_layer1', 'roughness_layer2', 'sld_layer1', 'sld_layer2']

• progress_bar – If True, a tqdm progress bar will be displayed.

Returns

List of ndarray of simulated scattering length density profiles (real part).

Return type

sld_profiles

mlreflect.data_generation.distributions module

mlreflect.data_generation.distributions.bolstered_uniform_distribution(min_value: float, max_value: float, n_samples: int, bolster_fraction: float, bolster_width: float) → Union[float, numpy.ndarray]

Sample from a modified uniform distribution that has a higher sampling density at the limits

Parameters

• min_value – lower limit of the distribution

• max_value – upper limit of the distribution

• n_samples – number of samples drawn from the distribution

• bolster_fraction – fraction of samples that are drawn around the limits (instead of uniformly)

• bolster_width – width of the normal distribution that is sampled from around both limits

Returns

ndarray

Return type

samples

mlreflect.data_generation.distributions.random_logarithmic_distribution(min_value: float, max_value: float, n_values: float) → Union[float, numpy.ndarray]

Sample uniformly from a logarithmic distribution.

mlreflect.data_generation.distributions.sample_distribution(number_of_values: int, **kwargs) → Union[float, numpy.ndarray]

Sample from the specified distribution

Parameters

• number_of_values – number of samples values

• **kwargs – distribution_type: ‘uniform’, ‘logarithmic’ or ‘bolstered’ min_value, max_value: float limits of the distribution bolster_fraction: float fraction of samples that are redistributed to the limits bolster_width: width of the normal distribution of the redistributed samples

Returns

ndarray

Return type

samples

mlreflect.data_generation.layers module

class mlreflect.data_generation.layers.AmbientLayer(name: str, sld: Union[float, complex, mlreflect.data_generation.parameters.ConstantParameter])

Bases: mlreflect.data_generation.layers.ConstantLayer

property ranges

class mlreflect.data_generation.layers.ConstantLayer(name: str, thickness: Union[float, mlreflect.data_generation.parameters.ConstantParameter], roughness: Union[float, mlreflect.data_generation.parameters.ConstantParameter], sld: Union[float, complex, mlreflect.data_generation.parameters.ConstantParameter])

Bases: mlreflect.data_generation.layers.Layer

Defines the name and constant parameter values of a single sample layer.

Parameters

• name – User defined name of this layer.

• thickness – Thickness of this layer in units of Å. Must be a float or int.

• roughness – Roughness of this layer in units of Å. Must be a float or int.

• sld – Scattering length density (SLD) of this layer in units of 1e-6 1/Å^2. Must be a float or int.

Returns

Layer object

property ranges

class mlreflect.data_generation.layers.Layer(name: str, thickness: Union[float, Iterable, mlreflect.data_generation.parameters.Parameter], roughness: Union[float, Iterable, mlreflect.data_generation.parameters.Parameter], sld: Union[float, complex, Iterable, mlreflect.data_generation.parameters.Parameter])

Bases: object

Defines the name and parameter ranges of a single sample layer.

Parameters

• name – User defined name of this layer.

• thickness – Thickness of this layer in units of Å. Can be a float for a constant vale or a tuple for a range.

• roughness – Roughness of this layer in units of Å. Can be a float for a constant vale or a tuple for a range.

• sld – Scattering length density (SLD) of this layer in units of 1e-6 1/Å^2. Can be a float for a constant vale or a tuple for a range.

Returns

Layer object

copy()

property ranges

to_dict()

class mlreflect.data_generation.layers.Substrate(name: str, roughness: Union[float, mlreflect.data_generation.parameters.ConstantParameter], sld: Union[float, complex, mlreflect.data_generation.parameters.ConstantParameter])

Bases: mlreflect.data_generation.layers.ConstantLayer

property ranges

mlreflect.data_generation.model_mixer module

class mlreflect.data_generation.model_mixer.ModelMixer(q_values)

Bases: object

Simulate reflectivity curves from given labels with different models with given probabilities.

Parameters

q_values – An array-like object (list, tuple, ndarray, etc.) that contains the q-values in units of 1/Å at which the reflected intensity will be simulated.

add_model(sample, weight=1)

property model_weights

property q

property sample_models

simulate_reflectivity(labels: pandas.core.frame.DataFrame, engine: str = 'refl1d')

mlreflect.data_generation.multilayer module

class mlreflect.data_generation.multilayer.LayerOnSubstrate

Bases: mlreflect.data_generation.multilayer.MultilayerStructure

Defines the structure of a multilayer sample through one or multiple Layer objects and an ambient SLD.

Can only contain one non-constant layer of class Layer, all others must be of class ConstantLayer.

Initializes with a default ambient and substrate layer.

Returns

MultilayerStructure

add_layer(layer: Union[mlreflect.data_generation.layers.Layer, mlreflect.data_generation.layers.ConstantLayer], index: Union[str, int] = 'next')

Add layer at given index position. If index='next' (default) layer is appended (added on top).

property has_variable_layer

class mlreflect.data_generation.multilayer.MultilayerStructure

Bases: object

Defines the structure of a multilayer sample through one or multiple Layer objects and an ambient SLD.

Initializes with a default ambient and substrate layer.

Returns

MultilayerStructure

add_layer(layer: mlreflect.data_generation.layers.Layer, index: Union[str, int] = 'next')

Add layer at given index position. If index='next' (default) layer is appended (added on top).

property ambient_layer

copy()

from_dict(sample_dict: dict)

Set the layers in the MultilayerStructure according to the dictionary representation.

property label_names: List[str]

Get list of all layer names in order.

move_layer(from_index: int, to_index: int)

Moves layer with given index to new index, shifting all layers with equal or higher index up.

rename_layer(layer_index, name)

Renames layer at given index to name.

property roughnesses: list

set_ambient_layer(ambient_layer: mlreflect.data_generation.layers.AmbientLayer)

Set the ambient layer.

set_substrate(substrate: mlreflect.data_generation.layers.Substrate)

Set the substrate layer.

property slds: list

property substrate

swap_layers(from_index: int, to_index: int)

Swaps the position of the two layers given by from_index and to_index.

property thicknesses: list

to_dict() → dict

Returns a dictionary representation of the MultilayerStructure

mlreflect.data_generation.noise module

mlreflect.data_generation.noise.apply_poisson_noise(reflectivity_curves: numpy.ndarray, rate_spread: Union[float, Tuple[float, float]]) → Tuple[numpy.ndarray, numpy.ndarray]

Returns reflectivity curves with applied shot noise based on shot_noise_spread.

Parameters

• reflectivity_curves – Array of normalized reflectivity curves

• rate_spread – Scaling factor c for the standard deviation sqrt(I*c) of the shot noise around the intensity of simulated reflectivity curves. Since the intensity is normalized, this is equivalent to setting the direct beam intensity I_0 = 1/c. If a tuple with two values is given, a random value between the two is chosen for each curve.

Returns

noisy_reflectivity, spreads

mlreflect.data_generation.noise.apply_scaling_factor(refl, scale_factor_range)

mlreflect.data_generation.noise.apply_shot_noise(reflectivity_curves: numpy.ndarray, shot_noise_spread: Union[float, Tuple[float, float]]) → Tuple[numpy.ndarray, numpy.ndarray]

Returns reflectivity curves with applied shot noise based on shot_noise_spread.

Parameters

• reflectivity_curves – Array of normalized reflectivity curves

• shot_noise_spread – Scaling factor c for the standard deviation sqrt(I*c) of the shot noise around the intensity of simulated reflectivity curves. Since the intensity is normalized, this is equivalent to setting the direct beam intensity I_0 = 1/c. If a tuple with two values is given, a random value between the two is chosen for each curve.

Returns

noisy_reflectivity, spreads

mlreflect.data_generation.noise.apply_uniform_noise(refl, noise_range)

mlreflect.data_generation.noise.generate_background(number_of_curves: int, number_of_q_values: int, background_base_level: Union[float, Tuple[float, float]], relative_background_spread: float) → Tuple[numpy.ndarray, numpy.ndarray]

Returns a background with a normal distribution that can be added to a reflectivity curve.

Parameters

• number_of_curves – Number of curves for which a background is generated

• number_of_q_values – Length of the generated array (should be same length as reflectivity curve)

• background_base_level – Range from which the mean of the normal distribution is chosen

• relative_background_spread – Relative standard deviation of the normal distribution (e.g. a value of 0.1 means the standard deviation is 10% of the mean)

Returns

background has dimensions (number_of_curves, number_of_q_values)

Return type

background, means

mlreflect.data_generation.noise.iterate_over_curves(func)

mlreflect.data_generation.parameters module

class mlreflect.data_generation.parameters.ConstantParameter(value, name: Optional[str] = None)

Bases: mlreflect.data_generation.parameters.Parameter

Defines a constant parameter that can be sampled to generate random training data.

Parameters

• value – value of the parameter

• name – optional name for the parameter (usually ‘thickness’, ‘roughness’ or ‘sld’)

copy()

property max

property min

sample(number_of_values: int, **distribution_params)

Returns ndarray with number_of_values repetitions of the parameter value.

property value

class mlreflect.data_generation.parameters.Parameter(min_value, max_value, name: Optional[str] = None)

Bases: object

Defines a parameter range that can be sampled to generate random training data.

Parameters

• min_value – minimum value of the parameter range

• max_value – maximum value of the parameter range

• name – optional name for the parameter (usually ‘thickness’, ‘roughness’ or ‘sld’)

copy()

sample(number_of_values: int, distribution_type: str = 'uniform', **distribution_params)

Samples random values in the given parameter range with the specified distribution.

Parameters

• number_of_values – number of sampled values

• distribution_type – distribution type ‘uniform’ is numpy.random.uniform(). ‘logarithmic’ is a uniformly sampled on a logarithmic scale. ‘bolstered’ is a uniform distribution where the sampling density is shifted towards both ends of the range.

• **distribution_params – catch-all for all parameters concerning the specified distribution min_value, max_value: float limits of the distribution bolster_fraction: float fraction of samples that are redistributed to the limits bolster_width: width of the normal distribution of the redistributed samples

Returns

ndarray

Return type

samples

property value

mlreflect.data_generation.reflectivity module

mlreflect.data_generation.reflectivity.multilayer_reflectivity(q_values: Iterable, thickness: Iterable, roughness: Iterable, scattering_length_density: Iterable, ambient_sld: float = 0.0)

Returns a normalized reflectivity curve for a set of stacked layers with the given parameters.

Parameters

• q_values – An array-like object (list, tuple, ndarray, etc.) that contains the q-values in SI base units (i.e. 1/m) at which the reflected intensity will be simulated.

• thickness – An array-like object (list, tuple, ndarray, etc.) that contains the thicknesses of the sample layers in SI base units (i.e. m) in order from bottom to top excluding the bottom most layer (substrate).

• roughness – An array-like object (list, tuple, ndarray, etc.) that contains the roughnesses of the sample interfaces in SI base units (i.e. m) in order from bottom to top.

• scattering_length_density – An array-like object (list, tuple, ndarray, etc.) that contains the scattering length densities of the sample layers in SI base units (i.e. 1/m^2) in order from bottom to top (excluding the ambient SLD).

• ambient_sld – Scattering length density of the ambient environment (above the top most layer).

Returns

ndrray of simulated intensity values with same length as q_values.

Example

The following code can be used to simulate the reflectivity of a model with two layers with 100 and 250 Å thickness on a substrate.

``` q = np.linspace(0.01, 0.20, 1001) * 1e10 ambient_sld = 0 thickness = np.array([100, 250]) * 1e-10 roughness = np.array([3, 11, 5]) * 1e-10 sld = np.array([12 + 0.012j, 2.36 + 0j, 4.2 + 0.016j]) * 1e14

simulated_curve = multilayer_reflectivity(q_values=q, thickness=thickness, roughness=roughness,

scattering_length_density=sld, ambient_sld=ambient_sld)

```

Module contents

class mlreflect.data_generation.AmbientLayer(name: str, sld: Union[float, complex, mlreflect.data_generation.parameters.ConstantParameter])

Bases: mlreflect.data_generation.layers.ConstantLayer

property ranges

class mlreflect.data_generation.ConstantLayer(name: str, thickness: Union[float, mlreflect.data_generation.parameters.ConstantParameter], roughness: Union[float, mlreflect.data_generation.parameters.ConstantParameter], sld: Union[float, complex, mlreflect.data_generation.parameters.ConstantParameter])

Bases: mlreflect.data_generation.layers.Layer

Defines the name and constant parameter values of a single sample layer.

Parameters

• name – User defined name of this layer.

• thickness – Thickness of this layer in units of Å. Must be a float or int.

• roughness – Roughness of this layer in units of Å. Must be a float or int.

• sld – Scattering length density (SLD) of this layer in units of 1e-6 1/Å^2. Must be a float or int.

Returns

Layer object

property ranges

class mlreflect.data_generation.ConstantParameter(value, name: Optional[str] = None)

Bases: mlreflect.data_generation.parameters.Parameter

Defines a constant parameter that can be sampled to generate random training data.

Parameters

• value – value of the parameter

• name – optional name for the parameter (usually ‘thickness’, ‘roughness’ or ‘sld’)

copy()

property max

property min

sample(number_of_values: int, **distribution_params)

Returns ndarray with number_of_values repetitions of the parameter value.

property value

class mlreflect.data_generation.Layer(name: str, thickness: Union[float, Iterable, mlreflect.data_generation.parameters.Parameter], roughness: Union[float, Iterable, mlreflect.data_generation.parameters.Parameter], sld: Union[float, complex, Iterable, mlreflect.data_generation.parameters.Parameter])

Bases: object

Defines the name and parameter ranges of a single sample layer.

Parameters

• name – User defined name of this layer.

• thickness – Thickness of this layer in units of Å. Can be a float for a constant vale or a tuple for a range.

• roughness – Roughness of this layer in units of Å. Can be a float for a constant vale or a tuple for a range.

• sld – Scattering length density (SLD) of this layer in units of 1e-6 1/Å^2. Can be a float for a constant vale or a tuple for a range.

Returns

Layer object

copy()

property ranges

to_dict()

class mlreflect.data_generation.LayerOnSubstrate

Bases: mlreflect.data_generation.multilayer.MultilayerStructure

Defines the structure of a multilayer sample through one or multiple Layer objects and an ambient SLD.

Can only contain one non-constant layer of class Layer, all others must be of class ConstantLayer.

Initializes with a default ambient and substrate layer.

Returns

MultilayerStructure

add_layer(layer: Union[mlreflect.data_generation.layers.Layer, mlreflect.data_generation.layers.ConstantLayer], index: Union[str, int] = 'next')

Add layer at given index position. If index='next' (default) layer is appended (added on top).

property has_variable_layer

class mlreflect.data_generation.MultilayerStructure

Bases: object

Defines the structure of a multilayer sample through one or multiple Layer objects and an ambient SLD.

Initializes with a default ambient and substrate layer.

Returns

MultilayerStructure

add_layer(layer: mlreflect.data_generation.layers.Layer, index: Union[str, int] = 'next')

Add layer at given index position. If index='next' (default) layer is appended (added on top).

property ambient_layer

copy()

from_dict(sample_dict: dict)

Set the layers in the MultilayerStructure according to the dictionary representation.

property label_names: List[str]

Get list of all layer names in order.

move_layer(from_index: int, to_index: int)

Moves layer with given index to new index, shifting all layers with equal or higher index up.

rename_layer(layer_index, name)

Renames layer at given index to name.

property roughnesses: list

set_ambient_layer(ambient_layer: mlreflect.data_generation.layers.AmbientLayer)

Set the ambient layer.

set_substrate(substrate: mlreflect.data_generation.layers.Substrate)

Set the substrate layer.

property slds: list

property substrate

swap_layers(from_index: int, to_index: int)

Swaps the position of the two layers given by from_index and to_index.

property thicknesses: list

to_dict() → dict

Returns a dictionary representation of the MultilayerStructure

class mlreflect.data_generation.Parameter(min_value, max_value, name: Optional[str] = None)

Bases: object

Defines a parameter range that can be sampled to generate random training data.

Parameters

• min_value – minimum value of the parameter range

• max_value – maximum value of the parameter range

• name – optional name for the parameter (usually ‘thickness’, ‘roughness’ or ‘sld’)

copy()

sample(number_of_values: int, distribution_type: str = 'uniform', **distribution_params)

Samples random values in the given parameter range with the specified distribution.

Parameters

• number_of_values – number of sampled values

• distribution_type – distribution type ‘uniform’ is numpy.random.uniform(). ‘logarithmic’ is a uniformly sampled on a logarithmic scale. ‘bolstered’ is a uniform distribution where the sampling density is shifted towards both ends of the range.

• **distribution_params – catch-all for all parameters concerning the specified distribution min_value, max_value: float limits of the distribution bolster_fraction: float fraction of samples that are redistributed to the limits bolster_width: width of the normal distribution of the redistributed samples

Returns

ndarray

Return type

samples

property value

class mlreflect.data_generation.ReflectivityGenerator(q_values: numpy.ndarray, sample: mlreflect.data_generation.multilayer.MultilayerStructure, random_seed: Optional[int] = None)

Bases: object

Generation of simulated reflectivity data and labels for neural network training.

Parameters

• q_values – An array-like object (list, tuple, ndarray, etc.) that contains the q-values in units of 1/Å at which the reflected intensity will be simulated.

• sample – MultilayerStructure object where the sample layers and their names and parameter ranges are defined.

• random_seed – Random seed for numpy.random.seed which affects the generation of the random labels (default None means random seed).

generate_random_labels(number_of_samples: int, distribution_type: str = 'bolstered', bolster_fraction: float = 0.15, bolster_width: float = 0.1) → pandas.core.frame.DataFrame

Generates random labels in the parameter ranges defined by the sample and returns them as pandas DataFrame.

Parameters

• number_of_samples – Number of label sets that will be generated.

• distribution_type – Can be 'bolstered' (default) or 'uniform'.

• bolster_fraction – Fraction of simulated samples that will be redistributed to the sides of the distribution.

• bolster_width – Width of the Gaussian distribution of the redistributed samples.

Returns

Pandas DataFrame with the randomly generated labels.

Return type

labels

make_sld_profile(thickness: numpy.ndarray, sld: numpy.ndarray, roughness: numpy.ndarray, sld_substrate: float, sld_ambient: float) → Tuple[numpy.ndarray, numpy.ndarray]

Generate scattering length density profile in units 1/Å^-2 * 10^-6 with height in units Å.

Parameters

• thickness – ndarray of layer thicknesses in units Å from bottom to top. For no layers (only substrate) provide empty tuple (,).

• sld – ndarray of layer scattering length densities in units 1/Å^-2 * 10^-6 from bottom to top. For no layers (only substrate) provide empty tuple (,).

• roughness – ndarray of RMS interface roughnesses in units Å from bottom to top. At least one has to be given.

• sld_substrate – Scattering length density of the used substrate in units 1/Å^-2 * 10^-6.

• sld_ambient – Scattering length density of the ambient medium in units 1/Å^-2 * 10^-6.

Returns

Tuple of ndarrays of sample height in units Å and the scattering length density profile in units 1/Å^-2 * 10^-6.

Return type

height, sld_profile

static separate_labels_by_category(labels: pandas.core.frame.DataFrame) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

simulate_reflectivity(labels: pandas.core.frame.DataFrame, q_noise_spread: float = 0, engine: str = 'refl1d', progress_bar=True) → numpy.ndarray

Simulates reflectivity curves for the given labels and returns them as ndarray.

Parameters

• labels – Must a pandas DataFrame with each column representing one label. The label order from left to right must be “thickness”, “roughness” and “scattering length density” with layers from bottom to top. Example for 2 layers: ['thickness_layer1', 'thickness_layer2', 'roughness_layer1', 'roughness_layer2', 'sld_layer1', 'sld_layer2']

• q_noise_spread – Standard deviation of the normal distribution of scaling factors (centered at 1) that are applied to each q-value during reflectivity simulation.

• engine – 'refl1d' (default): Uses C++-based simulation from the refl1d package. 'builtin': Uses the built-in python-based simulation (slower).

• progress_bar – If True, a tqdm progress bar will be displayed.

• labels – Must a pandas DataFrame with each column representing one label.

Returns

Simulated reflectivity curves.

Return type

reflectivity_curves

simulate_sld_profiles(labels: pandas.core.frame.DataFrame, progress_bar=True) → List[numpy.ndarray]

Simulates real scattering length density profiles for the given labels and returns them as ndarray.

Parameters

• labels – Must be pandas DataFrame with each column representing one label. The label order from left to right must be “thickness”, “roughness” and “scattering length density” with layers from bottom to top. Example for 2 layers: ['thickness_layer1', 'thickness_layer2', 'roughness_layer1', 'roughness_layer2', 'sld_layer1', 'sld_layer2']

• progress_bar – If True, a tqdm progress bar will be displayed.

Returns

List of ndarray of simulated scattering length density profiles (real part).

Return type

sld_profiles

class mlreflect.data_generation.Substrate(name: str, roughness: Union[float, mlreflect.data_generation.parameters.ConstantParameter], sld: Union[float, complex, mlreflect.data_generation.parameters.ConstantParameter])

Bases: mlreflect.data_generation.layers.ConstantLayer

property ranges

mlreflect.data_generation.interp_reflectivity(q_interp, q, reflectivity)

Interpolate data on a base10 logarithmic scale.

mlreflect.data_generation.multilayer_reflectivity(q_values: Iterable, thickness: Iterable, roughness: Iterable, scattering_length_density: Iterable, ambient_sld: float = 0.0)

Returns a normalized reflectivity curve for a set of stacked layers with the given parameters.

Parameters

• q_values – An array-like object (list, tuple, ndarray, etc.) that contains the q-values in SI base units (i.e. 1/m) at which the reflected intensity will be simulated.

• thickness – An array-like object (list, tuple, ndarray, etc.) that contains the thicknesses of the sample layers in SI base units (i.e. m) in order from bottom to top excluding the bottom most layer (substrate).

• roughness – An array-like object (list, tuple, ndarray, etc.) that contains the roughnesses of the sample interfaces in SI base units (i.e. m) in order from bottom to top.

• scattering_length_density – An array-like object (list, tuple, ndarray, etc.) that contains the scattering length densities of the sample layers in SI base units (i.e. 1/m^2) in order from bottom to top (excluding the ambient SLD).

• ambient_sld – Scattering length density of the ambient environment (above the top most layer).

Returns

ndrray of simulated intensity values with same length as q_values.

Example

The following code can be used to simulate the reflectivity of a model with two layers with 100 and 250 Å thickness on a substrate.

``` q = np.linspace(0.01, 0.20, 1001) * 1e10 ambient_sld = 0 thickness = np.array([100, 250]) * 1e-10 roughness = np.array([3, 11, 5]) * 1e-10 sld = np.array([12 + 0.012j, 2.36 + 0j, 4.2 + 0.016j]) * 1e14

simulated_curve = multilayer_reflectivity(q_values=q, thickness=thickness, roughness=roughness,

scattering_length_density=sld, ambient_sld=ambient_sld)

```