Industrial Radiography (RT), Ir-192 / X-Ray Weld Inspection & ASME Sec V Article 2
Radiographic NDT Geometric Unsharpness (Ug) & SFD Formula
Calculate Source-to-Object Distance D_o = SFD - t (mm), Penumbra Geometric Unsharpness U_g = F*t/(SFD - t) (mm), Minimum Code Source-to-Film Distance SFD_min (mm), and ASME Sec V Compliance.
Place an Ir-192 gamma source too close to a thick pipe weld and focal-spot penumbra blurs hairline cracks invisible!
Because industrial X-ray anodes and Iridium-192 / Cobalt-60 gamma pellets have finite Physical Focal-Spot Diameter F (mm, e.g. 2.5–3.5 mm), rays grazing an internal flaw on the source-side surface of a weld of Specimen-to-Film Thickness t (mm) cast a blurred penumbra shadow across the detector! By similar triangles between Source-to-Object Distance D_o = SFD - t and Object-to-Film Distance t (where SFD is total Source-to-Film Distance), ASME Boiler & Pressure Vessel Code Section V Article 2 defines Geometric Unsharpness U_g = (F * t) / (SFD - t) mm! For material under 50 mm thick, ASME caps U_g <= 0.51 mm (0.020 in), imposing a hard Minimum Source-to-Film Stand-Off SFD_min = t * (1 + F / U_g,max)—even though backing the source further away increases exposure time quadratically by the inverse-square law!
Verify on a 28.0 mm Heavy-Wall Pipeline Radiograph Using a 3.0 mm Ir-192 Pellet—Focal_Spot_Size F = 3.00 mm (B2), Source_Side_Object_to_Film t = 28.00 mm (B3), Actual_Source_to_Film_SFD = 650.0 mm (B4 -> Source-to-Object D_o = 622.0 mm in E2), and ASME_Max_Ug_Limit = 0.51 mm (B5): Geometric Unsharpness U_g hits (3.0 * 28.0) / 622.0 = 0.135 mm (E3), Minimum Code SFD equals 28 * (1 + 3.0 / 0.51) = 192.7 mm (E4), and Code Audit confirms "ASME UG COMPLIANT" (E5)!
| ASME Sec V Radiography KPI (F=3.0 mm, t=28 mm, SFD=650 mm, Ug,max=0.51 mm) | Formula | Verified Output |
|---|---|---|
| Source-to-Object Distance Do (mm) | Source_to_Film_SFD - Object_Film_t | 622.0 mm (132.0 mm @ tight 160 SFD) |
| Geometric Unsharpness Ug (mm) | (Focal_Spot_F * t) / (SFD - t) | 0.135 mm (0.636 > 0.51 @ 160 SFD!) |
| Minimum Code SFD_min (mm) | t * (1 + Focal_Spot_F / Max_Ug_Code) | 192.7 mm |
| ASME Sec V Art. 2 Penumbra Gate | Ug_mm <= Max_Ug_Code_mm | ASME UG COMPLIANT (FAIL @ 160 SFD!) |
ASME Section V Article 2 Geometric Unsharpness & Minimum SFD Formula
Validate Focal_Spot F > 0, Object_to_Film t > 0, SFD > 1.2 * t (source cannot touch the weld crown!), and Max_Ug_Code > 0!
=LET(fs_m, B2, tf_m, B3, sf_d, B4, ug_x, B5, IF(OR(fs_m <= 0, tf_m <= 0, sf_d <= 1.2 * tf_m, ug_x <= 0), "Invalid RT Setup", LET(ug_v, (fs_m * tf_m) / (sf_d - tf_m), IF(ug_v <= ug_x, "ASME UG COMPLIANT", "PENUMBRA BLUR EXCEEDS CODE"))))Cramped Pipe-Rack 160 mm Double-Wall Stand-Off Reject Check (Set SFD = 160.0 mm)
Crowd the gamma camera to SFD B4 = 160.0 mm (< 192.7 mm SFD_min in E4) inside a tight pipe rack: Source-to-Object Distance E2 shrinks to 132.0 mm, Geometric Unsharpness E3 balloons to 0.636 mm, and E5 rejects the shot with "PENUMBRA BLUR EXCEEDS CODE" (requiring a smaller fine-focus Se-75 / X-ray source)!
=IF(ISTEXT(E2), E2, ROUND((B2 * B3) / (B4 - B3), 3))Try the example
Use the original values or change them to test your understanding.