Appendix A. Explanations of the Errors Identified in the Original Article of Higlett and Colleagues: Higlett MP, O’Hagan JB, Khazova M. Safety of Light Emitting Diodes in Toys. J Radiol Prot 2012; 32: 51–72.
Error 1: incorrect assessment of the foreseeable misuse scenario
Two exposure scenarios were used by the authors to define the accessible emission limits (AELs) for visible light (page 54 of the original paper):
Scenario 1 corresponding to a worst-case condition of normal use at 200 mm from the eyes for 10 000 s,
Scenario 2 corresponding to a foreseeable misuse scenario at a viewing distance of 100 mm for 100 s.
In the first scenario (page 55), Higlett and colleagues used the blue light hazard exposure limit of 100 W·m-2·sr-1 (B-lambda weighted radiance) defined by the International Commission for Non-Ionizing Radiation Protection (ICNIRP) in their guidelines. They used the ICNIRP effective size of source of 0·11 rad (acceptance angle corresponding to a solid angle of 0·01 sr), leading to an exposure limit of 1 W·m-2 (B-lambda weighted irradiance) at the eye and a corresponding AEL of (0·04 × Ω) W in terms of B-lambda weighted flux emitted by the LED, where Ω is the solid angle of the LED beam.
Surprisingly, Higlett and colleagues used a different method for evaluating the AEL in the second scenario (page 55). They correctly used the ICNIRP exposure limit of 10 000 W·m-2·sr-1 (B-lambda weighted radiance) corresponding to an exposure of 100 s, but they multiplied it by the solid angle Ω of the LED beam and by the square of the viewing distance, thereby ignoring the ICNIRP acceptance angle. Their calculation gave an AEL of (100 × Ω) W, a value which is 2 500 times higher than the AEL of Scenario 1. They thus rejected Scenario 2 as they judged that it was not restrictive for optical safety, in comparison with Scenario 1.
Should Higlett and colleagues have used the ICNIRP acceptance angle as they did for the first scenario (for an exposure of 100 s, it is 0·011 rad, which is equivalent to a solid angle of 0·0001 sr), they would have found an AEL of (0·01 × Ω) W. Scenario 2 is actually 4 times more restrictive than Scenario 1. Scenario 2 should have been the one to consider in the assessment of optical safety.
Error 2: incorrect consideration of the ICNIRP luminance threshold of 10 000 cdm-2
The luminance threshold value of 10 000 cd·m
-2 was considered by Higlett and colleagues on page 56 of the original paper to establish safe limits for visible optical radiation, following the ICNIRP guidelines stating that below this indicative value, retinal exposure limits for the blue light hazard and thermal injury would not be exceeded in the case of light sources with a broad spectrum. [
3]
Higlett and colleagues calculated the luminous intensity value corresponding to a luminance of 10 000 cd·m-2 using Equation 3 on page 56 of the article. This equation contains a parameter named Area. Higlett and colleagues defined this parameter as being the area of the beam at the eye. This is incorrect because luminous intensity is the product of the luminance and the apparent source area, which is usually much smaller than the area of the beam at the eye. For instance, if an LED of 10 000 cd·m-2 has an apparent area of 4 mm², its luminous intensity is 0·04 cd.
In the paper, the luminous intensity values corresponding to a luminance of 10 000 cd·m-2 can reach 38·4 cd, as shown in Figure 7 (page 58 of the original article). Unfortunately, this luminous intensity value corresponds to LEDs having a very high luminance that may reach more than 1 000 times the ICNIRP guideline of 10 000 cd·m-2. For example, an LED of 38·4 cd with a typical apparent area of 4 mm² has a luminance of about 10 000 000 cd·m-2, far beyond the 10 000 cd·m-2 threshold considered by Higlett and colleagues to limit the luminance of LEDs.
Error 3: incorrect determination of emission limits expressed in unit of radiant intensity
A threshold of 0·76 W·sr-1 was used by Higlett and colleagues to provide a limit to the AEL curves expressed in unit of radiant intensity, as shown in Figure 9 (page 59 of the article). This value corresponds to luminous intensities that may largely exceed the limit of 38·4 cd, which was already overestimated due to Error 2. Based on our own calculations, we can conclude that Higlett and colleagues made an error of a factor of 10 in establishing the radiant intensity threshold.
To illustrate this error, we can consider a white LED having a radiant intensity of 0·76 W·sr-1 and a correlated colour temperature of 5 410 K. The corresponding luminous intensity is 250 cd, a value that exceeds the limit of 38·4 cd previously derived by the Higlett and colleagues. The combination of Error 2 and Error 3 would lead to wrongly considering that this white LED is safe for the eyes. If this white LED has an apparent area of 4 mm², its true luminance is 62 500 000 cd·m-2. Again, this value is far beyond the 10 000 cd·m-2 threshold considered by Higlett and colleagues as a limit to the luminance of LEDs.