Reconstruction of the Two-Dimensional Strain Tensor and Principal-Strain Hotspots from Indexed 4D-STEM Nanobeam Diffraction
Diffraction-peak detection and h/k indexing have already been completed for a set of nanobeam 4D-STEM data. The scan covers 21×17 positions, with 6 reciprocal-lattice peaks retained at each position; an independent standard sample was also acquired under the same detector conditions. The scan peak table, raw/certified q values for the standard sample, the undeformed reference reciprocal basis, ROI definitions, and quality requirements are provided in /app/input.
First calibrate the detector coordinates, then recover the local reciprocal basis and real-space deformation from the indexed peaks at each scan position. Separate lattice rotation from symmetric strain, and generate two-dimensional results for strain_xx, strain_yy, strain_xy, the principal strains, and the principal directions. Subsequently, perform ROI statistics, extract the centerline profile at y=160 nm, evaluate peak-fitting residuals, identify strain hotspots, and provide a conclusion regarding reconstruction quality.
Generate analysis.py, calibrated_diffraction_vectors.csv, strain_map.csv, region_summary.csv, strain_line_profile.csv, strain_qc.csv, strain_tensor_maps.png, principal_strain_map.png, strain_line_profile.png, and stem_strain_report.md under /app/output. Retain explicit units and mean/SD in the results, and ensure that the figures, tables, and report are consistent with the CSV files; do not read data from outside /app/input or hard-code reference results.
Deliverable Files
The following defines only the submission format and does not prescribe the analysis method or expected results. All 10 paths listed below are required. All CSV files must use UTF-8 encoding, comma delimiters, decimal-point notation, and no index column. Column order is unrestricted, and additional columns are permitted, but the required fields below must use the specified names.
/app/output/analysis.py
Text of the analysis script; it must be capable of generating the remaining deliverables from the public inputs in /app/input.
/app/output/calibrated_diffraction_vectors.csv
Each row corresponds to one indexed diffraction vector at one scan position, with (point_id, h, k) as the stable key.
| Field | Type | Unit | Meaning |
|---|---|---|---|
point_id |
string | — | Scan-position identifier |
grid_i, grid_j |
integer | — | Scan-grid indices |
scan_x_nm, scan_y_nm |
number | nm | Scan coordinates |
h, k |
integer | — | Diffraction-peak indices |
qx_raw_nm_inv, qy_raw_nm_inv |
number | nm⁻¹ | Raw reciprocal-vector components |
qx_calibrated_nm_inv, qy_calibrated_nm_inv |
number | nm⁻¹ | Calibrated reciprocal-vector components |
qx_predicted_nm_inv, qy_predicted_nm_inv |
number | nm⁻¹ | Reciprocal-vector components corresponding to the local reconstruction |
qx_residual_nm_inv, qy_residual_nm_inv |
number | nm⁻¹ | Reciprocal-vector residual components |
intensity_counts |
number | counts | Peak intensity |
peak_sigma_nm_inv |
number | nm⁻¹ | Peak-position uncertainty |
/app/output/strain_map.csv
Each row corresponds to one scan position, with point_id as the stable key.
| Field | Type | Unit | Meaning |
|---|---|---|---|
point_id |
string | — | Scan-position identifier |
grid_i, grid_j |
integer | — | Scan-grid indices |
scan_x_nm, scan_y_nm |
number | nm | Scan coordinates |
F11, F12, F21, F22 |
number | dimensionless | Components of the real-space deformation gradient |
strain_xx, strain_yy, strain_xy |
number | dimensionless | Components of the symmetric strain tensor |
rotation_deg |
number | degree | Lattice rotation angle |
principal_strain_max, principal_strain_min |
number | dimensionless | Principal strains |
principal_direction_deg |
number | degree | Axial orientation angle of the maximum principal strain |
determinant_F |
number | dimensionless | Determinant of the deformation gradient |
q_fit_rmse_nm_inv |
number | nm⁻¹ | Summary of the local reciprocal-vector fitting residuals |
/app/output/region_summary.csv
Each row corresponds to one reporting region, with region_id as the stable key.
| Field | Type | Unit | Meaning |
|---|---|---|---|
region_id |
string | — | Reporting-region identifier |
n_points |
integer | — | Number of scan positions within the region |
strain_xx_mean, strain_xx_sd, strain_yy_mean, strain_yy_sd, strain_xy_mean, strain_xy_sd |
number | dimensionless | Regional means and standard deviations of the strain-tensor components |
rotation_deg_mean, rotation_deg_sd |
number | degree | Regional mean and standard deviation of the lattice rotation angle |
principal_strain_max_mean, principal_strain_max_sd, principal_strain_min_mean, principal_strain_min_sd |
number | dimensionless | Regional means and standard deviations of the principal strains |
determinant_F_mean, determinant_F_sd |
number | dimensionless | Regional mean and standard deviation of the determinant of the deformation gradient |
q_fit_rmse_nm_inv_mean, q_fit_rmse_nm_inv_sd |
number | nm⁻¹ | Regional mean and standard deviation of the local reciprocal-vector fitting-residual summary |
principal_direction_axial_mean_deg |
number | degree | Regional axial mean angle of the principal direction |
/app/output/strain_line_profile.csv
Each row corresponds to one scan position along the centerline, with point_id as the stable key.
| Field | Type | Unit | Meaning |
|---|---|---|---|
point_id |
string | — | Scan-position identifier |
scan_x_nm, scan_y_nm |
number | nm | Scan coordinates |
strain_xx, strain_yy, strain_xy |
number | dimensionless | Components of the symmetric strain tensor |
rotation_deg |
number | degree | Lattice rotation angle |
principal_strain_max, principal_strain_min |
number | dimensionless | Principal strains |
principal_direction_deg |
number | degree | Axial orientation angle of the maximum principal strain |
q_fit_rmse_nm_inv |
number | nm⁻¹ | Summary of the local reciprocal-vector fitting residuals |
/app/output/strain_qc.csv
Single-row quality-summary table.
| Field | Type | Unit | Meaning |
|---|---|---|---|
calibration_a11, calibration_a12, calibration_a21, calibration_a22 |
number | dimensionless | Components of the linear calibration transformation |
calibration_b1_nm_inv, calibration_b2_nm_inv |
number | nm⁻¹ | Calibration offset components |
calibration_determinant |
number | dimensionless | Determinant of the linear calibration transformation |
calibration_rmse_nm_inv |
number | nm⁻¹ | Summary of the calibration residuals |
n_scan_points, n_diffraction_vectors |
integer | — | Numbers of scan positions and diffraction vectors |
mean_q_fit_rmse_nm_inv, maximum_q_fit_rmse_nm_inv |
number | nm⁻¹ | Summary statistics for the local reciprocal-vector fitting residuals |
maximum_principal_strain |
number | dimensionless | Summary of the maximum principal strain |
hotspot_point_id |
string | — | Hotspot scan-position identifier |
hotspot_x_nm, hotspot_y_nm |
number | nm | Hotspot scan coordinates |
hotspot_principal_direction_deg |
number | degree | Axial angle of the principal direction at the hotspot |
matrix_left_abs_strain_max |
number | dimensionless | Absolute-strain summary for the MATRIX_LEFT region |
strain_reconstruction_status |
string | — | Reconstruction quality status |
failure_reasons |
string | — | Explanation of the quality status |
/app/output/strain_tensor_maps.png
PNG image; display the two-dimensional results for the strain-tensor components and indicate the coordinates, units, and meaning of the colors.
/app/output/principal_strain_map.png
PNG image; display the two-dimensional results for the principal strains and principal directions, and indicate the coordinates, units, colors, and meaning of the directions.
/app/output/strain_line_profile.png
PNG image; display the centerline profile and indicate the coordinates, units, and meaning of the legend.
/app/output/stem_strain_report.md
UTF-8 Markdown report; cover detector calibration, conventions for reciprocal-space and real-space results, local reconstruction, strain and rotation, principal strains and principal directions, regional statistics, the centerline profile, hotspots, fitting residuals, and the conclusion regarding reconstruction quality, while remaining consistent with the CSV files and images.