Polarized Soft X-Ray Reflectivity Dataset (reflectivity-1m)

Synthetic polarized soft X-ray reflectivity (s and p channels) simulated with refloxide for uniaxial anisotropic thin films on native-oxide silicon:

vacuum | anisotropic film | SiO2 oxide | Si substrate

Each curve mimics an experimental angle scan at an arbitrary soft X-ray photon energy: 256 random grazing angles θ ∈ [0.5°, 65.0°] are drawn and sorted ascending, evaluated at a randomized photon energy E ∈ [200, 500] eV, and cast into momentum transfer q = (4π / λ) sin θ (1/Å). Photon energy is omitted from the saved labels so downstream models learn an energy-invariant mapping from (q, R_s, R_p) to structural and Cartesian uniaxial optical tensor parameters (delta_xx, delta_zz, beta_xx, beta_zz).

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Example Sample

Top: simulated s- and p-polarized power reflectivity R_s(q) and R_p(q) sampled at 256 random grazing angles and cast to q. Bottom: corresponding erf-smoothed uniaxial refractive-index depth profile (1 - n = δ - iβ) showing in-plane (δ_xx, β_xx) and out-of-plane (δ_zz, β_zz) components across the vacuum | film | oxide | silicon interfaces.

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Dataset Distributions (1,000,000 Curves · 256,000,000 Points)

Structural & Optical Parameter Priors

Sampling proceeds in two stages so every interface remains strictly inside the Nevot–Croce validity regime (thickness ≥ 2π · roughness): film and native oxide thicknesses are drawn first, followed by film roughness capped at min(40 Å, t_film / 2π) and oxide roughness coupled via σ_oxide = t_oxide / 2π. Uniaxial optical constants are drawn in polar form (component_xx = magnitude · cos(angle), component_zz = magnitude · sin(angle)) and stored directly as Cartesian tensor components (delta_xx, delta_zz, beta_xx, beta_zz).

Sampled q Grid & Fresnel-Compensated R · q⁴ Densities

Uniform sampling over (θ, E) produces dense coverage at low-to-intermediate q with a smooth high-q tail out to ~0.46 Å⁻¹, while p polarization exhibits broader dynamic range than s polarization due to Brewster-angle and birefringent contrast.

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Schema & Storage Layout

• Total rows: 1,000,000 across 10 Parquet shard(s) (data/train-*.parquet). All rows are stored in a single train split so train/validation/test splits can be chosen post-hoc.
• Substrate constants: Si (ρ = 2.33 g/cm³, σ = 1.2 Å), SiO2 (ρ = 2.2 g/cm³, σ_oxide = t_oxide / 2π).
• Optimized datatypes: Non-nullable FixedSizeList(float32, 256) curves + float32 scalars encoded with BYTE_STREAM_SPLIT + ZSTD—eliminating per-row list-offset and validity-bitmap overhead while preserving 38 decades of dynamic range (where float16 underflows below `6e-8`).

Column	Arrow Type	Units / Range	Description
q	fixed_size_list<float32>[256]	1/Å	Ascending momentum transfer grid cast from (θ, E)
s	fixed_size_list<float32>[256]	power reflectance	s-polarized reflectivity R_s(q)
p	fixed_size_list<float32>[256]	power reflectance	p-polarized reflectivity R_p(q)
film_thickness	float32	Å, [20.0, 800.0]	Anisotropic film thickness t_film
film_roughness	float32	Å, [0.0, min(40.0, t_film / 2π)]	Vacuum/film RMS roughness σ_film (Nevot–Croce capped)
oxide_thickness	float32	Å, [0.0, 15.0]	Native SiO2 thickness t_oxide (σ_oxide = t_oxide / 2π)
delta_xx	float32	[-5.0e-03, 5.0e-03]	In-plane (ordinary) dispersion δ_xx = δ cos α
delta_zz	float32	[-5.0e-03, 5.0e-03]	Out-of-plane (extraordinary) dispersion δ_zz = δ sin α
beta_xx	float32	[0.0, 5.0e-03]	In-plane (ordinary) absorption β_xx = β cos γ
beta_zz	float32	[0.0, 5.0e-03]	Out-of-plane (extraordinary) absorption β_zz = β sin γ
E	float64	eV	Photon energy the curve was simulated at (constant in fixed-q datasets, random in variable-q ones)

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Loading the Data

Polars -> Contiguous float32 NumPy / PyTorch Arrays

Because q, s, and p are stored as fixed-size non-nullable float32 arrays, Polars materializes them directly into C-contiguous (N, 256) tensors:

import numpy as np
import polars as pl

LABEL_COLS = [
    "film_thickness",
    "film_roughness",
    "oxide_thickness",
    "delta_xx",
    "delta_zz",
    "beta_xx",
    "beta_zz",
]

df = pl.read_parquet("hf://datasets/carbon-lab/reflectivity-1m/data/train-*.parquet")

q = df["q"].to_numpy()  # (1_000_000, 256) float32, C-contiguous
s = df["s"].to_numpy()  # (1_000_000, 256) float32, C-contiguous
p = df["p"].to_numpy()  # (1_000_000, 256) float32, C-contiguous

inputs = np.stack([s, p, q], axis=1)        # (1_000_000, 3, 256) float32
targets = df.select(LABEL_COLS).to_numpy()  # (1_000_000, 7) float32

Hugging Face datasets (with Post-Hoc Train/Validation Split)

from datasets import load_dataset

ds = load_dataset("carbon-lab/reflectivity-1m", split="train").with_format("torch")
splits = ds.train_test_split(test_size=0.1, seed=42)
train_ds, val_ds = splits["train"], splits["test"]

batch = train_ds[:64]
q, s, p = batch["q"], batch["s"], batch["p"]  # each torch.float32 of shape (64, 256)

Streaming Batches with PyArrow (Low Memory)

from huggingface_hub import snapshot_download
import pyarrow.dataset as ds

local_dir = snapshot_download(
    repo_id="carbon-lab/reflectivity-1m",
    repo_type="dataset",
    allow_patterns="data/train-*.parquet",
)

dataset = ds.dataset(f"{local_dir}/data", format="parquet")
for record_batch in dataset.to_batches(batch_size=4096):
    q = record_batch["q"].values.to_numpy().reshape(-1, 256)
    s = record_batch["s"].values.to_numpy().reshape(-1, 256)
    p = record_batch["p"].values.to_numpy().reshape(-1, 256)