228 J . -M . Deniel et al .: Radioprotection 2024 , 59 ( 3 ), 225 – 234
Fig . 4 . Red ( l ), Green ( l ) and Blue ( l ) relative spectral sensitivities for the three E-M5 camera color channels , along linear and log scale . Fig . 5 . Emissivity of refractive materials .
scaling factor h to obtain absolute radiance values from pixel c . s – 1 is not necessary . These Red ( l ) Green ( l ) and Blue ( l ) sensitivities are expressed in c . s – 1 W . m 2 sr and are null outside [ 380 ; 1000 nm ] wavelength range . They are shown in Figure 4 .
2.4
Spectral emissivity of materials
The spectral emissivity of two sets of materials was measured at the LNE laboratory , in the [ 250 ; 2500nm ] and [ 250 ; 3000 nm ] ranges . The first set was composed of refractive materials whose emissivity is shown in Figure 5 . The second set was composed of graphite and various cast iron , cast aluminium and steel samples 2 , whose emissivities are shown in Figure 6 .
2.5 From pixel color to radiance
The first principle of the method proposed is to relate any p pixel color to material m p and temperature T p . This color takes the form of three quantities r p , g p and b p expressed in counts ( c ) accumulated by the camera sensor during a t exposure time
2 Contifonte SAS , France , kindly gave us those cast iron and steel samples .
( in s ). We ensured that in [ 380 ; 1000nm � ], the camera response is linear with observed radiances inW : m �2 : sr �1 and t exposure time . Then , we can consider that r p t ; g p t
; b p
� t are flows in c : s �1 corresponding to observed radiances pondered by the corresponding Red � ( l ), Green ( l ) and Blue ( l ) channels relative sensitivities in c : s �1 : w �1 m 2 sr and a h scaling factor .
The relationship between observed materials and their temperature , and pixels color isestablished by integrating the
r camera response p t ; g p t
; b p t to observed radiances
� Bm p ; T p ; l over exposure time t and over the whole camera sensitivity wavelength range ( typically 380 nm to 1000 nm ).
In reality , the optical system is not perfect and several optical phenomena make sensor pixels react differently to a given radiance . A first reason is vignetting ( Ray , 2002 ; Britannica , 2023 ) also known as “ light fall-off ”: the farer the pixels are from the center of the sensor , the less amount of light they will receive from a same radiance originating on the camera focal plane , due to several optical phenomena as illustrated in Figure 7 . Other reasons can be dirt ( e . g .,( Deniel , 2002 ) p . 87 ) and imperfections in alignment of the optical component in the camera and its lens .
For those reasons , the relationship between observed materials and temperature , and camera response should account for a scaling factor dependent on each pixel . We assume that its dependency on wavelengths is negligible and denote it h p . Then the complete relationship between