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Probability of Hazardous Human Exposure from Space Based Lasers
K. Schulmeister1, G. Sonneck1, A. Simsek2, F. Rattay2, J. Mellerio3 and D. Sliney4
1
Austrian Research Centers Seibersdorf, A-2444 Seibersdorf, Austria
2
Technical University Vienna, Inst. f. Analysis a. Technical Math., A-1040 Wien, Austria
3
University of Westminster, School of Biosciences, W1M 8JS London, UK
4
U.S. Army Center for Health Promotion and Preventive Medicine, Aberdeen Proving Ground, MD 21010-5422,
USA
ABSTRACT
Laser (lidars) used from satellites and space stations for measurement of atmospheric properties may
represent an ocular hazard to people on the surface of the earth. The risk of an eye injury depends on a range of
parameters such as the energy per pulse, wavelength, beam divergence, space craft orbit, atmospheric conditions,
properties of telescopes and other viewing aids, and the viewing behaviour of potentially exposed people.
The probability of receiving an eye injury is a combination of the probability of being exposed and the
probability of the incident energy levels of radiation producing eye injury. Some aspects of this later probability
are discussed in another paper presented at this conference (1). Here we discuss a concept of an overall risk
assessment as applicable to satellite based lasers, and the probability that ocular exposure to the laser radiation
occurs.
The probability of sustaining eye damage varies with laser parameters and satellite path and, across the
globe, with population density and social habits. For the typical satellite based lidar, the probability of an
individual being exposed to the beam, and the probability of sustaining eye damage, are both very small and may
in some cases be zero.
INTRODUCTION
A quantitative probabilistic risk analysis model has been developed for a scenario where a laser beam is
emitted from a space craft in orbit around the earth and is incident on the earth surface. The two main
parameters for a quantitative risk analysis are the probability that ocular exposure occurs and the probability of
generating eye injury if exposure occurs, respectively. In terms of severity of a possible harmful event, which
also needs to be defined for a risk analysis, the present model considers minimal visible lesions, which are
characterised by being just detectable by ophthalmoscopic means. The lesion may be small, however the level
of severity can vary depending on the wavelength of the laser beam on the one hand and on the location of the
lesion on the other. If the wavelength is the range where the laser radiation is focussed onto the retina, and if the
location of the lesion on the retina is in the fovea or the optic nerve, then severe vision loss may occur. If the
wavelength of the laser beam is in the ultraviolet (UV) or far-infrared (far-IR), the kind of lesion which is
defined as minimal lesion will only produce a slight irritation of the cornea or might even go unnoticed. Also if a
minimal lesion is produced at the periphery of the retina, i.e. outside the central area of vision, it might go
unnoticed (2).
The probability for exposure, Pexp, depends on the orbit of the satellite, the geometrical and temporal
properties of the laser beam (i.e. diameter of the laser footprint on the earth surface and pulse repetition rate),
and, if one is employed, on the type of optical instrument and the way it is used (i.e. for instance the field of
view of the instrument and where it is pointed). The probability for ocular damage to occur per exposure, POD,
for a given laser wavelength and pulse duration, depends strongly on the laser energy, or radiant exposure, which
is incident on the eye. The radiant exposure, in units of J m-2, in turn will depend on the transmissivity of the
atmosphere and on the transmissivity of the optical instrument at the laser wavelength, and on the diameter of
the optical instrument. The energy collected with a 1 m telescope is a factor of 2⋅105 times larger than that
collected by an unaided dark adapted eye, which typically has a pupil diameter of 7 mm. However, this is only
the case in the visible and near infrared region, where the optics of the telescope are transmitting, while for farUV and far-IR wavelengths, the optical instrument will actually absorb the laser radiation and act as a protective
filter. Atmospheric turbulence and resulting scintillation effects might momentarily increase the exposure
significantly in comparison to the exposure without scintillation but only for the unaided eye and small optical
instruments such as binoculars (3). However for medium sized or large telescopes, scintillation does not play a
role as turbulence is small during the night and additionally the large size of the input optics leads to the effect of
aperture averaging, which reduces the variance of the momentary and local exposure (4).
The typical simplified approach to a laser safety assessment is to compare exposures with the ICNIRP
laser exposure limits (5), referred to here as maximum permissible exposure, MPE, as contained in the
international laser safety standard IEC 60825-1 (6). If the exposure is below the MPE1, the scenario is
1
MPEs are defined both for the eye and the skin. However as the MPEs for the eye are smaller or equal to the
MPE of the skin, often only the MPEs for the eye are considered in safety analysis.
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considered “safe”, if the exposure is above the MPE, it is considered as “hazardous”. The probability of an
exposure occurring is usually not considered, which can be interpreted as an assumption that exposure always
occurs. Also it is not considered that the MPE is defined with a safety factor, i.e. the probability of ocular
damage only gradually increases with increasing exposure and only becomes significant when the exposure is a
factor of 10 or so higher than the MPE. Such a risk analysis approach can be termed deterministic. For a
probabilistic laser risk assessment, the risk for injury to the skin or the eye will be a combination of the
probability that exposure occurs and the probability that an injury of given severity occurs per exposure. So far
probabilistic laser risk assessment models have been developed for applications mainly in the U.K. military field,
such as for the use of laser designators (7-9). However, to the knowledge of the authors, these models generally
are based on point estimates and associated uncertainties are not fully modelled, especially with regard to the
probability oh ocular damage. When point values are used, usually worst case assumptions have to be made for
the case where parameters vary within a given population or if there is an incomplete state of knowledge about
the parameters of the model. Both cases can, however, be quantified by specifying the uncertainty of the
parameters in the form of probability distributions and by using Monte Carlo simulation to combine distributions.
The different “levels of probability” of previous deterministic, probabilistic and this current fully probabilistic
approach are compared schematically in figure 1.
The risk model as discussed in this paper has been developed in a fully probabilistic approach, i.e.
where relevant, model parameters and output parameters are represented by probability distributions additionally
to worst case point estimates. In this paper, the overall risk model concept is presented and point estimates for
the probability for exposures are discussed.
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10
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10
10
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10
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-12
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-10
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Figure 1. Schematic comparison of the level of probability for different laser risk analyses. In a fully
probabilistic approach, uncertainties associated with the scenario parameters are carried through the model by
using the Monte Carlo technique to produce a final distribution.
Typical parameters of the space-based laser scenario are a footprint diameter in the range of a few
meters up to hundreds of meters, laser pulse energies of a few hundred millijoule, pulse durations smaller than 1
µs and pulse repetition rates of 10 – 100 Hz. Typical low earth orbits with altitudes of about 400 km above
ground result in a speed of the satellite’s footprint on the earth surface of about 7000 m s-1.
OVERALL RISK MODEL
The probability of exposure to laser radiation for a given scenario can be expressed as either individual
risk or as collective risk. The individual risk characterises the probability of exposure per hour of an activity.
When this figure is combined with the probability for injury it becomes an activity specific injury rate. For the
case of a satellite based lidar, this risk number can be calculated from the footprint speed, the laser parameters,
properties of the telescope, and in what way the telescope is used. The individual probability does not depend on
the distribution and density of the individuals on the earth or on how many hours a telescope is used per year,
which are parameters which have a relatively large associated uncertainty.
The individual risk measure is defined and used for different groups (amateur astronomers, birders, etc)
to account for specific groups with varying risks and to compare their risk from this activity to other risks such
as for playing football, driving a car, etc..
Additional to the individual risk, the collective risk (which is also termed global risk) can be
characterised, but the associated uncertainties are larger. The global risk describes the number of injured people
per mission which is simply derived from the number of injured people per mission hour. If further divided by
the number of people on earth, this corresponds to the risk measure often called “Injuries per Million” (with the
necessary adjustment of units) and might be used for the comparison with involuntary risks such as falls, fire, or
lightning.
In the following, the formulas for both the individual risk and the global risk are developed.
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Conceptually, two different prerequisites are needed for an actual ocular exposure to occur at a given
time and location: the laser beam has to be incident at this location and the person at this location has to have the
2
satellite in the field of view, FOV, of the particular optical instrument (see figure 2). This scenario can be
quantified by the probability that a given spot on the earth is illuminated, Pill, and the probability that the source
of the satellite is actually in the field of view of the optical instrument under consideration, PFOV. A combination
of the two figures yields the probability for exposure at a given point on the earth when a given type of optical
instrument is used.
.
.
.
.
FOV
Figure 2. In order for an exposure to occur, the laser beam has to be incident at a given location and the laser
source has to be in the field of view (FOV) of the optical instrument at the same time.
1) Pill: Probability, that a given spot on the earth is illuminated (per hour, as a function of latitude).
For satellite (or other spacecraft in orbit) based lidars, this probability is best calculated with reference
to a certain range of latitude, i.e. for a ring around the earth with width of e.g. 5 degrees. This ring has a certain
area Aring, depending on the latitude Λ. A footprint with known area Afoot takes the time tcross to cover the ring per
crossover. The area illuminated during the crossing is:
Afoot * f * tcross
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where f [1/s] is the laser pulse repetition rate and Afoot * f is the area covered per second .
This can be related to the area of the latitude ring and when multiplied with the number of crossovers
per hour (which can be calculated with the orbital period Tsat in hours), the probability for illumination per hour,
Pill(Λ) at a given latitude, Λ, is obtained:
Pill ( Λ ) :=
A foot⋅ f ⋅ t cross( Λ )
A ring( Λ )
⋅
2
Tsat
It should be noted that in contrast to other laser application scenarios, for instance with aeroplane based
lasers, due to the exact knowledge of the satellite path, the probability of illumination can be treated as exact
number without uncertainties.
Typical values for the probability of a spot on the surface on the earth are 10-4 and 10-6 per hour
depending on the type of orbit and the latitude.
2) PFOV The probability that the satellite is in the field of view of the optical instrument
The prerequisite for an actual ocular exposure is that a given location is illuminated and has the lidar
satellite in the field of view (FOV) of the optical instrument or the naked eye. Pexp is the probability for ocular
exposure per hour while using a given type of optical instrument:
Pexp = Pill * PFOV
PFOV is a factor from 0 to 1 describing the fraction of time in which the satellite is expected to be in the
FOV of the instrument. This number critically depends on the viewing behaviour of the individual for the
specific group of observers, the direction of the Line Of Sight of the lidar and the FOV of the instrument. For
instance, if the laser only points at nadir, FFOV is the time ratio the observer looks up in the direction of zenith ±
2
In this discussion, the naked eye is also seen as an “optical instrument“ with corresponding FOV, etc.
It is assumed that the pulse duration is so small that the footprint movement during the pulse is small
compared to the footprint diameter. If this is not the case, Afoot can be adjusted for a larger irradiated area
during a laser pulse.
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the FOV, e.g. 1 % of the time while using the instrument. With a larger FOV, the observer can be exposed even if
not pointing directly to zenith. For the case that the observer never has zenith in the FOV, no ocular exposure
can occur, and the factor is zero.
Often the observation behaviour can best be characterised in terms of the fraction of time, Ftime.FOV, for
which the pointing angle is in a certain elevated band (see figure 3) with the assumption that the probability for
looking in any direction in this ring is constant (i.e. homogeneous). Then the factor PFOV is determined by
P FOV :=
FOV
Ω
⋅Ftime.FOV
where Ω is the solid angle of the elevated band of the hemisphere (see figure 3) and FOV is also given as solid
angle. The formula is obviously only applicable when the satellite elevation for which exposure to the beam is
possible is contained in the elevated band, i.e. the band as pictured in figure 3 would not be appropriate to
describe a scenario where the laser beam points at nadir. For instance for birders, if the fraction of time looking
into a region of sky limited by 20° and 50° is, say, 20 % of the duration of “birding”, and the instrument’s FOV
is 8°, then FFOV = 5.7 10-3 * 0.2 = 1.1 10-3, where 5.7 10-3 is obtained by FOV/Ω.
Figure 3. PFOV can be derived from the ratio of the solid angle-FOV of the instrument and the solid angle of a
given elevated band which contains the elevation from which a laser beam can be incident, and the time fraction
of time one looks into that elevated band in relation to the total time spent using the optical instrument. Some
point estimates for a binocular and telescopes with very large and very small FOVs are shown also. Probability
distributions of this factor can be based on these extreme values.
3) “Activity specific injury rate” - Individual Risk, POD ind, of receiving ocular damage per hour of using a given
optical instrument
POD ind = Pexp * POD
POD is the probability of receiving ocular injury for given laser parameters, atmospheric conditions and optical
properties of the instrument, which will be discussed in another paper presented at this conference (1).
4) N: Number of humans versus latitude (per latitude degree). This curve can also be drawn for different groups
G (astronomers,...), i.e. numbers of users of instrument of given type per degree of latitude.
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800
Population (Million per degree)
700
600
500
400
300
200
100
85
75
65
55
45
35
25
5
15
5
15
25
35
45
55
65
75
85
0
Degrees 90° south to 90° north
Figure 4. Global population distribution represented in 5° latitude rings (adapted from Canadian Global
Emissions Inventory Centre http://grid2.cr.usgs.gov/globalpop/1-degree/).
The area below the curve is the total number of humans on earth N, or, for a group G, N(G).
5) Number of instances of ocular damages projected to occur per mission hour per latitude degree (for a given
group G and latitude Λ)
NOD (Λ,G) = POD ind(Λ,G) * N(Λ,G) * Ftime(Λ,G)
where Ftime is the fraction of time of usage of optical instrument of given type, such as 1 hour per 24 hours.
N(Λ,G) and Ftime can conveniently be grouped to one parameter Ntime (and corresponding distribution)
representing the number of optical instruments used at any time per degree latitude.
6) Assuming that the groups are exclusive, summations over all latitudes Λ and Groups G give the total numbers
of humans receiving ocular damage per mission hour
NOD (G)= NOD ( Λ, G)
∑
Λ
∑N
NOD =
OD (G)
G
7) The average risk for injury per person per hour is given by
R = NOD / N.
This risk can be compared to the risk measure: “Injuries per million” (with the necessary adjustment of
units) for other hazards, e.g. injury or death from flying.
Multiplication of NOD with the mission duration yields the total number of ocular injuries for a given
mission.
DISCUSSION
For typical space based lidar applications, the risk of injury occurring during a given mission most
critically depends on the laser wavelength, the laser energy per pulse and the laser footprint diameter. For
instance, if the laser emits in the UV or far-IR wavelength range, such as 355 nm or 2.1 µm respectively, for
typical lidar pulse energies and foot print diameters, the MPE cannot be exceeded and therefore the risk for eye
injury is zero even when exposure occurs behind a very large telescope4. Therefore the probability of being
exposed plays no role for such a scenario. However, if the laser emits in the visible or near infrared wavelength
range, i.e. in the retinal hazard region between 400 nm and 1400 nm, depending on the energy per pulse and the
footprint diameter, the MPE for the eye can be exceeded if exposure occurs behind large telescopes, as is shown
4
The maximum diameter of input optics of a telescope that needs to be considered for ocular damage is about 1
meter, as larger telescopes will not be used for visual observation through an eyepiece.
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for example values in table 1. For such a situation, both the probability for ocular damage as function of ocular
energy and the probability for exposure are important figures.
Table 1: For the example of a pulse energy of 100 mJ, a pulse duration of 100 ns and a footprint diameter of
100 meter (defined as 1/e points), the ocular exposure is compared to the MPE for the case of different laser
wavelengths, i.e. in the UV, VIS, near-IR and far-IR. The factors for the ocular exposure relative to the MPE is
given for a range of optical instrument’s diameters. If the factor is larger 1, the MPE is exceeded. An ocular
pupil diameter of 7 mm is assumed in the wavelength range of 400 to 1400 nm, i.e. the ocular exposure is
averaged over a 7 mm pupil even if the exit pupil of the telescope is smaller than 7 mm, for other wavelengths an
averaging aperture of 1 mm is assumed. The ocular energy is calculated by accounting for the atmospheric
transmission Tatm as calculated with FASCODE and MODTRAN (10) and for the transmissivity of the optical
instrument Topt, as measured for a simple telescope eyepiece.
Tatm Topt Exposure Factor eye Factor
Factor
Factor
Factor
WaveMPE
10 cm
30 cm
70 cm
100 cm
(J m-2)
length
(J m-2)
355 nm
56
0.37 0.2
9.4 ⋅ 10-7 2 ⋅ 10-8
2 ⋅ 10-4
2 ⋅ 10-3
8 ⋅ 10-3
2 ⋅ 10-2
-6
-3
-1
532 nm
0.005 0.67 0.95 8.1 ⋅ 10
3
16
33
2 ⋅ 10
3 ⋅ 10
-6
-4
-2
-1
1064 nm
0.05 0.88 0.6
1.3
2.7
1 ⋅ 10
3 ⋅ 10
2 ⋅ 10
6.7 ⋅ 10
2.1 µm 1000
0.95 0.2
2 ⋅ 10-5
2 ⋅ 10-4
1 ⋅ 10-3
2 ⋅ 10-3
2.4 ⋅ 10-6 2 ⋅ 10-9
If the MPE is exceeded for optics diameters of 30 cm, such as would be the case for the above
parameters if the laser wavelength were 532 nm, this means that for diameters of 1 m, the MPE is exceeded by a
factor of 10, which may lead to a probability of a minimal lesion of 10-2. As a risk figure on its own, this would
be considered as too large. However, for a complete risk analysis, the probability of an exposure occurring needs
to be considered. From an individual standpoint, the question which to be answered might be: “I am an amateur
astronomer, what probability do I have of being exposed?”. The probability of exposure, Pexp, is given by
Pill * PFOV. Pill for a polar orbit at 400 km altitude with a laser footprint diameter of 100 m and a repetition rate of
50 Hz is about 5⋅10-6 per hour, i.e. a given location on the earth surface is illuminated by the laser beam every
200000 hours. For the case that the telescope is pointed anywhere into the sky with a minimum elevation angle
of 30°, a very wide angle eyepiece with a FOV of 2.6° results in a Pexp of 3⋅10-9 per hour and an eyepiece with a
very small FOV of 0.06° gives a Pexp of 1.4⋅10-12 per hour of telescope use. To model the situation when the
satellite is visible, because sunlight is reflected from it, and the satellite can be followed with the telescope, PFOV
is set equal to 1 and Pexp = Pill. So far the probability of exposure is quantified in individual terms which can be
compared to risk figures for other activities, such as the probability for ocular injury per hour of playing golf.
The individual risk numbers however do not give information on the actual numbers of injuries. To calculate the
number of exposures with, for instance, telescopes of 60 cm in diameter and larger diameters, the number of
telescopes per degree² or per km² needs to be specified as well as the time ratio of usage, such as 10 hours per
month.
For the model as described here, an estimate of the number of amateur astronomers was obtained for a
range of countries by contacting amateur astronomers’ societies and individual astronomers. The data have a
substantial uncertainty, as some values are rough estimates made by individuals, and also because the term
amateur astronomer is not well defined. Often people are considered amateur astronomers who have a general
interest in astronomy but may not even have a telescope. Therefore, the number will probably be too large when
they are used to characterise people who use a telescope even if only sporadically. The weighted average
percentage of amateur astronomers in Europe, USA, Australia and Japan in relation to the general population is
about 0.1 %. For Russia, India, Chile and South Africa estimates were also obtained and the weighted average
percentage of amateur astronomers is about 0.002 %. The number of telescopes larger than 60 cm, used for
visual observation, will be less than 1 % of the number of amateur astronomers, and this percentage also includes
telescopes owned by observatories as inferred from data reported by the ISTeC (11) and the German
Astronomical Directory (12). It also should be noted that telescopes larger than about 25 cm are often not used
for visual observation but employ CCDs.
Depending on the mission parameters, the estimated frequency of exposure of observers which use a
telescope larger than 60 cm is less than 10-3 – 10-4 per mission year.
CONCLUSIONS
A fully probabilistic model for the exposure of different population groups to space-based lasers and for
ocular damage once exposure occurs, has been developed. Uncertainties are represented by probability density
functions and are carried through the model by Monte Carlo simulation. Particular emphasis has been placed on
the modelling of ocular exposures with large telescopes, i.e. with diameters of 60 cm and above, which can
critically increase the ocular exposure. For those large telescopes, depending on the laser energy per pulse and
the dimension of the laser footprint on the earth surface, the probability for minimal ocular injury for laser
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wavelengths in the retinal hazard region of 400 nm to 1400 nm, can be larger than 10-3 per exposure. This may
not be acceptable if looked at as an isolated risk but, due to the small field of view and the small number of these
large telescopes, the probability that an observer behind such a large telescope is exposed, is smaller than about
10-3 – 10-4 per mission year. These two figures combined yield a very small risk of harming any astronomer in
the region of less than 10-6 per year.
ACKNOWLEDGEMENTS
The probabilistic risk analysis models for exposure and for ocular injury described here were developed
under the European Space Agency contract number 13604/99/NL/GD.
REFERENCES
1.
D. H. Sliney, J. Mellerio, and K. Schulmeister, What is the Meaning of Thresholds in Laser Injury
Experiments, this conference
2. Sliney, D.H. and Worlbarsht, M., Safety with Lasers and Other Optical Sources, New York, Plenum
Publishing Corp., (1980)
3. Hill, R.J., Churnside, J.H., and Sliney, D.H., Measured statistics of laser beam scintillation in strong
refractive turbulence relevant to eye safety, Health Physics Vol. 53, 639-647, (1987)
4. Churnside, J. H., Aperture averaging of optical scintillations in the turbulent atmosphere, Applied Optics
Vol. 30, 1982-1994, (1982)
5. ICNIRP „Guidelines on Limits of Exposure to Laser Radiation of Wavelengths between 180 nm and 1,000
µm“, Health Physics Vol. 71, 804-819, (1997)
6. IEC Safety of Laser Products – Part 1: Equipment classification, requirements and user’s guide, Geneva,
IEC 60825-1, (1993)
7. Smerdon, W. S. A probabilistic approach to laser safety, In: Court, L.A.; Duchene, A.; Courant, D., eds.
First international symposium on laser biological effects and exposure limits, Cedex, France: Commisariat
á L’Énergie Atomique (1988)
8. Smith, P. A. Probabilistic laser safety: ocular damage models for Q-switched neodymium and ruby lasers.
Health Physics Vol. 66, 414 – 419 (1994)
9. NATO STANAG No. 3606, Edition 5, (1991)
10. Available from Air Force Research Laboratory, http://www-vsbm.plh.af.mil/
11. International Small Telescope Cooperative, http://www.astro.fit.edu/istec/
12. German Astronomical Directory, data kindly reviewed and forwarded by David Przewozny
http://www.astronomie.com/gad/
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