1. Fundamental Physics: Planck’s Law

• Planck’s Law describes the spectral radiance $B(\lambda ,T)$ of a blackbody (ideal emitter) as:B(λ,T)=λ52hc2​⋅eλkThc​−11​
  where:
  • $\lambda =$ wavelength
  • $T=$ absolute temperature (Kelvin)
  • $h=$ Planck constant, $c=$ speed of light, $k=$ Boltzmann constant
• Key Insight for MW:
  • At high temperatures (800–2000°C), the peak of the blackbody radiation curve shifts toward shorter wavelengths (MW range).
  • MW sensors are optimized to detect this intense radiation, providing high signal-to-noise ratios for accurate temperature measurements.

2. Emissivity and Material Interaction

• MW Advantages for Materials:
  • Metals: At high temperatures, we use high definition infrared camera, metals have relatively stable emissivity in the MW range (e.g., steel ≈ 0.1–0.3), reducing errors from surface reflections compared to long-wave infrared (8–14μm).
  • Transparent/Semi-Transparent Materials: MW radiation penetrates materials like glass, ceramics, or plastics more effectively than long-wave infrared, enabling measurement of internal temperatures (e.g., molten glass in furnaces).
  • Plasmas/Gases: MW interacts strongly with ionized gases and hot plasmas, making it suitable for high-energy physics research.

3. Atmospheric Transmission and Window

• MW Atmospheric Window:
  • The 3–5μm band experiences minimal absorption by water vapor, CO₂, and aerosols (compared to other IR bands), making it ideal for:
    • Long-range measurements in smoky/foggy environments (e.g., firefighting, industrial chimneys).
    • Aerospace applications (e.g., missile guidance through haze).
  • In contrast, the long-wave (8–14μm) window is more affected by water vapor, limiting range in humid conditions.

4. Sensor Technology and Detection

• Quantum-Based Detectors:
  • Indium Antimonide (InSb): Sensitive to 3–5μm, widely used in high-temperature industrial and military applications.
  • Mercury-Cadmium-Telluride (HgCdTe, MCT): Adjustable sensitivity across MW and long-wave bands, offering high detectivity for low-light or fast-response scenarios (e.g., missile seekers).
• Key Operational Features:
  • Fast Response Time: Nanosecond to millisecond-level speed, critical for tracking transient events (e.g., spark ignition, plasma dynamics).
  • High Spatial Resolution: MW cameras often achieve sub-millimeter pixel sizes, enabling detailed thermal imaging of small components (e.g., microchips, turbine blades).

5. Temperature Reconstruction

1. Measuring the radiant power in the 3–5μm band using calibrated detectors.
2. Applying the Stefan-Boltzmann Law for total radiation or solving Planck’s Law iteratively, accounting for:
   • Emissivity ($ϵ$) of the target material.
   • Atmospheric attenuation (e.g., path length, humidity, particulate matter).
   • Reflected background radiation (corrected via ambient temperature compensation).

• For dual-wavelength (ratio) thermometers, the intensity ratio at two MW wavelengths cancels out emissivity effects, enabling highly accurate measurements even for unknown or changing surface properties.

6. Comparison with Long-Wave (LW) Infrared

Conclusion