Laser safety assessments supported by analyses of reflections from metallic targets irradiated by high-power laser light

Abstract

When using kilowatt-class lasers in outdoor environments, ensuring laser safety turns out to be a complex issue due to the large safety areas that must be respected. For the special cases of collimated or focused laser radiation reflected from ideally flat but naturally rough metallic surfaces, the classical laser hazard analysis is deemed insufficient. In order to investigate the corresponding hazard areas for the aforementioned cases, we performed experiments on laser–matter interactions. Using high-power laser radiation, we studied the spatial and temporal reflection characteristics from four different metallic samples. For the evaluation of total reflection characteristics, we performed curve-fitting methods comprising Gaussian-like specular components, diffuse scattering components according to the ABg–scatter model and Lambertian components. For the investigation of occurring caustics, we developed a dedicated model in order to assess the divergence of the contained structures as a function of distance. Our evaluations have shown that the majority of the reflected power is scattered and based on these findings, that resulting nominal optical hazard distance values, even under worst-case assumptions, are significantly smaller than those of the non-reflected laser beam.

Full text

Research Article Vol. 60, No. 22 / 1 August 2021 / Applied Optics F71
Laser safety assessments supported by analyses
of reflections from metallic targets irradiated by
high-power laser light
Michael Henrichsen,* Bastian Schwarz, Gunnar Ritt, Adrian Azarian, AND
Bernd Eberle
Fraunhofer IOSB, Gutleuthausstr. 1, 76275 Ettlingen, Germany
*Corresponding author: michael.henrichsen@iosb.fraunhofer.de
Received 11 March 2021; revised 1 June 2021; accepted 1 June 2021; posted 3 June 2021 (Doc. ID 424722); published 1 July 2021
When using kilowatt-class lasers in outdoor environments, ensuring laser safety turns out to be a complex issue due
to the large safety areas that must be respected. For the special cases of collimated or focused laser radiation reflected
from ideally flat but naturally rough metallic surfaces, the classical laser hazard analysis is deemed insufficient. In
order to investigate the corresponding hazard areas for the aforementioned cases, we performed experiments on
laser–matter interactions. Using high-power laser radiation, we studied the spatial and temporal reflection char-
acteristics from four different metallic samples. For the evaluation of total reflection characteristics, we performed
curve-fitting methods comprising Gaussian-like specular components, diffuse scattering components according
to the ABg–scatter model and Lambertian components. For the investigation of occurring caustics, we developed
a dedicated model in order to assess the divergence of the contained structures as a function of distance. Our eval-
uations have shown that the majority of the reflected power is scattered and based on these findings, that resulting
nominal optical hazard distance values, even under worst-case assumptions, are significantly smaller than those
of the non-reflected laser beam. © 2021 Optical Society of America under the terms of the OSA Open Access Publishing
Agreement
https://doi.org/10.1364/AO.424722
1. INTRODUCTION
When working with lasers, the legally required occupational
safety and health regulations must be ensured in order to protect
the operators as well as uninvolved third parties from unin-
tended harmful irradiation. Inside buildings it is usually not
a major problem to establish laser safety in contrast to the use
of lasers in outdoor environments, where laser safety is often
not so easy to implement. However, if it is possible to work on
outdoor sites with controlled access, laser experiments can be
carried out with best practicable laser safety [1]; however, the
experiments are then also subject to many restrictions, which
limits the experimental possibilities. For example, in cases where
uncontrollable laser reflections, such as from moving or non-
fixed targets cannot be avoided (for instance, in laser weapon
scenarios), it is not obvious how to handle this kind of hazard.
Nowadays, in European or NATO countries, the level of
laser radiation to which an unprotected person may be exposed
without being injured, defined by the maximum permis-
sible exposure [MPE, in units of watts per square centimeter
(W/cm2) or joules per square centimeter (J/cm2)], is regulated
by legal occupational health and safety standards like ANSI
Z 136.1 [2] or the European Directive 2006/25/EC of the
European Parliament and of the Council of 5 April 2006 on the
minimum health and safety requirements regarding the expo-
sure of workers to risks arising from physical agents (artificial
optical radiation), 19th individual directive within the meaning
of Article 16(1) of Directive 89/391/EEC [3] (which replaces
EN 60825-1, which is still in use for laser classification pur-
poses). Once the MPE is determined, the potential laser hazard
distance for direct exposure to the laser beam, expressed by the
nominal ocular hazard distance (NOHD), can be estimated. In
the simplest and most pessimistic case, the NOHD is calculated
from only three parameters: the power of the laser beam, its
initial diameter, and its divergence.
For class 1 laser products, laser safety is inherently fulfilled
since their NOHD is zero, and thus no ocular hazards are posed
by such lasers. But if lasers of higher classes are used, each case
must be analyzed individually to determine whether the laser
can be used safely or not, according to the safety standards in
force. Industrial lasers, suitable for machining or manufactur-
ing, emitting tens of kilowatts of laser output power, can be
regarded as class 1 laser products, as long as they are operated
in closed cabins. On the other hand, for lasers with much less
output power that are to be operated outdoors and in situations
where potentially dangerous reflections cannot be completely
1559-128X/21/220F71-17 Journal © 2021 Optical Society of America

F72 Vol. 60, No. 22 / 1 August 2021 / Applied Optics Research Article
ruled out, laser operation will be prohibited since occupational
safety and health rules cannot be fulfilled. However, occupa-
tional safety and health rules are overly pessimistic, as they do
not take into account the probability that an observer will actu-
ally be irradiated, since risk management is not considered in
current laser safety standards. Risk expresses the likelihood that
harm from a particular hazard (something with the potential to
do harm) is realized. In other words, risk indicates the level of
safety, being related to both the harmful consequences and the
likelihood of occurrence.
Methods that address the risk aspect are, for example, quan-
titative or probabilistic risk assessment. Such approaches might
be true for scenarios in which the probability of irradiation, or
rather in terms of injury, is finite but very low. These procedures
make pessimistic assumptions to arrive at a “safe” use of lasers
related to the maximum hazard in a given scenario.
The difficulty behind such approaches is that laser safety
scenarios may vary widely,and so any treatment relating to a par-
ticular laser safety scenario must be assessed by an appropriate
authority. Analogous to the use of MPE in occupational safety
and health regulations, the key safety criterion in quantitative or
probabilistic risk assessment is that the expected harm to a per-
son is below an “acceptable” risk level that has been authorized
by the appropriate authority.
In order to estimate the laser hazard for a given scenario,
expressed as a risk, a whole range of parameters is needed, for
which normally no figures are known. The parameters comprise
the reflection or scattering properties of the target under con-
sideration, including the intensity distributions depending on
the distance to the target. Besides the reflectance of the target,
we need to know its spatial reflection characteristics, which may
be specular, diffuse, or a mixture of both. Specular means that
the beam is reflected purely geometrically, i.e., a flat surface
preserves the beam’s divergence, while purely diffuse reflections
mean Lambertian reflection, for which the reflected radiance
is equal at all viewing angles. These parameters characterize
the target at least during the initial phase of an illumination.
Considering target illumination with high laser intensities,
typically in excess of 1 kW/cm2, the scattering process becomes
dynamic, since the target’s surface and material properties start
to change, which affects its reflectivity and surface geometry. At
this point, the scenario becomes highly complex.
Based on their experimental results on kilowatt (kW)-class
high-energy laser (HEL) interaction with solids, Daigle et al.
[4] evaluated NOHD distances for reflected laser radiation. For
the reflection pattern from a flat carbon steel plate occurring
in the direction of the specular reflection, right after switching
the laser on, they measured an initial beam divergence close to
250 mrad, which is about 400 times higher than the divergence
of the incident beam. After the melting process of the irradi-
ated carbon steel plate had started, they found that at a distant
position in space where the specular reflection occurs, the reflec-
tions showed time variant intensity fluctuations, which they
described as pulse patterns. As a worst-case assumption, they
regarded these pulses as pure specular reflections, presuming
that the divergence of the reflected beam is the same as that of
the incident beam. Taking such specular reflection patterns into
arbitrarily directions into account, Daigle et al. concluded that
for their flat carbon steel plate, the resulting NOHD distances
are significantly shorter compared to the NOHD of several
kilometers, calculated according to the regular laser safety
standards.
In order to better understand the reflective characteristics of
materials with metallic surfaces and to gain reliable parameters
for hazard analyses, we performed investigations on different
metallic plates with different surface finishes, using high-power
lasers of two different wavelengths (Section 2). The first step
toward our aim was to analyze the time-dependent reflection
characteristics in the starting phase of the irradiation, includ-
ing the absorption aspects (Section 3.A). These investigations
are dedicated to understanding the concern of diffuse and the
specular components in the reflection properties and what beam
divergence they exhibit. The second step focused on investiga-
tions encompassing the time window of the melting process, i.e.,
when the material starts to change its surface geometry leading
to reflection caustics, also in dependence of the wavelength
(Section 3.B). Based on these findings, we calculated NOHDs
for the different reflection components assuming a 30 kW
high-power laser (Section 4.A) and explained some specifics for
thin samples (Section 4.B). Finally, the last step was dedicated to
the range dependency of the caustics (Section 4.C). Since such
investigations are practically not feasible, we developed specific
simulations for this purpose.
2. EXPERIMENTAL SETUP
In order to analyze the reflection and scattering characteristics of
four different samples (Section 2.A), two different experiments
were performed: the first experiment (Section 2.B) uses a low-
power laser, and it was necessary for the analysis of the second
experiment (Section 2.C), which uses high-power lasers.
A. Samples
The following four samples were used: two aluminum plates
with different thicknesses (labels A1 and A2), a (carbon) steel
plate (label CS), and a tinplate (label TP). The samples were
taken from the workshop of Fraunhofer IOSB and were used as
they were, i.e., without a special treatment (cleaning, grinding,
etc.) before the measurements. The samples are shown in Fig. 1
after the experiments, and their properties are listed in Table 1.
The surface roughness of the samples was measured using a
portable surface roughness tester Mitutoyo Surftest SJ-210. The
roughness measurements were performed both in the direction
of the long and the short edge of the rectangular samples. The
surface roughness can be different in these two directions due to
the manufacturing process. For the roughness measurements,
we used the standard settings of the roughness tester.
Fig. 1. Photographs of the samples. For details see Table 1.

Research Article Vol. 60, No. 22 / 1 August 2021 / Applied Optics F73
Table 1. Mechanical and Thermodynamic Properties of the Samples
Sample
A1 (#1) A2 (#2) TP (#3) CS (#4)
Material Aluminum Aluminum Tinplate Steel
Dimension [mm] (l ×w×t) 170 ×100 ×1 198 ×83 ×10 290 ×100 ×1 221 ×101 ×2
Roughness Rq [µm] (along the long/short edge) 0.115/0.446 0.705/0.958 0.385/0.552 1.727/1.951
Melting point [◦C] 660.3 [5] 660.3 [5] 232 [5] 1,425–1,540 [6]
Thermal conductivity [W/m K] ∼240 [5]∼240 [5]∼70 [5] 36–54 [7]
Reflectance at 1070 nma91.7% [8] 91.7% [8] 74.8% [9] 51.7% [9]
Reflectance at 1942 nma92.6% [8] 92.6% [8] 87.2% [9] 70.4% [9]
aThe given reflectance values are from the literature for polished, solid samples. The real reflectance values for the used samples may differ.
Table 2. Low-Power Experiments: Parameters of the
Camera and the Attached Lens and Filter
Camera
Manufacturer Allied Vision
Model Mako G-223B NIR
Detector type CMOS
Spectral range (µm) <1µm
Pixel size (µm) 5.5
Sensor size (pixel) 2048 ×1088
Lens
Manufacturer Schneider-Kreuznach
Model Xenoplan 2.8/50-0902
Focal length (mm) 50
f-number 5.6
FOV at screen/sample 16 cm ×8.5 cm
Filter
Manufacturer Newport
Model 10LF25-1064
Passband CWL: 1064 nm
FWHM: 25 nm
Thermodynamic properties of the different materials are also
listed in Table 1. These were not measured but taken from stand-
ard literature [5–9].
B. Low-Power Experimental Setup for Stray Light
Characterization
The experimental setup for the low-power experiments is shown
in Fig. 2. We used a Ventus 1064 laser from Laser Quantum to
illuminate the samples from a distance of 78 cm. The laser emits
at a wavelength of 1064 nm with a maximum output power of
∼1.5 W. For the experiments, the output power was limited
to 92 mW to record images that are not overexposed at 100
µs exposure time. The sample was slightly tilted with respect
to the incident laser beam so that the specular components
of the reflected laser beam hit the center of a reflection screen
Fig. 2. Sketch of the experimental setup for the low-power laser
reflection measurements.
(Thorlabs EDU–VS1/M) placed directly next to the laser
source. The diffuse reflection of the laser light at the screen
was monitored with a camera (Allied Vision G–223B NIR)
equipped with a camera lens (Schneider-Kreuznach Xenoplan
2.8/50–0902) with a focal length of 50 mm. The lens aperture
was set to an f-number of 5.6. Additionally, we placed a band-
pass filter (Newport 10LF25–1064, center wavelength: 1064
nm, FWHM: 25 nm) in front of the camera lens to suppress
disturbing ambient light. The camera had a field of view (FoV)
of 16 cm ×8.5 cm at the reflection screen. The parameters of
the cameras used are also listed in Table 2.
For each sample, we acquired a set of images with different
camera exposure times ranging from 100 µs to 1 s to be able to
reconstruct the irradiance distribution at the reflection screen in
the subsequent data analysis process (see Section 3.A).
For the low-power experiments, we additionally performed
measurements using a standard unprotected gold mirror
(Thorlabs PF10-03-M03) as the sample. The gold mirror was
used as a reference with a high specular contribution. The low-
power experiments are necessary to record a detailed profile
of the central part of the reflected beam. In the high-power
experiments, the central part of the profile is cut out due to an
aperture for a power meter. Here, this part can also be analyzed
without being sensitive to the duration of irradiation and by
using various camera integration times.
Before the measurements, the laser beam characteristics were
measured using an M2measurement device (Thorlabs M2MS–
BC106VIS/M). The beam diameter (1/e2) was estimated to
be 2.7 mm, and the full-angle beam divergence (1/e2) was esti-
mated to be 0.53 mrad; the beam quality was M2=1.06. These
quantities were used later for the data analysis; see Section 3.A.
C. High-Power Experimental Setup
Figure 3shows a sketch of our experimental setup to measure
the spatial and temporal properties of high-energy laser light
reflected by the different samples. To be able to monitor the spa-
tial distribution of the reflected laser light with high resolution,
we utilized a screen with diffuse reflection properties observed
by various cameras. The screen was constructed using six sand-
blasted aluminum panels of size 1 m ×1 m each, resulting in
a total screen size of 3 m ×2 m (horizontally/vertically). The
sample under test was placed at a distance of 2 m from the reflec-
tion screen. This geometry allowed us to cover a solid angle of
∼1 sr for observing the spatial distribution of the reflected laser
light.

F74 Vol. 60, No. 22 / 1 August 2021 / Applied Optics Research Article
Fig. 3. Sketch of the experimental setup for the high-power laser
reflection measurements. PM, power meter; PD, photodiode; BP,
bandpass filter, SP, short-pass filter.
The laser beam was transmitted through a central hole in the
reflection screen with a diameter of 20 mm. For safety reasons, a
laser beam dump was placed behind the sample to avoid uncon-
trolled laser propagation in case the intense laser beam would
burn a hole and penetrate the sample. In order to measure the
laser power of the specularly reflected part of the beam, we used a
power meter PM [Ophir Centauri +Ophir L50(300)A–LP2–
65]. To avoid too much obscuration of the reflection screen by
the power meter head, we placed it behind a second hole with a
diameter of 20 mm in the reflection screen, 45 cm below the first
one. Using low-power laser radiation, each sample was aligned
before the measurements so that the specular reflected portion
of the laser beam was directed to this second hole and fell onto
the power meter head.
For the experiments, we used two laser sources. A fiber laser
working at 1070 nm (IPG YLR–150/1500–QCW–AC) with
a maximum output power of 260 W and a fiber laser working
at 1942 nm (IPG TLR–200–WC) with a maximum output
power of 212 W. In the further course of this publication, we
will denote the lasers working at 1070 nm and 1942 nm as 1 µm
laser and 2 µm laser, respectively. The parameters of both laser
sources are listed in Table 3.
Both laser beams were spatially superimposed using an
optomechanical assembly, which is denoted as laser head in the
sketch of Fig. 3and is depicted in more detail in Fig. 4. The fiber
exit port of both lasers is connected to a corresponding fiber
collimator FC. The two laser beams are then superimposed by
Table 3. Parameters of the Laser Sources Used for
the Experiments
Laser 1 Laser 2
Manufacturer IPG IPG
Model YLR-150/1500-
QCW-AC
TLR-200-WC
Wavelength (nm) 1070 1942
Maximum output power (W) 260 212
Output beam diameter 1/e2(mm) 8.6 5.8
Divergence 1/e2(mrad) 0.4 0.45
Beam diameter on sample 1/e2
(mm)
8.6 5.9
Peak Irradiance on sample
(kW/cm2)
0.90 1.55
Fig. 4. Sketch of the laser head. FC, fiber collimator; DBS, dichroic
beam splitter; M, mirror.
using a mirror M (Linos DLHS IR 1064) and a dichroic beam
splitter DBS (Thorlabs DMLP1500).
For the experiments, five cameras were used:
Three measurement cameras (denoted as SWIR1, SWIR2,
and MWIR in Fig. 3) working in the short-wave and mid-wave
infrared spectral range, which recorded the spatial distribution
of reflected laser light on the reflection screen.
Two monitoring cameras (denoted as VIS1 and VIS2 in
Fig. 3) working in the visible spectral range to observe the sample
during laser irradiation for surveillance and documentation.
The task of cameras SWIR1 and SWIR2 was to record
the spatial distribution of the reflected light from the 1 µm
laser. The camera SWIR1 (Allied Vision Goldeye G–033
TEC1) was equipped with a camera lens with a focal length
of 35 mm (Edmund Optics 67716) and had a small (FoV) of
15.6◦×12.5◦. This camera was used specifically to monitor
the specularly reflected laser beam and was operated with a
rather short exposure time of 1 µs or 10 µs (depending on the
sample under test). For camera SWIR2 (Allied Vision Goldeye
G–032 TEC1), we used a camera lens with a focal length of
25 mm (Edmund Optics 67715), which resulted in a (FoV)
of 35.3◦×28.5◦and, therefore, allowed us to monitor the
reflected laser light on the whole reflection screen, i.e., this cam-
era was designated to monitor the diffusely reflected laser light.
For this camera, we chose an exposure time of 100 µs for the
image acquisition. For both cameras, we used a bandpass filter
BP1064 (Newport 10LF25–2064) with a center wavelength of
1064 nm and a full width at half-maximum of 25 nm to suppress
ambient light.
The camera MWIR (FLIR X8400sc) was used to record the
reflected light of the 2 µm laser. Using a camera lens with a focal
length of 50 mm, the camera’s(FoV) of 22◦×17◦corresponded
to a size of ∼2 m ×1.5 m at the reflection screen. For this cam-
era, we used a short-pass filter SP2600 (Spectrogon 713M) with
at a cutoff wavelength of 2600 nm to suppress infrared radiation
with wavelength above 2.6 µm.
For monitoring purposes during laser irradiation, we used
the two cameras VIS1 and VIS2. The color camera VIS1 (Allied
Vision Mako G–158C) was used to monitor the complete
target. This camera was placed next to the reflection screen in a
distance of ∼2.5 m from the target. For this camera, we used a
camera lens with a focal length of 24 mm (Schneider-Kreuznach
Apo-Xenoplan 2.0/24–2001).
The monochrome camera VIS2 (Allied Vision Mako
G–158B) was placed quite near to the target, in a distance

Research Article Vol. 60, No. 22 / 1 August 2021 / Applied Optics F75
Table 4. High-Power Experiments: Parameters of the Cameras and their Attached Lenses and Filters
VIS1 VIS2 SWIR1 SWIR2 MWIR
Camera
Manufacturer Allied Vision Allied Vision Allied Vision Allied Vision FLIR
Model Mako G-158C Mako G-158B Goldeye G-033 TEC1 Goldeye G-032 TEC1 X8400sc
Detector type CMOS CMOS InGaAs InGaAs InSb
Spectral range (µm) <1µm<1µm 0.9–1.7 0.9–1.7 1.5–5.1
Pixel size (µm) 3.45 3.45 15 25 15
Sensor size (pixel) 1456 ×1088 1456 ×1088 640 ×512 636 ×508 1280 ×1024
Lens
Manufacturer Schneider-Kreuznach Schneider-Kreuznach Edmund Optics Edmund Optics FLIR
Model Apo-Xenoplan
2.0/24-2001
Xenoplan 2.8/50-0902 67716 67715 L1002
Focal length (mm) 24 50 35 25 50
f-number 2 4 1.65 1.4 2
FOV, angular 11.9◦×8.9◦5.8◦×4.3◦15.6◦×12.5◦35.3◦×28.5◦22◦×17◦
FOV at screen/sample 53 cm ×40 cm 3.3 cm ×2.5 cm 1.4 m ×1.1 m 3.2 m ×2.5 m 2 m ×1.5 m
Filter
Manufacturer – Thorlabs Newport Newport Spectragon
Model – FESH0750 10LF25-1064 10LF25-1064 713M
Passband – <750 nm CWL: 1064 nm
FWHM: 25 nm
CWL: 1064 nm
FWHM: 25 nm
<2600 nm
of ∼30 cm, and a camera lens with a focal length of 50 mm
(Schneider-Kreuznach Xenoplan 2.8/50–0902) was used. A
selected area on the sample was observed in order to monitor the
laser beam on the target. To protect camera VIS2 from intense
laser radiation, it was equipped with a short-pass filter SP750
(Thorlabs FESH0750) with a cutoff wavelength of 750 nm.
The parameters of the cameras are listed in Table 4. The four
cameras SWIR1, SWIR2, VIS1, and VIS2 were synchronized
by using an external trigger source (Quantum Composer 9214)
with a period of 50 ms, which resulted in a recording frame rate
of 20 Hz.
Additional to the cameras, four photodiodes (Thorlabs
DET10D2) were used to record the temporal behavior of the
reflected light of the 1 µm laser at specific locations. For this
purpose, all photodiodes were equipped with a bandpass filter
(Thorlabs FBH1070–10) with a central wavelength of 1070 nm
and a full width at half-maximum of 10 nm. One of the photodi-
odes was located behind the reflection screen close to the second
hole and monitored the diffuse reflection of the potentially
specularly reflected laser beam from the active surface of the
power meter head. The three other photodiodes (only two are
depicted in the sketch of Fig. 3) were mounted at the side of the
reflection screen facing toward the target at arbitrary (but fixed)
positions and monitored the temporal behavior of the diffusely
reflected laser light. The signals of all four photodiodes were
recorded by a data logger (Graphtec GL820) with a temporal
resolution of 50 ms.
3. DATA ANALYSIS
A. Analysis of the Low-Power Experiment
The data for all four samples and the reference gold mirror
were analyzed in the same manner. To achieve a good inten-
sity resolution for the central specular region as well as for the
scattered peripheral part, we combined images with different
integration times to a high dynamic range (HDR) image at 100
µs integration time. All image parts were scaled linearly to their
integration time, as the camera response is linear. Therefore, we
took the image with the longest integration time (1 s) and sub-
tracted the dark image with the same integration time. Then the
portion of the image where the pixel values were less than 90%
of the maximum possible pixel value was extracted and scaled to
100 µs integration time. For the remaining portion (>90%),
the procedure was repeated with the next lower integration time,
and so forth until the full HDR image was extracted.
In the next step, the pixel positions of the HDR images were
recalculated to millimeter distances on screen with a factor of
0.08 mm/pixel. Then a model consisting of a central Gaussian
and an ABg-scattering part [10] was fitted to the data. The 1/e
width (beam diameter at 1/e) of the central Gaussian was fixed
to 2.0 mm on the screen as expected for the specular reflection:
the diameter of the beam waist at the laser output was measured
to be 2.7 mm with a full angle divergence of 0.53 mrad at 1/e2.
The 1/e width, important in regard to laser safety calculations,
is 1.9 mm, and the full angle divergence is 0.37 mrad. As the
distance from laser output to screen is smaller than the Rayleigh
length, the 1/e width on the screen is calculated as
wS=w0s1+d
zRayleigh 2
≈2.0 mm. (1)
The specular reflection on the screen is therefore expected
to have a 1/e width of 2.0 mm, if estimated with the measured
divergence. The fit function can be summarized as
I(x,y)=Ispec.(x,y)+Iscat. (x,y)+Ioffsetcos θ
d2+x2+y2.
(2)
Here, ddenotes the distance between the sample and the
scatter screen, and the angle to the normal measured from the

F76 Vol. 60, No. 22 / 1 August 2021 / Applied Optics Research Article
sample is given as θ=arctan(px2+y2/d). The specular part
is given as a Gaussian:
Ispec. =I0,spec.e−(x−x0)2+(y−y0)2
c2.(3)
Here, cis the 1/e radius of the Gaussian that was fixed to
c=2.0 mm/2. The ABg-scattering part is given as
Iscat. =I0,scat. ·Bx
Bx+x−x0
d
gx
By
By+y−y0
d
gy.(4)
Ai,Bi, and giare the ABg parameters with AxAy=
I0,scat. BxBy. The results of the fits are displayed in Figs. 5–9
for the horizontal and vertical profiles through the maximum
(x0,y0)of the reflection. The resulting 1/e widths from the
fits (Table 5) range from 0.4 mrad for the gold mirror (specular
reflection) up to 173 mrad for the aluminum plate (A1) in the
horizontal direction. It has to be taken into account that the
total width of the scattering screen is 190 mrad. Therefore, the
1/e widths of the ABg-scattering part may be underestimated.
Additional to the profiles, the radiant flux at two different
distances after the sample (16 and 70 cm) was measured with
an Ophir PD300-IR-ROHS power meter with an aperture of
re=5 mm in radius. Those distances represent field of views
from the samples of 62.4 mrad and 14.3 mrad, respectively. For
all measurements, the output power of the laser was measured
to be Pin =92 mW. For further evaluation, reflected power is
calculated as
Fig. 5. Horizontal (left) and vertical (right) profiles for the reflection at the unprotected gold mirror with logarithmic yaxis. The blue curves show
the profiles through (x0,y0); the orange curve shows the fit with function and a central Gaussian.
Fig. 6. Horizontal (left) and vertical (right) profiles for the reflection at the aluminum sample (A1) with logarithmic yaxis. The blue curves show
the profiles through (x0,y0); the orange curve shows the fit with function without a central Gaussian.
Fig. 7. Horizontal (left) and vertical (right) profiles for the reflection at the aluminum sample (A2) with the logarithmic yaxis. The blue curves
show the profiles through (x0,y0); the orange curve shows the fit with function without a central Gaussian.

Research Article Vol. 60, No. 22 / 1 August 2021 / Applied Optics F77
Fig. 8. Horizontal (left) and vertical (right) profiles for the reflection at the tinplate sample (TP) with the logarithmic yaxis. The blue curves show
the profiles through (x0,y0); the orange curve shows the fit with function and a central Gaussian.
Fig. 9. Horizontal (left) and vertical (right) profiles for the reflection at the steel plate sample (CS) with the logarithmic yaxis. The blue curves
show the profiles through (x0,y0); the orange curve shows the fit with function without a central Gaussian.
Table 5. 1/e Widths of the Total Fit and 1/e Widths of
the Scattering Part for the Investigated Samplesa
Sample wtotal
1/ewABg
1/e
in mrad Horizontal Vertical Horizontal Vertical
GM Unprotected
gold mirror
0.4 0.4 15.5 15.3
A1 Aluminum
plate
173 7.3 173 7.3
A2 Aluminum
plate
57.3 14.5 57.3 14.5
TP Tinplate 0.7 0.7 15.6 13.1
CS Carbon steel
plate
89.8 88.5 89.8 88.5
aThe relative error from the fit for the ABg-scatter widths range is below
2.5% for all values.
PR=Pin ·RS(5)
with the reflectance of the sample RSfrom Table 1. The fraction
of the total reflected power within the (FoV) of the power meter
is calculated as
ρFoV =8FoV
PR
.(6)
8FoV is the power measured by the power meter. In the following
considerations, we assume that there are three parts contributing
to the reflected power:
PR=Pspec. +PABg +PL.(7)
Here, Pspec. is the specular Gaussian contribution, being
present for the gold mirror and the tinplate sample. PABg
denotes the contribution that is scattered in an ABg-like man-
ner, and PLdenotes the Lambertian-like (uniform) scattered
contribution. The Lambertian contribution can be calculated
under the assumption that, within the FoV, its Lambertian
contribution is very small compared to the other contributions.
Its radiant intensity is then estimated as
LL≈PR−8FoV
2π.(8)
For comparison, we calculate the radiant flux of such
a Lambertian radiation within the two FoVs for the first
aluminum sample (A1):
8A1
L,64.4 =LL
πr2
e
d2=LL
π(5 mm)2
(16 cm)2≈38 µW,
8A1
L,14.3 =LL
π(5 mm)2
(70 cm)2≈2.1 µW. (9)
These results support the aforementioned assumptions.
Additionally, we calculated the portion of the total ABg-like
scattered power PABg that should contribute to 8FoV as

F78 Vol. 60, No. 22 / 1 August 2021 / Applied Optics Research Article
Table 6. Radiant Flux for a FoV of 62.4 mrad and the Derived Power Distribution
Sample 862.4 ρ62.4 νABg,62.4 pABg Pspec. PABg PL
GM Gold mirror 89.1 mW 98.9% 85.5% 1.2% 88.2 mW 1.1 mW 0.8 mW
A1 Aluminum 7.4 mW 8.8% 26.4% 33.3% – 24.5 mW 60.0 mW
A2 Aluminum n/aan/aan/aan/aan/aan/aan/aa
TP Tinplate 45.3 mW 65.9% 92.6% 55.5% 10.0 mW 38.1 mW 20.7 mW
CS Steel 1.2 mW 2.5% 16.4% 15.4% – 10.0 mW 37.6 mW
aNo data available for sample A2 at 62.4 mrad FoV.
Table 7. Radiant Flux for a FoV of 14.3 mrad and the Derived Power Distribution
Sample 814.3 ρ14.3 νABg,14.3 pABg Pspec. PABg PL
GM Gold mirror 88.5 mW 98.3% 32.2% 1.2% 88.2 mW 1.1 mW 0.8 mW
A1 Aluminum 1.2 mW 1.4% 4.9% 29.0% – 24.5 mW 60.0 mW
A2 Aluminum 1.2 mW 1.4% 9.8% 14.5% – 12.2 mW 71.9 mW
TP Tinplate 26.8 mW 39.0% 44.1% 55.5% 10.0 mW 38.1 mW 20.7 mW
CS Steel plate 0.1 mW 0.3% 1.2% 21.0% – 10.0 mW 37.6 mW
νABg,FoV =8ABg,FoV
PABg
.(10)
The ABg-like scattered portion of the total reflected power is
called
pABg =PABg
PR
.(11)
In the case in which there is no specular reflection, we can
conclude that
pABg ≈ρFoV
νABg,FoV
.(12)
In the contrary case with a specular reflection, we can
calculate the power scattered ABg-like as
PABg =862.4 −814.3
νABg,62.4 −νABg,14.3
(13)
and subsequently
Pspec. =8FoV −νABg,FoV PABg and
PL=PR−Pspec. −PABg.(14)
The calculated radiant fluxes and power distributions are listed
in Tables 6and 7.
B. Analysis of the High-Power Experiment
The images of the high-power experiment were analyzed to
determine the width of the ABg-like scattered part. The specular
contribution can be neglected in these fits, as the experimental
design contains a 20 mm diameter aperture in the reflection
screen (see Fig. 3). With a distance of 2.3 m from the laser out-
put to the sample and a distance of 2.0 m from the sample to the
screen, the diameter of the specular reflections on the reflection
screen are 8.6 mm and 6.1 mm for the 1 µm laser and 2 µm laser,
respectively. Compared to the size of the aperture, the remaining
specular component on the reflection screen can be neglected.
Therefore, only an ABg model has to be fitted to the data.
The scattering distribution was observed for irradiation times
of several tens of seconds for each sample. In total, there are
several thousands of images to be analyzed and, therefore, the
analysis has to be optimized so that the profiles and widths can
be extracted within a reasonable time. The analysis starts for
all images by subtracting a dark image and defining a region of
interest (ROI), see Fig. 10, to reduce fitting errors and reduce
calculation time.
The MATLAB blob detection algorithm is used with a
threshold of 1/e2of the maximum pixel value to determine the
largest blob within the ROI. The weighted center of the blob is
determined, and averaged profiles over 20 to 30 pixels through
this center point were extracted in horizontal and vertical orien-
tation. For these profiles, the 1/e width was determined using
three different algorithms:
1. Threshold Method
The first pixel position with P(p) > Pmax /ewas deter-
mined from both directions. The resulting width wth is
subsequently called the “threshold width” of the reflection.
2. ABg Fit Method
With the center position of the blob and the threshold
width as starting values, an ABg model, written as
a·1
b+|x−x0
dSS |gx·1
1+|x−x0
dSS |23/2,(15)
Fig. 10. Region of interests (ROIs) for both (a) 1 µm, SWIR1 and
(b) 2 µm, MWIR. P1 denotes the position of the aperture for the laser
beam exit, and P2 denotes the position of the aperture for measuring
the power in the bucket (PIB) of the central reflection. The distance
between both apertures (center to center) is 45 cm. During measure-
ments, the sample is visible in the camera image for 2 µm within the
orange box denoted by Target .

Research Article Vol. 60, No. 22 / 1 August 2021 / Applied Optics F79
is fitted to the profiles with the fit parameters a,b,gx, and
x0and the distance between sample and screen dSS. The 1/e
width of this function is the “fit width” of the reflection wfit.
3. Second Moment Method
The D4σwidth wD4σis calculated for the profiles by limit-
ing the profiles to a region of 2wth with
wD4σ=2√2·sPP(p)·(P(p)−Pmax)2
PP(p).(16)
The resulting widths at the beginning of the illumination
(first image, after laser was switched on) are detailed in Tables 8
and 9.
The power in the bucket (PIB) of the 2 cm aperture was
measured for the tinplate (TP) and the steel plate (CS) sample.
The aperture corresponds to a FoV of 10 mrad and the measured
output powers of lasers were 254 W for the 1 µm laser and 212
W for the 2 µm laser. The measured PIBs with the 1 µm laser
are displayed in Table 10, and the fraction of the total power
Table 8. Widths of the Reflection Distributions
Obtained by the Different Methods for 1 µm
Sample Horizontal Vertical
in mrad wth wfit wD4σwth wfit wD4σ
A1 Aluminum 202 198 243 13 13 14
A2 Aluminum 69 63 87 24 26 28
TP Tinplate 45 45 45 29 29 30
CS Steel plate 134 141 161 116 124 134
Table 9. Widths of the Reflection Distributions
Obtained by the Different Methods for 2 µm
Sample Horizontal Vertical
in mrad wth wfit wD4σwth wfit wD4σ
TP Tinplate 30 30 32 23 24 25
CS Steel plate 135 134 169 134 141 171
ρ10. Additionally, νABg,10 was calculated with the fits from the
low-energy measurements, and a predicted PIB was calculated.
This predicted PIB scales the results from the low-energy mea-
surements to the laser output power here. The PIBs for the 2 µm
laser are displayed in Table 11. The PIBs with the 2 µm laser are
notably higher than with the 1 µm laser as well as the fraction of
total power ρ10. With the fairly similar widths in Tables 8and 9,
a stronger specular contribution may be expected for 2 µm.
For each of the samples (TP and CS), three measurements
were performed. In the first measurement, the sample was irradi-
ated with 254 W of the 1 µm laser. In the second measurement,
the sample was irradiated with 212 W of the 2 µm laser. In the
third measurement, the sample was simultaneously irradiated
with 254 W of the 1 µm laser and 212 W of the 2 µm laser. In
Figs. 11–14, the reflections at the beginning of illumination are
displayed for the various samples and wavelengths.
During the first measurement (1 µm), the tinplate sample
(TP) was observed by the SWIR1 camera with an integration
time of 1 µs and the SWIR2 camera with an integration time
of 100 µs. In Fig. 15 the temporal evolvement of the reflection
structure is documented qualitatively. At the beginning, there is
Fig. 11. Analysis of the reflection of the 1 µm laser for aluminum sample A1 at the beginning of illumination. The upper left image shows the
detected blob and its weighted center, and the upper right image shows the 3Dplot of the ROI. The two lower images show the averaged horizontal
and vertical profiles and the respective ABg fits.

F80 Vol. 60, No. 22 / 1 August 2021 / Applied Optics Research Article
Table 10. Measured and Predicted PIB and Calculated Power Distributions for 1 µm
Sample PIB10 ρ10 νABg,10 PIBpred.,10 Pspec. PABg PL
TP Tinplate 59.1 W 31.1% 27.4% 56.4 W 27.5 W 105.3 W 57.1 W
CS Steel plate 0.14 W 0.1% 0.6% 0.12 W – 27.6 W 103.7 W
Table 11. Measured PIB for 2 µm
Sample PIB10 ρ10
TP Tinplate 94.0 W 50.1%
CS Steel plate 0.44 W 0.3%
a bright central spot (1). This spot remains for several seconds,
until after 20 s a ring shape of about 50 cm diameter is formed
(2), the origin of which explained in Section 4.B. Six seconds
later, with the first appearance of caustics, the ring becomes
immediately dim (3). The caustics evolve, and the ring slowly
disappears (4) until a bright caustic is formed that remains in a
similar shape (5).
For the second measurement on tinplate using the 2 µm
laser, our selected measurement duration of 50 s was too short
to observe a notable change in the reflection pattern. The slower
reaction is accounted to the 49% lower absorption of tinplate at
2µm than at 1 µm.
The third measurement on tinplate displays similar behavior
to the first measurement but on a substantially faster time scale
(Fig. 16). The 1 µm reflections are observed with the same
camera settings as in the first measurement, and the 2 µm reflec-
tions are observed with the MWIR camera with an integration
time of 100 µs. Additional to the faster time scale (caustics start
to form after 6.2 s), two moon-shaped reflections of opposite
orientation could be observed after 4.7 s (1) instead of the ring
structure as observed in the first measurement (see Section 4.B
for explanation). For both wavelengths the caustics evolving
after several seconds (2) of illumination are similar to each other
and similar to the caustics of the first measurement. After 24.7
s the 1 mm thin target is penetrated (3), and with the vanishing
of the reflection patterns only some scattering at the laser exit as
well as heat radiation from the sample is visible.
For the steel plate sample (CS), only during the third mea-
surement could notable changes in the reflection patterns be
observed during the measurement duration. The temporal
evolvement is shown in Fig. 17 for both the SWIR2 camera and
the MWIR camera, both set to an integration time of 100 µs.
In the beginning, a broadly scattered central spot is visible (1)
for both wavelengths. After several seconds, caustics begin to
form around the dimming central scatter spot (2). In contrast
to the only 1 mm thick tinplate sample, a ring structure is not
observed. After several tens of seconds, a prominent caustic
structure (3) very similar to the tinplate sample is formed.
Fig. 12. Analysis of the reflection of the 1 µm laser for aluminum sample A2 at the beginning of illumination. The upper left image shows the
detected blob and its weighted center, and the upper right image shows the 3Dplot of the ROI. The two lower images show the averaged horizontal
and vertical profiles and the respective ABg fits.

Research Article Vol. 60, No. 22 / 1 August 2021 / Applied Optics F81
Fig. 13. Analysis of the reflection of the 1 µm laser (left) and 2 µm laser (right) for the tinplate sample TP at the beginning of illumination. The
upper left images show the detected blob and its weighted center, and the upper right images show the 3D plot of the ROIs. The two pairs of lower
images each show the averaged horizontal and vertical profiles and the respective ABg fits.
Fig. 14. Analysis of the reflection of the 1 µm laser (left) and 2 µm laser (right) for the steel plate sample CS at the beginning of illumination. The
upper left images show the detected blob and its weighted center, and the upper right images show the 3D plot of the ROIs. The two pairs of lower
images each show the averaged horizontal and vertical profiles and the respective ABg fits.
Fig. 15. Temporal evolution of 1 µm reflection characteristics
from the tinplate sample observed with the SWIR2 camera (SWIR1
in inlay). From upper left to lower right: (1) Central reflection directly
after beginning of irradiation, (2) formation of a ring structure after
20 s of irradiation, (3) dimming of the ring and formation of caustics
after 26 s of irradiation, (4) evolution of caustics, and (5) pronounced
central caustic whose shape remains relatively stable.
As an example of the temporal evolution of the divergence
of the reflection patterns, we take a look at the reflections of the
tinplate sample (TP) when irradiated simultaneously with the
1µm laser and the 2 µm laser (Fig. 18). We selected tinplate for
this analysis, as it is the only of our four samples with a specular
component and therefore the most relevant for laser safety
considerations in the early phase of irradiation. The divergence
analysis can be performed only until the moon-shaped struc-
tures are formed. It can be observed that the divergence of the
scattered contribution stays fairly constant for about 3 s and
then starts to widen significantly. When this is compared to the
PIB in Fig. 19, it can be observed that this widening correlates
with the beginning of the decrease of the PIB. However, the
displayed curves have to be interpreted with care, as the power
meter has an integration time of 3 s and thus expresses a ramp up
of several seconds. Also, the diode looking at the power meter
responds nonlinearly above 80% of its maximum value. The
power meter and diode values cannot, therefore, be used to make

F82 Vol. 60, No. 22 / 1 August 2021 / Applied Optics Research Article
Fig. 16. Images of the reflections from tinplate observed by the
SWIR2 camera (left row) and the MWIR camera (right row) for
simultaneous irradiation with the 1 µm laser and the 2 µm laser. The
images were taken at different FoVs. From top to bottom: (1) After
4.7 s of irradiation, opposing moon structures emerge, (2) after about
15 s, characteristic caustics are visible, and (3) after more than 25 s the
glowing of the penetrated target is notable.
absolute statements, but it clearly gives an upper limit for the
duration of the specular reflection. Since the camera registered
no increase in maximum pixel value, we conclude that after
about 5 s the specular reflections irradiance must have decreased
significantly—because the specular reflection could not have
moved out of the central aperture. After about 10 s, spikes in the
maximal pixel value attributed to caustics become visible.
The maximum irradiance in the caustics can now be analyzed
under the assumption that the caustics do not change faster than
500 kHz (deduced from the 1 µs integration time). For the ABg
contribution, we calculate a central irradiance on the reflection
screen of 11.6 W/cm2. At the edge of the aperture, we calculate
an irradiance of 7.4 W/cm2in the horizontal direction and
6.2 W/cm2in the vertical direction. We can therefore appoint
a pixel value of 70 to an irradiance of 7.4 W/cm2. Therefore,
the maximum pixel value of 45 for caustics corresponds to an
irradiance of 4.8 W/cm2. For comparison, the peak irradiance
of the specular Gaussian contribution is 95 W/cm2. The cen-
tral peak irradiance as a combination of specular and scattered
contributions is therefore calculated to be 107 W/cm2. It can
be concluded that at a distance of 2 m from the sample, the
caustic’s maximum irradiance amounts to 1/20th of the central
irradiance at the beginning of irradiation.
Fig. 17. Image of the reflections from the steel plate sample
observed by the SWIR2 camera (left row) and the MWIR camera
(right row) for simultaneous irradiation with the 1 µm laser and the
2µm laser. The images were taken at different FoVs. From top to
bottom: (1) At the beginning of irradiation a broadly scattered spot is
visible, (2) after several seconds of illumination caustics start to form
around the dimming central spot, and (3) after several tens of seconds
prominent central caustics form.
4. RESULTS AND DISCUSSION
A. Laser Safety Assessment
For laser safety purposes, we calculate according NOHD val-
ues for the scattered and, if present, specular contributions.
To exploit our experimental results, we considered the fol-
lowing: (1) For the scatter component, the minimal scatter
1/e divergence of all measurements for each sample was used.
(2) For each component (specular, ABg), its complete radiant
power is assumed to be within the 1/e divergence. (3) A dedi-
cated reflection coefficient at the beginning of irradiation for
each component is calculated with Table 10 and displayed in
Table 12.
As an example of realistic parameters of a high-energy laser,
we consider a 30 kW laser emitting at 1070 nm from a 20 cm
aperture and focusing on a target in 500 m distance, resulting
in a focus of 20 mm diameter at 1/e (assuming turbulence and
jitter) and a 1/e divergence of 0.4 mrad for the specular com-
ponent reflected from the target. The power in each reflection
component was calculated with the aforementioned reflec-
tion coefficients (see Table 12). An exposure time of 0.25 s is
assumed as a conservative estimation for a dynamic process,
where target and laser beam are moving. The resulting NOHD
values (NOHDspec. for the specular contribution, NOHDscat.
for the ABg-like scattered component, and NOHDLfor the

Research Article Vol. 60, No. 22 / 1 August 2021 / Applied Optics F83
Fig. 18. Temporal evolvement of the scatter divergence of the horizontal and vertical profiles for tinplate (TP) calculated with different methods
for 1 µm (left) and 2 µm (right).
Fig. 19. Evolution of the central power. The maximum pixel value
in the surrounding of the central aperture (blue line), the diode signal
of the diode looking at the power meter (orange line), and the power
meter signal (orange markers).
Table 12. Dedicated Reflection Coefficients for the
Specular and ABg-Scatter Component for 1070 nm
Sample Rspec. RABg
A1 Aluminum –a26.6%
A2 Aluminum –a13.3%
TP Tinplate 10.9% 41.4%
CS Steel plate –a10.9%
aNo specular reflection observed.
Lambertian scattered component) are displayed in Table 13.
In Table 14 the NOHD values for the scattered component are
displayed for exposure times up to 10 s.
It is apparent that the Lambertian component may be
neglected for laser safety considerations, as the NOHD values
turn out to be only several meters despite the high integrated
radiant power in this component. Even if we assume the
Lambertian component not to be ideal and radiating into a
cone of 90◦, the NOHDLof the second aluminum sample (A2)
does not exceed 8 m. For the scattered component calculated
with the ABg model, we obtain NOHD values of several 100 m
with a maximum of 797 m for tinplate. Considering the tem-
poral evolution in Fig. 18, we expect this value to decrease after
the first few seconds as the divergence increases. Unsurprisingly,
the most critical component is the specular one. If a metallic
sample with a specular reflecting component is irradiated with
a high-energy laser, NOHD values of over 10 km (14.3 km for
tinplate) have to be considered, even if the specular component
is low (14.5% for our tinplate sample). However, this is only
true for a flat sample. If we assume the target to be curved in
one orientation with a large radius of 1 m, the NOHD already
decreases to 4.91 km. If the target is curved in both orientations,
the NOHD decreases to 1.69 km. Compared to the NOHD of
the laser itself of 43.3 km, these values are significantly smaller.
Additionally, with increasing target temperature, the power
in the specular component decreases within a few seconds.
Generally, one can assume that the higher the incident power,
the shorter the duration of the specular reflection component
will be.
B. Manifestation of Ring-Shaped Reflections for Thin
Samples
In the high-power experiments with the tinplate sample, a ring-
shaped reflection manifested after some seconds of irradiation
(Fig. 15). This could not be observed for the steel plate sam-
ple. Comparisons with unpublished previous measurements
showed that such ring structures only occurred for thin samples
≤1 mm. An investigation of the shape of the sample during the
irradiation showed that the thin samples deform around the
maximum of the irradiation; see Fig. 20. The point of time of
the deformation matches the beginning of the manifestation
of the ring-shaped structures. Ring structures can be formed
by a so-called axicon, a conical optical element. Thus, a conical
dent in the thin samples around the irradiation maximum was

F84 Vol. 60, No. 22 / 1 August 2021 / Applied Optics Research Article
Table 13. NOHDs for a 30 kW Laser at 1070 nm Assuming a Focus of 20 mm (1/e) and a Specular Divergence of 0.4
mrad (1/e)a
Sample Pspec. in kW NOHDspec. in km PABg in kW αABg (h/ v ) in mrad NOHDscat. in m PLin kW NOHDLin m
A1 Aluminum –b–b8.0 173/7c255 19.6 1.8
A2 Aluminum –b–b4.0 57/14c223 23.4 2.2
TP Tinplate 3.3 14.3 12.4 15/13c797 6.8 0.6
CS Steel plate –b–b3.3 90/88c64 12.3 1.2
aThe exposure time is assumed to be 0.25 s.
bNo specular reflection observed.
cDivergence values from the low-power measurements (Table 5) as worst-case assumptions.
Table 14. NOHDs for a 30 kW Laser at 1070 nm
Assuming a Focus of 20 mm (1/e) and a Specular
Divergence of 0.4 mrad (1/e) for Different Observation
Times
Sample NOHDscat. in m
Exposure Time in s 0.25 5 10
A1 Aluminum 255 373 409
A2 Aluminum 223 325 357
TP Tinplate 797 1160 1273
CS Steel plate 64 94 103
Fig. 20. Manifestation of a conical dent in the tinplate (TP) sample.
On the (a) left image, at the beginning of the illumination, a reflected
corner from within the room is outlined by a red line. After several
seconds, when the ring shape begins to form, the reflected corner is
deformed [blue line, right image (b)]. This is due to the formation of a
conical dent.
assumed, and geometrical optical considerations lead to a ring
on the reflection screen of radius
rR=dtan 2β.(17)
Here, dis the distance between the sample and the reflection
screen, and βis the tilt angle of the cone against the sample
surface. For the first measurement on tinplate in Fig. 15, a ring
structure with a diameter of 50 cm was observed. This can,
therefore, be led back to a conical dent with a slope of about
3.6◦.
In the case of simultaneous illumination with both laser
sources (third measurement on tinplate), the spots on the sam-
ple did not overlay completely. Therefore, the maximum of
combined irradiation lays in the center between the maxima of
each laser spot. As this is also the central point for physical stress,
both the laser beams hit the created conical dent off-axis. This
can be observed in the moon-shaped reflection patterns with
opposing orientations in Fig. 16. The formation of a ring struc-
ture does not necessarily lead to reduced intensities. However,
the maximum intensity then is not located in the centrum of the
reflection but on the ring. The width of the ring is determined by
the scatter component. For laser safety calculations, this process
may be neglected, as the intensities are not increased compared
to a central reflection. Moreover, in the here presented exper-
iments, only unclamped planar samples were used. It cannot
be concluded that the same process takes place in curved or
clamped samples.
C. Modeling the Reflected Intensity during the
Melting Process
Once the target begins to melt, the initial reflection pattern
transforms into a complicated structure called caustics, which
becomes increasingly difficult to predict. Figure 21 shows caus-
tics from reflections of a laser beam from our tinplate sample
at three different moments after the target started to melt. In
fact, the reflection is influenced by many parameters, which are
unknown or very difficult to measure, for example, the tem-
perature of the target, its temperature-dependent absorption
coefficient, the temperature of the air surrounding the target
(which can also include smoke), the depth of the dent in the
target, as well as the height and structure of the surface waves
of the liquefied metal in the laser spot. As it seems difficult to
simulate all the effects associated with the melting process with
great precision, we are looking for a model that is capable of
simulating similar caustics and which can be used to perform
laser safety or risk analyses.
Another challenge in assessing laser hazards is to model how
the intensity patterns develop with distance (from a few tens of
meters up to a kilometer, for example) based on the intensity
distribution measured at only 2 m from the target. The regions
showing high intensity on the screen, which correspond to
constructive interferences between the individual parts of the
reflected beam, might become zones of destructive interfer-
ences at another distance from the target. This means that the
intensity is changing with the distance from the target until
the far field is reached. A model should, therefore, be able to
generate intensity patterns similar to the ones measured at 2 m
distance, but it should also be able to propagate the beam to rel-
evant distances in order to perform laser safety or risk analyses.
Obviously, a model will not be able to grasp all the complexity
of the melting process. More importantly, the model should
be able to give worst-case approximations so that we do not
underestimate the risks of laser reflection from a melting target.

Research Article Vol. 60, No. 22 / 1 August 2021 / Applied Optics F85
Fig. 21. Measured reflected intensity from tinplate at three different
times after the melting of the target began.
Since we are interested in the reflections once the target is
melted, we first approximate the surface of the target according
to a liquid surface. In the literature, many liquid surface models
are used to simulate ocean waves’ heights. In these models, the
heights of the waves are described by a power spectral density. A
good review of the power spectrums can be found in [11]. Thus,
we propose here to take a spectrum used for water waves and
adapt its parameters for our molten metallic surface. The spec-
trum we choose is the Phillips spectrum Ph(E
k)as proposed in
[12], and we use it to generate the heights of the molten surface
structure:
Ph(E
k)=Aexp(−1/(kL)2)
k4exp(−k2l2)E
k· Ew
2
,(18)
where E
kis the spatial frequency vector, Ais a constant describing
the overall amplitudes of the waves, Lis the largest possible
waves arising from a continuous wind speed and is usually
expressed in terms of wind speed and gravitational constant,
lrepresents the smallest waves, and the cosine factor |E
k· Ew|2
eliminates waves that move perpendicular to the wind direction
Ew. For our purposes, we will slightly change this model since
wind does not matter here. First, we delete the cosine term, and
second, Lwill just represent the largest possible waves without
any consideration regarding the wind. The spectrum is there-
fore dependent on three parameters A,L, and l. The heights
hare created from the Fourier transform of Gaussian random
numbers filtered by the square root of the power spectrum:
h(x,y)=F T (ε1+iε2)qPh(E
k),(19)
where ε1and ε2are two Gaussian random variables These
heights can be converted into phase differences that can in turn
be applied on a laser beam. The phase differences are then calcu-
lated from the height hby subtracting its mean value h0from h
and multiplying by 2π/λ:
1ϕ =22π
λ(h−h0).(20)
The factor 2 arises from the fact that the beam is reflected, so
that the height differences are counted twice to account for the
phase differences. These phase differences are then considered as
a phase screen that will be applied on the electric field of the laser
beam for its propagation. The propagation starts at the target’s
surface, originating from a Gaussian beam of 4.3 mm 1/e2
radius, which was focused on the target (i.e., it has an infinite
radius of curvature on the target) and with a phase distribution
given by the surface’s heights. The beam is then propagated at a
desired distance using the same beam propagation methods used
to propagate laser beams in random media [13,14].
To make sure that the resulting intensity patterns are quan-
titatively similar to the experimental patterns, we generate 100
intensity patterns and average their autocorrelation function
(ACF). Each generated intensity distribution is a new ran-
dom realization of the phase screen. We then modify the input
parameters of the power spectrum in order to obtain an averaged
ACF, which has the same 1/e width as the ACF of the experimen-
tal data. We further use the 1/e width of the ACF as a criterion
to compare our simulated intensities with the measured ones
because this criterion is often used in speckle analysis [15,16] to
determine the roughness of a surface. We use the same criterion,
since we analyze a reflected intensity to model the surface of a
material as it is the case in speckle analysis. The ACFs on the
xand yaxes are shown in Fig. 22.
As one can see from Fig. 22, the experimental autocorrelation
function shows a sharp drop near the closest distance. This
can be explained by the applied noise filtering that consists of
a threshold filter. This filter basically sets all the pixels that are
below a certain value to zero. Of course, this also affects those
pixels the intensity of which cannot be distinguished from the
noise. While the 1/e widths between the experimental and
simulated autocorrelation functions are similar, the rest of the
autocorrelation functions might deviate from each other. We
again stress that we neither pretend to have a simulation able
to fully model the whole melting process nor are we looking
for such a simulation, as we are interested in a simulation able
to provide worst-case results. An example of the simulated
intensities at 2 m is given in Fig. 23.
Now that the input parameters for the Philips spectrum
have been determined using the ACF width as a criterion, the
beam can be propagated to any arbitrary distance in the far field.
In the far field the intensity pattern is no longer changing, so
the divergence of the incident beam can be adapted through a
simple scaling of the axes. Using the second-order moment of
the intensity, we measured in the case of the tinplate sample, in
which the smallest divergence is 8.5◦when the target is melting.
Fig. 22. Normalized averaged ACF for the xaxis (in dark and light
blue for the experimental and simulated data, respectively) and the y
axis (in orange and red for the experimental and simulated data, respec-
tively). The experimental ACF was time-averaged over the duration of
the target’s melting, while the simulated ACF was averaged over 100
intensity realizations. The 1/e width of the functions is indicated.

F86 Vol. 60, No. 22 / 1 August 2021 / Applied Optics Research Article
Fig. 23. Simulated intensity at 2 m distance from the target. Two different realizations of the phase screen were done.
Fig. 24. Simulated intensity at 500 m distance from the target. The phase screens used were the same as in Fig. 23. The intensity is given in watts
per square meter (W/m2).
Assuming a worst-case scenario, we round this value down to
5◦and calculate the intensity at 500 m distance from the target.
The intensities are shown in Fig. 24. The power of the laser is
assumed to be 30 kW.
In Fig. 24, the intensities at 500 m correspond to the use
of the same phase screens as in Fig. 23. Once the intensity is
known, a time constant of the change of the intensity is needed
to be able to calculate the fluence. It was not possible to derive
a time constant from our experiment, as our cameras and pho-
todiodes were not fast enough to clearly see the speed at which
the caustics are changing. Therefore, we take a time constant
measured in [4] (called pulse duration in their work) of 6 ms.
The simulated fluence is therefore about 2.4 J/m2. This fluence
can then be compared to the MPE, which is equal to 1.94 J/m2
for 6 ms and 1070 nm wavelength. We can therefore say that the
NOHD, once the caustics are formed, can be rounded to 500
m. Notice that we considered the whole 30 kW to be reflected
here (no sample absorption considered), so the NOHD here is a
worst-case scenario.
Of course, this simulation has limits and is not able to include
every phenomenon that occurs during the melting process.
For example, some of the melted material flows out of the hole
and creates a reflection that can be seen at the top of the screen
(compare Figs. 16 and 17). This effect is not modeled here, as it
is unclear if such an effect, among others, will happen in a real
engagement. In reality, wind might blow the melted metal away
or drops of material will fall from the hole, instead of slowly
flowing out of the hole, which can lead to a different intensity
pattern. Our simulation was a first step to create a laser safety
model. More importantly, we showed that the intensity mea-
sured at a short distance from the target cannot be directly used
to determine the intensity at a large distance, and the need for a
model describing caustics is imperative.
5. SUMMARY
For outdoor high-power laser applications, the legally required
laser safety assessments, as defined mostly in the scope of
occupational safety and health, potentially lead to vastly over-
estimated laser safety areas. However, the likelihood of an
accidental irradiation of an uninvolved person is not considered
there. In order to achieve a more realistic hazard assessment
of the scenario, those likelihoods have to be considered and
included in a risk analysis. Even though a risk analysis goes
beyond the scope of this paper, it is still important to understand
the difference between the laser safety assessment and a risk
analysis.
To deliver crucial basics for such a risk analysis, we performed
specific experiments to assess the complex reflection behavior of
metallic samples irradiated by high-power lasers. Four different
samples were investigated: two aluminum, a tinplate, and a
steel sample. During the experiments we measured the reflected
power in a narrow central (FoV) and the spatial and tempo-
ral distribution of the reflection patterns. We also performed

Research Article Vol. 60, No. 22 / 1 August 2021 / Applied Optics F87
modeling of the reflected beam and separated the reflections
into three components: a specular, a forward scattered, and a
Lambertian component. The Lambertian contribution leads to
NOHD values of under 10 m and may therefore be neglected
for such kinds of scenarios. The specular component leads to
the largest NOHD. It can exceed several kilometers depending
on the laser power and beam divergence. Still, our experiments
also showed that materials mostly reflect diffusely. Based on
our findings that materials like aluminum or steel do not reflect
specularly, we can assume that the likelihood of engaging a
target that possesses a pronounced specular component is
comparatively low. Considering a 30 kW laser and worst-case
assumptions regarding divergence, reflected power, sample
curvature, and atmospheric attenuation, we found NOHD
values for the aluminum and steel samples of up to 255 m. For
the tinplate sample, we observed a specular reflection and a
more pronounced forward scattering contribution. The result-
ing NOHD values are 800 m for the scattering contribution
and 14.3 km for the specular contribution. These worst-case
NOHD values are valid only for the very start of the irradi-
ation. Our experiments show that the radiant power values
decrease over the irradiation time; we can, therefore, expect
decreasing NOHD values, and the speed of this decrease scales
with incident laser power. In our experiments on tinplate, after
about 5 s, the components considered here almost vanish, and
other processes, like caustics, emerge. For a high-power laser as
assumed here, the time scale for these processes may be shorter.
For the caustics, we developed a specific model in order to cal-
culate intensities at arbitrary distances. These intensities can be
compared to MPE or ED50 values and used for risk analyses.
A proper risk analysis has to combine these findings with the
general irradiance probability derived from beam movement
and caustic fluctuations. Subsequently, a large NOHD is not
equivalent to a high risk: For a beam with a small divergence, the
beam size on the ground is small, and therefore the probability
to irradiate an uninvolved person may be low. The scattered
component, on the other hand, has a large divergence; the prob-
ability that a person gets irradiated might actually be higher.
However, the NOHD of the scattered contribution is small and
if the distance between a target and the ground, where a person
might be, is larger than this NOHD, an irradiated person will
not sustain any damage. Our present investigations, therefore,
enable us to define safety perimeters when performing outdoor
experiments and provide us with the first steps toward a risk
analysis.
Disclosures. The authors declare no conflicts of interest.
Data Availability. Data underlying the results presented in this paper are
not publicly available at this time but may be obtained from the authors upon
reasonable request.
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