Dec. 5-8, 2006, Curitiba, Brazil

Olivier Fudym

RAPSODEE UMR 2392 CNRS

11th Brazilian Congress of Thermal Sciences and Engineering -- ENCIT 2006Braz. Soc. of Mechanical Sciences and Engineering -- ABCM, Curitiba, Brazil

PROJETO DE COOPERAÇÃO SUL-AMERICANA EMIDENTIFICAÇÃO DE PROPRIEDADES FÍSICAS EMTRANSFERÊNCIA DE CALOR E MASSAPrograma CNPq/PROSUL

MINI-CURSOIDENTIFICAÇÃO DE PROPRIEDADES FÍSICAS

Infrared thermography for thermal characterization

2

• Ministère de l’Economie, des Finances, et de l’Industrie

• South West of France

• Civil Engineers (Major in Chemical Engineering )

RAPSODEE UMR 2392 CNRS=

Chemical Engineering Laboratoryfor Finely Divided Solids,Energy & Environment

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Aircraft signatureMultispectral imagery

Electrical control Security controlBuilding inspection

IR Imaging Systems : a widespread technic !!!

4

Art restoration

Vascular

Microcomponentanalysis

Skin & Fever

Underground Landmines Detectionfrom Thermal Imaging

5

Thermal Radiation

Infrared thermography : usually 1 – 15 µµµµm

10-5

0,001

0,1

10

1000

105

107

0,01 0,1 1 10

Luminance corps noir

Luminance spectrale (soleil)Luminance spectrale (lampe)Luminance spectrale (température fusion -aluminium)Luminance spectrale (ambiant)Luminance spectrale (azote liquide)

longueur d'onde en micromètre

T=5530°C

T=2530K

T=930 K

T=25°C

T= -196 °C

Energy � Signal / Noise

Sensitivity � Resolution

Black body spectral radiance

6

Calibration : Black body

After calibration, the optical properties

are necessary in order to measure

the surface temperature of the sample :

Emissivity

)(

)(

TnoirsCorp

E

Tobjet

E=ε

Signalcamera

Black BodyTemperature °C

50 100 150

V50

V100

V150

7

Infrared measurement : typical situation

0

10

20

30

40

50

60

1 10

Variation CN-température

Energie corps noir -50°CEnergie corps noir -100°CEnergie corps noir -150°C

longueur d'onde en micromètre

8 µm 13 µm

Atmospheric transmission

3-5 µm 8 - 12 µm Outdoor measurments

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Methane - Air

Combustion

CO2 spectral emissivityFlame instability

3-5 µm

« Spectre » de transmission IR du verre

transparent

opaque

Glass bottle process

Bottle Cooling / Surface Temperature

8 - 12 µm

Spectral Range of measurements

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Infrared thermography

Quantitative

Qualitative

Absolute temperature measurementsRelative temperature evolution

Pulsed ThermographyStep heating ThermographyLock-in ThermographyRandom Heating

Passive thermographyActive thermography testing Flash methods

Coating thickness

Periodic

0 50 100 150 200 250 300 350 400 4500

2

4

6

8

10

12

time (s)

T (K)

U/100 (V)

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Detector main characteristics

Noise Equivalent Temperature Difference (NETD)

Responsivity

( , , , )V

R x y fF

λ ∂=∂

1.V W −

incident optical flow

BlackBody

Changeof

temperature

IR Camera

Changeof

Signal-to-noise ratio= 1

T^m

Thermal sensitivity depends strongly on Temperature !!!

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Detector main characteristics

Spatial resolution

Line spread function (LSF)

Slit response function(SRF)

Recorded image = LSF * original image

T0 >> T1

w L

m = max(R(w)/max(R(w�)) as a function of w/L

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Detector main characteristics

Example SRF

IR Camera with 12° Aperture lens105 px / lineL = 1000 mm

Field of view 210x210 mm

If SRF curve gives 6 mrad at m = 100 % 6 mm

If you want m = 50 % and SRF� 2 mrad 2 mm

Spatial resolution at m %

Apparent resolution = 210 mm / 105 px ���� 2 mm / px

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Detector main characteristics

Focal Plane Array : matrix of sensors

Array of detectors

Commonly : 320 x 256 30 x 30 µµµµm

pixel

Thermal detectors = heated by incident radiation �

Measurement of electrical conductivity variations

« cheap » ; « slow » ; « noisy » ; « uncooled »

Photonic detectors �quantum = photon interactions � photoelectric

« fast » ; « cooled » ; « spectral range »CMT InSb

microbolometric

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Sensor : InSb, InGaAs, MCT, microbolometric…

Focal plane Array: 640x512 pixels or 320x256 pixels

Typical : 150 – 400 Hz !!!

thermal sensibility 30 °C: < 20 mK InSb, MCT

< 85 mK µµµµbolometric

Spectral Sens. : 1 - 5 µm or 3 - 5 µm (InSb), 8 - 12 µm

Integration time: about 10 µs

One pixel Sensor = 30 µm

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Hypothesis :- zero mean and additive errors- ββββ constant and unknown before the estimation and Xij known withouterror- constant variance (σσσσ known) and uncorrelated errors

Linear least squaresMaximum likelihood Estimator

Estimator

Estimation error

tS ( ) .( )= − −Y X� Y X�

=T X�

t 1 tˆ ( ) .−=� X X X Yt 1 2cov( ) ( ) .σ−=�e X X

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Example : Non-Stationary Signal -Estimation of one parameter

β

������

�

�

������

�

�

=

������

�

�

������

�

�

NN f

f

f

T

T

T

::

::

2

1

2

1

�

�

=

==N

ii

N

iii

f

Tf

1

2

1

ˆ

β̂�

=

=N

iif

1

2

22 σσ β

�=max

0

2 )()(t

dttftf 2

2max2

fN

t σσ β =

-If N small, Ti must be chosen as f is maximum

- Ti regularly spaced, N must be chosen as great as possible!

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Estimation of several parameters

( f and g assumed to be orthogonal )

T

T

T

f g

f g

f gN N N

1

2

1 1

2 2 1

2� � �

� �� ��

�

�

����

�

�

����

=

�

�

����

�

�

����

⋅�

��

�

��

X

ββ

( )β∧

∧

=⋅

� �

�

⋅1

f T

f f

t

t ( )β∧

∧

=⋅

� �

�

⋅2

g T

g g

t

t

( ) ( )( ) �

�

�

��

= −

−

1

12

00ˆcovgg

ffBt

t

σ

( )��

�

��

��

���

≈ −

−−

2

21

max

2

0

0ˆcovg

ftNσB ( )( )

2

2

ˆcovcondg

f≈B

- Ti regularly spaced, N must be chosen as great as possible!

-The conditioning number is non-dependant on N !

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Convective coefficients mapping

0 10 20 30 40 50 60 70 800

5

10

répo

nse

0 10 20 30 40 50 60 70 800

2

4

time

flux

Thermal characterizationof cyclist casque

hFlux

C

hT)t(dtdT

C −= ϕ

Characteristic frequencies are estimated :Ch

Imaging Systems with « matrix » of sensors