Laser Safety Calculations
Tom Lister
NOTES
• The following three calculations were given as
‘homework’ for delegates of the IPEM LPA
Update in Bath, 28th Nov 2014 and worked
through as an exercise during the afternoon.
• The answers given are not necessarily
‘correct’.
• There was a consensus agreement that the
consideration of pulsed sources and α< αmin are
appropriate conservative approaches for these
particular calculations
Laser Safety Measurements– 28th Nov 2014
Tom Lister
Calculation 1
• Alexandrite epilatory laser
– λ = 755 nm
– Aperture = 15 mm (‘focal spot’ 12 mm at 40 mm)
– Beam half angle = 2.7°
– Max Energy Density = 35 Jcm-2
– Pulse Duration = 20 ms
– Operating frequency = 1.5 Hz
Laser Safety Measurements– 28th Nov 2014
Tom Lister
MPE
• AOR Directive
– “In carrying out the assessment, measurement or calculation, the
employer must follow the [...] standards of the IEC”
• 60825-1:2014
– “The MPE levels represent the maximum level to which the eye or skin
can be exposed without consequential injury immediately or after a
long time and are related to the wavelength of the laser radiation, the
pulse duration or exposure duration, the tissue at risk and, for visible
and near infra-red laser radiation in the range 400 nm to 1 400 nm, the
size of the retinal image.”
Laser Safety Measurements– 28th Nov 2014
Tom Lister
Maximum Permissible Exposure
• 755 nm, 20 ms pulse
– Thermal effects on the retina
2.7°
12 mm
40 mm
x?
Laser Safety Measurements– 28th Nov 2014
Tom Lister
C6=1?
• 60825-1 page 27
– “Most laser sources have an angular subtense α less than αmin, and
appear as an apparent “point source” (small source) when viewed from
within the beam (intra-beam viewing).”
• If we assume α < αmin, C6=1
• Table A.1 in 60825-1
– MPE = 18·t0.75·C4
– Exposure time, t = 20 ms
• t0.75 = 5.3·10-2
– C4 = 100.002·(755-700) = 1.3
• MPE = 1.24 Jm-2
Laser Safety Measurements– 28th Nov 2014
Tom Lister
NOHD
• 60825-1:2014
– “distance from the output aperture beyond which
the beam irradiance or radiant exposure remains
below the appropriate corneal maximum
permissible exposure (MPE)”
Laser Safety Measurements– 28th Nov 2014
Tom Lister
NOHD C6=1
• Maximum energy output
– 35 Jcm-2 over a 12 mm diameter spot
• 35·π·(0.62) = 39.6 J
• Spot size required
– 39.6 J / 1.24 Jm-2 = 32 m2
– Radius = √(32/π) = 3.2 m
Laser Safety Measurements– 28th Nov 2014
Tom Lister
NOHD C6=1
• Distance required
– 3.2 m /47·10-3 = 68 m
3.2 m
47 mrad
68?m
• Manufacturer: NOHD = 100 m
Laser Safety Measurements– 28th Nov 2014
Tom Lister
C6≠1?
• 60825-1 p13:
• “The angular subtense of the laser source should not be
confused with the divergence of the beam. The angular
subtense of the laser source cannot be larger than the
divergence of the beam but it is usually smaller than the
divergence of the beam.”
2.7°
12 mm
40 mm
100 mm
100 mm
Laser Safety Measurements– 28th Nov 2014
smallest
spot size
α
17 mm
Tom Lister
C6≠1?
• 60825-1 p13:
– “The angular subtense of the laser source should not be confused with
the divergence of the beam. The angular subtense of the laser source
cannot be larger than the divergence of the beam but it is usually
smaller than the divergence of the beam.”
– If we assume α = beam divergence, C6≠1
• C6 = α/αmin = 47/1.5 = 31⅓
– MPE = 18·t0.75·C4·C6 (Table A.2)
– MPE = 1.24 x 31⅓
• MPE = 39.0 Jm-2
Laser Safety Measurements– 28th Nov 2014
Tom Lister
NOHD C6≠1
• Spot size required
– 39.6 / 39.0 = 1.0 m2
– Radius = √(1.0/π) = 0.57 m
• Distance required
– 0.57 m /47·10-3 = 12 m
0.57?m
47 mrad
12?m
Laser Safety Measurements– 28th Nov 2014
Tom Lister
Calculation 2
• EVLT laser
– λ = 1470 nm
– Aperture = 400 μm
– Numerical Aperture = 0.37
– Max Power = 12 W (±15%)
– Pulse Duration = 100-9900 ms
– Pulse Interval = 100-1000 ms
• Max pulse rate = 5 Hz
Laser Safety Measurements– 28th Nov 2014
Tom Lister
Maximum Permissible Exposure
• 1470 nm, >100 ms pulse length
– Thermal effects on the cornea
• If we assume α < αmin, C6=1
– MPE = 5600·t0.25
– Exposure time, t = 100 ms
• t0.25 = 0.56
• MPE = 3150 Jm-2
– Exposure time, t = 9900 ms
• t0.25 = 1.8
• MPE = 9933 Jm-2
Laser Safety Measurements– 28th Nov 2014
Tom Lister
NOHD 9900 ms
• Maximum energy output
– 12 W over 10 s; 9900 ms on, 100 ms off
• Approx. 108 J
• Spot size required
– 108 / 9933 = 1.09·10-2 m2
– Radius = √(1.09·10-2 /π) = 5.9 cm
Laser Safety Measurements– 28th Nov 2014
Tom Lister
Beam Divergence
• NA = 0.37
• NA = n·sin
– Refractive index of fibre = 1.62 (Wikipedia)
–  = sin-1(NA/n) = 230 mrad
Laser Safety Measurements– 28th Nov 2014
Tom Lister
NOHD 9900 ms
• Distance required
– 0.059 m /0.23 rad = 26 cm
5.9 cm
230 mrad
26?cm
Laser Safety Measurements– 28th Nov 2014
Tom Lister
NOHD 100 ms
• Maximum energy output
– 12 W over 10 s; 100 ms on, 100 ms off
• Approx 6 J
• Spot size required
– 6 / 3150 = 1.90·10-3 m2
– Radius = √(1.90·10-3 /π) = 2.5 cm
• Distance required
– 0.025 m /0.23 = 10.8 cm
Laser Safety Measurements– 28th Nov 2014
Tom Lister
Calculation 3
• Ophthalmic YAG Laser
– λ = 1064 nm
– Aperture = 50 mm (8 μm spot size)
– Focal length 107 mm
– Cone Angle = 16°
– Max Energy = 10 mJ
– Pulse Duration = 4 ns
– Single pulse
Laser Safety Measurements– 28th Nov 2014
Tom Lister
Maximum Permissible Exposure
• 1064 nm, 4 ns pulse length
– Thermal effects on the retina (any pulse length)
• Assume α < αmin, C6=1
– MPE = 2·10-2·C7
– C7 = 1
• MPE = 20 mJm-2
Laser Safety Measurements– 28th Nov 2014
Tom Lister
Divergence
• Cone angle (16°)?
– Divergence 8° (140 mrad)?
Laser Safety Measurements– 28th Nov 2014
Tom Lister
NOHD
• Spot size required
– 20 mJm-2 / 10 mJ = 2 m2
– Radius = √(2 /π) = 80 cm
• Distance required
– 0.80 /0.14 = 5.7 m
– Effect of ionisation?
80 cm
?
140 mrad
5.7? m
Laser Safety Measurements– 28th Nov 2014
Tom Lister
Thank you
Laser Safety Measurements– 28th Nov 2014
Tom Lister
Beam diameter
• d63 definition?
– If d86 is 12 mm, then d63 = 8.5 mm
Laser Safety Measurements– 28th Nov 2014
Tom Lister
LaserBee NOHD
• Assume full power of 12 W for different times.
– Set power profile to continuous and enter 12 W.
This gives the default 100 s NOHD of 25.8 cm.
– If you change the exposure time to 100 ms then the
NOHD is 47.0 cm
Laser Safety Measurements– 28th Nov 2014
Tom Lister
LaserBee NOHD
• Assume that the cone angle is the required full
angle d63 divergence
– source diameter of 8 m (we are measuring the
NOHD from the focal spot).
– Enter a pulse energy of 10 mJ and lookup the
NOHD from the tab to get 2.84 m.
• Increasing the energy by 20% to allow for
fluctuations makes the NOHD 3.1 m
Laser Safety Measurements– 28th Nov 2014
Tom Lister
BS EN 50825-1:2014
• Page 69: x = 100 mm
Laser Safety Measurements– 28th Nov 2014
Tom Lister
Maximum Exposure
• Assume 7 mm pupil
– 50825-1 p90:
• “The pupil is a variable aperture but the diameter may
be as large as 7 mm when maximally dilated in the
young eye.”
• 18.8 Jcm-2 x π·(0.352) = 7.25 J
Laser Safety Measurements– 28th Nov 2014
Tom Lister