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.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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 unintended 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 permissible exposure [MPE, in units of watts per square centimeter (${\rm W}/{{\rm cm}^2}$) or joules per square centimeter (${\rm J}/{{\rm cm}^2}$)], 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 exposure 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 purposes). 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 manufacturing, 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 ruled out, laser operation will be prohibited since occupational safety and health rules cannot be fulfilled. However, occupational safety and health rules are overly pessimistic, as they do not take into account the probability that an observer will actually 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, quantitative 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 particular 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 person 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 consideration, 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 ${1}\;{{\rm kW/cm}^2}$, 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 irradiated carbon steel plate had started, they found that at a distant position in space where the specular reflection occurs, the reflections 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.

 figure: Fig. 1.

Fig. 1. Photographs of the samples. For details see Table 1.

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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, including 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 investigations 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.

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Table 1. Mechanical and Thermodynamic Properties of the Samples

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Table 2. Low-Power Experiments: Parameters of the Camera and the Attached Lens and Filter

Thermodynamic properties of the different materials are also listed in Table 1. These were not measured but taken from standard literature [59].

 figure: Fig. 2.

Fig. 2. Sketch of the experimental setup for the low-power laser reflection measurements.

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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 ${\sim}{1.5}\;{\rm W}$. 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 (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 bandpass 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 ${16}\;{\rm cm} \times {8.5}\;{\rm cm}$ 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 ${{\rm M}^2}$ measurement device (Thorlabs M2MS–BC106VIS/M). The beam diameter (${{1/e}^2}$) was estimated to be 2.7 mm, and the full-angle beam divergence (${{1/e}^2}$) was estimated to be 0.53 mrad; the beam quality was ${{\rm M}^2} = {1.06}$. These quantities were used later for the data analysis; see Section 3.A.

C. High-Power Experimental Setup

Figure 3 shows 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 spatial 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 ${1}\;{\rm m} \times {1}\;{\rm m}$ each, resulting in a total screen size of ${3}\;{\rm m} \times {2}\;{\rm m}$ (horizontally/vertically). The sample under test was placed at a distance of 2 m from the reflection screen. This geometry allowed us to cover a solid angle of ${\sim}{1}\;{\rm sr}$ for observing the spatial distribution of the reflected laser light.

 figure: Fig. 3.

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.

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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 uncontrolled 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.

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Table 3. Parameters of the Laser Sources Used for the Experiments

Both laser beams were spatially superimposed using an optomechanical assembly, which is denoted as laser head in the sketch of Fig. 3 and 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 using a mirror M (Linos DLHS IR 1064) and a dichroic beam splitter DBS (Thorlabs DMLP1500).

 figure: Fig. 4.

Fig. 4. Sketch of the laser head. FC, fiber collimator; DBS, dichroic beam splitter; M, mirror.

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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 ${15.6}^\circ \times {12.5}^\circ$. 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 ${35.3}^\circ \times {28.5}^\circ$ and, therefore, allowed us to monitor the reflected laser light on the whole reflection screen, i.e., this camera 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 ${22}^\circ \times {17}^\circ$ corresponded to a size of ${\sim}{2}\;{\rm m} \times {1.5}\;{\rm m}$ at the reflection screen. For this camera, 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 ${\sim}{2.5}\;{\rm m}$ 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).

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Table 4. High-Power Experiments: Parameters of the Cameras and their Attached Lenses and Filters

The monochrome camera VIS2 (Allied Vision Mako G–158B) was placed quite near to the target, in a distance of ${\sim}{30}\;{\rm cm}$, 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 photodiodes 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 intensity 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 subtracted 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 (${\gt}{90}\%$), the procedure was repeated with the next lower integration time, and so forth until the full HDR image was extracted.

 figure: Fig. 5.

Fig. 5. Horizontal (left) and vertical (right) profiles for the reflection at the unprotected gold mirror with logarithmic $y$ axis. The blue curves show the profiles through $({x_0},\;{y_0})$; the orange curve shows the fit with function and a central Gaussian.

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 figure: Fig. 6.

Fig. 6. Horizontal (left) and vertical (right) profiles for the reflection at the aluminum sample (A1) with logarithmic $y$ axis. The blue curves show the profiles through $({x_0},\;{y_0})$; the orange curve shows the fit with function without a central Gaussian.

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 figure: Fig. 7.

Fig. 7. Horizontal (left) and vertical (right) profiles for the reflection at the aluminum sample (A2) with the logarithmic $y$ axis. The blue curves show the profiles through $({x_0},\;{y_0})$; the orange curve shows the fit with function without a central Gaussian.

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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 ${{1/e}^2}$. 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

$${w_S} = {w_0}\sqrt {1 + {{\left({\frac{d}{{{z_{{\rm Rayleigh}}}}}} \right)}^2}} \approx 2.0\;{\rm mm}.$$

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

$$I(x,y) = \left({{I_{{\rm spec}.}}(x,y) + {I_{{\rm scat}{\rm .}}}(x,y) + {I_{{\rm offset}}}} \right)\frac{{\cos \theta}}{{{d^2} + {x^2} + {y^2}}}.$$

Here, $d$ denotes the distance between the sample and the scatter screen, and the angle to the normal measured from the sample is given as $\theta = \arctan ({{{\sqrt {{x^2} + {y^2}}} / d}})$. The specular part is given as a Gaussian:

$${I_{{\rm spec}{\rm .}}} = {I_{0,{\rm spec}{\rm .}}}{e^{- \frac{{{{(x - {x_0})}^2} + {{(y - {y_0})}^2}}}{{{c^2}}}}}.$$

Here, $c$ is the 1/e radius of the Gaussian that was fixed to ${c = 2.0\;{\rm mm}/2}$. The ABg-scattering part is given as

$${I_{{\rm scat}{\rm .}}} = {I_{0,{\rm scat}{\rm .}}} \cdot \frac{{{B_x}}}{{{B_x} + {{\left| {\frac{{x - {x_0}}}{d}} \right|}^{{g_x}}}}}\frac{{{B_y}}}{{{B_y} + {{\left| {\frac{{y - {y_0}}}{d}} \right|}^{{g_y}}}}}.$$
 figure: Fig. 8.

Fig. 8. Horizontal (left) and vertical (right) profiles for the reflection at the tinplate sample (TP) with the logarithmic $y$ axis. The blue curves show the profiles through $({x_0},\;{y_0})$; the orange curve shows the fit with function and a central Gaussian.

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 figure: Fig. 9.

Fig. 9. Horizontal (left) and vertical (right) profiles for the reflection at the steel plate sample (CS) with the logarithmic $y$ axis. The blue curves show the profiles through $({x_0},\;{y_0})$; the orange curve shows the fit with function without a central Gaussian.

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${A_i}$, ${B_i}$, and ${g_i}$ are the ABg parameters with ${A_x}{A_y} = {I_{0,{\rm scat}{\rm .}}}\;{B_x}{B_y}$. The results of the fits are displayed in Figs. 59 for the horizontal and vertical profiles through the maximum $({x_0},\;{y_0})$ 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 ${r_e} = 5\;{\rm mm}$ 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 ${P_{\textit{in}}} = 92\;{\rm mW}$. For further evaluation, reflected power is calculated as

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Table 5. 1/e Widths of the Total Fit and 1/e Widths of the Scattering Part for the Investigated Samplesa

$${P_R} = {P_{\textit{in}}} \cdot {R_S}$$
with the reflectance of the sample ${R_S}$ from Table 1. The fraction of the total reflected power within the (FoV) of the power meter is calculated as
$${\rho _{{\rm FoV}}} = \frac{{{\Phi _{{\rm FoV}}}}}{{{P_R}}}.$$
${\Phi _{{\rm FoV}}}$ is the power measured by the power meter. In the following considerations, we assume that there are three parts contributing to the reflected power:
$${P_R} = {P_{{\rm spec}{\rm .}}} + {P_{{\rm ABg}}} + {P_L}.$$

Here, ${P_{{\rm spec}{\rm .}}}$ is the specular Gaussian contribution, being present for the gold mirror and the tinplate sample. ${P_{{\rm ABg}}}$ denotes the contribution that is scattered in an ABg-like manner, and ${P_L}$ denotes 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

$${L_L} \approx \frac{{{P_R} - {\Phi _{{\rm FoV}}}}}{{2\pi}}.$$

For comparison, we calculate the radiant flux of such a Lambertian radiation within the two FoVs for the first aluminum sample (A1):

$$\begin{split}&\Phi _{L,\;64.4}^{A1} = {L_L}\frac{{\pi r_e^2}}{{{d^2}}} = {L_L}\frac{{\pi {{(5\;{\rm mm})}^2}}}{{{{(16\;{\rm cm)}}^2}}} \approx 38\;{\unicode{x00B5} \rm W},\\&\Phi _{L,\;14.3}^{A1} = {L_L}\frac{{\pi {{(5\;{\rm mm})}^2}}}{(70\;{\rm cm})^2} \approx 2.1\;{\unicode{x00B5} \rm W}.\end{split}$$
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Table 6. Radiant Flux for a FoV of 62.4 mrad and the Derived Power Distribution

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Table 7. Radiant Flux for a FoV of 14.3 mrad and the Derived Power Distribution

These results support the aforementioned assumptions. Additionally, we calculated the portion of the total ABg-like scattered power ${P_{{\rm ABg}}}$ that should contribute to ${\Phi _{{\rm FoV}}}$ as

$${\nu _{{\rm ABg},\;{\rm FoV}}} = \frac{{{\Phi _{{\rm ABg},\;{\rm FoV}}}}}{{{P_{{\rm ABg}}}}}.$$

The ABg-like scattered portion of the total reflected power is called

$${p_{{\rm ABg}}} = \frac{{{P_{{\rm ABg}}}}}{{{P_R}}}.$$

In the case in which there is no specular reflection, we can conclude that

$${p_{{\rm ABg}}} \approx \frac{{{\rho _{{\rm FoV}}}}}{{{\nu _{{\rm ABg},\;{\rm FoV}}}}}.$$

In the contrary case with a specular reflection, we can calculate the power scattered ABg-like as

$${P_{{\rm ABg}}} = \frac{{{\Phi _{62.4}} - {\Phi _{14.3}}}}{{{\nu _{{\rm ABg},\;62.4}} - {\nu _{{\rm ABg},\;14.3}}}}$$
and subsequently
$$\begin{split}&{P_{{\rm spec}{\rm .}}} = {\Phi _{{\rm FoV}}} - {\nu _{{\rm ABg},\;{\rm FoV}}}{P_{{\rm ABg}}}\;{\rm and}\\&{P_L} = {P_R} - {P_{{\rm spec}{\rm .}}} - {P_{{\rm ABg}}}.\end{split}$$
The calculated radiant fluxes and power distributions are listed in Tables 6 and 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 output 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.

 figure: Fig. 10.

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 measurements, the sample is visible in the camera image for 2 µm within the orange box denoted by Target.

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 figure: Fig. 11.

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 3D plot of the ROI. The two lower images show the averaged horizontal and vertical profiles and the respective ABg fits.

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The MATLAB blob detection algorithm is used with a threshold of ${{1/e}^2}$ of 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 orientation. For these profiles, the 1/e width was determined using three different algorithms:

  • 1. Threshold Method

    The first pixel position with $P(p) \gt {P_{{\rm max}}}/e$ was determined from both directions. The resulting width ${w_{{\rm th}}}$ 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

    $$a \cdot \frac{1}{{b + |\frac{{x - {x_0}}}{{{d_{\textit{SS}}}}}{|^{{g_x}}}}} \cdot \frac{1}{{{{\left({1 + |\frac{{x - {x_0}}}{{{d_{\textit{SS}}}}}{|^2}} \right)}^{3/2}}}},$$
    is fitted to the profiles with the fit parameters $a$, $b$, ${g_x}$, and ${x_0}$ and the distance between sample and screen ${d_{\textit{SS}}}$. The 1/e width of this function is the “fit width” of the reflection ${w_{{\rm fit}}}$.

  • 3. Second Moment Method

    The ${{{\rm D}4\sigma}}$ width ${w_{{\rm D}4\sigma}}$ is calculated for the profiles by limiting the profiles to a region of $2{w_{\textit{th}}}$ with

    $${w_{{\rm D}4\sigma}} = 2\sqrt 2 \cdot \sqrt {\frac{{\sum {P(p) \cdot {{(P(p) - {P_{{\rm max}}})}^2}}}}{{\sum {P(p)}}}} .$$

The resulting widths at the beginning of the illumination (first image, after laser was switched on) are detailed in Tables 8 and 9.

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Table 8. Widths of the Reflection Distributions Obtained by the Different Methods for 1 µm

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Table 9. Widths of the Reflection Distributions Obtained by the Different Methods for 2 µm

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 ${\rho _{10}}$. Additionally, ${\nu _{{\rm ABg},\;10}}$ 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 measurements 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 ${\rho _{10}}$. With the fairly similar widths in Tables 8 and 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 irradiated 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. 1114, 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 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).

 figure: Fig. 12.

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 3D plot of the ROI. The two lower images show the averaged horizontal and vertical profiles and the respective ABg fits.

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Table 10. Measured and Predicted PIB and Calculated Power Distributions for 1 µm

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Table 11. Measured PIB for 2 µm

 figure: Fig. 13.

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.

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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 2 µm than at 1 µm.

 figure: Fig. 14.

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.

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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 reflections 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.

 figure: Fig. 15.

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.

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For the steel plate sample (CS), only during the third measurement 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.

 figure: Fig. 16.

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.

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 figure: Fig. 17.

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 2 µm 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.

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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 1 µm 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 structures 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 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 ${11.6}\;{{\rm W/cm}^2}$. At the edge of the aperture, we calculate an irradiance of ${7.4}\;{{\rm W/cm}^2}$ in the horizontal direction and ${6.2}\;{{\rm W/cm}^2}$ in the vertical direction. We can therefore appoint a pixel value of 70 to an irradiance of ${7.4}\;{{\rm W/cm}^2}$. Therefore, the maximum pixel value of 45 for caustics corresponds to an irradiance of ${4.8}\;{{\rm W/cm}^2}$. For comparison, the peak irradiance of the specular Gaussian contribution is ${95}\;{{\rm W/cm}^2}$. The central peak irradiance as a combination of specular and scattered contributions is therefore calculated to be ${107}\;{{\rm W/cm}^2}$. 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.

4. RESULTS AND DISCUSSION

A. Laser Safety Assessment

For laser safety purposes, we calculate according NOHD values for the scattered and, if present, specular contributions. To exploit our experimental results, we considered the following: (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 dedicated reflection coefficient at the beginning of irradiation for each component is calculated with Table 10 and displayed in Table 12.

 figure: Fig. 18.

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).

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 figure: Fig. 19.

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).

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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 component reflected from the target. The power in each reflection component was calculated with the aforementioned reflection 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 (${{\rm NOHD}_{{\rm spec}{\rm .}}}$ for the specular contribution, ${{\rm NOHD}_{{\rm scat}{\rm .}}}$ for the ABg-like scattered component, and ${{\rm NOHD}_L}$ for the 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.

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Table 12. Dedicated Reflection Coefficients for the Specular and ABg-Scatter Component for 1070 nm

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 ${\rm NOHD}_{\rm L}$ of 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 temporal 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.

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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

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 sample. Comparisons with unpublished previous measurements showed that such ring structures only occurred for thin samples ${\le} {1}\;{\rm mm}$. 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 assumed, and geometrical optical considerations lead to a ring on the reflection screen of radius

$${r_R} = d\tan 2\beta .$$

Here, $d$ is the distance between the sample and the reflection screen, and $\beta$ is 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°.

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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

 figure: Fig. 20.

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.

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In the case of simultaneous illumination with both laser sources (third measurement on tinplate), the spots on the sample 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 structure 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 experiments, 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 caustics 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 temperature 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 interferences 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 relevant 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.

 figure: Fig. 21.

Fig. 21. Measured reflected intensity from tinplate at three different times after the melting of the target began.

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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 spectrum we choose is the Phillips spectrum ${P_h}(\vec k)$ as proposed in [12], and we use it to generate the heights of the molten surface structure:

$${P_h}(\vec k) = A\frac{{\exp (- 1/{{(kL)}^2})}}{{{k^4}}}\exp (- {k^2}{l^2}){\left| {\vec k \cdot \vec w} \right|^2},$$
where $\vec k$ is the spatial frequency vector, $A$ is a constant describing the overall amplitudes of the waves, $L$ is the largest possible waves arising from a continuous wind speed and is usually expressed in terms of wind speed and gravitational constant, $l$ represents the smallest waves, and the cosine factor ${| {\vec k \cdot \vec w} |^2}$ eliminates waves that move perpendicular to the wind direction $\vec w$. For our purposes, we will slightly change this model since wind does not matter here. First, we delete the cosine term, and second, $L$ will just represent the largest possible waves without any consideration regarding the wind. The spectrum is therefore dependent on three parameters $A$, $L$, and $l$. The heights $h$ are created from the Fourier transform of Gaussian random numbers filtered by the square root of the power spectrum:
$$h(x,y) = FT\left[{({\varepsilon _1} + i{\varepsilon _2})\sqrt {{P_h}(\vec k)}} \right],$$
where ${\varepsilon _1}$ and ${\varepsilon _2}$ are 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 calculated from the height $h$ by subtracting its mean value ${h_0}$ from $h$ and multiplying by $2\pi /\lambda$:
$$\Delta \varphi = 2\frac{{2\pi}}{\lambda}\left({h - {h_0}} \right).$$

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 ${{1/e}^2}$ 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].

 figure: Fig. 22.

Fig. 22. Normalized averaged ACF for the $x$ axis (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, respectively). 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.

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To make sure that the resulting intensity patterns are quantitatively similar to the experimental patterns, we generate 100 intensity patterns and average their autocorrelation function (ACF). Each generated intensity distribution is a new random 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 experimental 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 $x$ and $y$ axes 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.

 figure: Fig. 23.

Fig. 23. Simulated intensity at 2 m distance from the target. Two different realizations of the phase screen were done.

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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. 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.

 figure: Fig. 24.

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 (${\rm W}/{{\rm m}^2}$).

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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 photodiodes 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 ${2.4}\;{{\rm J/m}^2}$. This fluence can then be compared to the MPE, which is equal to ${1.94}\;{{\rm J/m}^2}$ 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 measured 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 overestimated 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 temporal distribution of the reflection patterns. We also performed 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 resulting 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 irradiation. 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 calculate 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 probability 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.

REFERENCES

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2. LIA, ANSI Z136.1 – Safe Use of Lasers (Laser Institute of America, 2014).

3. European Union, “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 exposure of workers to risks arising from physical agents (artificial optical radiation) (19th individual Direct),” (2019).

4. J.-F. Daigle, D. Pudo, F. Théberge, and M. Châteauneuf, “Laser safety evaluation for high-energy laser interaction with solids,” Opt. Eng. 56, 026106 (2017). [CrossRef]  

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15. F. Schwenger and K. Braesicke, “Simulation of laser speckle patterns generated by random rough surfaces,” Proc. SPIE 11406, 1140609 (2020). [CrossRef]  

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References

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  1. B. Eberle, W. T. Kinerk, M. Koerber, J. Öhgren, G. Ritt, C. N. Santos, B. Schwarz, O. Steinvall, S. M. Tipper, M. Vandewal, and C. L. Westgate, “NATO SET-249 joint measurement campaign on laser dazzle effects in airborne scenarios,” Proc. SPIE 11161, 111610C (2019).
    [Crossref]
  2. LIA, ANSI Z136.1 – Safe Use of Lasers (Laser Institute of America, 2014).
  3. European Union, “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 exposure of workers to risks arising from physical agents (artificial optical radiation) (19th individual Direct),” (2019).
  4. J.-F. Daigle, D. Pudo, F. Théberge, and M. Châteauneuf, “Laser safety evaluation for high-energy laser interaction with solids,” Opt. Eng. 56, 026106 (2017).
    [Crossref]
  5. Y. S. Touloukian, R. W. Powell, C. Y. Ho, and M. C. Nicolaou, Thermal Diffusivity—Thermophysical Properties of Matter (IFI/Plenum, 1973), Vol. 10.
  6. Steelforge, “Melting point of metals & alloys,” https://www.steelforge.com/literature/metal-melting-ranges/ .
  7. Engineering ToolBox, “Thermal conductivity of metals, metallic elements and alloys,” https://www.engineeringtoolbox.com/thermal-conductivity-metals-d_858.html .
  8. M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, Handbook of Optics (McGraw-Hill, 1995), Vol. II.
  9. Z. Song, J. Qin, J. Qu, J. Song, W. Zhang, Y. Shi, T. Zhang, X. Xue, R. Zhang, H. Zhang, Z. Zhang, and X. Wu, “A systematic investigation of the factors affecting the optical properties of near infrared transmitting cool non-white coatings,” Sol. Energy Mater. Sol. Cells 125,206–214 (2014).
    [Crossref]
  10. R. N. Pfisterer, “Models for stray light analysis,” Opt. Photon. News 22(10), 16–17 (2011).
    [Crossref]
  11. M. Ryabkova, V. Karaev, J. Guo, and Y. Titchenko, “A review of wave spectrum models as applied to the problem of radar probing of the sea surface,” J. Geophys. Res. Oceans 124, 7104–7134 (2019).
    [Crossref]
  12. J. Tessendorf, “Simulating ocean water,” in SIG-GRAPH’99 Course Note (2001).
  13. J. Schmidt, Numerical Simulation of Optical Wave Propagation with Example in MATLAB (SPIE, 2010).
  14. A. Belmonte, “Feasibility study for the simulation of beam propagation: consideration of coherent lidar performance,” Appl. Opt. 39, 5426–5445 (2000).
    [Crossref]
  15. F. Schwenger and K. Braesicke, “Simulation of laser speckle patterns generated by random rough surfaces,” Proc. SPIE 11406, 1140609 (2020).
    [Crossref]
  16. E. Kayahan, O. Gundogdu, F. Hacizade, and H. Nasibov, “Autocorrelation analysis of spectral dependency of surface roughness speckle patterns,” in International Symposium Optomechatronic Technology (ISOT) (2009), pp. 235–240.

2020 (1)

F. Schwenger and K. Braesicke, “Simulation of laser speckle patterns generated by random rough surfaces,” Proc. SPIE 11406, 1140609 (2020).
[Crossref]

2019 (2)

M. Ryabkova, V. Karaev, J. Guo, and Y. Titchenko, “A review of wave spectrum models as applied to the problem of radar probing of the sea surface,” J. Geophys. Res. Oceans 124, 7104–7134 (2019).
[Crossref]

B. Eberle, W. T. Kinerk, M. Koerber, J. Öhgren, G. Ritt, C. N. Santos, B. Schwarz, O. Steinvall, S. M. Tipper, M. Vandewal, and C. L. Westgate, “NATO SET-249 joint measurement campaign on laser dazzle effects in airborne scenarios,” Proc. SPIE 11161, 111610C (2019).
[Crossref]

2017 (1)

J.-F. Daigle, D. Pudo, F. Théberge, and M. Châteauneuf, “Laser safety evaluation for high-energy laser interaction with solids,” Opt. Eng. 56, 026106 (2017).
[Crossref]

2014 (1)

Z. Song, J. Qin, J. Qu, J. Song, W. Zhang, Y. Shi, T. Zhang, X. Xue, R. Zhang, H. Zhang, Z. Zhang, and X. Wu, “A systematic investigation of the factors affecting the optical properties of near infrared transmitting cool non-white coatings,” Sol. Energy Mater. Sol. Cells 125,206–214 (2014).
[Crossref]

2011 (1)

R. N. Pfisterer, “Models for stray light analysis,” Opt. Photon. News 22(10), 16–17 (2011).
[Crossref]

2000 (1)

Bass, M.

M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, Handbook of Optics (McGraw-Hill, 1995), Vol. II.

Belmonte, A.

Braesicke, K.

F. Schwenger and K. Braesicke, “Simulation of laser speckle patterns generated by random rough surfaces,” Proc. SPIE 11406, 1140609 (2020).
[Crossref]

Châteauneuf, M.

J.-F. Daigle, D. Pudo, F. Théberge, and M. Châteauneuf, “Laser safety evaluation for high-energy laser interaction with solids,” Opt. Eng. 56, 026106 (2017).
[Crossref]

Daigle, J.-F.

J.-F. Daigle, D. Pudo, F. Théberge, and M. Châteauneuf, “Laser safety evaluation for high-energy laser interaction with solids,” Opt. Eng. 56, 026106 (2017).
[Crossref]

Eberle, B.

B. Eberle, W. T. Kinerk, M. Koerber, J. Öhgren, G. Ritt, C. N. Santos, B. Schwarz, O. Steinvall, S. M. Tipper, M. Vandewal, and C. L. Westgate, “NATO SET-249 joint measurement campaign on laser dazzle effects in airborne scenarios,” Proc. SPIE 11161, 111610C (2019).
[Crossref]

Gundogdu, O.

E. Kayahan, O. Gundogdu, F. Hacizade, and H. Nasibov, “Autocorrelation analysis of spectral dependency of surface roughness speckle patterns,” in International Symposium Optomechatronic Technology (ISOT) (2009), pp. 235–240.

Guo, J.

M. Ryabkova, V. Karaev, J. Guo, and Y. Titchenko, “A review of wave spectrum models as applied to the problem of radar probing of the sea surface,” J. Geophys. Res. Oceans 124, 7104–7134 (2019).
[Crossref]

Hacizade, F.

E. Kayahan, O. Gundogdu, F. Hacizade, and H. Nasibov, “Autocorrelation analysis of spectral dependency of surface roughness speckle patterns,” in International Symposium Optomechatronic Technology (ISOT) (2009), pp. 235–240.

Ho, C. Y.

Y. S. Touloukian, R. W. Powell, C. Y. Ho, and M. C. Nicolaou, Thermal Diffusivity—Thermophysical Properties of Matter (IFI/Plenum, 1973), Vol. 10.

Karaev, V.

M. Ryabkova, V. Karaev, J. Guo, and Y. Titchenko, “A review of wave spectrum models as applied to the problem of radar probing of the sea surface,” J. Geophys. Res. Oceans 124, 7104–7134 (2019).
[Crossref]

Kayahan, E.

E. Kayahan, O. Gundogdu, F. Hacizade, and H. Nasibov, “Autocorrelation analysis of spectral dependency of surface roughness speckle patterns,” in International Symposium Optomechatronic Technology (ISOT) (2009), pp. 235–240.

Kinerk, W. T.

B. Eberle, W. T. Kinerk, M. Koerber, J. Öhgren, G. Ritt, C. N. Santos, B. Schwarz, O. Steinvall, S. M. Tipper, M. Vandewal, and C. L. Westgate, “NATO SET-249 joint measurement campaign on laser dazzle effects in airborne scenarios,” Proc. SPIE 11161, 111610C (2019).
[Crossref]

Koerber, M.

B. Eberle, W. T. Kinerk, M. Koerber, J. Öhgren, G. Ritt, C. N. Santos, B. Schwarz, O. Steinvall, S. M. Tipper, M. Vandewal, and C. L. Westgate, “NATO SET-249 joint measurement campaign on laser dazzle effects in airborne scenarios,” Proc. SPIE 11161, 111610C (2019).
[Crossref]

Nasibov, H.

E. Kayahan, O. Gundogdu, F. Hacizade, and H. Nasibov, “Autocorrelation analysis of spectral dependency of surface roughness speckle patterns,” in International Symposium Optomechatronic Technology (ISOT) (2009), pp. 235–240.

Nicolaou, M. C.

Y. S. Touloukian, R. W. Powell, C. Y. Ho, and M. C. Nicolaou, Thermal Diffusivity—Thermophysical Properties of Matter (IFI/Plenum, 1973), Vol. 10.

Öhgren, J.

B. Eberle, W. T. Kinerk, M. Koerber, J. Öhgren, G. Ritt, C. N. Santos, B. Schwarz, O. Steinvall, S. M. Tipper, M. Vandewal, and C. L. Westgate, “NATO SET-249 joint measurement campaign on laser dazzle effects in airborne scenarios,” Proc. SPIE 11161, 111610C (2019).
[Crossref]

Pfisterer, R. N.

R. N. Pfisterer, “Models for stray light analysis,” Opt. Photon. News 22(10), 16–17 (2011).
[Crossref]

Powell, R. W.

Y. S. Touloukian, R. W. Powell, C. Y. Ho, and M. C. Nicolaou, Thermal Diffusivity—Thermophysical Properties of Matter (IFI/Plenum, 1973), Vol. 10.

Pudo, D.

J.-F. Daigle, D. Pudo, F. Théberge, and M. Châteauneuf, “Laser safety evaluation for high-energy laser interaction with solids,” Opt. Eng. 56, 026106 (2017).
[Crossref]

Qin, J.

Z. Song, J. Qin, J. Qu, J. Song, W. Zhang, Y. Shi, T. Zhang, X. Xue, R. Zhang, H. Zhang, Z. Zhang, and X. Wu, “A systematic investigation of the factors affecting the optical properties of near infrared transmitting cool non-white coatings,” Sol. Energy Mater. Sol. Cells 125,206–214 (2014).
[Crossref]

Qu, J.

Z. Song, J. Qin, J. Qu, J. Song, W. Zhang, Y. Shi, T. Zhang, X. Xue, R. Zhang, H. Zhang, Z. Zhang, and X. Wu, “A systematic investigation of the factors affecting the optical properties of near infrared transmitting cool non-white coatings,” Sol. Energy Mater. Sol. Cells 125,206–214 (2014).
[Crossref]

Ritt, G.

B. Eberle, W. T. Kinerk, M. Koerber, J. Öhgren, G. Ritt, C. N. Santos, B. Schwarz, O. Steinvall, S. M. Tipper, M. Vandewal, and C. L. Westgate, “NATO SET-249 joint measurement campaign on laser dazzle effects in airborne scenarios,” Proc. SPIE 11161, 111610C (2019).
[Crossref]

Ryabkova, M.

M. Ryabkova, V. Karaev, J. Guo, and Y. Titchenko, “A review of wave spectrum models as applied to the problem of radar probing of the sea surface,” J. Geophys. Res. Oceans 124, 7104–7134 (2019).
[Crossref]

Santos, C. N.

B. Eberle, W. T. Kinerk, M. Koerber, J. Öhgren, G. Ritt, C. N. Santos, B. Schwarz, O. Steinvall, S. M. Tipper, M. Vandewal, and C. L. Westgate, “NATO SET-249 joint measurement campaign on laser dazzle effects in airborne scenarios,” Proc. SPIE 11161, 111610C (2019).
[Crossref]

Schmidt, J.

J. Schmidt, Numerical Simulation of Optical Wave Propagation with Example in MATLAB (SPIE, 2010).

Schwarz, B.

B. Eberle, W. T. Kinerk, M. Koerber, J. Öhgren, G. Ritt, C. N. Santos, B. Schwarz, O. Steinvall, S. M. Tipper, M. Vandewal, and C. L. Westgate, “NATO SET-249 joint measurement campaign on laser dazzle effects in airborne scenarios,” Proc. SPIE 11161, 111610C (2019).
[Crossref]

Schwenger, F.

F. Schwenger and K. Braesicke, “Simulation of laser speckle patterns generated by random rough surfaces,” Proc. SPIE 11406, 1140609 (2020).
[Crossref]

Shi, Y.

Z. Song, J. Qin, J. Qu, J. Song, W. Zhang, Y. Shi, T. Zhang, X. Xue, R. Zhang, H. Zhang, Z. Zhang, and X. Wu, “A systematic investigation of the factors affecting the optical properties of near infrared transmitting cool non-white coatings,” Sol. Energy Mater. Sol. Cells 125,206–214 (2014).
[Crossref]

Song, J.

Z. Song, J. Qin, J. Qu, J. Song, W. Zhang, Y. Shi, T. Zhang, X. Xue, R. Zhang, H. Zhang, Z. Zhang, and X. Wu, “A systematic investigation of the factors affecting the optical properties of near infrared transmitting cool non-white coatings,” Sol. Energy Mater. Sol. Cells 125,206–214 (2014).
[Crossref]

Song, Z.

Z. Song, J. Qin, J. Qu, J. Song, W. Zhang, Y. Shi, T. Zhang, X. Xue, R. Zhang, H. Zhang, Z. Zhang, and X. Wu, “A systematic investigation of the factors affecting the optical properties of near infrared transmitting cool non-white coatings,” Sol. Energy Mater. Sol. Cells 125,206–214 (2014).
[Crossref]

Steinvall, O.

B. Eberle, W. T. Kinerk, M. Koerber, J. Öhgren, G. Ritt, C. N. Santos, B. Schwarz, O. Steinvall, S. M. Tipper, M. Vandewal, and C. L. Westgate, “NATO SET-249 joint measurement campaign on laser dazzle effects in airborne scenarios,” Proc. SPIE 11161, 111610C (2019).
[Crossref]

Tessendorf, J.

J. Tessendorf, “Simulating ocean water,” in SIG-GRAPH’99 Course Note (2001).

Théberge, F.

J.-F. Daigle, D. Pudo, F. Théberge, and M. Châteauneuf, “Laser safety evaluation for high-energy laser interaction with solids,” Opt. Eng. 56, 026106 (2017).
[Crossref]

Tipper, S. M.

B. Eberle, W. T. Kinerk, M. Koerber, J. Öhgren, G. Ritt, C. N. Santos, B. Schwarz, O. Steinvall, S. M. Tipper, M. Vandewal, and C. L. Westgate, “NATO SET-249 joint measurement campaign on laser dazzle effects in airborne scenarios,” Proc. SPIE 11161, 111610C (2019).
[Crossref]

Titchenko, Y.

M. Ryabkova, V. Karaev, J. Guo, and Y. Titchenko, “A review of wave spectrum models as applied to the problem of radar probing of the sea surface,” J. Geophys. Res. Oceans 124, 7104–7134 (2019).
[Crossref]

Touloukian, Y. S.

Y. S. Touloukian, R. W. Powell, C. Y. Ho, and M. C. Nicolaou, Thermal Diffusivity—Thermophysical Properties of Matter (IFI/Plenum, 1973), Vol. 10.

Van Stryland, E. W.

M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, Handbook of Optics (McGraw-Hill, 1995), Vol. II.

Vandewal, M.

B. Eberle, W. T. Kinerk, M. Koerber, J. Öhgren, G. Ritt, C. N. Santos, B. Schwarz, O. Steinvall, S. M. Tipper, M. Vandewal, and C. L. Westgate, “NATO SET-249 joint measurement campaign on laser dazzle effects in airborne scenarios,” Proc. SPIE 11161, 111610C (2019).
[Crossref]

Westgate, C. L.

B. Eberle, W. T. Kinerk, M. Koerber, J. Öhgren, G. Ritt, C. N. Santos, B. Schwarz, O. Steinvall, S. M. Tipper, M. Vandewal, and C. L. Westgate, “NATO SET-249 joint measurement campaign on laser dazzle effects in airborne scenarios,” Proc. SPIE 11161, 111610C (2019).
[Crossref]

Williams, D. R.

M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, Handbook of Optics (McGraw-Hill, 1995), Vol. II.

Wolfe, W. L.

M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, Handbook of Optics (McGraw-Hill, 1995), Vol. II.

Wu, X.

Z. Song, J. Qin, J. Qu, J. Song, W. Zhang, Y. Shi, T. Zhang, X. Xue, R. Zhang, H. Zhang, Z. Zhang, and X. Wu, “A systematic investigation of the factors affecting the optical properties of near infrared transmitting cool non-white coatings,” Sol. Energy Mater. Sol. Cells 125,206–214 (2014).
[Crossref]

Xue, X.

Z. Song, J. Qin, J. Qu, J. Song, W. Zhang, Y. Shi, T. Zhang, X. Xue, R. Zhang, H. Zhang, Z. Zhang, and X. Wu, “A systematic investigation of the factors affecting the optical properties of near infrared transmitting cool non-white coatings,” Sol. Energy Mater. Sol. Cells 125,206–214 (2014).
[Crossref]

Zhang, H.

Z. Song, J. Qin, J. Qu, J. Song, W. Zhang, Y. Shi, T. Zhang, X. Xue, R. Zhang, H. Zhang, Z. Zhang, and X. Wu, “A systematic investigation of the factors affecting the optical properties of near infrared transmitting cool non-white coatings,” Sol. Energy Mater. Sol. Cells 125,206–214 (2014).
[Crossref]

Zhang, R.

Z. Song, J. Qin, J. Qu, J. Song, W. Zhang, Y. Shi, T. Zhang, X. Xue, R. Zhang, H. Zhang, Z. Zhang, and X. Wu, “A systematic investigation of the factors affecting the optical properties of near infrared transmitting cool non-white coatings,” Sol. Energy Mater. Sol. Cells 125,206–214 (2014).
[Crossref]

Zhang, T.

Z. Song, J. Qin, J. Qu, J. Song, W. Zhang, Y. Shi, T. Zhang, X. Xue, R. Zhang, H. Zhang, Z. Zhang, and X. Wu, “A systematic investigation of the factors affecting the optical properties of near infrared transmitting cool non-white coatings,” Sol. Energy Mater. Sol. Cells 125,206–214 (2014).
[Crossref]

Zhang, W.

Z. Song, J. Qin, J. Qu, J. Song, W. Zhang, Y. Shi, T. Zhang, X. Xue, R. Zhang, H. Zhang, Z. Zhang, and X. Wu, “A systematic investigation of the factors affecting the optical properties of near infrared transmitting cool non-white coatings,” Sol. Energy Mater. Sol. Cells 125,206–214 (2014).
[Crossref]

Zhang, Z.

Z. Song, J. Qin, J. Qu, J. Song, W. Zhang, Y. Shi, T. Zhang, X. Xue, R. Zhang, H. Zhang, Z. Zhang, and X. Wu, “A systematic investigation of the factors affecting the optical properties of near infrared transmitting cool non-white coatings,” Sol. Energy Mater. Sol. Cells 125,206–214 (2014).
[Crossref]

Appl. Opt. (1)

J. Geophys. Res. Oceans (1)

M. Ryabkova, V. Karaev, J. Guo, and Y. Titchenko, “A review of wave spectrum models as applied to the problem of radar probing of the sea surface,” J. Geophys. Res. Oceans 124, 7104–7134 (2019).
[Crossref]

Opt. Eng. (1)

J.-F. Daigle, D. Pudo, F. Théberge, and M. Châteauneuf, “Laser safety evaluation for high-energy laser interaction with solids,” Opt. Eng. 56, 026106 (2017).
[Crossref]

Opt. Photon. News (1)

R. N. Pfisterer, “Models for stray light analysis,” Opt. Photon. News 22(10), 16–17 (2011).
[Crossref]

Proc. SPIE (2)

B. Eberle, W. T. Kinerk, M. Koerber, J. Öhgren, G. Ritt, C. N. Santos, B. Schwarz, O. Steinvall, S. M. Tipper, M. Vandewal, and C. L. Westgate, “NATO SET-249 joint measurement campaign on laser dazzle effects in airborne scenarios,” Proc. SPIE 11161, 111610C (2019).
[Crossref]

F. Schwenger and K. Braesicke, “Simulation of laser speckle patterns generated by random rough surfaces,” Proc. SPIE 11406, 1140609 (2020).
[Crossref]

Sol. Energy Mater. Sol. Cells (1)

Z. Song, J. Qin, J. Qu, J. Song, W. Zhang, Y. Shi, T. Zhang, X. Xue, R. Zhang, H. Zhang, Z. Zhang, and X. Wu, “A systematic investigation of the factors affecting the optical properties of near infrared transmitting cool non-white coatings,” Sol. Energy Mater. Sol. Cells 125,206–214 (2014).
[Crossref]

Other (9)

LIA, ANSI Z136.1 – Safe Use of Lasers (Laser Institute of America, 2014).

European Union, “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 exposure of workers to risks arising from physical agents (artificial optical radiation) (19th individual Direct),” (2019).

Y. S. Touloukian, R. W. Powell, C. Y. Ho, and M. C. Nicolaou, Thermal Diffusivity—Thermophysical Properties of Matter (IFI/Plenum, 1973), Vol. 10.

Steelforge, “Melting point of metals & alloys,” https://www.steelforge.com/literature/metal-melting-ranges/ .

Engineering ToolBox, “Thermal conductivity of metals, metallic elements and alloys,” https://www.engineeringtoolbox.com/thermal-conductivity-metals-d_858.html .

M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, Handbook of Optics (McGraw-Hill, 1995), Vol. II.

E. Kayahan, O. Gundogdu, F. Hacizade, and H. Nasibov, “Autocorrelation analysis of spectral dependency of surface roughness speckle patterns,” in International Symposium Optomechatronic Technology (ISOT) (2009), pp. 235–240.

J. Tessendorf, “Simulating ocean water,” in SIG-GRAPH’99 Course Note (2001).

J. Schmidt, Numerical Simulation of Optical Wave Propagation with Example in MATLAB (SPIE, 2010).

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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Figures (24)

Fig. 1.
Fig. 1. Photographs of the samples. For details see Table 1.
Fig. 2.
Fig. 2. Sketch of the experimental setup for the low-power laser reflection measurements.
Fig. 3.
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.
Fig. 4.
Fig. 4. Sketch of the laser head. FC, fiber collimator; DBS, dichroic beam splitter; M, mirror.
Fig. 5.
Fig. 5. Horizontal (left) and vertical (right) profiles for the reflection at the unprotected gold mirror with logarithmic $y$ axis. The blue curves show the profiles through $({x_0},\;{y_0})$; the orange curve shows the fit with function and a central Gaussian.
Fig. 6.
Fig. 6. Horizontal (left) and vertical (right) profiles for the reflection at the aluminum sample (A1) with logarithmic $y$ axis. The blue curves show the profiles through $({x_0},\;{y_0})$; the orange curve shows the fit with function without a central Gaussian.
Fig. 7.
Fig. 7. Horizontal (left) and vertical (right) profiles for the reflection at the aluminum sample (A2) with the logarithmic $y$ axis. The blue curves show the profiles through $({x_0},\;{y_0})$; the orange curve shows the fit with function without a central Gaussian.
Fig. 8.
Fig. 8. Horizontal (left) and vertical (right) profiles for the reflection at the tinplate sample (TP) with the logarithmic $y$ axis. The blue curves show the profiles through $({x_0},\;{y_0})$; the orange curve shows the fit with function and a central Gaussian.
Fig. 9.
Fig. 9. Horizontal (left) and vertical (right) profiles for the reflection at the steel plate sample (CS) with the logarithmic $y$ axis. The blue curves show the profiles through $({x_0},\;{y_0})$; the orange curve shows the fit with function without a central Gaussian.
Fig. 10.
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 measurements, the sample is visible in the camera image for 2 µm within the orange box denoted by Target.
Fig. 11.
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 3D plot of the ROI. The two lower images show the averaged horizontal and vertical profiles and the respective ABg fits.
Fig. 12.
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 3D plot of the ROI. The two lower images show the averaged horizontal and vertical profiles and the respective ABg fits.
Fig. 13.
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.
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.
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.
Fig. 16.
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.
Fig. 17.
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 2 µm 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.
Fig. 18.
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.
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).
Fig. 20.
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.
Fig. 21.
Fig. 21. Measured reflected intensity from tinplate at three different times after the melting of the target began.
Fig. 22.
Fig. 22. Normalized averaged ACF for the $x$ axis (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, respectively). 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.
Fig. 23.
Fig. 23. Simulated intensity at 2 m distance from the target. Two different realizations of the phase screen were done.
Fig. 24.
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 (${\rm W}/{{\rm m}^2}$).

Tables (14)

Tables Icon

Table 1. Mechanical and Thermodynamic Properties of the Samples

Tables Icon

Table 2. Low-Power Experiments: Parameters of the Camera and the Attached Lens and Filter

Tables Icon

Table 3. Parameters of the Laser Sources Used for the Experiments

Tables Icon

Table 4. High-Power Experiments: Parameters of the Cameras and their Attached Lenses and Filters

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Table 5. 1/e Widths of the Total Fit and 1/e Widths of the Scattering Part for the Investigated Samplesa

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Table 6. Radiant Flux for a FoV of 62.4 mrad and the Derived Power Distribution

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Table 7. Radiant Flux for a FoV of 14.3 mrad and the Derived Power Distribution

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Table 8. Widths of the Reflection Distributions Obtained by the Different Methods for 1 µm

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Table 9. Widths of the Reflection Distributions Obtained by the Different Methods for 2 µm

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Table 10. Measured and Predicted PIB and Calculated Power Distributions for 1 µm

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Table 11. Measured PIB for 2 µm

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Table 12. Dedicated Reflection Coefficients for the Specular and ABg-Scatter Component for 1070 nm

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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

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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

Equations (20)

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w S = w 0 1 + ( d z R a y l e i g h ) 2 2.0 m m .
I ( x , y ) = ( I s p e c . ( x , y ) + I s c a t . ( x , y ) + I o f f s e t ) cos θ d 2 + x 2 + y 2 .
I s p e c . = I 0 , s p e c . e ( x x 0 ) 2 + ( y y 0 ) 2 c 2 .
I s c a t . = I 0 , s c a t . B x B x + | x x 0 d | g x B y B y + | y y 0 d | g y .
P R = P in R S
ρ F o V = Φ F o V P R .
P R = P s p e c . + P A B g + P L .
L L P R Φ F o V 2 π .
Φ L , 64.4 A 1 = L L π r e 2 d 2 = L L π ( 5 m m ) 2 ( 16 c m ) 2 38 µ W , Φ L , 14.3 A 1 = L L π ( 5 m m ) 2 ( 70 c m ) 2 2.1 µ W .
ν A B g , F o V = Φ A B g , F o V P A B g .
p A B g = P A B g P R .
p A B g ρ F o V ν A B g , F o V .
P A B g = Φ 62.4 Φ 14.3 ν A B g , 62.4 ν A B g , 14.3
P s p e c . = Φ F o V ν A B g , F o V P A B g a n d P L = P R P s p e c . P A B g .
a 1 b + | x x 0 d SS | g x 1 ( 1 + | x x 0 d SS | 2 ) 3 / 2 ,
w D 4 σ = 2 2 P ( p ) ( P ( p ) P m a x ) 2 P ( p ) .
r R = d tan 2 β .
P h ( k ) = A exp ( 1 / ( k L ) 2 ) k 4 exp ( k 2 l 2 ) | k w | 2 ,
h ( x , y ) = F T [ ( ε 1 + i ε 2 ) P h ( k ) ] ,
Δ φ = 2 2 π λ ( h h 0 ) .

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