4. Neutron reflectometry use#
import torch
import numpy as np
import matplotlib.pyplot as plt
from reflectorch import InferenceModel, Layer, Structure, Backing, EXP_DATA_DIR
from reflectorch.inference.plotting import print_prediction_results, plot_reflectivity
torch.manual_seed(0); # set seed for reproducibility
In this tutorial, we build upon the concepts introduced in the previous tutorial, where we demonstrated inference on XRR data, by highlighting key considerations specific to NR data.
4.1. Handling linear resolution smearing#
We consider the following NR data for a 1-layer stucture of Ni on Si (air as ambient), measured at a resolution dq/q = 0.1 (i.e. 10%):
data = np.loadtxt(EXP_DATA_DIR / 'Ni500.dat', delimiter='\t', skiprows=0)
print(data.shape)
q_exp = data[..., 0]
curve_exp = data[..., 1]
sigmas_exp = data[..., 2]
print(curve_exp.shape, q_exp.shape, q_exp.min(), q_exp.max())
print(sigmas_exp.shape, sigmas_exp.max(), sigmas_exp.min(), (sigmas_exp / curve_exp).max())
(174, 3)
(174,) (174,) 0.01333 0.22399
(174,) 8.83715e-05 4.23214e-07 0.3282606076124776
Show code cell source
fig, ax = plot_reflectivity(
q_exp=q_exp,
r_exp=curve_exp,
yerr=sigmas_exp,
)
We initialize an inference object for a model trained for neutron reflectometry and a standard parameterization with 1 layer (for more details on the InferenceModel class see the previous tutorial). Notably, the parameterization has 2 additional nuisance parameters: a scaling factor for the intensity of the reflectivity curve and the constant backround (in log10 representation). Here we load the models from the ‘reflectorch-ILL’ Huggingface repository which is a repository for selected NR models mainly targeting use cases relevant at the Institut Laue-Langevin (ILL), as opposed to the default research-based Huggingface repository ‘valentinsingularity/reflectivity’.
config_name = "NR-1layer-basic-v1"
inference_model = InferenceModel(
config_name=config_name,
repo_id="reflectorch-ILL",
device='cpu',
)
Configuration file `D:\Github Projects\reflectorch\reflectorch\configs\NR-1layer-basic-v1.yaml` found locally.
Weights file `D:\Github Projects\reflectorch\reflectorch\saved_models\model_NR-1layer-basic-v1.safetensors` found locally.
Model NR-1layer-basic-v1 loaded. Number of parameters: 21.90 M
The model corresponds to a `standard_model` parameterization with 1 layers (7 predicted parameters)
Parameter types and total ranges:
- thicknesses: [1.0, 1500.0]
- roughnesses: [0.0, 60.0]
- slds: [-8.0, 16.0]
- r_scale: [0.9, 1.1]
- log10_background: [-10.0, -4.0]
Allowed widths of the prior bound intervals (max-min):
- thicknesses: [0.01, 1500.0]
- roughnesses: [0.01, 60.0]
- slds: [0.01, 5.0]
- r_scale: [0.001, 0.2]
- log10_background: [0.01, 6.0]
The model was trained with linear resolution smearing (dq/q) in the range [0.01, 0.12]
The following quantities are additional inputs to the network: prior bounds, the resolution dq/q.
We set some prior bounds for the parameters:
prior_bounds = [
(300., 900.), #layer thicknesses (top to bottom)
(0., 20.), #interlayer roughnesses (top to bottom)
(0., 20.),
(9., 11.), #real layer slds: Ni, glass
(3., 5.),
(0.9, 1.1), #intensity scaling factor
(-10, -4), #log10 background
]
For performing the prediction we need to provide the q_resolution argument. When this argument is a float, its meaning is dq/q. This value is always used for simulating the reflectivity curve corresponding to the predicted parameters and as a keyword argument to the reflectivity function during polishing. Depending on the training scenario, it might also be used as an additional input to the network.
Since NR data can have points with high error bars which can disturb the neural network prediction, the preprocess_and_predict method can filter out the points with high error bars for the purpose of the prediction (they are still used for the polishing step), if the array of error bars (sigmas) is provided and enable_error_bars_filtering is True. Then the points where the error bar to intensity ratio is higher than the filter_threshold argument will be removed before the neural network inference. One can also manually truncate the part of the data seen by the network via the truncate_index_left and truncate_index_right arguments.
prediction_dict = inference_model.preprocess_and_predict(
reflectivity_curve=curve_exp,
prior_bounds=prior_bounds,
q_values=q_exp,
q_resolution=0.1,
sigmas=sigmas_exp,
clip_prediction=True,
polish_prediction=True,
use_sigmas_for_polishing=False,
calc_pred_curve=True,
calc_pred_sld_profile=True,
calc_polished_sld_profile=True,
sld_profile_padding_left=0.3,
sld_profile_padding_right=1.3,
enable_error_bars_filtering=True,
filter_threshold=0.3,
truncate_index_left=None,
truncate_index_right=None,
)
pred_params = prediction_dict['predicted_params_array']
pred_curve = prediction_dict['predicted_curve']
polished_curve = prediction_dict.get('polished_curve')
q_plot = prediction_dict['q_plot_pred']
print_prediction_results(prediction_dict)
Parameter Predicted Polished
----------------------------------------
Thickness L1 498.954 497.006
Roughness L1 6.429 6.504
Roughness sub 6.793 7.226
SLD L1 9.939 10.232
SLD sub 3.138 3.415
r_scale 0.944 0.977
log10_background -7.238 -6.277
fig, ax = plot_reflectivity(
q_exp=q_exp, r_exp=curve_exp, exp_style='errorbar', exp_marker='o', exp_ms=3, exp_color='blue', exp_facecolor='blue', exp_alpha=1.0, exp_label='exp. curve', exp_zorder=1,
yerr=sigmas_exp, xerr=None, exp_errcolor='purple', exp_elinewidth=1.0, exp_capsize=1, exp_capthick=1.0,
q_pred=q_plot, r_pred=pred_curve, pred_color='red', pred_lw=1.0, pred_ls='-', pred_label='pred. curve', pred_alpha=1.0, pred_zorder=2,
q_pol=q_exp, r_pol=polished_curve, pol_color='orange', pol_lw=2.0, pol_ls='--', pol_label='polished pred. curve', pol_alpha=1.0, pol_zorder=3,
plot_sld_profile=True, z_sld=prediction_dict['predicted_sld_xaxis'],
sld_pred=prediction_dict['predicted_sld_profile'], sld_pred_color='red', sld_pred_lw=2.0, sld_pred_ls='-', sld_pred_label='pred. SLD',
sld_pol=prediction_dict['sld_profile_polished'], sld_pol_color='orange', sld_pol_lw=2.0, sld_pol_ls='--', sld_pol_label='polished SLD',
)
Next, we load data for a different measurement of a similar structure (also Ni on Si). The differences are that the Ni layer is thicker, the resolution is dq/q = 0.015 (i.e. 1.5 %) and the data has a constant background.
data = np.loadtxt(EXP_DATA_DIR / 'Ni_on_glass.dat', delimiter='\t', skiprows=0)
print(data.shape)
q_exp = data[..., 0]
curve_exp = data[..., 1]
print(curve_exp.shape, q_exp.shape, q_exp.min(), q_exp.max())
(757, 2)
(757,) (757,) 0.00508981 0.175655
prior_bounds = [
(300., 900.), #layer thicknesses (top to bottom)
(0., 20.), #interlayer roughnesses (top to bottom)
(0., 20.),
(9., 11.), #layer slds: Ni, glass
(3., 5.),
(0.9, 1.1), #intensity scaling factor
(-10, -4), #log10 background
]
Tip
Alternatively, one can define the prior bounds in the following manner:
Ni_layer = Layer(thickness_bounds=(300, 900), roughness_bounds=(0, 20), sld_bounds=(9, 11))
backing = Backing(roughness_bounds=(0, 20), sld_bounds=(3, 5))
structure = Structure(
layers=[Ni_layer, backing],
r_scale_bounds=(0.9, 1.1),
log10_background_bounds=(-10, -4),
)
prior_bounds = structure.prior_bounds
Now we provide the new value of dq/q as argument:
prediction_dict = inference_model.preprocess_and_predict(
reflectivity_curve=curve_exp,
prior_bounds=prior_bounds,
q_values=q_exp,
q_resolution=0.015,
sigmas=None,
clip_prediction=True,
polish_prediction=True,
calc_pred_curve=True,
calc_pred_sld_profile=True,
calc_polished_sld_profile=True,
sld_profile_padding_left=0.3,
sld_profile_padding_right=1.3,
truncate_index_left=None,
truncate_index_right=None,
)
pred_params = prediction_dict['predicted_params_array']
pred_curve = prediction_dict['predicted_curve']
polished_curve = prediction_dict.get('polished_curve')
q_plot = prediction_dict['q_plot_pred']
print_prediction_results(prediction_dict, precision=2)
Parameter Predicted Polished
----------------------------------------
Thickness L1 831.42 827.32
Roughness L1 10.53 8.52
Roughness sub 1.55 0.00
SLD L1 9.05 9.19
SLD sub 4.39 3.91
r_scale 0.98 0.91
log10_background -4.00 -4.00
fig, ax = plot_reflectivity(
q_exp=q_exp, r_exp=curve_exp, exp_style='scatter', exp_marker='o', exp_ms=3, exp_color='blue', exp_facecolor='none', exp_alpha=1.0, exp_label='exp. curve', exp_zorder=1,
yerr=None,
q_pred=q_plot, r_pred=pred_curve, pred_color='red', pred_lw=2.0, pred_ls='-', pred_label='pred. curve', pred_alpha=1.0, pred_zorder=2,
q_pol=q_exp, r_pol=polished_curve, pol_color='orange', pol_lw=2.0, pol_ls='--', pol_label='polished pred. curve', pol_alpha=1.0, pol_zorder=3,
plot_sld_profile=True, z_sld=prediction_dict['predicted_sld_xaxis'],
sld_pred=prediction_dict['predicted_sld_profile'], sld_pred_color='red', sld_pred_lw=2.0, sld_pred_ls='-', sld_pred_label='pred. SLD',
sld_pol=prediction_dict['sld_profile_polished'], sld_pol_color='orange', sld_pol_lw=2.0, sld_pol_ls='--', sld_pol_label='polished SLD',
)
4.2. Handling pointwise resolution smearing#
We load NR data of a thick silicon oxide layer on top of a silicon substrate. Notably the data is in 4 colums format [q, R, dR, dQ], the last column being the pointwise resolution smearing.
data = np.loadtxt(EXP_DATA_DIR / 'D17_SiO.dat', skiprows=3)
print(data.shape)
q_exp = data[..., 0]
curve_exp = data[..., 1]
sigmas_exp = data[..., 2]
q_res_exp = data[..., 3]
print(curve_exp.shape, q_exp.shape, q_exp.min(), q_exp.max())
print(sigmas_exp.shape, sigmas_exp.max(), sigmas_exp.min())
print(q_res_exp.shape, (q_res_exp / q_exp).min(), (q_res_exp / q_exp).max())
(2166, 4)
(2166,) (2166,) 0.00610735 0.277902
(2166,) 1.39997 4.75674e-07
(2166,) 0.01295813163759255 0.020793481155227386
config_name = "NR-1layer-basic-v1"
inference_model = InferenceModel(
config_name=config_name,
repo_id="reflectorch-ILL",
device='cpu',
)
Configuration file `D:\Github Projects\reflectorch\reflectorch\configs\NR-1layer-basic-v1.yaml` found locally.
Weights file `D:\Github Projects\reflectorch\reflectorch\saved_models\model_NR-1layer-basic-v1.safetensors` found locally.
Model NR-1layer-basic-v1 loaded. Number of parameters: 21.90 M
The model corresponds to a `standard_model` parameterization with 1 layers (7 predicted parameters)
Parameter types and total ranges:
- thicknesses: [1.0, 1500.0]
- roughnesses: [0.0, 60.0]
- slds: [-8.0, 16.0]
- r_scale: [0.9, 1.1]
- log10_background: [-10.0, -4.0]
Allowed widths of the prior bound intervals (max-min):
- thicknesses: [0.01, 1500.0]
- roughnesses: [0.01, 60.0]
- slds: [0.01, 5.0]
- r_scale: [0.001, 0.2]
- log10_background: [0.01, 6.0]
The model was trained with linear resolution smearing (dq/q) in the range [0.01, 0.12]
The following quantities are additional inputs to the network: prior bounds, the resolution dq/q.
Show code cell source
fig, ax = plot_reflectivity(
q_exp=q_exp,
r_exp=curve_exp,
yerr=sigmas_exp,
logx=True,
)
prior_bounds = [
(500., 1500.), #layer thicknesses (top to bottom)
(0., 30.), #interlayer roughnesses (top to bottom)
(0., 30.),
(3, 4), #layer slds (top to bottom)
(1.7, 2.5),
(0.9, 1.1), #intensity scaling factor
(-10, -4), #log10 background
]
prediction_dict = inference_model.preprocess_and_predict(
reflectivity_curve=curve_exp,
prior_bounds=prior_bounds,
q_values=q_exp,
q_resolution=q_res_exp,
sigmas=sigmas_exp,
clip_prediction=True,
polish_prediction=True,
use_sigmas_for_polishing=True,
calc_pred_curve=True,
calc_pred_sld_profile=True,
calc_polished_sld_profile=True,
sld_profile_padding_left=0.3,
sld_profile_padding_right=1.3,
enable_error_bars_filtering=True,
filter_threshold=0.3,
)
pred_params = prediction_dict['predicted_params_array']
pred_curve = prediction_dict['predicted_curve']
polished_curve = prediction_dict.get('polished_curve')
q_plot = prediction_dict['q_plot_pred']
print_prediction_results(prediction_dict)
Parameter Predicted Polished
----------------------------------------
Thickness L1 1246.756 1244.731
Roughness L1 5.675 3.070
Roughness sub 4.594 0.007
SLD L1 3.536 3.473
SLD sub 2.207 2.198
r_scale 0.903 0.934
log10_background -5.929 -6.561
Show code cell source
fig, ax = plot_reflectivity(
q_exp=q_exp, r_exp=curve_exp, exp_style='errorbar', exp_marker='o', exp_ms=3, exp_color='blue', exp_facecolor='none', exp_alpha=1.0, exp_label='exp. curve', exp_zorder=1,
yerr=sigmas_exp, xerr=None, exp_errcolor='purple', exp_elinewidth=1.0, exp_capsize=1, exp_capthick=1.0,
q_pred=q_plot, r_pred=pred_curve, pred_color='red', pred_lw=2.0, pred_ls='-', pred_label='pred. curve', pred_alpha=1.0, pred_zorder=2,
q_pol=q_exp, r_pol=polished_curve, pol_color='orange', pol_lw=2.0, pol_ls='--', pol_label='polished pred. curve', pol_alpha=1.0, pol_zorder=3,
plot_sld_profile=True, z_sld=prediction_dict['predicted_sld_xaxis'],
sld_pred=prediction_dict['predicted_sld_profile'], sld_pred_color='red', sld_pred_lw=2.0, sld_pred_ls='-', sld_pred_label='pred. SLD',
sld_pol=prediction_dict['sld_profile_polished'], sld_pol_color='orange', sld_pol_lw=2.0, sld_pol_ls='--', sld_pol_label='polished SLD',
logx=True,
)
4.3. Structures with fronting medium different than air#
We load neutron reflectometry (NR) data for a multilayer structure composed of silicon/silicon oxide/polymer/D₂O. Notably, the fronting medium in this case is not air, meaning the fronting SLD is non-zero. Although all models in Reflectorch are trained assuming a fronting SLD of zero, inference on data with non-zero fronting SLD is still valid. This is due to the invariance property of reflectivity under uniform SLD shifts, where R(SLD(z)) = R(SLD(z)+A) for any constant A.
data = np.loadtxt(EXP_DATA_DIR / 'ORSO_example.ort')
print(data.shape)
q_exp = data[..., 0]
curve_exp = data[..., 1]
sigmas_exp = data[..., 2]
q_res_exp = data[..., 3]
print(curve_exp.shape, q_exp.shape, q_exp.min(), q_exp.max())
print(sigmas_exp.shape, sigmas_exp.max(), sigmas_exp.min(), (sigmas_exp / curve_exp).max())
print(q_res_exp.shape, (q_res_exp / q_exp).min(), (q_res_exp / q_exp).max())
(408, 4)
(408,) (408,) 0.00806022 0.465555
(408,) 0.125959 1.19257e-07 1.784325740151806
(408,) 0.017461305621930916 0.020605159300190096
Show code cell source
fig, ax = plot_reflectivity(
q_exp=q_exp,
r_exp=curve_exp,
yerr=sigmas_exp,
)
config_name = "NR-2layers-basic-v1"
inference_model = InferenceModel(
config_name=config_name,
repo_id="reflectorch-ILL",
device='cpu',
)
Configuration file `D:\Github Projects\reflectorch\reflectorch\configs\NR-2layers-basic-v1.yaml` found locally.
Weights file `D:\Github Projects\reflectorch\reflectorch\saved_models\model_NR-2layers-basic-v1.safetensors` found locally.
Model NR-2layers-basic-v1 loaded. Number of parameters: 22.00 M
The model corresponds to a `standard_model` parameterization with 2 layers (10 predicted parameters)
Parameter types and total ranges:
- thicknesses: [1.0, 1500.0]
- roughnesses: [0.0, 60.0]
- slds: [-8.0, 16.0]
- r_scale: [0.9, 1.1]
- log10_background: [-10.0, -4.0]
Allowed widths of the prior bound intervals (max-min):
- thicknesses: [0.01, 1500.0]
- roughnesses: [0.01, 60.0]
- slds: [0.01, 5.0]
- r_scale: [0.001, 0.2]
- log10_background: [0.01, 6.0]
The model was trained with linear resolution smearing (dq/q) in the range [0.01, 0.12]
The following quantities are additional inputs to the network: prior bounds, the resolution dq/q.
prior_bounds = [
(10., 40.), #layer thicknesses: SiOx, polymer
(50., 500.),
(1.0, 20.0), #interlayer roughnesses: Si/SiOx, SiOx/polymer, polymer/D2O
(1.0, 20.0),
(1.0, 20.0),
(2.5, 4.0), #layer slds: SiOx, polymer, D2O
(1., 5.),
(6.3, 6.4),
(0.9, 1.1), #intensity scaling factor
(-10, -4), #log10 background
]
For inference we need to additionally provide the SLD of the fronting medium (here silicon) as the ambient_sld argument of the preprocess_and_predict method:
prediction_dict = inference_model.preprocess_and_predict(
reflectivity_curve=curve_exp,
prior_bounds=prior_bounds,
q_values=q_exp,
q_resolution=q_res_exp,
sigmas=sigmas_exp,
ambient_sld=2.07, #Si
clip_prediction=True,
polish_prediction=True,
use_sigmas_for_polishing=False,
calc_pred_curve=True,
calc_pred_sld_profile=True,
calc_polished_sld_profile=True,
sld_profile_padding_left=0.3,
sld_profile_padding_right=1.3,
enable_error_bars_filtering=True,
filter_threshold=0.3,
truncate_index_left=None,
truncate_index_right=None,
)
pred_params = prediction_dict['predicted_params_array']
pred_curve = prediction_dict['predicted_curve']
polished_curve = prediction_dict.get('polished_curve')
q_plot = prediction_dict['q_plot_pred']
print_prediction_results(prediction_dict)
Parameter Predicted Polished
----------------------------------------
Thickness L1 33.264 37.770
Thickness L2 261.801 259.244
Roughness L1 6.719 7.671
Roughness L2 6.727 10.235
Roughness sub 3.454 3.143
SLD L1 3.402 3.521
SLD L2 2.367 2.438
SLD sub 6.320 6.342
r_scale 0.900 0.900
log10_background -6.424 -6.471
fig, ax = plot_reflectivity(
q_exp=q_exp, r_exp=curve_exp, exp_style='errorbar', exp_marker='o', exp_ms=3, exp_color='blue', exp_facecolor='blue', exp_alpha=1.0, exp_label='exp. curve', exp_zorder=1,
yerr=sigmas_exp, xerr=None, exp_errcolor='purple', exp_elinewidth=1.0, exp_capsize=1, exp_capthick=1.0,
q_pred=q_plot, r_pred=pred_curve, pred_color='red', pred_lw=1.0, pred_ls='-', pred_label='pred. curve', pred_alpha=1.0, pred_zorder=2,
q_pol=q_exp, r_pol=polished_curve, pol_color='orange', pol_lw=2.0, pol_ls='--', pol_label='polished pred. curve', pol_alpha=1.0, pol_zorder=3,
plot_sld_profile=True, z_sld=prediction_dict['predicted_sld_xaxis'],
sld_pred=prediction_dict['predicted_sld_profile'], sld_pred_color='red', sld_pred_lw=2.0, sld_pred_ls='-', sld_pred_label='pred. SLD',
sld_pol=prediction_dict['sld_profile_polished'], sld_pol_color='orange', sld_pol_lw=2.0, sld_pol_ls='--', sld_pol_label='polished SLD',
)
