Experimental and simulation assessments of underwater light propagation

Abstract

This paper investigates the light propagation through several types of water by experimental and simulation. The Zemax-ray tracing software allowed to simulate the propagation of light in water and to observe the receiver response by reproducing the real conditions of propagation. The underwater environment has been reproduced by a 1.2 m long water tube and 20 cm in diameter with a glass window fitted on one side. The use of tap water with different amounts of sand leads toward three types of water with different attenuation coefficients (0.133, 0.343, 0.580 m⁻¹). The light transmission in the three types of water was experimentally evaluated using a doubled Nd:YAG laser with energy of 4.3 mJ and a pulse width of 20 ns. Comparisons were done between simulation and experimental results.

Keywords

underwater light propagation / attenuation coefficient / telescope / laser range finder

Introduction

Since several decades, sound waves have been used in underwater ranging techniques [¹]. This allowed the development of several applications, such as sea bed structure [²], bathymetry and imaging [³,⁴]. Nowadays, laser sources are used in underwater for imaging [⁵,⁶], scanning [⁷], predicting water turbidity [⁸], underwater laser induced breakdown spectroscopy (LIBS) [⁹], remote sensing [¹⁰], and obstacle detection [¹¹].

An underwater time of flight laser range finder [¹²] requires a receiver channel to achieve the ranging measurement. This receiver comprises a telescope and a photo-detector. The goal of the telescope is to focus the reflected optical signal on the active area of the photo-detector [¹³,¹⁴]. This latter converts the optical signal to photo-current.

This paper is a contribution to the state-of-the-art in the study of the transmission of light in water media through simulation and experiment.

Section 2 of this paper describes the parameters influencing the light propagation in water and the water types used in the assessment. In Section 3, the simulation results of underwater light transmission are presented. In Section 4, the experimental results are discussed. Finally, concluding remarks are given in Section 5.

Method and experimental setup

The water environment is characterized by its attenuation coefficient which is several times higher than in the atmosphere. Therefore, for long distances of propagation in water, the appropriate wavelengths are the blue and green ones [¹⁵,¹⁶].

The attenuation coefficient c(\lambda ), where \lambda refers to the wavelength of light, is the decay constant associated with the removal of light intensity as given by Eq. (1) [¹⁷].

(1)I\left(z\right)=I\left(0\right)\exp (-c\left(\lambda \right)\cdot z),

where z is the distance of propagation, I(\mathrm{0}) and I(z) are respectively the intensities at position z=\mathrm{0} and z=z.

As reported in Table 1 [¹⁶], this coefficient varies from one water type to another, such as turbid harbor, coastal ocean, and clear ocean [¹⁸].

To reproduce experimentally an underwater environment with different kinds of water as in Table 1, we use tap water with different amounts of sand. Two amounts of sand were added to the water: 250 and 350 g. A scanning electron microscopy (SEM) allowed to specify the particle sizes of sand in the range of 100 to 400 µm. The attenuation coefficients of three types of water defined as W1, W2, and W3 were experimentally determined similarly to the work of Boivin et al. [¹⁹]. As summarized in Table 2, the attenuation coefficient of tap water W1 is 0.130 m^-1, which corresponds approximately to that of clear ocean. Besides, the attenuation coefficient of tap water plus 250 g of sand W2 takes the value of 0.343 m^-1 that is nearly close to that of coastal ocean (0.348 m^-1) according to Sverdrup et al. [²⁰]. Finally, the attenuation coefficient of tap water plus 350 g of sand W3 is 0.580 m^-1, which probably corresponds to the lowest turbid harbor water since nowhere similar value has been reported for coastal water at 532 nm.

The underwater environment is reproduced by 1.2 m long water tube and 20 cm in diameter with a glass window fitted on one side. For each water type, the experiment is performed with an intra-cavity frequency-doubling of a Nd:YAG laser passively Q-switched to generate the 532 nm wavelength. The output laser energy is 4.3 mJ for a pulse width of 20 ns at a repetition rate of 1 Hz. This corresponds to a peak power of 2.15´10⁵ W.

Simulation of underwater light propagation

The Zemax-ray tracing software [²¹,²²] is used to reproduce the receiving telescope and to simulate the propagation of light in the real environment of propagation. As shown in Fig. 1(a), the arrangement of the receiving telescope is achieved in the sequential mode of Zemax [²³]. It is constituted of an objective (Plano-convex lens with a diameter D = 50 mm and a focal length FL= 100 mm), a Bi-concave lens (D = 45 mm, FL= -50 mm), and a Plano-convex lens (D = 25 mm, FL= 35 mm). As observed in Fig. 1(b), the received laser rays are focused inside the active area (diameter of 800 µm) of the photo-detector. The 3-D profile of the telescope is illustrated in Fig. 2.

To observe the light transmission through the different water types, the telescope is translated to the non-sequential mode (NSC) of Zemax [²¹]. According to the experimental conditions, the water media is reproduced in 1.2 m water tank in length and situated 5 m far from the telescope. For each water type presented in Table 2 and the turbid harbor (Table 1), the attenuation coefficient is considered to evaluate the laser power arriving at the object. This evaluation is necessary in Zemax because the object is considered as the laser source. Considering the attenuation coefficient of one travel of the laser source through each water type, the reflected laser power being reflected by the object is evaluated by Eq. (1). The parameters used in the NSC simulations are summarized in Table 3.

The 2-D and 3-D profiles of the simulated laser source are displayed in Fig. 3. In the window of the 2-D profile, the color bar represents the peak irradiance (W/cm²).

The first simulation was done for water type W1 with an attenuation coefficient of 0.130 m^-1. Figure 4 depicts the 2-D and 3-D profiles of the reflected laser beam recorded on the detector area. The collected laser power is equal to 1.17´10⁵ W, which corresponds to 54.4% of the laser source power (2.15´10⁵ W) as seen in Fig. 4(b).

In the case of water type W2, corresponding to the increase of the attenuation coefficient from 0.130 to 0.343 m^-1, the obtained 2-D and 3-D profiles of the reflected laser beam are illustrated in Figs. 5(a) and 5(b). The transmitted laser power is of 6.8´10⁴ W, which represents 31.4% of the laser source power. Under such conditions, the attenuation is more important since we observe a decrease of the reflected power versus the increase of the attenuation coefficient of water.

The third simulation was performed for water type W3 representing the attenuation coefficient of 0.580 m^-1. The 2-D and 3-D profiles of the reflected laser beam are displayed in Figs. 6(a) and 6(b). The transmitted laser power is about 3.72´10⁴ W, which corresponds to 17.3% of the laser source power.

The last simulation was done for turbid harbor water as reported in Table 1. Figure 7 depicts the 2-D and 3-D profiles of the transmitted laser light. The laser power as shown in the detector area is equal to 979 W, which corresponds to 0.45% of the transmitted laser power (2.15´10⁵ W) as seen in Fig. 7(b). For this water type, the transmitted laser light is strongly attenuated comparing with the others simulated water types. This is the fact of the attenuation coefficient which is higher (2.190 m⁻¹) than the others attenuation coefficients (0.130, 0.343, 0.580 m⁻¹) of the specified types of water.

One can observe from the recorded profiles that the received laser powers decrease with the increase of the attenuation coefficient of water. Also, the laser beam size as seen by the telescope is practically the same. This last fact reflects directly on the optimization of the detector area and on the magnification of the telescope. However, we should note that increasing the active area of the detector may have a negative impact on the increase of the noise of the system. A detector with larger area will show more intrinsic noise and will increase the effective field of view of the detector, making it more exposed to the background radiation.

Experimental results

The experimental setup is shown in Fig. 8. The laser source is oriented to the glass window of the water tube situated 5 m far. A Teflon (PTFE) cube (70´70´70 mm³) is immersed in water through a hole about 12 cm in diameter. The cube has a reflection coefficient of up to 98% in the wavelength range of 250 to 2500 nm. The telescope presented in the previous section was achieved and positioned parallel to the laser source to collect the reflected laser beam from the object. A charge coupled device (CCD) camera records the reflected laser beam profiles at the output of the telescope. This camera has a sensor size of 6.16´4.62 mm², a video resolution of 1280´720 pixels (high quality) and an optical zoom 5´. The 2-D and 3-D profiles of the laser spot are displayed on the computer screen.

The 2-D and 3-D profiles of the Q-switched laser source are depicted in Figs. 9(a) and 9(b).

Figures 10(a) and 10(b) depict the 2-D and 3-D profiles of the reflected laser beam obtained in case of water type W1 at a temperature of 20°C (293 K). These profiles look like the laser source profiles (Figs. 9(a) and 9(b)) with a certain attenuation of intensity due to the propagation in water. The received laser power at the output of the telescope is of 1.22´10⁵ W, which corresponds to 57% of the laser source power (2.15´10⁵ W). This value is nearly close to that of simulated one (1.17´10⁵ W) for the same water type (Fig. 4). As shown in the 2-D profile, the beam spot diameter is under 800 µm.

In the second experiment with water type W2, the 2-D and 3-D profiles of the reflected laser beam are shown in Figs. 11(a) and 11(b). As expected, the intensity is less than that in case of W1 (Figs. 10(a) and 10(b)). The reflected laser power is of 6.15´10⁴ W, which corresponds to 28.6% of the laser source power. This value is nearly close to that of simulated one (6.8´10⁴ W) for the same water W2.

In the last experiment with water type W3, the reflected 2-D and 3-D profiles are depicted in Figs. 12(a) and 12(b). Here, the attenuation is more pronounced as expressed by the decrease of the reflected laser power due to the increase of the amount of sand from 250 to 350 g. The reflected power is of 3.65´10⁴ W, which corresponds to 17% of the laser source power. This value is the same to that obtained by simulation (3.72´10⁴ W) in case of W3.

In summary, the transmitted laser powers recorded from simulation and experiment are approximately the same for each water type. This leads us to conclude that the implemented optical model within Zemax software reproduces well the conditions of light propagation in a real underwater environment.

Conclusions

In this paper, the underwater light propagation was investigated by simulation and experiment. The Zemax-ray tracing software allowed us to simulate the light propagation and to observe the receiver response of a laser range finder in underwater environment. This latter was reproduced experimentally by adding different amounts of sand to tap water. Three types of water (W1, W2, and W3) were obtained with different attenuation coefficients (0.133, 0.343, 0.580 m^-1). It was observed that the three water types result in different transmitted laser powers and the experimental data validate those obtained from simulations. Therefore, the conclusion that can be drawn is that Zemax software can be effectively used to assess the light propagation in underwater environment by reproducing the appropriate water type, the receiver optics, and the laser source.

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