328 J-M Deniel : Radioprotection 2024 , 59 ( 4 ), 327 – 337 Fig . 1 . Scheme of cataract risk assessment from an image with incandescent opaque materials .
The second principle is illustrated in the left and bottom parts of Figure 1 . First , each pixel p is considered as a rectangular window corresponding to a solid angle , which is projected onto the sensor plane as a form factor ff p . The characteristics of the camera perspective are used to compute ff p ( also called configuration factor )( Howell et al ., 2021 ).
Then the incident IR irradiance through the solid angle corresponding to pixel p is simply p * ff p * B ( m p , T p , l ).
Finally , E IR is the sum of the irradiance from all pixels corresponding to incandescent materials and not too dark .
As risk indices from exposure to IR usually vary from tens to hundreds , such an estimation does not require the accuracy of radiometry . In such situations , even a ± 50 % E IR estimation would be useful to obtain information on the risk and lead employers to investigate and prevent workers from being subject to cataracts . This paper presents the use of the ff p geometry terms in order to compute E IR , and the influence of image resolution and noise on E IR appraisal , compared to measured and theoretical irradiance .
2 Materials and method
The equipment to compare the estimated and measured irradiance are exactly the same as that used in ( Deniel , 2024 ). As illustrated in Figure 2 , the camera and the spectroradiometer had to be placed close to each other , in front of the INRS furnace .
We had to compare the irradiance measured with the spectroradiometer and the irradiance estimated from camera images taken at the same distance from the optical radiation sources . While measuring the distance from the source opening to the spectroradiometer optics is easy , measuring the distance from sources opening to the camera optical center is not straightforward . Figure 3 shows the arbitrary reference point on the camera body , at which we placed the spectroradiometer optics , at distance Z from the source opening . We determined a Z 0 = -7.33 cm distance offset along the camera view axis , between the reference point on the camera body and the opening of a pinhole approximation of the camera lens . We could verify that ZþZ 0 successfully matched up the objects seen in the pictures with their virtual projection in the camera perspective .
The far field assumption that irradiance varies as the inverse squared distance , applies when the irradiance distance exceeds 5 times the size of the light source ( see DiLaura et al ., 2011a Fig . 9-3 p . 389 ). In the case of our blackbody , error on irradiance will be ± 7 % at 97mm , ± 2 % at 172mm and neglictible at 492mm . This assumption allowed comparison of the method
Z with the measured irradiances scaled by 2
2.1 Pixel form factor calculation
. ðZþZ 0 Þ 2
The second principle of the proposed method is to sum the IR irradiance of each p pixel , as expressed in equation ( 2.1 ).
E IR ¼ p X pixelpff p B IR ; p ð2:1Þ
This technique is called hemicube in realistic image synthesis ( Cohen and Greenberg , 1985 ) when five planes are considered ( see Fig . 4a ). In our case , just one plane must be considered ; it is called the hemiplane method ( Sillion and Puech 1989 ) ( see Fig . 4b ).