13.3 Radiographic Physics, Geometric Unsharpness, Density & IQI Sensitivity

13.2 Volumetric Radiography (RT): Geometric Unsharpness & Film/Digital Imaging

Quick Answer: Industrial Radiographic Testing (RT) evaluates internal volumetric soundess by directing ionizing radiation through a weldment onto photographic film or a digital detector. Differential absorption follows the Beer-Lambert law ($I = I_0 e^{-\mu t}$). Image penumbra is controlled by the geometric unsharpness formula ($U_g = \frac{f \cdot d}{D}$), where code limits mandate $U_g \le 0.020\text{ in}$ ($0.51\text{ mm}$) for steel under $2\text{ in}$ ($50\text{ mm}$). Optical density must fall between $1.8\text{ and }4.0$ for X-ray and $2.0\text{ and }4.0$ for gamma rays. Image Quality Indicators (hole-type plaques or wire IQIs) verify standard 2-2T sensitivity. While volumetric flaws (porosity, slag, tungsten) are readily identified, planar lack of fusion and cracks require beam alignment within $\pm 5^\circ\text{ to }10^\circ$ of the flaw plane.

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1. Physics of Industrial Radiography: Sources, Spectra & Attenuation

Radiographic examination relies on high-energy electromagnetic photons possessing wavelengths between $10^{-4}\text{ and }10\text{ nm}$. As radiation penetrates steel, photons undergo absorption and scattering primarily through the Photoelectric Effect (predominant at low energies, $< 100\text{ keV}$), Compton Scattering (predominant across industrial welding energies, $100\text{ keV to }5\text{ MeV}$), and Pair Production (occurring at high energies, $> 1.022\text{ MeV}$).

                    VOLUMETRIC RADIOGRAPHIC EXPOSURE GEOMETRY

                               Source / Focal Spot (f)
                                      +-----+
                                      |  *  |
                                      +--+--+
                                         |  \
                                         |   \
                    Source-to-Object     |    \
                     Distance (SOD = D)  |     \
                                         |      \
                                         V       V
                     ====================[===WELD===]==================== Plate
                     ====================================================
                     Object-to-Film (d)  |        |
                     --------------------+--------+----------------------
                                         [==FILM==]
                                   Source-to-Film Distance
                                       (SFD = D + d)

X-Ray Machines vs. Radioisotope Gamma Sources

• Industrial X-Ray Generators: X-rays are produced when high-velocity electrons accelerated across an electrical potential ($kV_p$) strike a heavy metal target (tungsten). The deceleration produces a continuous Bremsstrahlung spectrum superimposed with sharp characteristic emission lines. The tube voltage ($kV_p$) dictates photon energy (penetrating power), while tube current ($mA$) and exposure time ($s$) dictate total photon flux (intensity).
• Gamma-Ray Radioisotopes: Gamma rays originate from the spontaneous nuclear decay of unstable radioactive isotopes, yielding discrete, monochromatic photon energy lines.

Attenuation Mathematics: Beer-Lambert Law, HVL & TVL

Radiation passing through matter attenuates exponentially according to the Beer-Lambert Law:

$$I = I_0 e^{-\mu t}$$

where $I_0$ is the incident beam intensity, $I$ is the transmitted beam intensity, $\mu$ is the linear attenuation coefficient of the material ($\text{cm}^{-1}$ or $\text{in}^{-1}$), and $t$ is the material thickness.

• Half-Value Layer (HVL): The thickness of absorber required to reduce the beam intensity to exactly $50\%$ ($1/2$) of its initial value: $$\frac{I}{I_0} = 0.5 = e^{-\mu \cdot HVL} \implies HVL = \frac{\ln(2)}{\mu} = \frac{0.69315}{\mu}$$
• Tenth-Value Layer (TVL): The thickness of absorber required to attenuate the beam intensity to $10\%$ ($1/10$): $$TVL = \frac{\ln(10)}{\mu} = \frac{2.3026}{\mu} \approx 3.32 \times HVL$$

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2. Geometric Unsharpness ($U_g$) Mechanics & Code Limits

Because radiation sources possess finite physical dimensions (focal spot width $f$ in an X-ray tube, or the physical diameter of a radioactive isotope pellet), rays originate from multiple points across the source face. This geometric dispersion casts a blurred shadow boundary—known as the geometric penumbra or geometric unsharpness ($U_g$)—along every feature edge on the film.

                         GEOMETRIC UNSHARPNESS MECHANICS

                            Source Diameter / Spot (f)
                                 |<- f ->|
                                 +-------+
                                /         \
                               /           \
                              /             \
          Source-to-Object   /               \
           Distance (SOD = D)/                 \
                            /                   \
                           /                     \
                          /   Object / Defect     \
     --------------------+------[=======]----------+--------------------
     Weldment Plate             |<--w-->|
     Object-to-Film (d)  /                 \
     -------------------+-------------------+---------------------------
                        |<--Ug->|           |<--Ug->|
                         Blur    Full Shadow Blur
                              Film Plane / Detector

Governing Formula

From similar triangles across the optical projection:

$$U_g = \frac{f \cdot d}{D}$$

where:

• $U_g$ = Geometric unsharpness (penumbra width on film)
• $f$ = Source size (effective focal spot dimension of X-ray tube or active diameter of radioisotope capsule)
• $d$ = Object-to-film distance (OFD, distance from the source-side surface of the weldment to the recording media)
• $D$ = Source-to-object distance (SOD, distance from radiation source to the source-side surface of the weldment)
• Note: Source-to-Film Distance is $SFD = D + d = SOD + OFD$.

To minimize geometric unsharpness ($U_g$), the welding engineer must:

1. Select the smallest practical source/focal spot size ($f$).
2. Minimize object-to-film distance ($d$) by placing film cassettes in direct contact with the weld root/face.
3. Maximize source-to-object distance ($D$), balancing penumbra reduction against the Inverse Square Law ($I \propto 1 / SFD^2$), which increases exposure time quadratically.

Code Acceptance Limits for Geometric Unsharpness

ASME BPVC Section V Article 2 (Table T-274.2) and AWS D1.1 Clause 8 impose maximum permissible $U_g$ thresholds based on material thickness:

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3. Radiographic Sensitometry, Density & Film Viewing

Optical Density Formulation

Radiographic film consists of a polyester base coated with a photographic emulsion of silver halide crystals ($AgBr$). Photons ionize halide atoms, creating a latent image reduced to metallic silver grains during chemical development. The blackening of the processed radiograph is quantified as Optical Density ($D$):

$$D = \log_{10}\left(\frac{I_0}{I_t}\right)$$

where $I_0$ is the light intensity incident on the film from a calibrated industrial viewer, and $I_t$ is the light intensity transmitted through the radiograph, measured via a calibrated transmission densitometer.

• $D = 1.0 \implies 10\%$ of light transmitted ($10^{-1}$).
• $D = 2.0 \implies 1\%$ of light transmitted ($10^{-2}$).
• $D = 3.0 \implies 0.1\%$ of light transmitted ($10^{-3}$).
• $D = 4.0 \implies 0.01\%$ of light transmitted ($10^{-4}$).

                       HURTER & DRIFFIELD (H&D) CURVE

     Optical Density (D)
       ^
   4.0 |                                       .--- Shoulder (Saturation)
       |                                      /
   3.0 |                                    / <-- Linear Region
       |                                   /      (Maximum Film Gradient & Contrast)
   2.0 |                                 / 
       |                    .-----------' <-- Toe (Under-exposed, low contrast)
   1.0 |                   /
       |   _______________/
       +---+---+---+---+---+---+---+---+---+---> Log Relative Exposure

Code Optical Density Boundaries (ASME Section V / AWS D1.1)

• Single Film Viewing:
  • X-Ray Radiographs: Density must be within $1.8 \le D \le 4.0$ throughout the area of interest.
  • Gamma-Ray Radiographs: Density must be within $2.0 \le D \le 4.0$ throughout the area of interest.
• Composite Viewing of Double Film Exposures: Density must be within $2.6 \le D \le 4.0$, with neither individual film falling below $1.3$.
• Density Variation Limitations: The optical density across the weldment area of interest must not vary by more than $-15\%$ to $+30\%$ from the density measured through the body of the Image Quality Indicator (IQI).

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4. Image Quality Indicators (IQI / Penetrameters) & Sensitivity Calibration

Radiographic sensitivity measures the smallest discontinuity that can be discerned on the film. Sensitivity is verified using Image Quality Indicators (IQIs) positioned on the weldment during exposure.

       HOLE-TYPE PLAQUE (ASTM E1025)             WIRE-TYPE IQI (ASTM E747)

          T = 2% of Specimen Thickness                 6 Graduated Wires
         +---------------------------+              +-----------------------+
         | (1T)    (2T)        (4T)  |              | |   |   |   |   |   | |
         |  o       O           ( )  |              | |   |   |   |   |   | |
         |     Lead ID: "25"         |              | Lead ID: "SET B"      |
         +---------------------------+              +-----------------------+
              Hole Diameters:                           Essential Wire:
             1T, 2T, 4T Plaque Thick.                   Must be Clearly Visible

Plaque-Type vs. Wire-Type IQI Systems

1. Hole-Type Plaques (ASTM E1025): Rectangular metal strips manufactured from radiographically similar alloys. The plaque thickness ($T$) is typically fabricated to equal $2\%$ of nominal weldment thickness. The plaque contains three drilled holes with diameters proportional to plaque thickness: $1T$, $2T$, and $4T$.
   • Standard Radiographic Sensitivity (2-2T): The radiograph must clearly display the $2\%$ thick plaque and resolve the $2T$ hole (whose diameter equals twice the plaque thickness, $d = 2T$). Resolving the smaller $1T$ hole represents higher sensitivity ($2-1T$).
2. Wire-Type IQIs (ASTM E747 / ISO 19232-1): Six plastic-encapsulated parallel wires of graduated diameters (Sets A, B, C, and D). ASTM E747 Table 4 establishes the mandatory Essential Wire Number that must be resolved across the weld area based on joint thickness.

Source-Side vs. Film-Side Placement Rules

• Standard Source-Side Placement: Codes mandate placing the IQI on the source side of the joint (the side facing the radiation source), aligned parallel to and within $1/8\text{ in}$ ($3.2\text{ mm}$) of the weld toe.
• Film-Side Placement: When physical geometry precludes source-side access (e.g., closed pressure vessels, unpiggable pipelines), the IQI is placed on the film side. To warn the interpreter of lower sensitivity due to reduced penumbra magnification, a lead letter "F" at least $1/4\text{ in}$ ($6.4\text{ mm}$) high must be placed immediately adjacent to the IQI on the film cassette.
• Weld Reinforcement Shims: When a weld possesses high external crown reinforcement, the base metal under the IQI is thinner than the total weld cross-section. A radiographically similar compensating shim must be placed beneath the IQI to elevate it to the total thickness of the weld plus allowable reinforcement.

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