5.2 Emissivity Determination and Measurement Technique

5.2 Emissivity Determination and Measurement Technique

In quantitative infrared thermography, calculating true target temperatures requires precise knowledge of the target's emissivity (ε). A frequent error among non-certified personnel is selecting generic emissivity values from standard reference tables or relying on the camera's default setting (typically ε = 0.95). While non-metallic materials (plastics, rubber, masonry, wood, organic coatings) generally display stable, high emissivity values between 0.85 and 0.95, unpainted metals display wildly variable values ranging from 0.02 for clean, polished aluminum to 0.80 for heavily oxidized carbon steel.

Emissivity is an extrinsic surface condition, not a fixed bulk material property. It varies substantially with:

• Surface oxidation state and patina thickness
• Surface roughness and microscopic profile
• Surface contamination (oils, soot, dust, slag)
• Spectral waveband of the camera detector (SWIR vs MWIR vs LWIR)
• Viewing angle relative to the surface normal

Recall the radiosity balance for an opaque target viewed through a non-attenuating atmosphere: $W_{\text{tot}} = \varepsilon \cdot \sigma T_{\text{obj}}^4 + (1 - \varepsilon) \cdot \sigma T_{\text{refl}}^4$

Solving for target emissive power reveals that when emissivity ε is small, the term (1 - ε) dominates, causing reflected ambient radiation to overwhelm the target's self-emission. Any uncertainty in ε or reflected apparent temperature (T_refl) produces an exponential error in calculated temperature. Consequently, thermographers must determine true in-situ emissivity using standardized protocols established by ASTM E1933 (Standard Test Methods for Measuring and Compensating for Emissivity Using Infrared Imaging Radiometers).

ASTM E1933 Method A: Contact Thermometer Cross-Check

The contact thermometer method determines emissivity by cross-referencing radiometric camera measurements against an independent, calibrated contact temperature sensor.

Required Test Apparatus

• Calibrated contact thermometer: Type K thermocouple with surface-contact probe, platinum resistance temperature detector (RTD), or precision thermistor (accuracy ± 0.5°C or better).
• Heat-conductive couplant: Silicone thermal grease, heat sink compound, or conductive elastomer pad to eliminate microscopic air gaps at the contact interface.
• Supplemental heating source (if target is unheated): Laboratory hot plate, industrial heat gun, or band heater.
• Reflected apparent temperature (T_refl) measurement tool: Crumpled and flattened aluminum foil reflector card.

Step-by-Step Execution Protocol

1. Establish Thermal Differential: Ensure the target material is at least 20°C (preferably ≥ 30°C) above or below the ambient reflected apparent temperature: $\Delta T = |T_{\text{obj}} - T_{\text{refl}}| \ge 20^\circ\text{C}$ Allow the target to stabilize under steady-state thermal equilibrium.
2. Determine and Input Reflected Apparent Temperature (T_refl): Measure T_refl following ASTM E1862 (reflector method) and input the numerical value into the camera's measurement parameter menu.
3. Set Environmental Parameters: Measure and enter target distance, ambient air temperature, and relative humidity.
4. Apply Contact Sensor: Coat the contact probe tip with a thin layer of thermal grease. Press the probe firmly against the target surface. Shield the probe from ambient convective air currents and radiant sources using an insulating backing.
5. Record True Contact Temperature: Allow the contact thermometer to achieve steady-state reading and record this baseline temperature as T_contact.
6. Focus Thermal Camera on Target: Position the thermal camera perpendicular to the target surface (± 15° from normal) at a distance satisfying the measurement field of view (MFOV). Focus sharply on the surface area immediately adjacent to the contact probe (ensuring the probe itself and its thermal grease are excluded from the measurement spotmeter).
7. Iterative Emissivity Tuning: In the camera's live measurement menu, adjust the emissivity setting (ε) up or down until the radiometric temperature reported by the camera spotmeter matches T_contact exactly.
8. Record and Validate: Document the calibrated emissivity value. Repeat the test across three separate locations on the material surface to account for localized surface roughness variations.

ASTM E1933 Method B: Reference Coating / Electrical Tape Method

When physical contact probes cannot achieve reliable thermal contact, or when inspecting delicate, thin, or irregularly shaped targets, Method B utilizes a reference coating of known, pre-calibrated emissivity.

Standard Reference Materials

• Scotch Super 33+ Professional Vinyl Electrical Tape: Highly standardized across the thermography industry with an accepted emissivity of ε_ref = 0.95 across the 8–14 µm LWIR waveband for temperatures up to 105°C (221°F).
• High-Temperature Matte Black Paint / Lacquer: Specialized thermographic black spray (e.g., Krylon Flat Black or Nextel Velvet Coating) with ε_ref = 0.95–0.96, capable of operating up to 300°C or higher.
• Water-Soluble Chalk / High-Emissivity Paste: Non-destructive paste with ε_ref = 0.95 for polished surfaces where tape adhesive residues are unacceptable.

Step-by-Step Execution Protocol

1. Thermal Excitation: Ensure the target satisfies the thermal differential requirement (ΔT = |T_obj - T_refl| ≥ 20°C).
2. Apply Reference Standard: Clean the target surface of loose debris. Apply a piece of Scotch Super 33+ tape (minimum 25 mm × 25 mm to exceed the camera's MFOV). Press firmly to eliminate trapped air pockets, which act as thermal insulators.
3. Wait for Thermal Equilibrium: Allow sufficient time (typically 30 to 60 seconds) for the thin vinyl tape to conduct heat from the substrate and reach equilibrium temperature.
4. Measure Substrate True Temperature:
   • Program the camera parameters: set ε = 0.95 and enter the measured T_refl.
   • Place spotmeter 1 directly on the taped section.
   • Record this temperature as the true substrate surface temperature T_true.
5. Target Bare Substrate:
   • Place spotmeter 2 on the bare, un-taped target surface immediately adjacent to the tape (within 10–20 mm).
   • Because the bare surface has high reflectivity and low emissivity, spotmeter 2 will initially report an erroneous apparent temperature.
6. Adjust Emissivity: In the camera menu, modify the emissivity parameter for spotmeter 2 until its reported temperature equals T_true from spotmeter 1.
7. Read Determined Emissivity: The resulting numerical value displayed in the camera menu represents the true emissivity (ε_target) of the bare material.

Method C: Cavity Radiator / Drilled Hole Method

When working with thick metallic blocks, castings, or machine components in a laboratory or machine shop, an artificial blackbody cavity can be fabricated directly into the target.

Physics of Cavity Emissivity

An isothermal cavity with a small aperture behaves as a near-perfect blackbody absorber and emitter regardless of the internal wall emissivity. Photons entering the cavity undergo multiple internal specular and diffuse reflections. At each reflection, a fraction (1 - ε) is absorbed. After multiple bounces, virtually no radiant energy escapes without absorption, driving effective emissivity toward unity: $\varepsilon_{\text{eff}} \approx 1 - (1 - \varepsilon)^N$ Where N is the average number of reflections before an internal ray exits the aperture.

Geometric Standard

To achieve an effective cavity emissivity of ε_eff ≥ 0.98 on unpolished metal surfaces, the cavity must satisfy an aspect ratio of depth (L) to diameter (D) of: $\frac{L}{D} \ge 5:1 \quad (\text{ideally } 6:1 \text{ to } 8:1)$ The hole should be drilled with a standard 118° drill point, which naturally creates a conical bottom that scatters reflections away from the entrance aperture.

Measurement Procedure

1. Heat the component to ΔT ≥ 20°C above ambient.
2. Aim the thermal imager directly down the longitudinal axis of the drilled cavity. Ensure the cavity diameter completely fills the camera's measurement field of view (MFOV).
3. Set the camera emissivity to ε = 1.00 (or 0.99).
4. Read the temperature at the bottom of the cavity. This represents the true thermodynamic temperature of the component (T_true).
5. Move the measurement spot to the adjacent outer flat metal surface.
6. Adjust the camera emissivity setting until the surface reading matches T_true. The resulting setting is the material's surface emissivity.

Summary Comparison of Emissivity Determination Methods

Practical Limitations and Critical Boundary Conditions

The Minimum Temperature Rise Rule (ΔT ≥ 20°C)

ASTM E1933 strictly specifies that the target must be at least 20°C hotter or colder than the reflected apparent temperature (|T_obj - T_refl| ≥ 20°C). The mathematical justification lies in the sensitivity derivative of detected radiosity with respect to emissivity: $\frac{\partial W_{\text{tot}}}{\partial \varepsilon} = \sigma (T_{\text{obj}}^4 - T_{\text{refl}}^4)$

If T_obj = T_refl, this derivative equals zero. At thermal equilibrium with the environment, the total radiosity leaving the surface is identical regardless of whether ε = 0.05 or ε = 0.95. Adjusting the camera's emissivity setting produces zero change in measured temperature. If the temperature difference is small (e.g., ΔT = 2°C), minor sensor noise or a 0.5°C error in T_refl causes calculated emissivity to swing wildly between 0.10 and 1.50 (an impossible non-physical result).

Curved Surfaces and Directional Emissivity Falloff

Emissivity is directional. For dielectric materials (electrical tape, plastics, paints, ceramics), emissivity remains constant and follows Lambert's Cosine Law up to approximately 45° to 55° from the surface normal. Beyond 60° (grazing angles), directional emissivity plummets toward zero, while surface reflectivity surges toward 1.0. For clean metals, directional emissivity exhibits a slight peak near 70° before collapsing toward zero at 90°. Thermographers must never attempt to determine emissivity or record radiometric temperatures on the curved shoulders of cylindrical conductors, pipes, or transformer bushings where the angle of incidence exceeds 45°. Always align the camera optical axis perpendicular (± 30°) to the surface normal.

High-Voltage Energized Equipment Safety Constraints

On energized electrical distribution equipment (such as 480 V switchgear, 13.8 kV busbars, or 230 kV substation breakers), applying contact thermocouples or electrical tape while energized is strictly prohibited by NFPA 70E (Standard for Electrical Safety in the Workplace) and OSHA regulations. Entering the Restricted Approach Boundary or Arc Flash Boundary with handheld tools creates fatal flashover and shock hazards. Thermographers must either:

• Apply permanent reference dots, stickers, or high-emissivity ceramic coatings during scheduled de-energized maintenance outages.
• Measure on adjacent, connected non-energized grounded surfaces (e.g., external enclosure casings or bolted structural supports) using conductive thermal modeling.
• Utilize qualitative thermal pattern recognition rather than quantitative temperature calculation.

Worked Field Calibration Calculation: Industrial Busbar Emissivity

During a plant outage, a thermographer calibrates the emissivity of a newly installed unpainted aluminum busbar. The plant electrical room ambient temperature and reflected apparent temperature are measured at T_refl = 22.0°C (295.15 K).

The busbar is artificially heated with an inductive heater until stable at elevated temperature. The thermographer applies a square of Scotch Super 33+ tape (ε_ref = 0.95) to the busbar.

1. Measuring True Temperature on Taped Section: With camera ε = 0.95 and T_refl = 22.0°C, the spotmeter on the tape reads: $T_{\text{true}} = 82.0^\circ\text{C} = 355.15\text{ K}$ Verify ΔT criterion: ΔT = 82.0 - 22.0 = 60.0°C ≥ 20°C (valid).

2. Measuring Apparent Temperature on Bare Aluminum: Moving the spotmeter to the bare aluminum surface immediately adjacent to the tape, with camera still set to default ε = 0.95, the camera displays an uncorrected apparent reading of: $T_{\text{app}} = 29.5^\circ\text{C} = 302.65\text{ K}$ (The hot 82°C busbar appears to be barely above room temperature because it reflects 22°C background radiation).

3. Theoretical Calculation of Busbar Emissivity: Using the Stefan-Boltzmann constant σ = 5.670374 × 10⁻⁸ W/(m²·K⁴):

   • Radiosity detected by camera corresponding to T_app: $W_{\text{tot}} = \sigma T_{\text{app}}^4 = 5.670374 \times 10^{-8} \times (302.65)^4 = 476.5\text{ W/m}^2$
   • Blackbody emissive power of target at true temperature: $W_{\text{true}} = \sigma T_{\text{true}}^4 = 5.670374 \times 10^{-8} \times (355.15)^4 = 901.8\text{ W/m}^2$
   • Reflected incident environmental flux: $W_{\text{refl}} = \sigma T_{\text{refl}}^4 = 5.670374 \times 10^{-8} \times (295.15)^4 = 429.3\text{ W/m}^2$

   Setting up the radiosity balance: $W_{\text{tot}} = \varepsilon_{\text{bus}} W_{\text{true}} + (1 - \varepsilon_{\text{bus}}) W_{\text{refl}}$ $476.5 = \varepsilon_{\text{bus}} (901.8) + (1 - \varepsilon_{\text{bus}}) (429.3)$ $476.5 - 429.3 = \varepsilon_{\text{bus}} (901.8 - 429.3)$ $47.2 = \varepsilon_{\text{bus}} (472.5)$ $\varepsilon_{\text{bus}} = \frac{47.2}{472.5} \approx 0.0998 \approx 0.10$

4. Camera Tuning Verification: When the thermographer turns the camera emissivity dial from 0.95 down to 0.10, the displayed temperature of the bare aluminum jumps from 29.5°C directly to 82.0°C, matching the true surface temperature.