1 Introduction

Laser rangefinder is a kind of equipment [1,2,3,4] widely used in laser technology in the military. Laser rangefinders can be used with a variety of tactical weapons to make the first hit rate of more than 80%. It has been widely used in multi-type photoelectric tracking, alerting, and search equipment [5].

The ranging ability, i.e. the maximum range, is an important indicator of a laser rangefinder, and its size depends on the environmental conditions and the characteristics of the rangefinder itself. At present, the research on the influencing factors of ranging ability is mainly focused on the visibility of the atmosphere, the size of the target, and the characteristics of the rangefinder itself [6,7,8]. Based on the characteristics of laser ranging targets, this paper analyzes the impact of cooperative targets on laser ranging capabilities.

2 Theoretical Model of Ranging Ability

The laser ranging ability is mainly related to the detection sensitivity of the detector and the laser energy received by the detector. When the equivalent noise power of the laser received by the detector is greater than the equivalent noise power of the detector, the ranging distance can be achieved, otherwise, The equivalent noise power of the laser received by the detector is less than the equivalent noise power of the detector, so the ranging distance cannot be achieved.

2.1 Theoretical Model of Detector Equivalent Noise Power

For laser rangefinders, the target’s laser echo is very weak, in order to improve the receiving sensitivity of the target echo, an avalanche photodiode (APD tube) is usually used as the photodetector. For a typical InGaAs avalanche photodiode, its equivalent noise power is shown in (27.1).

$${\text{NEP}} = 330/\sqrt f$$
(27.1)

Among them, NEP is the equivalent noise power of the detector, and f is the bandwidth of the avalanche photodiode.

2.2 Theoretical Model of Laser Equivalent Noise Power

Laser equivalent noise power is received by laser rangefinder P as shown in (27.2).

$$P = P_{r} /{\text{SNR}}$$
(27.2)

among them, Pr The laser power is received by the laser rangefinder.

Assumptions: the propagation of laser light in the atmosphere obeys the laws of geometric optics; the atmosphere is uniform and isotropic; the reflection of the incident light by the target is either diffuse or specular; the energy distribution in the laser beam is approximately uniform or at least axially symmetric; the receiving system and the transmitting system are tightly coupled, and the optical axes are parallel to each other, the laser power intercepted by the target at a distance r Ps for [9]:

$$P_{s} = \frac{{4P_{t} \tau_{t} A_{s} \cos \theta }}{{\pi^{2} \theta_{t}^{2} R^{2} }}e^{ - \mu R}$$
(27.3)

among them, Pt is the laser emission power; τr is the transmittance of the transmitting optical system; As the target area illuminated by the laser beam; θ is the angle between the average surface normal of the illuminated part and the incident ray; θr The beam divergence angle of the optical system; μ the attenuation coefficient of the laser energy through the unit length of the atmosphere. Here, an empirical formula is used to determine the atmospheric attenuation coefficient during the laser transmission. The empirical formula is to calculate the atmospheric attenuation coefficient by using the normalized contrast between the target and the background and the line-of-sight relationship, as shown in (27.4).

$$\mu = \frac{3.91}{V}\left( {\frac{\lambda }{0.55}} \right)^{ - q}$$
$$q = \left\{ {\begin{array}{*{20}c} {\begin{array}{*{20}c} {1.6,} & {{\text{when}}\;V\;{\text{is}}\;{\text{large}}} \\ \end{array} } \\ {\begin{array}{*{20}c} {{1}{\text{.3}},} & {{\text{moderate}}} \\ \end{array} } \\ {\begin{array}{*{20}c} {{0}{\text{.585}}\,V^{{{1}/{3}}} ,} & {{\text{when}}\;V \le {6}\,{\text{km}}} \\ \end{array} } \\ \end{array} } \right.$$
(27.4)

where v is the visibility of the atmosphere; λ is the laser wavelength.

Diffuse target

When the target surface is rough and irregular, we consider it to be a diffuse reflection target. The rough surface of the diffuse reflection target does not reflect the incident laser light uniformly in all directions. The reflection in the incident direction is the strongest, and the reflection gradually decreases as the angle between the incident light and the incident light increases. π/2, the reflected light intensity, decreases to almost zero at the time. Because the specific angular distribution of the reflected light intensity varies with the target surface, it is more practical to use a cosine distribution instead of a uniform distribution. In addition, the laser beam energy distribution is also non-uniform, which can be considered the energy distribution in the beam is an axisymmetric Gaussian distribution. After the above analysis, the ranging model for diffuse reflection targets is shown in (27.5).

$$P_{r} = \frac{{4P_{t} \tau_{t} \tau_{r} A_{r} A_{SM} \rho }}{{\pi^{2} \theta_{t}^{2} R^{4} }}e^{ - 2\mu R}$$
(27.5)

where: Pr the laser power received by the laser rangefinder; τr is the transmittance of the receiving optical system; Ar effective receiving area for receiving optical system; ASM effective receiving area for diffuse targets; ρ is the diffuse reflection coefficient of the target.

Cooperation goals

For an ideal Lambertian target, the scattering space is hemispherical space, while for an ideal cooperative target, because the beam does not change its properties after reflection, the energy is concentrated after the reflection and returns in the direction of incidence. Therefore, the distance measurement equation for laser ranging on the cooperative target is as follows, (27.6).

$$P_{r} = \frac{{16P_{t} \tau_{t} \tau_{r} A_{r} A_{SH} \rho_{S} }}{{\pi^{2} \theta_{t}^{2} R^{4} \theta_{S}^{2} }}e^{ - 2\mu R}$$
(27.6)

where: ASH effective reception area for cooperation goals; ρs the reflection coefficient of the cooperative target; θs reflection divergence angle for cooperative targets.

2.3 SNR Theoretical Model

The ranging capability index is inseparable from the detection probability and false alarm rate indicators. In order to ensure that the laser rangefinder meets a certain false alarm rate and detection probability, the received laser power should meet a certain signal-to-noise ratio requirement. Under white noise, noise current in to fit a zero-mean random variable with a normal distribution, let the root mean square error be In, Then the distribution probability is:

$$P(i_{n} ) = \frac{1}{{\sqrt {2\pi } I_{n} }}\exp \left( { - \frac{{i_{n}^{2} }}{{2I_{n}^{2} }}} \right)$$
(27.7)

Set the detection threshold to It, the laser echo pulse width is τ, the number of false alarms per second caused by the above noise is PF. It can be expressed by the following formula:

$$\overline{P}_{F} = \frac{1}{2\sqrt 3 \tau }\exp \left( { - \frac{{I_{t}^{2} }}{{2I_{n}^{2} }}} \right)$$
(27.8)

Let the signal current be Is, detection probability Pd can be expressed as:

$$P_{d} = P\left( {I_{s} + i_{n} \rangle I_{t} } \right) = \int_{{I_{t} - I_{s} }}^{\infty } {P\left( {i_{n} } \right)} di_{n} = \frac{1}{{\sqrt {2\pi } I_{n} }}\int_{{I_{t} - I_{s} }}^{\infty } {\exp \left( { - \frac{{i_{n}^{2} }}{{2I_{n}^{2} }}} \right)} di_{n}$$
(27.9)

The above formula can be expressed as an error function:

$$P_{d} = \frac{1}{2} + \frac{1}{2}erf\left( {\frac{{I_{s} - I_{t} }}{{\sqrt 2 I_{n} }}} \right)$$
(27.10)

According to Formulas (27.8) and (27.10), the signal-to-noise ratio of the laser rangefinder under a certain detection probability and false alarm rate can be obtained.

According to Formulas (27.1), (27.2), (27.4)–(27.6), (27.8), (27.10), the theoretical laser ranging capability index for diffuse reflection targets and cooperative targets can be obtained.

3 Impact Analysis of Cooperative Targets on Laser Ranging

3.1 Influence of Cooperative Targets on Ranging Ability Under Different Atmospheric Visibility Conditions

The relevant parameters of the laser rangefinder for numerical simulation calculation are shown in Table 27.1. Under different visibility conditions, the relationship between the receiver power and the equivalent noise power of the detector at different ranging distances for diffuse reflection targets is shown in Fig. 27.1a. This range can be achieved when the laser power received by the detector is greater than the equivalent noise power of the detector. The relationship between the received power and the equivalent noise power of the detector at different ranging distances for the cooperative target under different visibility conditions is shown in Fig. 27.1b. It can be seen from Fig. 27.1b that when the cooperative target is configured, when the visibility is 5 km, the maximum range of the laser rangefinder can reach more than 15 km. With the increase of the visibility of the atmosphere, the maximum range can reach more than 50 km. Therefore, the laser ranging ability can be significantly improved under the condition of cooperative targets. In addition, the laser rangefinder has significantly reduced requirements for environmental and atmospheric conditions, enabling the laser rangefinder to work in harsher conditions.

Table 27.1 Parameter of the laser rangefinder
Full size table
Fig. 27.1
figure 1

The received power of laser rangefinder at different visibility

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3.2 Analysis of the Influence of Cooperative Targets on Ranging Ability Under Different Laser Beam Divergence Angles

Using the parameters in Table 27.1, under the condition of visibility of 5 km and different laser emission beam divergence angles, for diffuse reflection targets and cooperative targets, the receiving power of laser rangefinder detectors with different ranging distances is shown in Fig. 27.2. The smaller the divergence angle of the laser emission beam, the more obvious the difference in laser ranging ability is with and without the cooperative target. When the ranging distance is 10 km and the laser beam divergence angle is 0.5 mrad, configure the cooperative target. The received power of the lower detector is about 10 three times without the cooperation target.

Fig. 27.2
figure 2

The received power of laser rangefinder at different beam divergence angles

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3.3 Theoretical Calculation of Laser Emission Power Under the Condition of Configuring Cooperative Targets

According to the analysis in Sect. 3.1, when the same range is required, configuring the cooperation target can reduce the laser transmission power. The reduction of the laser transmission power can reduce the weight and volume of the laser rangefinder on the one hand and can further ensure the use of Personnel safety. According to the parameters of the rangefinder shown in Table 27.1, the Formula (27.6) can be used to obtain the distance of the cooperative target under different laser emission power conditions. The equivalent noise power received by the detector is shown in Fig. 27.3. Figure 27.3 shows that when the atmospheric visibility is greater than 3 km and the laser emission energy is less than 10 mJ, the laser rangefinder can achieve a maximum range of 15 km. According to the laser hazard type determination method [10], when the laser output energy is 10 mJ, the laser can be guaranteed The rangefinder laser is a Class 3A laser, and the laser emitted by the rangefinder will not cause damage to the eyes of the person on the measured target when the measurement distance is greater than 100 m under the condition that the atmospheric attenuation is ignored. Effectively reduce the laser transmission power of the laser rangefinder, thereby effectively reducing the weight and volume of the rangefinder and ensuring human eye safety.

Fig. 27.3
figure 3

The received noise equivalent power of laser rangefinder at different visibility and different emission power

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4 Conclusion

Based on the characteristics of laser ranging targets, this paper analyzes the influence of cooperative targets on laser ranging capabilities under different atmospheric visibility conditions and different laser emission beam divergence angles. The analysis results show that the configuration of cooperative targets can effectively improve ranging capabilities. The laser rangefinder has significantly reduced the requirements for environmental and atmospheric conditions and can make the laser rangefinder work in harsh conditions; the smaller the laser emission beam divergence angle, the laser ranging ability with and without the cooperation target The more obvious the difference is; in addition, the configuration of cooperation targets can effectively reduce the laser emission power and further provide protection for improving personnel safety.