J . -M . Deniel et al .: Radioprotection 2024 , 59 ( 3 ), 225 – 234 229 Fig . 6 . Non-refractive materials emissivity . ( g / r ; b / r ) camera color response and IR radiance
3000 lnm
B IR ¼ ∫ Bm ð ; T ; lÞ∂l . Then , B l¼780 IR ; m and T are stored in ( g / r ; b / r ) indexed matrices , keeping the most dangerous cases ( i . e ., the highest B IR , m ).
This � way , we can associate any g p = r p ; b p = r p pixel hue with a m p ; T p worst case and the corresponding BIR ; p radiance ( or no radiance if the cell in the matrix is empty ). To account for camera chromatic noise , our method considers the worst case ± 0.02 around both coordinates . Figure 8 shows the nonnull part of the ðg = r ; b = rÞ to T E-M5 matrix .
Fig . 7 . Schematic examples of non-uniformities in the sensor reaction to a uniform radiance in the focal camera plane . ( a ) and ( c ) are pixels in the border of the sensor , while ( b ) is at its center . In yellow : the optical paths from the observed radiance to the ( a ), ( b ) and ( c ) pixels . Optical vignetting reasons : ( a ) receives less light than ( b ) because light is partially occluded at ( e ); pixel irradiance differ between ( a ) and ( b ) because of different optical paths ( e . g ., ( f ) and ( g )) from observed radiance to pixels . Vignetting due to defects : less light reaches the sensor at ( c ) than elsewhere due to dirt at ( d ).
observed radiance and sensor response is expressed in equations ( 4 ):
1000 nm r p = t ¼ h h p ff p ∫ l¼380 RedðlÞBm � p ; T p ; l ∂l
1000 nm g p = t ¼ h h p ff p ∫ l¼380 GreenðlÞBm � p ; T p ; l ∂l b p = t ¼ h h p ff p ∫ 1000nm l¼380 BlueðlÞBm � p ; T p ; l ∂l ð4Þ
Since incandescent materials in the 800 to 1300 ° C range emit more red radiations than green and blue , we normalize pixels color against the red channel , so that g p = r p ; b p = r p 2 ½ 0 ; 1Š 2 represents the p pixel hue independent of ff p ; h p t exposure time and h sensitivity scaling factor .
Furthermore , knowing RedðlÞ ; GreenðlÞ ; BlueðlÞ and collections of emissivities for mðlÞevery T 2½800 ° C ; 1300 ° CŠ per 1 ° C step , we compute the corresponding
2.6 Estimating temperature of materials inside the metal furnace
As illustrated in Figure 3 , the metal furnace was filled with graphite , firebricks and metal samples at 800 ° C to 1100 ° C every 100 ° C , plus 1140 ° C . As this is not an item of calibrated equipment , the air temperature from the furnace probe must be considered with caution . In addition , after opening the furnace door even for a few tens of seconds , materials close to the opening become noticeably less hot than those in the back of the cavity . Consequently , only consistency between the estimated temperature of the materials and probe temperature should be considered .
3 Results
We analyzed pictures of the HGH RCN 1350 N1 blackbody and metal furnace , to estimate material m and temperature T . In the first case ( blackbody ), the emissivity database was reduced to mðlÞ ¼ 1 . In the second case ( heated materials ), it contained all the emissivity data in Figure 5 and 6 .
3.1 Blackbody temperature estimation
We analyzed pictures of the HGH RCN 1350 N1 blackbody . This device was set at every 100 ° C from 800 ° C to 1300 ° C . Camera measurement uncertainty takes the form of color noise in pictures , influencing temperature estimates . This is why , each time , we noted the mean , lowest and highest