Alfredo Dubra's PhD thesis - Imperial College London

B. Laser safety calculations
if the LEDs were lasers, as indicated by the standard. The LEDs have a built-in lens
after the diode, making the apparent angular size of each LED the diameter of this
lens, that is 5mm, which then divided by the distance from the eye (50 mm), gives an
apparent subtended angle α ≈ 100 mrad. Then, the MPE for one LED is given by
MP E 1 (t > 100 s; λ = 880 nm, α > 100 mrad) = 18 C 4 C 6 C 7 A pupil × 100 −0.25 Wm −2
(B.7)
where C 4 and C 7 are wavelength dependent factors which for 880nm take the values
2.29 and 1, respectively. Again, we will consider the most restrictive case, i.e. exposures
greater than 100s and a value of 67 for C 6 , which gives the MPE for a single
LED
MP E 1 (t > 100 s; λ = 880 nm, α > 100 mrad) ≈ 33 mW (B.8)
If we have a very restrictive approach, we can assume that the power of the 4 LEDs
is coming from a subtended angle equal to that subtended by only one of them,
simplifying the calculation. Thus, we can safely say that the MPE for the combination
of the 4 LEDs at 50mm from the eye is
MP E 1 (t > 100 s; λ = 880 nm, α > 100 mrad) ≥ 33 mW
(B.9)
B.4 MPE for infrared laser
The source used for the Shack-Hartmann sensor was a laser diode emitting at λ =
780 nm. The apparent angular size of the source to be considered is 1.5 mrad as the
beam entering the eye is collimated, making the viewing distance infinite. For these
conditions and exposures times larger than 10s, the MPE is given by
MP E(t > 10 s; λ = 780 nm, α = 1.5 mrad) = 10 C 4 C 7 A pupil Wm −2
(B.10)
where C 4 and C 7 are wavelength dependent factors which for 780 nm take the values
1.45 and 1, respectively, yielding
MP E(t > 100 s; λ = 880 nm, α > 100 mrad) ≈ 0.6 mW
(B.11)
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