3.3 Reflected Apparent Temperature (RAT) and the Reflector Method

Reflected Apparent Temperature (RAT) and the Reflector Method

1. The Physics of Reflected Apparent Temperature

In quantitative thermography, obtaining an accurate temperature measurement requires the thermographer to account for all sources of radiation entering the camera lens. When an infrared camera is aimed at a target, the focal plane array detector does not collect radiation solely from the object itself. Instead, because all real surfaces have a reflectivity greater than zero (ρ = 1 - ε > 0), radiation originating from surrounding environmental objects strikes the target surface and reflects into the camera lens.

This background environmental radiation is characterized radiometrically by Reflected Apparent Temperature (RAT, commonly designated as T_refl, T_bkg, or background temperature in camera menus). Formally, RAT is defined as the apparent radiant temperature of all objects and energy sources whose thermal radiation reflects off the target surface into the camera detector.

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2. The Comprehensive Radiometric Calibration Equation

Modern radiometric thermal imaging cameras compute true object temperature by continuously solving the radiometric equation within their internal microprocessors. The total radiant flux arriving at the camera detector (W_cam) is the linear superposition of three primary physical components:

$W_{\text{cam}} = \tau_{\text{atm}} \cdot \varepsilon_{\text{obj}} \cdot W(T_{\text{obj}}) + \tau_{\text{atm}} \cdot (1 - \varepsilon_{\text{obj}}) \cdot W(T_{\text{refl}}) + (1 - \tau_{\text{atm}}) \cdot W(T_{\text{atm}})$

Where:

• τ_atm is the spectral transmission of the atmosphere over the measurement distance (0 < τ_atm ≤ 1).
• ε_obj is the target surface emissivity (0 < ε_obj ≤ 1).
• (1 - ε_obj) = ρ_obj is the target surface reflectivity (for opaque materials, τ_obj = 0).
• W(T_obj) is the blackbody radiant power at the target's true temperature T_obj.
• W(T_refl) is the blackbody radiant power corresponding to the Reflected Apparent Temperature T_refl.
• W(T_atm) is the blackbody radiant power of the surrounding ambient air path at temperature T_atm.

During an inspection, the camera measures the total radiant flux (W_cam). The thermographer inputs four critical environmental compensation parameters into the camera firmware:

1. Object Emissivity (ε_obj)
2. Reflected Apparent Temperature (T_refl)
3. Target Distance (d, from which the camera estimates τ_atm)
4. Atmospheric Temperature (T_atm) and Relative Humidity (RH)

The camera firmware isolates the true target emissive power W(T_obj) by rearranging the radiometric equation:

$W(T_{\text{obj}}) = \frac{W_{\text{cam}} - (1 - \tau_{\text{atm}}) W(T_{\text{atm}}) - \tau_{\text{atm}} (1 - \varepsilon_{\text{obj}}) W(T_{\text{refl}})}{\tau_{\text{atm}} \cdot \varepsilon_{\text{obj}}}$

Once W(T_obj) is isolated, the camera applies its internal detector calibration curves (governed by Planck's radiation law) to calculate and display the true object temperature T_obj.

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3. Sensitivity Analysis: Why RAT Errors Scale Inversely with Emissivity

Examining the numerator of the radiometric isolation equation reveals why entering an accurate RAT is vital:

$\text{Reflected Flux Subtracted} = \tau_{\text{atm}} (1 - \varepsilon_{\text{obj}}) W(T_{\text{refl}})$

The magnitude of the reflected radiation subtracted by the camera is directly weighted by the target's reflectivity: ρ_obj = 1 - ε_obj.

• High-Emissivity Target (ε = 0.95): Reflectivity is only ρ = 0.05. Reflected ambient energy constitutes only 5% of the total radiosity signal. A substantial error of 10.0°C in the entered RAT parameter produces a negligible target temperature measurement error of less than 0.5°C.
• Low-Emissivity Target (ε = 0.15): Reflectivity is ρ = 0.85. Reflected radiation constitutes 85% of the total signal received by the detector! An identical 10.0°C error in the entered RAT parameter causes a catastrophic error of 25.0°C to 40.0°C in the calculated target temperature.

This mathematical reality establishes the foundational Level I rule of thumb: Never attempt quantitative temperature measurement on surfaces with emissivity below 0.60 (ε < 0.60) without surface modification. For targets with ε < 0.60, the reflected background radiation swamps target self-emission, rendering uncorrected temperature calculations scientifically unreliable.

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4. Standard Measurement Protocols: ASTM E1862 Reflector Method

Entering an arbitrary room ambient temperature (e.g., 20°C) as the default RAT is a primary source of measurement error in industrial environments. Standardized procedures for accurately determining RAT are codified in ASTM E1862 (Standard Test Methods for Measuring and Compensating for Reflected Temperature Using Infrared Imaging Radiometers).

ASTM E1862 defines two standardized measurement methodologies:

Method 1: The Reflector Method (Crumpled Aluminum Foil)

The Reflector Method is the universal industry standard for measuring diffuse hemispherical background radiation:

1. Prepare the Reflector: Take a sheet of heavy-duty commercial aluminum foil, crumple it firmly into a tight ball, and then carefully unfold and flatten it across a rigid piece of cardboard or plywood.
2. Physical Rationale: Aluminum foil is a near-perfect specular reflector (ρ ≈ 0.95–0.97, ε ≈ 0.03–0.05). However, a flat mirror sheet reflects radiation from only a single specular direction. Firmly crumpling and re-flattening the foil creates thousands of randomly oriented microscopic facets, transforming the specular sheet into a diffuse (Lambertian) reflector. The crumpled foil integrates radiant energy arriving from all angles across the surrounding 180° hemisphere.
3. Position the Reflector: Mount the foil reflector directly over or immediately adjacent to the target surface, oriented with its reflective face facing the camera from the exact perspective of the target.
4. Configure Camera Parameters:
   • Set the camera emissivity parameter to 1.00 (ε = 1.00).
   • Set the measurement distance to 0 (or the exact target distance).
5. Measure and Record: Aim the camera at the center of the crumpled foil reflector. With ε set to 1.00, the camera assumes all exiting energy is emitted. Because the foil has an actual emissivity near zero and reflectivity near 1.0, virtually 100% of the flux exiting the foil is the diffuse reflection of the thermal environment. Measure the average apparent temperature across the foil using an area measurement box.
6. Input RAT into Camera: Record this measured value and enter it directly into the camera's Reflected Apparent Temperature (T_refl) parameter field.
7. Reset Emissivity: Reset the camera emissivity setting back to the true emissivity of the target material before beginning inspections.

Method 2: The Direct Method

When a target is located in a benign, highly uniform thermal environment (such as an enclosed, temperature-controlled office or warehouse), or when a single massive radiant source (such as an open boiler face) dominates the line of sight:

• Point the camera directly at the dominant background radiator.
• Measure its average surface temperature with emissivity set to that surface's true value.
• Enter the resulting value as T_refl.

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5. Outdoor Substation Pitfall: The Cold Sky Reflection

The most dramatic demonstration of RAT error occurs during outdoor high-voltage substation inspections under a cloudless sky.

In the long-wave infrared band (7.5–14 μm), atmospheric water vapor and greenhouse gases are concentrated near the earth's surface. Looking upward through a cloudless sky, the infrared camera views the upper troposphere and stratosphere. Because of extremely low molecular density and minimal water vapor, the effective radiometric temperature of a clear blue sky ranges between -20.0°C and -50.0°C!

When an inspector scans outdoor high-voltage disconnect switches or aluminum busbars (ρ ≈ 0.90–0.95), the angled surfaces reflect the frigid upper sky directly into the camera lens. If the inspector leaves the camera's RAT setting at the ground ambient air temperature of +25.0°C, the camera's microprocessor assumes the incoming reflection carries +25°C of flux. In reality, the reflection carries only -40°C of flux. The camera subtracts the assumed +25°C flux, finds the total received flux to be far lower than expected, and calculates an absurdly low apparent temperature for the switch (often displaying -10°C to -15°C). This cold sky reflection completely suppresses the thermal signature of severe electrical resistance, allowing a burning electrical joint to appear completely cool!

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6. Worked Step-by-Step Calculation: Quantitative Impact of Incorrect RAT

To quantify the exact temperature error resulting from an uncalibrated RAT setting, consider an indoor electrical switchgear panel:

• Target: Oxidized copper busbar joint with known emissivity ε = 0.65.
• True Object Temperature: T_true = 75.0°C (348.15 K).
• Actual Thermal Environment: An adjacent variable frequency drive (VFD) cabinet heats the local background to an actual RAT of T_refl, actual = 55.0°C (328.15 K).
• Measurement Distance: Short distance indoor scan, so atmospheric attenuation is negligible (τ_atm = 1.0).

Step 1: Calculate the true radiant flux arriving at the camera detector (W_cam): $W(T_{\text{true}}) = \sigma (348.15)^4 = 5.670374 \times 10^{-8} \times 1.46904 \times 10^{10} \approx 833.00\text{ W/m}^2$ $W(T_{\text{refl, actual}}) = \sigma (328.15)^4 = 5.670374 \times 10^{-8} \times 1.15954 \times 10^{10} \approx 657.50\text{ W/m}^2$ $W_{\text{cam}} = \varepsilon \cdot W(T_{\text{true}}) + (1 - \varepsilon) \cdot W(T_{\text{refl, actual}})$ $W_{\text{cam}} = 0.65 \times 833.00 + 0.35 \times 657.50 = 541.45 + 230.13 = 771.58\text{ W/m}^2$

Case A: Thermographer correctly executes ASTM E1862 and inputs T_refl = 55.0°C (328.15 K): The camera firmware subtracts the true reflected flux (230.13 W/m²): $W(T_{\text{calc}}) = \frac{771.58 - 0.35 \times 657.50}{0.65} = \frac{771.58 - 230.13}{0.65} = \frac{541.45}{0.65} = 833.00\text{ W/m}^2$ $T_{\text{calc}} = \left[ \frac{833.00}{5.670374 \times 10^{-8}} \right]^{1/4} = 348.15\text{ K} = 75.0^\circ\text{C} \quad (\text{Error} = 0.0^\circ\text{C})$

Case B: Thermographer leaves the camera at default room ambient T_refl = 20.0°C (293.15 K): The camera calculates blackbody flux for 20.0°C: $W(T_{\text{refl, default}}) = \sigma (293.15)^4 = 5.670374 \times 10^{-8} \times 7.3848 \times 10^9 \approx 418.75\text{ W/m}^2$ The camera subtracts only 0.35 × 418.75 = 146.56 W/m²: $W(T_{\text{calc}}) = \frac{771.58 - 146.56}{0.65} = \frac{625.02}{0.65} = 961.57\text{ W/m}^2$ $T_{\text{calc}} = \left[ \frac{961.57}{5.670374 \times 10^{-8}} \right]^{1/4} = \left[ 1.6958 \times 10^{10} \right]^{1/4} \approx 360.65\text{ K} = 87.5^\circ\text{C}$

Result: Failing to measure and enter the true RAT caused the camera to over-report the joint temperature by +12.5°C! This severe error could falsely escalate an operable joint into a critical emergency shutdown under NETA or Infraspection severity criteria.

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7. Field Best Practices: Surface Modification and the 0.60 Emissivity Threshold

When facing targets with emissivity below 0.60 (ε < 0.60), attempting to calibrate RAT cannot fully overcome measurement uncertainty. Level I thermographers must implement physical surface modifications before performing quantitative thermography:

1. High-Emissivity Electrical Tape: Apply a square of premium vinyl electrical tape (such as Scotch Super 33+, ε = 0.95, rated up to 105°C) to the clean target surface. Ensure firm mechanical bonding to eliminate air gaps. Allow 60 seconds for thermal conduction to equalize surface temperatures.
2. High-Emissivity Matte Spray/Paint: For high-temperature piping or complex geometric castings, apply a light mist of flat black high-temperature engine paint (ε = 0.96) or removable emissivity chalk spray.
3. Safety Mandate (NFPA 70E): Never touch, apply tape to, or spray energized electrical equipment! All surface modifications on electrical systems must be installed while the equipment is de-energized, locked out, and tagged out in an electrically safe work condition.