midas-saxs

Differentiable small-angle X-ray scattering for MIDAS. Two source terms, one detector:

• Density contrast — voids, gas bubbles, precipitates. Sphere / ellipsoid / cylinder form factors, lognormal polydispersity, Percus-Yevick S(Q), Guinier and Porod analysis. These came from midas_pdf.saxs, which now re-exports them from here, so MIDAS has one definition of "SAXS form factor".
• Strain contrast — dislocation loops, driven by a midas_ddd network read from ExaDiS. Optional extra: pip install 'midas-saxs[dislocations]'.

from midas_saxs import SAXSGeometry, SpherePopulation, simulate_frame

geom = SAXSGeometry(lsd_um=2.0e6, bcy_px=512, bcz_px=512, px_um=75.0,
                    wavelength_A=0.7293, n_pix_y=1024, n_pix_z=1024,
                    beamstop_radius_px=30)
voids = SpherePopulation(radius_A=50.0, number_density_per_A3=1e-8,
                         delta_rho_e_per_A3=-2.45, label="voids")
frame = simulate_frame(geom, particles=[voids], sample_volume_A3=1e15)

dev/paper/loop_vs_void_demo.py renders the five-panel figure that motivates the whole package.

Read this before promising anyone a loop measurement

Three numbers, all reproducible from the demo script.

1. Loops are faint. A dislocation loop of radius R displaces only its relaxation volume pi R^2 b; a void of the same radius displaces 4 pi R^3 / 3. For R = 5 nm in Cu that is 26x in volume and 680x in forward intensity. The loop scatters like a sphere of radius 1.7 nm.

2. What separates a loop from a void is shape, not size. The loop's small-angle amplitude is direction-dependent — kappa dV in its own plane, dV along its normal, with kappa = lambda/(lambda + 2 mu). Intensity is therefore modulated by 1 - kappa^2 (0.84 for lambda = 100, mu = 75). A void is isotropic. Radially averaging a frame destroys exactly this, which is why this package renders 2-D frames and offers azimuthal_profile alongside radial_average.

3. Real voids bury the signature. Measured on the demo: 24 aligned loops alone give an azimuthal contrast of 6.30x (the closed form predicts 1/kappa^2 = 6.25). Add equal-radius voids at the same number density — the physically realistic irradiated case — and the contrast collapses to 1.002x, with the voids outshining the loops by 1089x integrated over the frame.

So: loops are detectable at small angle in a clean matrix, and essentially undetectable alongside a void or bubble population of comparable size. If the question is defect-type discrimination in an irradiated material, near-Bragg diffuse (Huang) scattering is stronger than the small-angle signal by (G/q)^2 ~ 1e4 to 1e7 and is the better measurement.

Identifiability — what a frame determines, and what it only appears to

Loop number density is not recoverable from a single SAXS frame. A study in this package claimed 2.6 % on loop number density and 0.6 % on loop radius, at 1e6 photons/q-point with voids at volume fraction 5.2e-5, from a loop-block condition number of 639. It was REFUTED on 2026-09-04 by adversarial review. Every number in it reproduces, several bit-identically — the arithmetic was never the problem. The numbers describe a different parameter vector, a different void loading and a different sample mounting than the claim stated.

Six ways it fails, each measured by a refuter rather than read from the study's own output:

At the claim's own operating point voids already supply 97.9 % of the photons and the whole result rides on a 3.54 % azimuthal modulation. Over 99 % of the claimed information is azimuthal anisotropy, not scattering-curve shape.

A condition number cannot be a confirm criterion here. A Fisher matrix scales linearly with photon budget, so its condition number is exactly scale-invariant: measured at 639.5832 to seven digits across 1e0, 1e3, 1e6, 1e9 and 1e12 photons/q-point while SE[log n_loop] ran 2580 % to 0.0026 %. Across four decades of void loading it moved 639.6 to 640.2 while SE went 2.58 % to 101 %, straight through the refute threshold with the criterion passing untouched.

What survived. Loop radius at 0.6 % is robust — it held under every lens, including the ones that destroyed the number density, and is unaffected by freeing the absolute scale. State it with its condition: q_max * R >~ 3.

What this means for the code. Nothing here is wrong. Three independent lenses confirmed the Fourier kernel, the Laue correction, the Fisher assembly and the Schur profiling. The forward model is sound; the claim was wrong about what it measured. If you build a Fisher or CRB analysis on this package, include the degenerate directions (signed dV, a loop-vs-plate shape parameter), use a habit distribution that can actually reach isotropy, put the void population at its realistic loading, and report the sample mounting -- because the answer depends on all four.

Scope

Closed dislocation loops only. A cut surface exists only for a closed circuit. Open lines — the deformation population — enclose no area, carry no relaxation volume, and contribute nothing as q -> 0; their small-angle signature is a weak transverse streak that is not modelled. simulate_frame reports how much line length it ignored rather than returning a number that looks complete.

Units

The 1e4 between the last two is easy to lose, so inv_A_to_inv_um / inv_um_to_inv_A exist and strain_source uses them rather than a literal.

Detector geometry

pixel_to_q goes through midas_transforms.apply_tilt_distortion — the same tilt (R_z R_y R_x) and 15-coefficient distortion model the HEDM side uses. That is deliberate: a SAXS geometry and an FF geometry calibrated from the same detector must agree about where q sits. Transmission SAXS has no omega, so lab q is sample q.

Migration note

form_factors, model, wide_band and core_shell moved here from midas_pdf.saxs. Both the package-level path (from midas_pdf.saxs import SAXSModel) and the deep path (from midas_pdf.saxs.form_factors import ...) still resolve, to the same objects — asserted by test_midas_pdf_reexports_the_same_objects. midas_pdf.saxs keeps the genuinely PDF-coupled part: joint SAXS + PDF refinement and its Bayesian variants.

One convention worth knowing: sphere_form_factor_squared returns V^2 |F|^2, not the normalised |F|^2. SpherePopulation.intensity multiplies it by n * delta_rho^2 and nothing else, which is only correct because the volume is already in there.