Computed Tomography

Computed Tomography (manufacturing-quality/ndt/computed-tomography)

Use when you must plan and interpret a volumetric X-ray computed tomography (CT) inspection of an aerospace part: turning the source, object and detector geometry into the magnification and voxel size, checking the achievable spatial resolution against the smallest flaw to detect, sizing the cone beam projection count, estimating the scan time and the required tube energy, converting measured attenuation into CT numbers, and measuring the porosity volume fraction in a segmented region of interest. This leaf is volumetric CT only; 2D radiographic film and digital setup (geometric unsharpness, IQI sensitivity, film density, inverse square exposure) belongs to manufacturing-quality/ndt/radiographic-inspection. It pairs with manufacturing-quality/ndt/ndt-method-selection, which decides when CT is the chosen method for an internal defect class. This leaf implements the planning model in pure Python, stdlib only.

Domain quick reference

• Geometric magnification: M = (SOD + ODD) / SOD, with SOD the source to object distance and ODD the object to detector distance.
• Voxel size: the detector pixel pitch p_det maps to the approximate isotropic voxel size v = p_det / M.
• Spatial resolution: the smallest reliably detected feature spans about 2 to 3 voxels; this module uses the module constant detect_factor = 3, so the check passes when v * detect_factor is at or below the required flaw size.
• Projection count (Nyquist-ish rule of thumb for cone beam): N_proj ~= pi / 2 * N_col, where N_col is the number of detector columns spanned by the object projection (reference-only guidance).
• Tube energy (rule of thumb, paraphrased reference-only guidance): roughly 60 to 80 kV per 10 mm of aluminum equivalent at moderate density, with steel about 2 times that; this module uses a representative kV per mm material table (aluminum 7, titanium 9, steel 14, nickel 16 kV per mm).
• Scan time: t_scan = N_proj * t_per_proj with the exposure time per projection as input; total in seconds.
• CT number: HU = 1000 * (mu - mu_water) / mu_water for a voxel with measured linear attenuation mu against the water attenuation mu_water; the material class follows the CT number band (air-or-gas, low-density-void, polymer-composite, light-alloy, high-density-metal).
• Porosity: porosity fraction = V_voids / V_total from the segmented void voxel count and the region of interest total voxel count, reported as percent; the equivalent spherical void diameter follows from the void voxel count and the voxel size by volume conservation.
• Units are SI throughout (m, s) except thickness in mm for the tube energy rule and porosity in percent.
• AS9100 frames the NDT process control context; the relations above are standard engineering methodology and reference-only guidance, summary-only.

Workflow

1. Fix the scan geometry: SOD and ODD in m, detector pixel pitch p_det in m. Compute magnification with magnification(sod, odd) and the voxel size with voxel_size(pixel_pitch, sod, odd).
2. State the smallest required flaw and run resolution_check(voxel, flaw) for the pass or fail verdict on spatial resolution.
3. Span the object on the detector: with the number of detector columns crossed by the object projection, size the scan with projection_count(columns_span).
4. Estimate the tube energy with tube_energy_kv(material, thickness_mm) using the material table, and the total scan time with scan_time(num_projections, exposure_s_per_proj).
5. Convert measured attenuation to the CT scale with ct_number(mu, mu_water) and classify the voxel population with material_class_from_ct_number(hu).
6. Measure porosity: porosity_fraction(void_voxels, total_voxels) gives the percent, void_diameter(void_voxels, voxel_size) the equivalent spherical void diameter.
7. For the planning summary call ct_inspection_verdict(...) once; it returns the magnification, voxel size, resolution verdict, projection count, tube energy, and any scan time, porosity and CT number fields supplied.
8. Confirm the deterministic checks with the contract test scripts/test_computed_tomography.py.

Worked example

Aluminum casting 50 mm diameter on a 200 micron pixel detector with SOD 300 mm and ODD 300 mm, required flaw 0.5 mm, 1024 detector columns, 0.1 s per projection, 0.8 percent porosity in a region of interest of 8,000,000 voxels.

• Magnification: M = (300 + 300) / 300 = 2.0 (magnification(0.300, 0.300)).
• Voxel size: v = 200 micron / 2 = 1.000e-4 m (100 micron) (voxel_size(200e-6, 0.300, 0.300)).
• Spatial resolution: smallest detectable feature 3 * 1.000e-4 = 3.000e-4 m, at or below the required 5.000e-4 m flaw, verdict PASS.
• Projection count: N_proj = ceil(pi / 2 * 1024) = 1609 (projection_count(1024)).
• Tube energy: 7.0 kV per mm * 50 mm = 350.0 kV (tube_energy_kv("aluminum", 50.0)).
• Scan time: 1609 * 0.1 s = 160.9 s (scan_time(1609, 0.1)).
• Porosity: 64,000 void voxels over 8,000,000 total voxels = 0.8 percent (porosity_fraction(64000, 8000000)); equivalent spherical void diameter void_diameter(64000, 1.000e-4) = 4.963e-3 m.
• CT number example: mu = 1.4 * mu_water gives ct_number(28.0, 20.0) = 400 HU, material class light-alloy.

Verification

• Confirm magnification(0.300, 0.300) returns 2.0 and voxel_size(200e-6, 0.300, 0.300) returns 1.000e-4 m.
• Confirm resolution_check(1.000e-4, 5.000e-4) returns a PASS verdict and resolution_check(1.000e-4, 2.000e-4) returns FAIL.
• Confirm projection_count(1024) returns 1609 and scan_time(1609, 0.1) returns 160.9 s.
• Confirm tube_energy_kv("aluminum", 50.0) returns 350.0 kV and that the steel value is about 2 times the aluminum value per mm.
• Confirm ct_number round-trips: ct_number(mu, mu_water) then mu_water * (1 + hu / 1000) recovers mu.
• Confirm porosity_fraction(64000, 8000000) returns 0.8 percent and the void volume conserved by void_diameter equals the voxel count times the voxel volume.
• Confirm every non-positive distance, pitch, flaw size, thickness, exposure and projection count, void count above the total, and unknown material raises ValueError.
• Run the contract test offline: python3 scripts/test_computed_tomography.py (59 tests, deterministic).

Related leaves

• manufacturing-quality/ndt/ndt-method-selection: decides when CT is the chosen method among the NDT families for an internal defect class on a cast or additive part.
• manufacturing-quality/ndt/radiographic-inspection: the 2D radiographic counterpart (geometric unsharpness, IQI sensitivity, film density and exposure), used when planar radiography is chosen over the volumetric CT scan.
• manufacturing-quality/additive/lpbf-parameter-development: the build process context for additive parts whose build region porosity this leaf measures volumetrically.

Pitfalls

• Trusting a resolution verdict for flaws smaller than the voxel rule: the smallest reliably detected feature spans about 2 to 3 voxels (detect_factor = 3 here), so a 0.2 mm flaw under a 1.000e-4 m voxel scan FAILS while the same flaw passes at 0.5 mm - features below 3 voxels are not a valid claim.
• Treating the planning rules as exact standards: the projection count (pi / 2 * N_col) and the tube energy table (aluminum 7, titanium 9, steel 14, nickel 16 kV per mm, steel about 2 times aluminum) are reference-only rules of thumb for moderate density, not a substitute for the scan developer's validated technique.
• Reading a CT number band as material identification: HU = 1000 * (mu - mu_water) / mu_water classifies a voxel into a band (air-or-gas through high-density-metal) - two materials can share a band, so the class is not a chemical identification.
• Mixing units: the geometry and exposure inputs are SI (m, s) while thickness enters the tube energy rule in mm and porosity is reported in percent, so a cm source distance or a fraction porosity silently corrupts the plan.
• Quoting porosity without the segmentation: the fraction is void voxels over the region-of-interest total (0.8 percent from 64,000 of 8,000,000 voxels in the worked example), and a void count above the total raises ValueError - the ROI definition is part of the measurement.
• Reaching for this leaf for 2D setups: it is volumetric CT only; geometric unsharpness, IQI sensitivity, film density and inverse square exposure belong to radiographic-inspection.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_computed_tomography.py

The test covers the worked example contract (magnification 2.0, voxel 1.000e-4 m, PASS at the 0.5 mm flaw, 1609 projections, 350 kV, 160.9 s, 0.8 percent porosity, void diameter 4.963e-3 m), magnification and voxel scaling, the resolution boundary at exactly 3 voxels, the projection count rule of thumb, the tube energy material table and scaling, scan time scaling, CT number conversion with the round trip, material class bands, porosity fraction bounds, void diameter volume conservation, the combined ct_inspection_verdict, and ValueError rejection of non-physical inputs and unknown materials.

Compliance

• Standards referenced, not reproduced: AS9100 frames the NDT process control and personnel qualification context; CT physics standard forms (magnification, voxel mapping, cone beam sampling rule, tube energy rule, Hounsfield scale) are paraphrased reference-only guidance, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.