L 5 -B: Measurements without contact in heat transfer: principles, - PowerPoint PPT Presentation

L 5 -B: Measurements without contact in heat transfer: principles, implementation and pitfalls Jean-Claude Krapez ONERA DOTA/MVA 13300 Salon de Provence Eurotherm Seminar 94Advanced Spring School: Thermal Measurements & Inverse Techniques 5th edition Station Biologique de ROSCOFF -June 13-18 2011

Outline Temperature measurement by sensing the thermal emissive power • Basics : Planck’s law, Wien’s law and s.o. • Emissivity-Temperature Separation problem (ETS) • Pyrometry • single-color, bispectral pyrometry • multispectral pyrometry • ETS in airborne/satellite remote sensing • atmosphere compensation • Spectral-Smoothness method • Multi-temperature method • Conclusion METTI 2011 2/

Thermal radiation Matter emits EM radiation Monitoring of emitted radiation offers a mean for Intensity increases with temperature measurement temperature X Visible Microwaves Radio UV IR 1m 100m 1km 10nm 100nm 1µm 10µm 100µm 1mm 10mm 100mm 10m METTI 2011 MidWave = 3 � 5,5 �m LongWave = 7 � 14 �m 3/

Thermal radiation monitoring Advantages of the radiation method : - non-contact - surface probing (opaque material), - surface to sub-surface probing (semi-transparent material) - rapid : detectors with up to GHz bandwidth (and even higher) - long distance measurement (airborne and satellite remote sensing, astronomy) - point detectors (local measurement or 2D images by mechanical scanning) - focal plane arrays (instantaneous 2D images) METTI 2011 - possibility of spectral measurements (multispectral, hyperspectral) 4/

Radiation sensing is dependant on the atmosphere transmission, (absorption bands of air constituents : H 2 O, CO 2 , O 3 , CH 4 , …) MidWave: 3 � 5,5 �m ShortWave: 0.7 � 2,5 �m LongWave: 7 � 14 �m METTI 2011 5/

Basics (1/4) • Blackbody: perfect absorber, perfect emitter (~Holy Grail…) ( ) C 1 λ = • Spectral radiance given by Planck’s law: 1 B , T λ   5 C −   2 exp 1 λ • Wien’s approximation:    −  T ( ) C C 1 exp λ =   2 , B W T λ λ   5 T 10 10 Planck 1100K 9 Wien 10 Radiance (W/m 3 /sr) 900K 8 10 Maximum given by Wien’s 700K λ = displacement law: T 2898 µmK 7 10 max 500K 6 10 Error of Wien’s approximation is less 300K λ < than 1% providing that T 3124 µmK 5 METTI 2011 10 0 1 10 10 Wavelength ( µ m) 6/

Basics (2/4) Wavelength selection for temperature measurement λ = • Maximum of radiance given by Wien’s displacement law: T 2898 µmK max λ = ∂ 9 . 65 µm B • Radiance sensitivity to temperature ( absolute sensitivity): for T = 300K ∂ T 8 10 1100K 7 dB/dT (W/m 3 /sr/K) 10 900K 6 10 λ = Maximum corresponding to: T 2410 µmK 700K 5 10 500K λ = 8 . 05 µm 300K for T = 300K 4 10 0 1 METTI 2011 10 10 Wavelength ( µ m) 7/

Basics (3/4) Wavelength selection for temperature measurement ∂ • Radiance sensitivity to temperature ( relative sensitivity): 1 B B ∂ T 0 10 for T = 300K : 2% radiance increase per K at 8µm 16% radiance increase per K at 1µm -1 dB/BdT (1/K) 10 300K Advantage of performing 500K measurements at short wavelengths 700K (sensitivity is nearly in inverse -2 10 900K proportion to wavelength) 1100K Interest in visible pyrometry or even UV pyrometry ? -3 10 0 1 METTI 2011 10 10 Wavelength ( µ m) 8/

Basics (4/4) Real materials (non-perfect emitters) ( ) λ θ ϕ • with respect to blackbody, the emitted radiance is reduced by L , T , , a factor called emissivity: ( ) ( ) ( ) λ θ ϕ = ε λ θ ϕ λ ≤ ε ≤ L , T , , , T , , B , T 0 1 • emissivity depends on wavelength, temperature, and direction • second Kichhoff’s law between emissivity and absorptance: ( ) ( ) ε λ θ ϕ = α λ θ ϕ , , , , θ ϕ • relation between absorptance and directional hemispherical reflectance from the energy conservation law for an opaque material (the energy that is not absorbed by the surface is reflected in all directions): ( ) ( ) α λ θ ϕ + ρ ∩ λ θ ϕ = ' , , , , 1 METTI 2011 Emissivity can be inferred from a reflectance measurement (integrating sphere) Drawback : need to bring the integrating sphere close to the surface 9/

Contributors to the optical signal • the surface reflects the incoming radiation (non-perfect absorber) ( ) ↓ λ θ ϕ L , , • downwelling radiance: i i ( ) ρ λ θ ϕ θ i ϕ ' ' , , , , • bidirectional reflectance : i • the radiation leaving the surface is attenuated along the optic path (absorption, scattering by atmosphere constituents: gases, aerosols – dust, water/ice particles) ( ) τ λ θ ϕ , , • transmission coefficient : • atmosphere emits and scatters radiation towards the sensor ( ) ↑ λ θ ϕ L , , • upwelling radiance at-sensor radiance ( ) ( ) ( ) ( ) ↑ λ θ ϕ = τ λ θ ϕ λ θ ϕ + λ θ ϕ L s , T , , , , L , T , , L , , surface leaving radiance ( ) ( ) ( ) ( ) ( ) ∫ ↓ λ θ ϕ = ε λ θ ϕ λ + ρ λ θ ϕ θ ϕ λ θ ϕ θ Ω ' ' , , , , , , , , , , , , cos L T B T L d i i i i i i METTI 2011 π 2 10/

First considered case • Pyrometry of high temperature surfaces • sensor at close range (limited or even negligible atmosphere contributions) • environment much colder than the analyzed surface ( ) ( ) ( ) λ θ ϕ = ε λ θ ϕ λ L s , T , , , , B , T METTI 2011 11/

Second considered case • Airborne/satellite remote sensing • hypothesis of lambertian surface: isotropic reflectance isotropic emissivity ( ) ( ) 1 ∫ ↓ λ = λ θ ϕ θ Ω L L , , cos d • mean downwelling radiance π env i i i i π 2 • need for atmosphere compensation step ( ) ( ) ( ) ( ) ↑ λ θ ϕ = τ λ θ ϕ λ + λ θ ϕ L s , T , , , , L , T L , , ( ) ( ) ( ) ( ( ) ) ( ) ↓ λ = ε λ λ + − ε λ λ L , T B , T 1 L METTI 2011 12/

What about emissivity ? In all cases we need an information on emissivity to get temperature • relations for emissivity : only for ideal materials , for example Drude law for pure metals λ > (satisfactory only for , not valid for corroded or rough surfaces) 2 µm • databases for specific materials in particular state of roughness, corrosion, coatings, contaminant, moisture content … • Practical solution : simultaneous evaluation of temperature and METTI 2011 emissivity 13/

Single-color pyrometry • Measurement is performed in a narrow to large spectral band • In any case, after sensor calibration, the retrived radiance is of the form ( ) ( ) ( ) λ = ε λ λ L s , T B , T One equation, two unknown parameters One has to estimate the emissivity (a priori knowledge) • Sensitivity of temperature to an error in emissivity estimation: − 1 ε λ ε   dT T dB d T d = − ≈ −   ε ε   T B dT C 2 at 1µm and T= 1100K : -0.8K/% error at 10 µm and T= 300K : -0.6K/% error • advantage in working at short wavelength (visible or UV pyrometry): sensitivity to emissivity error drops. • However, the signal drops at short wavelength compromise METTI 2011 14/

Two-color pyrometry (1/2) • Adding a new wavelength adds an equation but also an unknown parameter namely the emissivity a this additional wavelength. ( ) ( ) ( ) λ = ε λ λ • Two spectral signals:  L , T B , T 1 1 1  ( ) ( ) ( ) λ = ε λ λ  L , T B , T 2 2 2 ( ) ( )     ε C 1 1     λ − λ = − − • by ratioing the signals: 5 5 2 2 ln ln ln L L     ε λ λ 2 2 1 1   T   1 2 1 λ λ λ = 1 2 effective wavelength: λ − λ 12 2 1 Effective wavelength can be high : bad news !! • The problem can be solved if one has a knowledge about the emissivity ratio. ( ) ( ) ε λ = ε λ • Common hypothesis (but not necessary) : « greybody » assumption 1 2 • Sensitivity of temperature to an error in emissivity estimation: λ  ε ε  dT T d d   ≈ − − 12 1 2   ε ε   T C 2 1 2 at 1µm/1.5µm and T= 1100K : -2.5K/% error = 3 times higher METTI 2011 at 10µm/12µm and T= 300K : -3.7K/% error = 6 times higher 15/

Ratio pyrometry vs 1-color pyrometry 1-color 2-color 3-color ε ε 2 2 2 ε ε ε ε Input 1 1 1 3 (slope) (curvature) Error λ λ × T amplification − λ ∆ λ 2   ×   C on 2 ∆ λ   temperature METTI 2011 16/