226 J . -M . Deniel et al .: Radioprotection 2024 , 59 ( 3 ), 225 – 234 Fig . 1 . Scheme of cataract risk assessment from an image with incandescent opaque materials .
Employers must assess workers ’ exposure to IR , for example , by using the INRS freeware CatRayon ( CR 1 )( INRS , 2018 ). For all optical radiation domains covered by the regulation ( European Union , 2006 ), this freeware indicates risk indices that are the ratio of the worker ' s exposure over the daily limit .
When incandescent materials are heated ( e . g ., absorbing forge hammer kinetic energy ) or cooled down , when they move and change form ( e . g ., forged and rolled iron ), irradiance varies over time ( Lydahl et al ., 1984 ). As CatRayon does not cover these cases , in situ irradiance measurements are necessary . Radiometers and spectroradiometers capable of measuring E IR cost thousands and tens of thousands euros , respectively , making them unaffordable for most people in charge of safety at work .
We assert that incandescent opaque materials worked in industry ( e . g ., metals , firebricks ) can be represented as colored bodies . They differ from black bodies and grey bodies in that their radiance accounts for the spectral variation in the emissivity of the material . We note B ( m , T , l ) the spectral radiance at wavelength l of a colored body made of an m material at temperature T ( in K ). Eq . ( 2 ) shows that B ( m , T , l ) follows Planck ' s law weighted by m spectral emissivity m ( l ) For ease of reading , l is expressed in meter in this equation :
Bm ð ; T ; lÞ ¼ 2hc2 l 5
�
1 exp hc klT
mðlÞ ; � 1 ð2Þ
where h is the Planck constant , c is the speed of light in the vacuum , k is the Boltzmann constant .
From equation ( 2 ), it appears that the hue of the incandescent opaque materials radiance ( i . e ., B ( m , T , l ) relative distribution ) depends on emissivity and temperature .
As depicted in the flow chart in Figure 1 , this paper shows how to exploit this relationship in order to estimate E IR from
1 CatRayon is a free software created , distributed and maintained by
INRS , to assess risk from optical radiation sources and workers description and positioning in 3D , and propose effective protective equipment . camera pictures , which can be a cheap way to help preventing workers from risks of cataract .
A color camera picture is a matrix of ( r p , g p , b p ) pixel colors , each pixel p corresponding to a direction in space from the point of view of the camera . Assessing IR exposure from such a camera consists in summing irradiances at the optical centre of the camera , from incoming directions limited by the camera ' s field of view .
This assessment relies on two principles . The first is the subject of this paper . It is to associate a p pixel hue with a material m p and temperature T p , hence radiance B ( m p , T p , l ) according to Eq . ( 2 ). This is illustrated in the right part of Figure 1 .
The second principle is exposed in the left part of Figure 1 and will be covered in a next paper : it considers that every p pixel in the picture corresponds to a ff p solid angle . It is illustrated in Figure 2 .
Incoming IR irradiance through the solid angle corresponding to pixel p is simply p times the product of ff p and B ( m p , T p , l ). Then , E IR is the sum of irradiance from all the relevant pixels p ( that correspond to incandescent materials and are not too dark ), as indicated in the lower part of Figure 1 and expressed in equation ( 3 ):
E IR ¼ p X pixelp
2 Materials and method
3000 nm ff p ∫ l¼780 nm Bm p ; T p ; l
� ∂l ; ð3Þ
First , we present the devices used in this paper and their conditions of use . Then we give details about the first of the principles presented above .
2.1 Spectro radiometric measurements
Spectral irradiance in the [ 380 ; 1040 nm ] range was measured using an Avantes AvaSpec2048-14 single grating CCD array spectroradiometer ( now discontinued and replaced