Abstract

This paper presents a method of estimation of the nominal ocular hazard distance (NOHD) and the nominal ocular dazzle distance (NODD) for multibeam laser radiation. For the analysis, laser beams propagating in the same optical path (overlapping) but with different wavelength, power, and divergences in two perpendicular planes were assumed. To the authors’ best knowledge, such a comprehensive analysis of multiple beams, considering the above parameters, is being presented for the first time. The dazzling possibilities described thus far assumed a single beam of radiation with a circular cross-section. This article also presents the calculation results of the NOHD and the NODD values for three laser beams with wavelengths in the red, green, and blue radiation spectrum with assumed parameters. Similar calculations were also made for a commercial laser source with potential use for laser dazzling. The presented analysis did not take into account the attenuation of radiation by the atmosphere. Moreover, the study provides recommendations on how to design effective, but safe, multiwavelength laser dazzlers.

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

Corrections

Jaroslaw Mlynczak, Krzysztof Kopczynski, Miron Kaliszewski, and Maksymilian Wlodarski, "Estimation of nominal ocular hazard distance and nominal ocular dazzle distance for multibeam laser radiation: publisher’s note," Appl. Opt. 60, 6849-6849 (2021)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-60-23-6849

1. INTRODUCTION

Death of the enemy should be a last resort in military or preventive actions carried out by the military or other state services. If possible, the opponent should be overpowered and kept alive. One of the ways to neutralize an opponent in this way is to induce a glare effect on him, which disables his ability to carry out his tasks effectively. Thus, dazzling allows one to disrupt the opponent’s activity and, as a result, overpower him while keeping him alive. This makes it possible to minimize fatalities, protect the innocent, and limit collateral damage [1]. There are already available many commercial laser dazzlers mainly emitting radiation at the green wavelength. However, there are also devices emitting violet, blue, or red wavelengths that can be used as laser dazzlers [2]. The available dazzlers can be handheld or vehicle-mountable and can be used not only to dazzle people but also birds to scare them away from airport areas [3].

When analyzing the possibilities of dazzling caused by laser radiation, one cannot forget about the potential damage to the human eye. There is an increasing amount of news information and scientific articles about the reckless use of laser radiation emitted mainly by laser pointers, which are becoming increasingly available on the market. Currently, the so-called laser pointers emitting green, red, or blue radiation with a power of up to several W can be easily purchased using the Internet [4]. Such devices are especially dangerous when in the hands of children who, unknowingly, may hurt themselves and others. An extensive review of the literature on this subject is presented in [5]. Even toys for children that emit laser radiation do not necessarily meet the safety requirements [6]. The increasing number of incidents of illuminating airplanes with lasers and cases of damage to the eyesight of pilots should also be mentioned [7]. Such situations are particularly dangerous because they may lead to air crashes and death. The potential for eye damage has been already defined in the relevant standards [8,9].

One of the basic parameters of a dazzler is the distance range, within which it can produce a glare effect. In the case of a divergent laser beam (the most common situation), this range extends from the radiation source to the nominal ocular dazzle distance (NODD) [10]. In addition to the dazzling range, one should also bear in mind the distance range where the eye damage may occur, from the radiation source to the nominal ocular hazard distance (NOHD). The knowledge of the two mentioned parameters allows potentially safe use of a dazzler, which can cause glare without damaging the human eye. Their calculation for a single beam has already been described in the literature [11].

It is relatively easy to counteract dazzling caused by one expected wavelength. This can be done, for example, by using appropriate attenuating filters. Such filters suppress the radiation responsible for the glare effect and at the same time allows the remaining radiation in the visible range to pass. This residual radiation must be sufficient to maintain an adequate level of vision so that certain activities can still be performed. There are commercially available laser protection spectacles that can attenuate the green, blue, and near-infrared radiation [12]; however, they still transmit some radiation mainly in the red wavelength range. Thus, the chance to dazzle an adversary who wears them still exist. Moreover, to limit the possibilities of counteracting glare, several radiation beams can be used in different wavelength ranges. By using three beams in the red, green, and blue band of radiation, potential filters to suppress this radiation would also significantly reduce the level of vision, effectively preventing a person using such filters from performing properly. Therefore, it becomes reasonable to use many beams of radiation for dazzling. Thus, there is a need to develop a simple model for the analysis of multibeam radiation with different wavelengths in the band of visible light. The paper presents a simple way to determine the NODD and the NOHD for such radiation. Laser beams with homogeneous and constant power distribution in the cross-section of a beam, the so-called “top-hat,” propagating in the same optical path, with different power, different wavelengths, and different divergences in two perpendicular planes were considered for the analysis. The presented analysis did not take into account the attenuation of radiation by the atmosphere.

2. DERIVING OF NOHD FOR MULTIBEAM RADIATION

The nominal ocular hazard distance (NOHD) is defined as the distance from a radiation source at which eye exposure to laser radiation equals the maximum permissible exposure (MPE). The MPE has been defined in the relevant standards [8,9] based on research and case studies, for various ranges of wavelength and exposure times. Thus, determination of the NOHD for a single laser beam with a defined wavelength is a simple task. For the given beam power $P$, the divergence $\emptyset$ (in the case of a beam with circular cross-section), and the beam width at the output aperture $w$, it can be expressed using the following equation:

$${\rm NOHD} = \frac{{\sqrt {\frac{{4P}}{{\pi {\rm MPE}}}} - w}}{{tg\emptyset}}.$$

The problem becomes more complex when dealing with several laser beams with different wavelengths, power, and elliptical cross-sections. If the radiation beams belong to different wavelength ranges but affect the same tissue, they should be treated as additive. A typical example can be radiation at a wavelength of 1064 and 532 nm. Both wavelengths are transmitted to the interior of the eye and focused onto the retina, which is affected due to the absorption. If the beams do not affect the same tissue, they should be treated independently. Here, a typical example can be radiation with a wavelength of 532 and 1500 nm. The former affects the retina; the latter affects the cornea because it is absorbed by it and does not reach the retina.

In the case of radiation used for dazzling, it should be in the wavelength range that is visible to the human eye, i.e., 400–700 nm. Due to the fact that radiation in this range affects the same tissue, specifically the retina of the eye, it should be treated additively.

In the case of the additivity of the beams, each of the beams contribute to a specific effect, to an extent that can be defined as the ratio of the exposure level to the level necessary for the given effect to occur for a given wavelength. Therefore, to induce this effect, the sum of the ratios defined in this way should be equal to 1. In the case of the effect of eye damage, the sum of the ratios of the exposure level El to the MPE for individual beams should be equal to 1. For $n$ beams with different wavelengths, this can be expressed by the equation

$$\frac{{{{{\rm El}}_1}}}{{{{{\rm MPE}}_1}}} + \frac{{{{{\rm El}}_2}}}{{{{{\rm MPE}}_2}}} + \ldots + \frac{{{{{\rm El}}_n}}}{{{{{\rm MPE}}_n}}} = 1.$$

The exposure level should be expressed in the same units as the MPE, which is expressed in ${\rm J}/{{\rm cm}^2}$ or ${\rm W}/{{\rm cm}^2}$ in accordance with the relevant standards [8,9]. Therefore, knowing the power or energy of the emitted radiation, it becomes necessary to determine the cross-sectional area of the laser beam, at a distance from the radiation source where the exposure takes place. For beams with an elliptical cross-section, it can be done based on their divergence in two perpendicular planes. The diagram of three beams with an elliptical cross-section is shown in Fig. 1.

 figure: Fig. 1.

Fig. 1. Diagram of three beams with different elliptical cross-section.

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The area of the cross-section of a single beam $S$ at exposure distance $d$ can be expressed by the following equation:

$$\!\!\!S = \frac{\pi}{4}ab = \frac{\pi}{4}\left({2d \cdot tg\frac{{{\phi _x}}}{2} + {w_x}} \!\right) \cdot \left({2d \cdot tg\frac{{{\phi _y}}}{2} + {w_y}}\! \right),\!$$
where $a$ is the beam diameter in the $x$ plane, $b$ is the beam diameter in the $y$ plane, $d$ is the distance from the output aperture to the exposure place, ${\phi _x}$ is the angle of divergence in the $x$ plane, ${\phi _y}$ is the angle of divergence in the $y$ plane, ${w_x}$ is the beam diameter at the output aperture in the $x$ plane, and ${w_y}$ is the beam diameter at the output aperture in the $y$ plane.

In most cases, the beam diameter at the exit aperture is small compared with the diameter of the beam at the exposure site, so it can be neglected. Such neglecting of the beam diameter at the exit aperture increases the NOHD, which is advantageous from a safety point of view. Thus, the Eq. (3) can be expressed as

$$S \cong \pi {d^2} \cdot tg\frac{{{\phi _x}}}{2} \cdot tg\frac{{{\phi _y}}}{2}.$$

When the power of the emitted radiation is known for each beam, Eq. (2) can be written as follows:

$$\frac{{\frac{{{P_1}}}{{\pi {d^2} \cdot tg\frac{{{\phi _{x1}}}}{2} \cdot tg\frac{{{\phi _{y1}}}}{2}}}}}{{{{{\rm MPE}}_1}}} + \frac{{\frac{{{P_2}}}{{\pi {d^2} \cdot tg\frac{{{\phi _{x2}}}}{2} \cdot tg\frac{{{\phi _{y2}}}}{2}}}}}{{{{{\rm MPE}}_2}}} + \ldots + \frac{{\frac{{{P_n}}}{{\pi {d^2} \cdot tg\frac{{{\phi _{{xn}}}}}{2} \cdot tg\frac{{{\phi _{{yn}}}}}{2}}}}}{{{{{\rm MPE}}_n}}} \cong 1.$$

It is tempting to assume that the exposure time of potential adversaries to visible radiation is limited to natural aversion to too intense radiation. It is usually related to eyelid closure time, which is estimated for approximately 0.25 s. For such exposure time, the MPE value for all wavelengths in the range of 400–700 nm is the same and is equal to ${25.46}\;{{\rm W/m}^2}$. However, for laser dazzlers, applied in a hostile engagement scenario, a more appropriate assumption is persistent viewing when the person being dazzled intentionally looks at the dazzle beam for a relatively long time. It is therefore appropriate to use the MPE value that relates to exposures from 10 to 30,000 s. For this exposure time, according to the standard [8], the MPE is wavelength dependent.

Thus, Eq. (5) can be written as follows:

$$\frac{1}{{\pi {d^2}}}\left({\frac{{{P_1}}}{{{{{\rm MPE}}_1}tg\frac{{{\phi _{x1}}}}{2} \cdot tg\frac{{{\phi _{y1}}}}{2}}} + \frac{{{P_2}}}{{{{{\rm MPE}}_2}tg\frac{{{\phi _{x2}}}}{2} \cdot tg\frac{{{\phi _{y2}}}}{2}}} + \ldots + \frac{{{P_n}}}{{{{{\rm MPE}}_n}tg\frac{{{\phi _{{xn}}}}}{2} \cdot tg\frac{{{\phi _{{yn}}}}}{2}}}} \right) \cong 1.$$

Knowing that $d$ is identical to the NOHD, Eq. (6) can be transformed to

$${\rm NOHD} \cong \sqrt {\frac{1}{\pi}\left({\frac{{{P_1}}}{{{{{\rm MPE}}_1}tg\frac{{{\phi _{x1}}}}{2} \cdot tg\frac{{{\phi _{y1}}}}{2}}} + \frac{{{P_2}}}{{{{{\rm MPE}}_2}tg\frac{{{\phi _{x2}}}}{2} \cdot tg\frac{{{\phi _{y2}}}}{2}}} + \ldots + \frac{{{P_n}}}{{{{{\rm MPE}}_n}tg\frac{{{\phi _{{xn}}}}}{2} \cdot tg\frac{{{\phi _{{yn}}}}}{2}}}} \right)} .$$

For small divergence angles, which for most laser sources are up to several milliradians, the $tg\phi = \phi$ approximation can be introduced; then, Eq. (7) can be simplified to

$$\begin{split}&{\rm NOHD} \cong 2 \\&\cdot\sqrt {\frac{1}{\pi}\left(\!{\frac{{{P_1}}}{{{{{\rm MPE}}_1}{\phi _{x1}}{\phi _{y1}}}} + \frac{{{P_2}}}{{{{{\rm MPE}}_2}{\phi _{x2}}{\phi _{y2}}}} + \ldots + \frac{{{P_n}}}{{{{{\rm MPE}}_n}{\phi _{{xn}}}{\phi _{{yn}}}}}} \!\right)} .\end{split}$$

After calculating the constant values and rounding, we obtain

$$\begin{split}&{\rm NOHD} \cong 1.128 \\& \cdot\sqrt {\frac{{{P_1}}}{{{{{\rm MPE}}_1}{\phi _{x1}}{\phi _{y1}}}} + \frac{{{P_2}}}{{{{{\rm MPE}}_2}{\phi _{x2}}{\phi _{y2}}}} + \ldots + \frac{{{P_n}}}{{{{{\rm MPE}}_n}{\phi _{{xn}}}{\phi _{{yn}}}}}} .\end{split}$$

In order to determine the NOHD expressed in meters, the power of individual beams, expressed in Watts, and their divergence in two perpendicular planes, expressed in radians, should be inserted into the above equation. Further, the values of the MPE should be expressed in ${\rm W} / {\rm m}^2$.

According to the standard [8] for exposure durations of 10 s or longer, the additive photochemical effects (400 to 600 nm) and the additive thermal effects (400 to 1400 nm) shall be assessed independently and the most restrictive value used. However, the laser sources used for dazzling are usually characterized by angular subtense below 1.5 mrad; thus, factor C6 can be assumed equal to 1, and the values of the MPE defined in Table A1 in the standard [8] should be used. In this table, two exposure time ranges from 10s to ${{10}^2}\;{\rm s}$ and ${{10}^2}\;{\rm s}$ to ${{3\cdot 10}^4}\;{\rm s}$ are defined. The second one is the most restrictive for all wavelengths in the range of 400–700 nm for photochemical as well as for thermal effects, and the values of the MPE for this exposure time should be used. Moreover, for this exposure time, there are no different values of the MPE for thermal and photochemical effects.

3. DERIVING OF NODD FOR MULTIBEAM RADIATION

The nominal ocular dazzle distance (NODD) is defined as the distance from the radiation source at which eye exposure to laser radiation is equal to the maximum dazzle exposure (MDE). Here, the additivity of spectral sensitivity of the eye for visible radiation can be assumed again; however, it has not been firmly proven for laser exposure [13,14]. Thus, Eq. (2) can be used to find the NODD, but the MPE should be replaced by the MDE. Equation (5) will then take the form

$$\frac{{\frac{{{P_1}}}{{\pi {d^2} \cdot tg\frac{{{\phi _{x1}}}}{2} \cdot tg\frac{{{\phi _{y1}}}}{2}}}}}{{{{{\rm MDE}}_1}}} + \frac{{\frac{{{P_2}}}{{\pi {d^2} \cdot tg\frac{{{\phi _{x2}}}}{2} \cdot tg\frac{{{\phi _{y2}}}}{2}}}}}{{{{{\rm MDE}}_2}}} + \ldots + \frac{{\frac{{{P_n}}}{{\pi {d^2} \cdot tg\frac{{{\phi _{{xn}}}}}{2} \cdot tg\frac{{{\phi _{{yn}}}}}{2}}}}}{{{{{\rm MDE}}_n}}} \cong 1.$$

Standard ${\rm MDE}_S$ values, for maximum eye sensitivity, for four different dazzle levels (the angular size of the visual field that is obscured within an observer’s field of vision: 2°, 10°, 20°, 40°) and for three ambient luminance levels (night ${0.1}\;{{\rm cd/m}^2}$, dusk ${10}\;{{\rm cd/m}^2}$, day ${1000}\;{{\rm cd/m}^2}$) were proposed for the first time by Williamson and McLin [11]. The dazzle levels are schematically shown in Fig. 2, where the area seen by the observer is marked with blue, and the area obscured by the dazzle effect is marked with green.

The standard ${\rm MDE}_S$ values were determined based on a number of experiments and extensive analysis, taking into account such parameters as the angular subtense of the object, the contrast of the object, the observer’s age, and the eye pigmentation [11]. The values of the above parameters, adopted for the determination of the ${\rm MDE}_S$, are presented in Table 1, and the ${\rm MDE}_S$ values are presented in Table 2.

The above ${\rm MDE}_S$ values were defined for the maximum eye sensitivity, which is for the eye’s photopic sensitivity ${\rm V}(\lambda)$ equal to 1 (for a wavelength of 556.1 nm) [15]. To determine the MDE for other wavelengths, the value from Table 2 should be divided by the appropriate ${\rm V}(\lambda)$ value in accordance with the expression

$${\rm MDE} = \frac{{{{\rm MDE}_{\rm S}}}}{{\rm V}({\lambda} )}.$$

The ${\rm V}(\lambda)$ values for several basic wavelengths, which are used in calculations presented later in this paper, are given in Table 3.

 figure: Fig. 2.

Fig. 2. Four dazzle levels.

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Table 1. Parameters Adopted for the Determination of the ${\rm MDE}_S$ [11]

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Table 2. ${\rm MDE}_S$ Values for Different Dazzle and Ambient Light Levels [11]

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Table 3. ${\rm V}(\lambda)$ Values for Several Basic Wavelengths [15]

Taking the above considerations into account and assuming small angles of divergence of the beams and identifying $d$ with the NODD, Eq. (10) can be transformed as follows:

$${\rm NODD} \cong 2 \sqrt {\frac{1}{\pi}\left({\frac{{{P_1}}}{{{{{\rm MDE}}_1}{\phi _{x1}}{\phi _{y1}}}} + \frac{{{P_2}}}{{{{{\rm MDE}}_2}{\phi _{x2}}{\phi _{y2}}}} + \ldots + \frac{{{P_n}}}{{{{{\rm MDE}}_n}{\phi _{{xn}}}{\phi _{{yn}}}}}} \right)} .$$

After calculating the constant values and rounding, we obtain

$$\begin{split}&{\rm NODD} \cong 1.128 \\&\cdot \sqrt {\frac{{{P_1}}}{{{{{\rm MDE}}_1}{\phi _{x1}}{\phi _{y1}}}} + \frac{{{P_2}}}{{{{{\rm MDE}}_2}{\phi _{x2}}{\phi _{y2}}}} + \ldots + \frac{{{P_n}}}{{{{{\rm MDE}}_n}{\phi _{{xn}}}{\phi _{{yn}}}}}} .\end{split}$$

In order to determine the NODD expressed in meters, the power of individual beams, expressed in Watts, their divergence in two perpendicular planes, expressed in radians, and MDE expressed in ${\rm W}/{{\rm m}^2}$ should be substituted to the above equation. It is worth noting that the values of the ${{\rm MDE}_1},\;{{\rm MDE}_2}, \ldots ,\;{{\rm MDE}_n}$ should be considered for the same ambient light levels and dazzle levels.

4. ANALYSIS OF NOHD AND NODD FOR THREE RADIATION BEAMS

In order to analyze the effect of the additivity of laser beams on the values of the NOHD and the NODD, calculations were performed for three hypothetical radiation sources, with beam parameters presented in Table 4. Wavelengths were selected based on the availability in the market, of simple and small radiation sources such as laser diodes. For all three sources, the same power and same divergence in both perpendicular planes, 1 W and 2 mrad, respectively, were assumed. In Table 4, the values of the MPE for exposure time longer than 100 s according to the standard [8] are also shown.

Using Eq. (8), the NOHD values for the above sources were determined, which were approximately 564 m for the blue source and 178 m for the green and red sources; for all sources simultaneously (taking into account additivity), it was approximately 618 m.

Using Eq. (12), the calculations of the NODD were made. The results of the calculations for four dazzle levels and three ambient light levels are presented graphically in Figs. 36. The highest values of the NODD, determined under the same ambient light levels and dazzle levels, were obtained for the green beam. This is due to the highest value of the eye’s photopic sensitivity (${\rm V}(\lambda) = {0.7181}$) compared with the other beams. The maximum NODD value of over 151 km was obtained for the night conditions and the dazzle level of 2°. The smallest NODD values were obtained for the blue beam for which the ${\rm V}(\lambda)$ coefficient equals only 0.0574. For the dazzle level of 40° and day conditions, the dazzle effect may appear only at distance up to 8 m from the source of this radiation.

The analysis also shows that the highest NODD values are obtained for night conditions and, depending on the beam and the dazzle level, range from approximately 1.7 km for the blue beam and 40° dazzle level to over 151 km for the green beam and 2° dazzle level. In turn, the lowest NODD values are obtained for day conditions, and it ranges from approximately 8 m for the blue beam and 40° dazzle level to approximately 756 m for the green beam and 2° dazzle level.

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Table 4. Parameters of Beams Emitted by Hypothetical Sources and Their MPE

 figure: Fig. 3.

Fig. 3. NODD values for 445 nm beam.

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 figure: Fig. 4.

Fig. 4. NODD values for 520 nm beam.

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 figure: Fig. 5.

Fig. 5. NODD values for 638 nm beam.

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 figure: Fig. 6.

Fig. 6. NODD values for all beams.

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It should also be noted that there are some distance ranges for specific ambient light levels and dazzle levels, where the NOHD is greater than the NODD. It covers the distances where the eye can be damaged without dazzle effect. In this case, the exposure level is high enough to damage the retina of the eye but does not yet cause a dazzle effect due to the low contrast to ambient light and the assumed high dazzle level. These ranges obviously appear for day conditions and high dazzle levels. For the assumed beam parameters, such a situation occurs for day conditions and all dazzle levels for the blue beam and 10°, 20°, and 40° dazzle levels for the green and red beams. For dusk conditions, it occurs again for the blue beam at 10°, 20°, and 40° dazzle levels and for the red beam at 40° dazzle level.

If three beams are analyzed simultaneously and their additivity is taken into account, all the NODD values are increased. The maximum NODD≅177 km, similarly to a single beam, is obtained for night conditions and a dazzle level of 2°. The minimum NODD value of approximately 32 m, occurs again for day conditions and the dazzle level of 40°. The ranges where the NOHD≅618 m is greater than the NODD occurs for day conditions and the dazzle levels of 10°, 20°, and 40° as well as for dusk conditions and dazzle levels of 20° and 40°.

It is also worth noting that the presented analysis did not take into account the attenuation of radiation by the atmosphere; therefore, the NOHD and the NODD values will be lower in real conditions.

The analysis also included calculations of the NOHD and ODD values in function of the power of the emitted radiation for a wavelength of 520 nm and divergence in both perpendicular planes of 2 mrad. Due to the common availability of laser pointers with power up to several mW, on the market, the analysis was limited to this range. Figure 7 shows the results of the NOHD calculations, while Figs. 810 show the results of the NODD calculations for power up to 10 mW. The NOHD value for the power of 10 mW was approximately 18 m. The NODD values for 10 mW power are presented in Table 5.

 figure: Fig. 7.

Fig. 7. NOHD values in the function of beam power for a wavelength of 520 nm and a divergence of 2 mrad.

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 figure: Fig. 8.

Fig. 8. NODD values in the function of beam power for a wavelength of 520 nm, divergence of 2 mrad, and night conditions.

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 figure: Fig. 9.

Fig. 9. NODD values in the function of beam power for a wavelength of 520 nm, divergence of 2 mrad, and dusk conditions.

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 figure: Fig. 10.

Fig. 10. NODD values in the function of beam power for a wavelength of 520 nm, divergence of 2 mrad, and day conditions.

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The analysis shows that the beam of radiation with a wavelength of 520 nm, a divergence of 2 mrad, and a power of 10 mW can damage the eye up to a distance of approximately 18 m, while the distance at which the dazzle effect may occur varies widely depends on the ambient light conditions and the dazzle level that need to be achieved. The highest NODD values are obtained for night conditions, which reach over 15 km for the dazzle level of 2° and decrease to approximately 617 m for the dazzle level of 40°. In turn, the lowest NODD values are obtained for day conditions, which is approx. 76 m for the dazzle level of 2°, but it drops to about 3 m for the dazzle level of 40°. As can be seen from the presented analysis, despite the relatively low beam power, it is possible to cause dazzling at relatively large distances under appropriate conditions. Due to the lower contrast in day conditions, these distances are much smaller. It should also be noted that for day conditions and the dazzle levels of 10°, 20°, and 40°, there are distance ranges at which the eye can be injured without causing the dazzle effect. For the dazzle level of 40°, dazzling will occur only at a distance of up to approximately 3 m, while eye damage may occur at a distance of up to approximately 18 m.

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Table 5. NODD Values for a Laser Beam of 10 mW Power, 520 nm Wavelength, and 2 mrad Divergence

For the 638 nm wavelengths and the same divergencies, the NOHD value in function of the beam power will have the same values as for the 520 nm wavelength due to the same MPE value. However, for the 445 nm wavelength, the values of the NOHD will be much higher, reaching approximately 56 m at 10 mW beam power. The NODD values for 638 and 445 nm wavelengths will be correspondingly lower due to the dependence of the MDE on the eye’s photopic sensitivity ${\rm V}(\lambda)$.

Assuming the additivity of three beams with a wavelength of 445, 520, and 638 nm and 2 mrad divergence and 10 mW power of each beam, the NOHD value will be approximately 62 m. This is more than a threefold increase in the distance up to which eye can be damaged compared with a single beam at 520 nm. In contrast, the NODD values will increase slightly due to the relatively low ${\rm V}(\lambda)$ values for 445 and 638 nm. Figure 11 shows the dependence of the NODD on the power of emitted radiation, assuming the same power for each beam for night conditions and different dazzle levels. For the remaining ambient light levels, the NODD values will be much lower, as presented for a single beam of 520 nm wavelength. Results of the calculations of the NODD value for the maximum power of 10 mW are presented in Table 6.

 figure: Fig. 11.

Fig. 11. NODD values in the function of power for three beams with a wavelength of 445, 520, and 638 nm; divergence of 2 mrad; and night conditions.

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Table 6. NODD Values for Three Beams with a Wavelength of 445, 520, and 638 nm, Power of 10 mW and Divergence of 2 mrad

It can be seen from the analysis that the additivity of the beams of different wavelengths causes a slight increase in the distance range of eye damage compared with the blue beam. Also, the increase in the range of the distance at which the dazzle effect can occur is relatively small and becomes smaller the farther the wavelengths are away from 556.1 nm.

5. ANALYSIS OF NOHD AND NODD FOR COMMERCIAL RADIATION SOURCES WITH POTENTIAL APPLICATION TO LASER DAZZLERS

The above analysis shows that the parameters influencing the NOHD and the NODD are the power of the beams and their divergence. Moreover, they are affected by the wavelength due to different tabularized values of the MPE and the dependence of the MDE on the eye’s photopic sensitivity ${\rm V}(\lambda)$. The beam divergence can always be adjusted and changed using appropriately designed optical systems. On the other hand, the radiation power and the wavelength are usually characteristic for a given source. Therefore, when selecting potential sources of radiation for use in a dazzler, besides a simple and rigid construction, small dimensions and weight, these last two parameters are decisive. There are many light sources available on the market, but laser diodes deserve special attention due to their simple construction, small dimensions and weight, and the ability to generate relatively high powers, reaching several watts. Examples include laser diodes produced by Nichia (generating blue and green radiation) [16] and Ushio (generating red radiation) [17]. One can also find laser modules that are based on laser diodes, whereby applying appropriate optical systems, much smaller beam divergence can be obtained [18]. There are also ready-to-use modules emitting radiation at three wavelengths of different colors [18]. The parameters of such exemplary module 4 W-RGB are presented in Table 7.

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Table 7. Parameters of Laser Beams Generated by the Exemplary Laser Module [18]

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Table 8. NOHD Values for the Analyzed Laser Module

Using Eqs. (8) and (12), analysis of the values of the NOHD and the NODD was carried out for the laser module. Table 8 presents the NOHD values for each source separately, taking into account the additivity of the beams emitted by the module.

The results presented in Table 8 show that the laser module can damage the eye at distances up to 887, 198, and 208 m for the blue, green, and red beams, respectively. The additivity of the beams causes slight increases in the NOHD value compared with the blue wavelength beam, due to the low value of the power of the other two beams (red and green), as well as a tenfold smaller value of the MPE.

Table 9 presents the results of the NODD calculated in meters for the analyzed laser module. The results show that applying commercial laser modules allows one to develop a sufficient dazzling device that can cause a dazzle effect at long distances under defined ambient light and dazzle levels. It should also be noted that, for high ambient light and dazzle levels, there are distance ranges where eye damage may occur without the dazzle effect.

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Table 9. Results of the NODD Calculations in Meters for the Analysed Laser Module

6. CONCLUSION

The paper shows the method of the NOHD and the NODD determination for multiple laser beams. The above equations allow simple calculation of these values on the basis of the MPE and the MDE for specific ambient light and dazzle levels, taking into account the additivity of the beams. The proposed calculation method may turn out to be particularly desirable in the current situation when more radiation sources using multiple laser beams become available. The analysis also showed that, for high ambient light and dazzle levels, there are distance ranges where the NOHD values are greater than the NODD values. In these ranges, the eye may be damaged, while the dazzle effect does not occur. Such information is particularly important in order to ensure the safety of those being dazzled. Thus, the presented results can be used as a reference for designers developing devices for applications related to dazzling.

From the point of view of safety, for exposures lasting more than 100 s, the most dangerous wavelengths are those in the 400–450 nm range due to the low MPE value of ${1}\;{{\rm W/m}^2}$. Wavelengths in the 450–500 nm range are characterized by the different MPE values varying from ${1}\;{{\rm W/m}^2}$ to ${10}\;{{\rm W/m}^2}$. However, the safest wavelengths are those in the 500–700 nm range due to the highest MPE value of ${10}\;{{\rm W/m}^2}$. For dazzling, wavelengths in the vicinity of 556 nm are the most effective. The dazzle efficiency decreases gradually moving away from this wavelength in both the longer and shorter wavelength directions. Thus, it can be concluded that the most desirable wavelengths, from the point of view of safety and dazzle efficiency, are those in the vicinity of 556 nm. However, in order to ensure the widest possible spectral range for dazzling while ensuring safety and high dazzle efficiency, one could conclude that the most appropriate wavelength range is 510–610 nm where the ${\rm V}(\lambda)$ is still higher than 0.5. These are the colors between cyan (almost blue) and orange. Applying wavelengths from this range to multibeam dazzlers can provide the maximum increase of the NODD with the minimum increase of the NOHD. Unfortunately, the availability of such lasers is much more limited than in the case of the exemplary lasers described in the paper.

When using commercial lasers, such as those described here, in multiwavelength dazzlers, the NODD is mainly determined by the green beam and the NOHD by the blue beam. Thus, combining the red and blue beams to the green beam only slightly increases the NODD and significantly increases the NOHD. Nevertheless, in justified cases, it may be rational to use such multiwavelength dazzlers, especially in night conditions and low dazzle levels. The reason may be the need to cover the wider spectrum of visible radiation because of the possible use of laser filters by the adversary.

Regarding different ambient light levels, the best results are definitely obtained for night conditions when effective dazzling and appropriate safety can be ensured for almost the whole spectrum of visible radiation. However, for daytime conditions, effective dazzling and safety can only be achieved for the lowest dazzle level and for the limited spectrum of visible radiation.

It should also be noted that the standard MDEs values have been estimated on the basis of the specific angular subtense and contrast of the object, the observer’s age, and the eye pigmentation; therefore, they may vary depending on the individual, applications, and intended dazzle effect.

The analysis was limited to the ideal conditions where no laser beam attenuation in the atmosphere was considered. One can assume that the NOHD and NODD values will be lower under real conditions. The introduction of such a supplement may be the subject of further work on the problem of dazzling people by laser radiation.

The results presented in this paper concern only laser sources that generate continuous wave (cw) radiation. However, the calculations of the NOHD can be expanded to single-pulse or repetitively pulsed sources by applying appropriate values of the MPE for the right exposure time according to the relevant standards. In case of the NODD, the situation is not so simple. The values of MDE were determined for cw radiation. Thus, to expand the presented calculations to single-pulse or repetitively pulsed sources, the new values of MDE should be determined, which has not been done thus far. Expansion of the calculation to single-pulse or repetitively pulsed sources should be the subject of future work.

Moreover, it would be useful to explore the dazzle additivity assumption experimentally, i.e., exploring whether the human perception of multiple lasers does actually equal the effect calculated by simply adding MDE values, as was done in this paper.

Funding

Narodowe Centrum Badań i Rozwoju (DOB-1-6/1/PS/2014).

Disclosures

The authors declare no conflicts of interest.

Data Availability

No data were generated or analyzed in the presented research.

REFERENCES

1. “Joint non-lethal weapons program, non-lethal optical distracters fact sheet,” 2016, https://jnlwp.defense.gov/Portals/50/Documents/Press_Room/Fact_Sheets/NL_Optical_Distracters_Fact_Sheet_May_2016.pdf.

2. https://www.beamq.com/.

3. https://www.jetlasers.org/.

4. J. Marshall, J. B. O’Hagan, and J. R. Tyrer, “Eye hazards of laser ‘pointers’ in perspective,” Br. J. Ophthalmol. 100, 583–584 (2016). [CrossRef]  

5. J. E. Neffendorf, G. D. Hildebrand, and S. M. Downes, “Handheld laser devices and laser-induced retinopathy (LIR) in children: an overview of the literature,” Eye 33, 1203–1214 (2019). [CrossRef]  

6. J. Mlynczak, “Laser toys fail to comply with safety standards–case study based on laser product classification,” Adv. Opt. Technol. (to be published).

7. D. B. Gosling, J. B. O’Hagan, and F. M. Quhill, “Blue laser induced retinal injury in a commercial pilot at 1300 ft,” Aerosp. Med. Human Perform. 87, 69–70 (2016). [CrossRef]  

8. “Safety of laser products—part 1: equipment classification and requirements,” IEC 60825-1:2014 (International Electrotechnical Commission, 2014).

9. “American National standard for safe use of lasers,” ANSI Z136.1-2014 (American National Standards Institute, 2014).

10. C. A. Williamson and L. N. McLin, “Nominal ocular dazzle distance (NODD),” Appl. Opt. 54, 1564–1572 (2015). [CrossRef]  

11. C. A. Williamson and L. N. McLin, “Determination of a laser eye dazzle safety framework,” J. Laser Appl. 30, 032010 (2018). [CrossRef]  

12. https://ownthenight.com/.

13. P. Lennie, J. Pokorny, and V. C. Smith, “Luminance,” J. Opt. Soc. Ame. A 10, 1283–1293 (1993). [CrossRef]  

14. H. Cai and T. Chung, “Evaluating discomfort glare from non-uniform electric light sources,” Light. Res. Technol. 45, 267–294 (2012). [CrossRef]  

15. “CVRL Database, CVRL functions, Luminous efficiency functions, 2-deg functions,” http://www.cvrl.org/.

16. http://www.nichia.co.jp/.

17. http://www.ushio-optosemi.com/.

18. https://optlasers.com/.

References

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  1. “Joint non-lethal weapons program, non-lethal optical distracters fact sheet,” 2016, https://jnlwp.defense.gov/Portals/50/Documents/Press_Room/Fact_Sheets/NL_Optical_Distracters_Fact_Sheet_May_2016.pdf .
  2. https://www.beamq.com/ .
  3. https://www.jetlasers.org/ .
  4. J. Marshall, J. B. O’Hagan, and J. R. Tyrer, “Eye hazards of laser ‘pointers’ in perspective,” Br. J. Ophthalmol. 100, 583–584 (2016).
    [Crossref]
  5. J. E. Neffendorf, G. D. Hildebrand, and S. M. Downes, “Handheld laser devices and laser-induced retinopathy (LIR) in children: an overview of the literature,” Eye 33, 1203–1214 (2019).
    [Crossref]
  6. J. Mlynczak, “Laser toys fail to comply with safety standards–case study based on laser product classification,” Adv. Opt. Technol. (to be published).
  7. D. B. Gosling, J. B. O’Hagan, and F. M. Quhill, “Blue laser induced retinal injury in a commercial pilot at 1300 ft,” Aerosp. Med. Human Perform. 87, 69–70 (2016).
    [Crossref]
  8. “Safety of laser products—part 1: equipment classification and requirements,” IEC 60825-1:2014 (International Electrotechnical Commission, 2014).
  9. “American National standard for safe use of lasers,” ANSI Z136.1-2014 (American National Standards Institute, 2014).
  10. C. A. Williamson and L. N. McLin, “Nominal ocular dazzle distance (NODD),” Appl. Opt. 54, 1564–1572 (2015).
    [Crossref]
  11. C. A. Williamson and L. N. McLin, “Determination of a laser eye dazzle safety framework,” J. Laser Appl. 30, 032010 (2018).
    [Crossref]
  12. https://ownthenight.com/ .
  13. P. Lennie, J. Pokorny, and V. C. Smith, “Luminance,” J. Opt. Soc. Ame. A 10, 1283–1293 (1993).
    [Crossref]
  14. H. Cai and T. Chung, “Evaluating discomfort glare from non-uniform electric light sources,” Light. Res. Technol. 45, 267–294 (2012).
    [Crossref]
  15. “CVRL Database, CVRL functions, Luminous efficiency functions, 2-deg functions,” http://www.cvrl.org/ .
  16. http://www.nichia.co.jp/ .
  17. http://www.ushio-optosemi.com/ .
  18. https://optlasers.com/ .

2019 (1)

J. E. Neffendorf, G. D. Hildebrand, and S. M. Downes, “Handheld laser devices and laser-induced retinopathy (LIR) in children: an overview of the literature,” Eye 33, 1203–1214 (2019).
[Crossref]

2018 (1)

C. A. Williamson and L. N. McLin, “Determination of a laser eye dazzle safety framework,” J. Laser Appl. 30, 032010 (2018).
[Crossref]

2016 (2)

D. B. Gosling, J. B. O’Hagan, and F. M. Quhill, “Blue laser induced retinal injury in a commercial pilot at 1300 ft,” Aerosp. Med. Human Perform. 87, 69–70 (2016).
[Crossref]

J. Marshall, J. B. O’Hagan, and J. R. Tyrer, “Eye hazards of laser ‘pointers’ in perspective,” Br. J. Ophthalmol. 100, 583–584 (2016).
[Crossref]

2015 (1)

2012 (1)

H. Cai and T. Chung, “Evaluating discomfort glare from non-uniform electric light sources,” Light. Res. Technol. 45, 267–294 (2012).
[Crossref]

1993 (1)

P. Lennie, J. Pokorny, and V. C. Smith, “Luminance,” J. Opt. Soc. Ame. A 10, 1283–1293 (1993).
[Crossref]

Cai, H.

H. Cai and T. Chung, “Evaluating discomfort glare from non-uniform electric light sources,” Light. Res. Technol. 45, 267–294 (2012).
[Crossref]

Chung, T.

H. Cai and T. Chung, “Evaluating discomfort glare from non-uniform electric light sources,” Light. Res. Technol. 45, 267–294 (2012).
[Crossref]

Downes, S. M.

J. E. Neffendorf, G. D. Hildebrand, and S. M. Downes, “Handheld laser devices and laser-induced retinopathy (LIR) in children: an overview of the literature,” Eye 33, 1203–1214 (2019).
[Crossref]

Gosling, D. B.

D. B. Gosling, J. B. O’Hagan, and F. M. Quhill, “Blue laser induced retinal injury in a commercial pilot at 1300 ft,” Aerosp. Med. Human Perform. 87, 69–70 (2016).
[Crossref]

Hildebrand, G. D.

J. E. Neffendorf, G. D. Hildebrand, and S. M. Downes, “Handheld laser devices and laser-induced retinopathy (LIR) in children: an overview of the literature,” Eye 33, 1203–1214 (2019).
[Crossref]

Lennie, P.

P. Lennie, J. Pokorny, and V. C. Smith, “Luminance,” J. Opt. Soc. Ame. A 10, 1283–1293 (1993).
[Crossref]

Marshall, J.

J. Marshall, J. B. O’Hagan, and J. R. Tyrer, “Eye hazards of laser ‘pointers’ in perspective,” Br. J. Ophthalmol. 100, 583–584 (2016).
[Crossref]

McLin, L. N.

C. A. Williamson and L. N. McLin, “Determination of a laser eye dazzle safety framework,” J. Laser Appl. 30, 032010 (2018).
[Crossref]

C. A. Williamson and L. N. McLin, “Nominal ocular dazzle distance (NODD),” Appl. Opt. 54, 1564–1572 (2015).
[Crossref]

Mlynczak, J.

J. Mlynczak, “Laser toys fail to comply with safety standards–case study based on laser product classification,” Adv. Opt. Technol. (to be published).

Neffendorf, J. E.

J. E. Neffendorf, G. D. Hildebrand, and S. M. Downes, “Handheld laser devices and laser-induced retinopathy (LIR) in children: an overview of the literature,” Eye 33, 1203–1214 (2019).
[Crossref]

O’Hagan, J. B.

J. Marshall, J. B. O’Hagan, and J. R. Tyrer, “Eye hazards of laser ‘pointers’ in perspective,” Br. J. Ophthalmol. 100, 583–584 (2016).
[Crossref]

D. B. Gosling, J. B. O’Hagan, and F. M. Quhill, “Blue laser induced retinal injury in a commercial pilot at 1300 ft,” Aerosp. Med. Human Perform. 87, 69–70 (2016).
[Crossref]

Pokorny, J.

P. Lennie, J. Pokorny, and V. C. Smith, “Luminance,” J. Opt. Soc. Ame. A 10, 1283–1293 (1993).
[Crossref]

Quhill, F. M.

D. B. Gosling, J. B. O’Hagan, and F. M. Quhill, “Blue laser induced retinal injury in a commercial pilot at 1300 ft,” Aerosp. Med. Human Perform. 87, 69–70 (2016).
[Crossref]

Smith, V. C.

P. Lennie, J. Pokorny, and V. C. Smith, “Luminance,” J. Opt. Soc. Ame. A 10, 1283–1293 (1993).
[Crossref]

Tyrer, J. R.

J. Marshall, J. B. O’Hagan, and J. R. Tyrer, “Eye hazards of laser ‘pointers’ in perspective,” Br. J. Ophthalmol. 100, 583–584 (2016).
[Crossref]

Williamson, C. A.

C. A. Williamson and L. N. McLin, “Determination of a laser eye dazzle safety framework,” J. Laser Appl. 30, 032010 (2018).
[Crossref]

C. A. Williamson and L. N. McLin, “Nominal ocular dazzle distance (NODD),” Appl. Opt. 54, 1564–1572 (2015).
[Crossref]

Aerosp. Med. Human Perform. (1)

D. B. Gosling, J. B. O’Hagan, and F. M. Quhill, “Blue laser induced retinal injury in a commercial pilot at 1300 ft,” Aerosp. Med. Human Perform. 87, 69–70 (2016).
[Crossref]

Appl. Opt. (1)

Br. J. Ophthalmol. (1)

J. Marshall, J. B. O’Hagan, and J. R. Tyrer, “Eye hazards of laser ‘pointers’ in perspective,” Br. J. Ophthalmol. 100, 583–584 (2016).
[Crossref]

Eye (1)

J. E. Neffendorf, G. D. Hildebrand, and S. M. Downes, “Handheld laser devices and laser-induced retinopathy (LIR) in children: an overview of the literature,” Eye 33, 1203–1214 (2019).
[Crossref]

J. Laser Appl. (1)

C. A. Williamson and L. N. McLin, “Determination of a laser eye dazzle safety framework,” J. Laser Appl. 30, 032010 (2018).
[Crossref]

J. Opt. Soc. Ame. A (1)

P. Lennie, J. Pokorny, and V. C. Smith, “Luminance,” J. Opt. Soc. Ame. A 10, 1283–1293 (1993).
[Crossref]

Light. Res. Technol. (1)

H. Cai and T. Chung, “Evaluating discomfort glare from non-uniform electric light sources,” Light. Res. Technol. 45, 267–294 (2012).
[Crossref]

Other (11)

“CVRL Database, CVRL functions, Luminous efficiency functions, 2-deg functions,” http://www.cvrl.org/ .

http://www.nichia.co.jp/ .

http://www.ushio-optosemi.com/ .

https://optlasers.com/ .

https://ownthenight.com/ .

“Safety of laser products—part 1: equipment classification and requirements,” IEC 60825-1:2014 (International Electrotechnical Commission, 2014).

“American National standard for safe use of lasers,” ANSI Z136.1-2014 (American National Standards Institute, 2014).

J. Mlynczak, “Laser toys fail to comply with safety standards–case study based on laser product classification,” Adv. Opt. Technol. (to be published).

“Joint non-lethal weapons program, non-lethal optical distracters fact sheet,” 2016, https://jnlwp.defense.gov/Portals/50/Documents/Press_Room/Fact_Sheets/NL_Optical_Distracters_Fact_Sheet_May_2016.pdf .

https://www.beamq.com/ .

https://www.jetlasers.org/ .

Data Availability

No data were generated or analyzed in the presented research.

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Figures (11)

Fig. 1.
Fig. 1. Diagram of three beams with different elliptical cross-section.
Fig. 2.
Fig. 2. Four dazzle levels.
Fig. 3.
Fig. 3. NODD values for 445 nm beam.
Fig. 4.
Fig. 4. NODD values for 520 nm beam.
Fig. 5.
Fig. 5. NODD values for 638 nm beam.
Fig. 6.
Fig. 6. NODD values for all beams.
Fig. 7.
Fig. 7. NOHD values in the function of beam power for a wavelength of 520 nm and a divergence of 2 mrad.
Fig. 8.
Fig. 8. NODD values in the function of beam power for a wavelength of 520 nm, divergence of 2 mrad, and night conditions.
Fig. 9.
Fig. 9. NODD values in the function of beam power for a wavelength of 520 nm, divergence of 2 mrad, and dusk conditions.
Fig. 10.
Fig. 10. NODD values in the function of beam power for a wavelength of 520 nm, divergence of 2 mrad, and day conditions.
Fig. 11.
Fig. 11. NODD values in the function of power for three beams with a wavelength of 445, 520, and 638 nm; divergence of 2 mrad; and night conditions.

Tables (9)

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Table 1. Parameters Adopted for the Determination of the M D E S [11]

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Table 2. M D E S Values for Different Dazzle and Ambient Light Levels [11]

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Table 3. V ( λ ) Values for Several Basic Wavelengths [15]

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Table 4. Parameters of Beams Emitted by Hypothetical Sources and Their MPE

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Table 5. NODD Values for a Laser Beam of 10 mW Power, 520 nm Wavelength, and 2 mrad Divergence

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Table 6. NODD Values for Three Beams with a Wavelength of 445, 520, and 638 nm, Power of 10 mW and Divergence of 2 mrad

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Table 7. Parameters of Laser Beams Generated by the Exemplary Laser Module [18]

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Table 8. NOHD Values for the Analyzed Laser Module

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Table 9. Results of the NODD Calculations in Meters for the Analysed Laser Module

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

N O H D = 4 P π M P E w t g .
E l 1 M P E 1 + E l 2 M P E 2 + + E l n M P E n = 1.
S = π 4 a b = π 4 ( 2 d t g ϕ x 2 + w x ) ( 2 d t g ϕ y 2 + w y ) ,
S π d 2 t g ϕ x 2 t g ϕ y 2 .
P 1 π d 2 t g ϕ x 1 2 t g ϕ y 1 2 M P E 1 + P 2 π d 2 t g ϕ x 2 2 t g ϕ y 2 2 M P E 2 + + P n π d 2 t g ϕ x n 2 t g ϕ y n 2 M P E n 1.
1 π d 2 ( P 1 M P E 1 t g ϕ x 1 2 t g ϕ y 1 2 + P 2 M P E 2 t g ϕ x 2 2 t g ϕ y 2 2 + + P n M P E n t g ϕ x n 2 t g ϕ y n 2 ) 1.
N O H D 1 π ( P 1 M P E 1 t g ϕ x 1 2 t g ϕ y 1 2 + P 2 M P E 2 t g ϕ x 2 2 t g ϕ y 2 2 + + P n M P E n t g ϕ x n 2 t g ϕ y n 2 ) .
N O H D 2 1 π ( P 1 M P E 1 ϕ x 1 ϕ y 1 + P 2 M P E 2 ϕ x 2 ϕ y 2 + + P n M P E n ϕ x n ϕ y n ) .
N O H D 1.128 P 1 M P E 1 ϕ x 1 ϕ y 1 + P 2 M P E 2 ϕ x 2 ϕ y 2 + + P n M P E n ϕ x n ϕ y n .
P 1 π d 2 t g ϕ x 1 2 t g ϕ y 1 2 M D E 1 + P 2 π d 2 t g ϕ x 2 2 t g ϕ y 2 2 M D E 2 + + P n π d 2 t g ϕ x n 2 t g ϕ y n 2 M D E n 1.
M D E = M D E S V ( λ ) .
N O D D 2 1 π ( P 1 M D E 1 ϕ x 1 ϕ y 1 + P 2 M D E 2 ϕ x 2 ϕ y 2 + + P n M D E n ϕ x n ϕ y n ) .
N O D D 1.128 P 1 M D E 1 ϕ x 1 ϕ y 1 + P 2 M D E 2 ϕ x 2 ϕ y 2 + + P n M D E n ϕ x n ϕ y n .