334 J-M Deniel : Radioprotection 2024 , 59 ( 4 ), 327 – 337 Fig . 7 . Differences in irradiance from a blackbody : ( a ) theoretically as a gain by passing from [ 1,000 ; 2,500 nm ] to [ 780 ; 3,000 nm ] integral wavelength range , ( b ) in practice as a loss due to air absorbency above 2,500 nm , as measured in front of a metal melting furnace at 1,200 ° C ( image from CR 5 ).
in Table 1 shows that enlarging the wavelength range contributes þ28 % to þ65 % to the theoretical irradiance , as illustrated in Figure 7a . In practice , this difference is reduced by strong air CO 2 and H 2 O absorption of [ 2,500 ; 3,00 nm ] radiations ( AMETSOC , 2012 ), as illustrated in Figure 7b .
Differences in irradiance between columns in Table 1 are given in Table 6 . They should be assessed considering :
– the gain in irradiance when enlarging the irradiance integration wavelength range ,
– the loss in irradiance by air absorption , ignored in calculations ( E th , E IR , th , E IR , CR 5 , E IR , pic ).
Second , E 5 IR , CR and E IR , th are very close : both are based on the blackbody model , and differ in the numerical integration of form factors .
Third , it appears that measured irradiance E m is under theoretical irradiance E IR , th by �20 % to �3.4 % ( except at 800 ° C ). The first reason is air absorbency , as described before . A second reason is the misalignment of the spectroradiometer and the black body . The third reason is the systematic lowering of the ratio with distance to the black body : the spectroradiometer cosine correction overestimates out of axis irradiance .
Fourth , as stated in Stephan-Boltzman law ( Boltzmann , 1884 ), the total energy radiated by a black body is proportional with T 4 . What is the influence of e T error on the estimated blackbody temperature , hence on E IR , th , E 5 I , CR and E IR , pic ? As these depend on Planck ’ s integral limited to [ 1,000 ; 3,000 nm ], they will vary differently from it . For example at ZþZ 0 = 97 mm , E IR , th and e IR error on E IR , th due to e T are approximated as follows :
� E IR ; th ðTÞ≈ 5:670E � 11 T 4 : 405 R 2 ≈ 1
IR ≈ 8:440 2 T þ 4 : 370 � T R 2 ð4:1Þ
≈ 1
In Table 6 , E IR , th ! E IR , pic and e T columns do not show such a relationship . Then , we assume that the difference between E IR , th and E IR , pic mainly comes from geometrical reasons like the Z o value and misalignment .
Generally , irradiance from the blackbody and calculated by picture analysis seems close enough to reality , given the need for accuracy expressed in the introduction .
4.2 Consistency of irradiance between the furnace measurements and the method proposed
The comparison in Table 2 shows that our method is consistent with the measurements performed in front of the metal furnace . As written in introduction , risk indices from IR are usually tens or even hundreds . Despite IR air absorption and the wavelength range difference between E m and E IR , our method is accurate enough to inform on the need to protect against IR and choose the right protection . Nevertheless , a number of observations should be made .
First , the method proposed is sensitive to camera orientation , in the same way as a radiometer . Using a cross in the viewfinder of the camera will help centering the exposure evaluation on objects of interest .
Second , as seen in Table 3 , the method proposed underestimates E IR from the cut-out incandescent silhouettes in inverse proportion to the picture definition . Thus , it should capture pictures with the highest definition .
Third , measuring a physical quantity from a device response relies on the established relationship between the two . In our case , sensor linearity to observed radiance is the key . It is absolutely necessary to make pixel levels proportional with exposure time and the observed radiance . The first part of the solution consists in bracketing ( Halford , 2022 ) and analyzing only pixel colors whose all channels lie within the sensor ’ s