Underwater blue-green LED communication using a double-layered, curved compound-eye optical system

Xizheng Ke; Xizheng Ke; Xizheng Ke; Shangjun Yang; Yu Sun; Jingyuan Liang; Xiya Pan

doi:10.1364/OE.457052

1. Introduction

As the world's resources become increasingly scarce, ground resources can no longer meet the demand, and the utilization of marine resources has become particularly important [1]. Therefore, the timeliness and reliability of underwater communication technology are of great significance for the exploration of the ocean [2–3]. Optical antennas are an important component of underwater optical wireless communication, and in recent years, many scholars around the world have conducted extensive research on receiving antennas [4].

Due to the absorption and scattering characteristics of seawater, the divergence angle of blue-green light reaching the receiving end becomes larger and the power decreases [5]. Researchers have found that an optical receiving system with a single-lens structure, such as plano-convex lens [6–7] or gradient-index lens [8], has limited communication performance in complex seawater environments owing to its small field of view and low sensitivity [9]. The receiving structure of array lens is adopted to improve the channel’s capacity and reliability [10–11]. Conventional lens is difficult to meet the requirements of the system for the size and weight of optical antenna. Compared with conventional lens, Fresnel lens has the advantages of strong convergence ability, small volume and light weight [12–14]. However, Fresnel lens is very sensitive to the angle change of incident light, which is suitable for high gain and small field of view, and only for parallel incident light. The compound eyes of animals such as flies and insects have attracted the attention of researchers owing to their compact structure, large field of view, and high sensitivity [15]. Therefore, inspired by these compound eyes, researchers have proposed an artificial fly-eye lens system composed of microlens arranged in an array to simulate the ommatidium of insects, forming a multi-channel structure to obtain a large field of view [16]. Chen proposed a new polynomial fractional projection model by analyzing the energy distribution of the imaging spot of the fisheye lens during the system acquisition [17]. Cheng proposed a compound eye sensor based on a spatially deformed, curved microlens array [18]. He designed a diverse-array receiving antenna composed of a Fresnel lens and a hemispherical lens [19]. Cheng used a fisheye lens with an ultra-wide field of view along with a polynomial projection model to obtain high-quality light-intensity reception on the imaging receiving plane [20]. Most of these systems are in the form of a microlens array. Although the structure and function are closer to those of biological compound eyes, the high-precision microlens design increases the complexity of the processing technology. Chen designed an optical receiving antenna coupled with a spherical bionic fly-eye microlens group and compound parabolic concentrator, which can effectively improve the anti-shadow occlusion performance of an optical communication system. However, with the increase in the included angle of the optical axis, the ability of the antenna to collect light energy is greatly affected [21]. Li designed a compact fly-eye plano-convex lens antenna based on the optimization of the plano-convex microlens structure by combining a fly-eye lens with a sunflower plano-convex lens. However, the design of its planar structure leads to a small field of view of the receiving antenna [22]. Improving the field of view and optical receiving efficiency of the compound-eye optical system and reducing its cost are the keys to further developing the bionic compound-eye optical system.

Scholars have widely used the bionic structure of fly-eye lens optical antennas in visual imaging systems, but few have applied it to the field of wireless optical communication. Therefore, drawing inspiration from the aforementioned biological systems, this paper proposes a wide-angle-focusing wireless optical communication system that can be used underwater and is composed of both a fly-eye lens and convex lens to receive light signals from an LED array. The main research aims were to design a visible-light system of a fly-eye lens, analyze the optical concentrating efficiency of the receiving antenna, determine the received optical power, and improve this optical power through the fly-eye lens, which was verified by simulation and experiment.

2. Transmission model of the LED light source in water

The attenuation of light by seawater is mainly reflected in the absorption and scattering characteristics of the seawater, which are mainly influenced by the large amount of dissolved substances, suspended particles, and organic matter. However, light waves with wavelengths of 400–550 nm exhibit the smallest attenuation during underwater transmission. In this study, a green LED light source with a wavelength of 550 nm was used for the research of the transmission model and subsequent experimental design.

As mentioned above, light transmission is affected by the absorption and scattering of substances in the water, and its attenuation coefficient is the linear sum of the absorption attenuation coefficient and scattering attenuation coefficient [23]:

(1)$$c(\lambda ) = \alpha (\lambda ) + \beta (\lambda )$$

where α(λ) is the total absorption coefficient, β(λ) is the total scattering coefficient, and c(λ) is the total attenuation coefficient of seawater. The attenuation coefficient α(λ) for absorption can be expressed as follows [24]:

(2)$$\alpha (\lambda ) = {\alpha _p}(\lambda ) + {\alpha _y}(\lambda ) + {\alpha _c}(\lambda ) + {\alpha _s}(\lambda )$$

where α_p(λ), α_y(λ), α_c(λ), and α_s(λ) are the attenuation coefficients for the absorption of light by pure water, yellow substances, plankton, and suspended particles, respectively. The attenuation coefficient β(λ) for scattering can thus be expressed as follows [25]:

(3)$$\beta (\lambda ) = {\beta _p}(\lambda ) + {\beta _s}(\lambda )$$

where β_p(λ) and β_s(λ) represent the attenuation coefficients for the scattering of light by pure seawater and suspended particles, respectively. Table 1 shows the typical values of the attenuation coefficient of green light transmitted through different water bodies [23].

Table 1. Typical values of attenuation coefficients

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Figure 1 shows the radiation transmission model of the LED light signal in the seawater channel. During the underwater transmission process, the LED light source is regarded as a Lambertian light source, and its light intensity distribution satisfies the Lambertian radiation law [26]. Owing to the complex seawater channel, the LED optical signal is easily affected by the attenuation of the water body during the transmission process, resulting in serious loss of the LED optical signal. For long-distance underwater blue-green LED communication, the power loss of optical communication is related to the communication distance, the receiving aperture, and the divergence angle of the light source at the transmitting end, and the beam expansion increase with distance [27]. The power received by the receiver within the field of view after the beam has expanded is described by the following equation [28]:

(4)$${P_r} = {P_0} \cdot {\eta _t} \cdot {\eta _r} \cdot \eta \cdot \frac{{D_r^2}}{{{{\left( {{D_t} + 2d \cdot \tan \frac{\theta }{2}} \right)}^2}}} \cdot {e^{ - c(\lambda ) \cdot d}}$$

where P_r is the power after the light-transmission distance, P₀ is the transmitted light power, D_r is the aperture size of the receiver, D_t is the aperture size of the transmitter, d is the distance from the LED light source to the photodetector, θ is the divergence angle of the light source, and c(λ) is the total attenuation coefficient of seawater. At the transmitting end, the emitting device of the light source will produce a certain loss during the light-emitting process, and the emission efficiency is η_t. At the receiving end, the beam is affected by the receiving antenna and optical design among other factors, resulting in receiving loss; therefore, the receiving efficiency η_r. The influence of turbulence in the underwater light wave transmission process is described by η.

Fig. 1. Model of the radiative transfer from the LED light source to the receiver.

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LED light expands in the radial direction during the propagation of the seawater channel, causing the emitted light to expand with the increase in the distance. Therefore, it cannot be completely received by the receiving end, resulting in partial loss of the light energy. As such, it is particularly important to increase the light intensity reaching the receiving surface of the photodetector by designing the optical system of the receiving end in an underwater blue-green LED communication system.

3. Structural design and analysis of fly-eye lens optical receiving antenna

3.1 Lens array structure of fly-eye lens receiving antenna

The principle of the fly-eye lens system is to divide the object space into several small fields of view, and the beam channel of each lens corresponds to a small field of view. The light beam of this small field of view is concentrated on the image surface so that a group of small light spots are obtained on the image plane, which are combined to form superimposed light spots. The working principle of this lens system is very similar to that of insect compound eyes. Each ommatidium of insect compound eyes is equivalent to each beam channel of the compound eye system, and each beam channel is distributed along the spherical surface [29].

Figure 2(a) shows a schematic of a single-layered, curved fly-eye lens. Since most current detectors have a flat structure, the quality of light-spot convergence at the edge of the field of view for this type of system is greatly reduced. As shown in Fig. 2(b), the lens located in the center of the array has the best convergence effect; however, with the radial movement of the lens position, the convergence effect of the lens gradually decreases, and the outermost lens cannot effectively focus the light on the light-detection surface [30].

Fig. 2. Schematic diagram of the optical system of a single-layered, curved fly-eye lens array (a) structure (b) ray tracing.

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To solve the defocus phenomenon of the beam during the convergence process, a double-layered, curved fly-eye lens array optical system was designed based on a single layer. Figure 3 shows a schematic diagram of an optical system comprising a double-layered, curved fly-eye lens array. Firstly, the focal length of each small curved lens on the first layer of the system is determined by the position of the semicircular surface where the lens is located, that is, the distance from the field-of-view ray direction at the center of the small lens to the surface of the large lens; in any position, the small lens can obtain the ideal beam convergence effect on the surface of the large lens. Secondly, the large curved mirror on the second layer is concentrated on the surface of the detector so that the optical signal can be focused on the surface simultaneously, reducing the loss of light energy caused by the inability of the edge lens to focus.

Fig. 3. Schematic diagram of the double-layered, curved fly-eye lens array optical system (a) structure (b) ray tracing.

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3.2 Evaluation indicators

3.2.1 Optical efficiency

The purpose of the fly-eye lens optical receiving antenna is to increase the effective receiving area and field of view and to gather sufficiently strong optical signals on the surface of the detector. Therefore, the optical efficiency is an important indicator for evaluating the performance of an optical receiving antenna. The optical efficiency of the optical receiving antenna is shown in Fig. 2 and Fig. 3, and the ratio of the total energy E₀ of the output surface to the total energy E of the input surface is as follows [31]:

(5)$$\eta = \frac{{{E_0}}}{E} \times 100\%$$

where E₀ is the total energy received by the optical antenna, and E is the total energy of the incident light.

3.2.2 Bit-error rate

When the optical signal is modulated by OOK and the light beam is transmitted in seawater, the water molecules and particles in the seawater have the greatest influence on the light beam. However, the influence of other noise sources on the beam, including background noise, dark-current noise, thermal noise and shot noise generated by the input signal and background radiation [32], as well as the reduction of communication performance caused by the turbulence of the beam passing through the seawater medium cannot be ignored [33].

During the process of light-beam transmission, when outside natural light irradiates the water, it causes great interference to the propagation of the light beam, resulting in background noise. The variance of the background noise is [34]

(6)$${\sigma _{BG}}^2 = 2q\Re {P_{BG}}B$$

where q = 1.6 × 10^–19 C represents the electron charge, ℜ represents the response, P_BG represents the background noise power, and B is the response bandwidth of the detector. In addition to the background noise, there is another source of shot noise, mainly the dark-current noise generated by the photodiode at the receiving end when the current passes through and photoelectric conversion occurs. The variance σ_DC² of the dark-current noise is [35]

(7)$${\sigma _{DC}}^2 = 2q{I_{DC}}B$$

where I_DC is the current flowing through the photodiode. At the receiving end of the underwater blue-green LED communication system, the thermal noise generated by the load resistance R of the detector during the impedance conversion process also has a certain influence on the bit error rate performance of the system (i.e., the thermal noise). The variance σ_TH² of the thermal noise is

(8)$${\sigma _{TH}}^2 = \frac{{4KTB}}{R}$$

where the Boltzmann constant is K = 1.38×10^–23 J/K, T is the absolute temperature of the system. In practice, a load resistance R of 50 Ω is generally adopted. Shot noise is caused by the dispersion of carriers that form the current and is mainly found in active devices such as detectors. The variance σ_SS² of the shot noise is

(9)$${\sigma _{SS}}^2 = 2q\Re {P_0}B$$

where P₀ denotes the signal power. Through a large number of experiments, Ref. [36] showed that the generalized gamma distribution well fits the fluctuation of received light intensity under the influence of turbulence and describes weak to strong fading. The probability density is [36]

(10)$${f_R}(r) = \frac{{2v}}{{{{(\Omega /m)}^m}\Gamma (m)}}{r^{2vm - 1}}\exp ( - \frac{{m{r^{2v}}}}{\Omega }),r > 0$$

where m and v represent the shape parameters, and Ω denotes the scale parameters. The i^th moment of the generalized Gamma distribution is expressed as

(11)$$E[{R^i}] = \frac{{{{(\frac{\Omega }{m})}^{\frac{i}{{2v}}}}\Gamma (m + \frac{i}{{2v}})}}{{\Gamma (m)}}$$

Then, according to the definition of the flicker index, we obtain,

(12)$${\sigma _0}^2 = \frac{{\Gamma (m)\Gamma (m + \frac{1}{v})}}{{{\Gamma ^2}\left( {m + \frac{1}{{2v}}} \right)}} - 1$$

Therefore, the expression of the average signal-to-noise ratio of the detector output at the receiving end is [37]

(13)$$\left\langle {SNR} \right\rangle = \frac{{SN{R_0}}}{{\sqrt {1 + \sigma _0^2SNR_0^2} }},SN{R_0} = \sqrt {\frac{{{{(\Re {P_S})}^2}}}{{{\sigma _{BG}}^2 + {\sigma _{DC}}^2 + {\sigma _{TH}}^2 + {\sigma _{SS}}^2}}}$$

The average bit-error rate is

(14)$$\left\langle {BER} \right\rangle = \frac{1}{2}\int_0^\infty {{f_I}(I )erfc\left( {\frac{{\left\langle {SNR} \right\rangle I}}{{2\sqrt 2 }}} \right)} dI$$

where erfc(x) is the complementary error function, f_I(I) is the channel fading probability density function, and I is the signal light intensity at the receiving end.

3.3 Received optical power of fly-eye lens

The double-layered fly-eye-lens receiving antenna is a simple linear-diversity combination, namely, an equal-gain combination (EGC) [38]. The double-layered fly-eye lens receiving antenna is composed of a lens array and curved mirror. The curved lens of the second layer converges and superimposes the light beams collected by the lens array so that the light passing through each small lens is combined and output on the surface of the detector. According to the Huygens–Fresnel principle, the power of the light beam after reaching the compound-eye receiving antenna and passing through the k^th microlens is

(15)$$E({P_k}) = C\int\!\!\!\int\limits_\Sigma {\frac{1}{2}} (1 + \cos {\theta _k})E(P)\frac{{{e^{ik{r_k}}}}}{{{r_k}}}d{s_k}$$

where C is a constant; θ_k is the angle between the light wave and the k^th microlens when the light is incident; E(P) is the optical power when the light reaches the surface of the receiving antenna; r_k is the distance from the microlens to the second-layer, curved converging lens; and s_k is the aperture area of the k^th microlens. As shown in Fig. 3(b), the output power of the double-layered compound-eye receiving antenna is the superposition sum of the output signals of each microlens in the microlens array, which can be expressed as follows:

(16)$$\begin{array}{l} \mathop {{P_r}}\limits^ \wedge{=} \sum\limits_{k = 1}^{{N_r}} {{C_k}\int\!\!\!\int\limits_\Sigma {\frac{1}{2}} (1 + \cos {\theta _k})E(P)\frac{{{e^{ik{r_k}}}}}{{{r_k}}}d{s_k}} \\ = C\sum\limits_{k = 1}^{{N_r}} {\int\!\!\!\int\limits_\Sigma {\frac{1}{2}} (1 + \cos {\theta _k})({P_0} \cdot ({\eta _t} \cdot {\eta _r} \cdot \eta \cdot \frac{{D_{kr}^2}}{{{{\left( {{D_t} + 2d\tan \frac{\theta }{2}} \right)}^2}}} \cdot {e^{ - c(\lambda ) \cdot d}}))\frac{{{e^{ik{r_k}}}}}{{{r_k}}}d{s_k}} \end{array}$$

where D_kr is the aperture size of the k^th microlens, D_t is the aperture size of the transmitter.

3.4 Design and simulation analysis of optical receiving antenna with curved fly-eye lens

3.4.1 Optical design

First, the arrangement position of each microlens on the surface is determined according to the included angle. Then, the aperture size of each microlens is calculated, and the microlens of the curved fly-eye lens are graded. The microlens located in the center is designated as level 0, and the number of microlens levels increases layer by layer to k levels as it expands to the periphery. The focal length of the 0-level microlens is l₀, and the focal length of each microlens is l_k, where the value of k is 1, 2, 3, etc. The distances of the other microlens from the image surface along the optical axis, that is, the image-side focal lengths of each microlens are l₁, l₂, l₃……l_k, and the sagittal height of each microlens is h₀.

The focal length l_k of each microlens is equal to the focal point f’ of the image side, r_k₁ and r_k₂ are the radius of curvature of the k^th level microlens:

(17)$${l_k} = {f^{\prime}}\textrm{ = }\frac{{n{r_{k1}}{r_{k2}}}}{{({n - 1} )[{n({{r_{k2}} - {r_{k1}}} )+ ({n - 1} )\Delta } ]}}$$

where n is the refractive index of lens material, and Δ is the thickness of biconvex lens.

From the positional relationship between the central microlens and the peripheral microlens of the curved fly-eye lens, the following relationship can be obtained:

(18)$$\frac{{R + {h_0} + {l_0}}}{{\cos \alpha }} = {l_k} + R + {h_0}$$

where α is the angle between the optical axis of the k-level microlens and the 1-level microlens, R is the radius of curvature of the spherical crown of the curved fly-eye lens, and h₀ is the sagittal height of the spherical cap of the microlens. Combining Eqs. (17) and (18), we obtain:

(19)$$\frac{{R + {h_0} + {l_0}}}{{\cos \alpha }} - (R + {h_0}) = \frac{{n{r_{k1}}{r_{k2}}}}{{({n - 1} )[{n({{r_{k2}} - {r_{k1}}} )+ ({n - 1} )\Delta } ]}}$$

When r_k₁ = r_k₂ = r, the equation for the change in the curvature radius r of a small lens with α can be calculated as follows:

(20)$$r = (n - 1) \cdot \sqrt {\frac{\Delta }{n}} \cdot \sqrt {\frac{{R + {h_0} + {l_0}}}{{\cos \alpha }} - (R + {h_0})}$$

According to the curvature radius r, the chord length S of the spherical cap of the microlens is:

(21)$$S = \sqrt {{r^2} - {{(r - {h_0})}^2}}$$

3.4.2 Single-layered fly-eye-lens optical simulations

The parameters of the curved fly-eye lens were obtained according to the aforementioned optical design, and Zemax was used to simulate a single-light-source emission to a fly-eye-lens optical receiving antenna in non-sequential mode. First, a single-layered, curved fly-eye-lens optical antenna system was designed. Table 2 shows the simulated device components and their corresponding parameters, where the first component is the light source with a divergence angle, the second is the overall system of the single-layered, curved, compound-eye optical receiving antenna; and the third is the detector.

Table 2. Design parameters of the single-layered, curved fly-eye lens

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Figure 4 shows a simulation diagram of a three-dimensional (3D), single-layered fly-eye-lens receiving antenna, where the light beam is focused on the detector surface after being focused by a single-layered fly-eye lens. The output light power of the light source was 500 µW, the distance from the light source to the fly-eye lens was 1 m, and the number of ray traces of the light source was 100,000.

Fig. 4. 3D simulation of a single-layered fly-eye-lens optical receiving antenna.

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Using Zemax to trace the single-layered fly eye lens system, the spot distribution of light passing through the fly-eye lens on the surface of the photodetector was mapped. As can be seen from the simulation results in Fig. 5, the light spot was scattered on the detector surface, and the energy value received by the detector was relatively scattered. The peak irradiance of the light spot was 2.6860×10^–2 W/cm², and the optical power received by the detector was 1.8042×10^–5 W.

Fig. 5. Spot irradiation diagrams on the detector surface of light passing through the single-layered fly-eye lens.

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Because the incident angle of the source to be considered, based on the compound fly-eye lens model, the insertion loss corresponding to the different incident angle is analyzed. The insertion loss is the power difference between the incident power to the fly-eye lens and the incident power to the active area of the detector. According to formula (4) and the corresponding parameters in the above ZEMAX calculation environment, it can be calculated that the incident power to the fly-eye-lens is 4.29×10⁻⁵ W, and the incident power to the active area of the detector is 1.80×10^–5 W. The insertion loss of the single-layered fly-eye lens is 3.77 dB.

Similarly, by changing the incident angle of the optical source (the incident angle is the angle between the main optical axis of the optical source and the central optical axis of the compound eye lens), detector power and insertion loss under the condition of single-layered fly-eye lens are calculated respectively. Figure 6 is a ray tracing diagram of changing the incident angle of light, and the results are shown in Table 3.

Fig. 6. A single-layered fly-eye-lens optical receiving antenna by changing the incident angle of the optical source.

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Table 3. Incident angle and insertion loss of the single-layered, curved fly-eye lens

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By changing the incident angle of the optical source, the insertion loss of the single-layered fly-eye lens will be directly affected. The insertion loss increases with the increase of incident angle.

3.4.3 Double-layered fly-eye-lens optical simulations

Based on the design of a single-layered fly-eye lens, Zemax was used to simulate the double-layered fly-eye lens optical receiving antenna, and the same single light source as the single-layered fly-eye lens was used as the transmitting end for emission. Table 4 shows the device components and corresponding parameters for the simulation. The first component is the light source with a divergent angle, the second to fourth components represent the overall system, and the fifth is the detector.

Table 4. Design parameters of bilayered, curved fly-eye lens

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The double-layered, curved fly-eye-lens optical receiving antenna was composed of 16 small curved lenses in the first layer and converging lenses in the second layer. Figure 7 shows a simulated 3D diagram of a double-layered fly-eye-lens optical receiving antenna, which shows that after the light beam is converged by the fly-eye lens, it converges at the focal point of the optical lens, and the optical lens of the second layer converges the light beam to a point, which increases the light energy received by the detector surface. The output light power of the light source was 500 µW, the distance from the light source to the fly-eye lens was 1 m, and the number of ray traces of the light source was 100,000.

Fig. 7. 3D simulation of the double-layered fly-eye-lens optical receiving antenna.

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Using Zemax to perform ray tracing on the double-layered fly-eye-lens optical receiving antenna system, a diverging light source was used to simulate the scattering of light underwater. The spot distribution of the light passing through the double-layered fly-eye lens on the surface of the photodetector is shown in Fig. 8. The energy received by the detector was concentrated in the center, the surface of the detector had a circular illuminated surface, and the illumination was relatively uniform throughout the entire area. The simulation results are shown in Fig. 8, where the peak irradiance of the light spot was 4.8987×10^–3 W/cm², and the optical power received by the detector was 3.0695×10^–5 W.

Fig. 8. Spot irradiation diagrams on the detector surface of light passing through the double-layered fly-eye lens.

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It can be seen by comparing the simulation results in Fig. 5 and Fig. 8 that the optical power received by the double-layered fly-eye lens is 3.0695×10^–5 W, which is 70% higher than that of the single-layered fly-eye lens (1.8042×10^–5 W). Moreover, the optical system of the double-layered fly-eye lens can not only successfully converge the light received by the small lens through the converging lens but can also realize the superposition of light intensity by the double-layered fly-eye lens.

Similarly, by changing the incident angle of the optical source, the incident power to the fly-eye lens, detector power and insertion loss under the condition of double-layer compound eye lens are calculated respectively, as shown in Fig. 9, and the results data are shown in Table 5.

Fig. 9. A double-layered fly-eye-lens optical receiving antenna by changing the incident angle of the optical source.

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Table 5. Incident angle and insertion loss of the double-layered, curved fly-eye lens

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From Table 5, by increasing the incident angle of the optical source, the insertion loss will increase. Compared Table 3 and Table 5, under the same conditions, the insertion loss of the double-layered fly-eye-lens is significantly less than that of the single-layered fly-eye-lens, which shows that the double-layered fly-eye-lens can effectively improve the received optical power.

4. Experiment

4.1 Double-layered fly-eye-lens optical receiving antenna structure design

To evaluate the performance of the double-layered fly-eye-lens optical receiving antenna system, using the proposed geometrical optics design and simulation based on the lens array, the double-layered compound eye structure was fabricated and the optical system at the receiving end was assembled, as shown in Fig. 10.

Fig. 10. Receiver prototype with double-layered compound-eye array: (a) front view and (b) top view.

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The first layer is composed of seven identical biconvex microlenses (the focal length of the biconvex is the same), with a lens diameter of 30 mm, and a focal length of 50 mm. The lens of the second layer is a biconvex focusing lens (the focal length of the biconvex is the same), in which the lens diameter is 90 mm, and the focal length is 50 mm; The central microlens of the first layer and the focusing lens of the second layer are coaxial optical systems. The second layer focusing lens is located at the focal length of the central microlens of the first layer, and the included angle between the optical axis of each microlens and the optical axis of the focusing lens is 20°. The microlenses in the first-layer of fly-eye lens are distributed in a symmetrical hexagonal shape.

4.2 Insertion loss measurement

By measuring the power of LED light source and according to the Lambert radiation model, we can approximately estimate the light power on the incident surface of double-layer compound eye lens. The incident power behind the pinhole is measured by changing the position of the incident angle relative to the main optical axis. The distance from the LED light source to the compound eye lens incident surface is 25 cm, and the effective diameter of the pinhole is 400 µm. The power meter model is Ophir-PD300-UV. Figure 11 shows the measurement diagram, and the results are shown in Table 6.

Fig. 11. Schematic diagram of insertion loss measurement of double-layer compound eye lens.

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Table 6. Measurement of incident angle and insertion loss of the double-layered fly-eye lens

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With the increase of the incident angle, the pinhole output power decreases and the insertion loss increases, which is almost consistent with the results obtained by theoretical calculation.

4.3 Experimental design

To measure the receiving efficiency of the optical system for the LED light source, a measurement system was built in the laboratory (Fig. 12) that consisted of an arbitrary function waveform generator (AWG; RIGOL DG5105), an optical power meter, and a photodetector (PDA10A2).

Fig. 12. Schematic diagram of optical-power test system.

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As shown in Fig. 12, an AWG was used to load a square-wave signal to the LED transmitter. The modulation sheme is On-off key modulation with 2 MHz, simulate seawater channels through water pipes. An optical power meter or a photodetector was placed at the rear of the fly-eye-lens receiving antenna, and the probe of the optical power measuring instrument was fixed on the image plane of the fly-eye-lens receiving antenna system. The received optical signal is directly detected by the photodetector, and the waveform is displayed by oscilloscope.

The results from the power meter were displayed on the computer, the optical power meter was replaced with a photodetector, and an oscilloscope was used to read the output waveform. The test procedure was as follows:

(1) The green LED (λ = 550 nm) light source was turned on, and the optical power meter was used to measure the optical power of the LED after the square-wave signal was loaded, determined as the optical power of the transmitting end of the test system.
(2) The test system was built according to Fig. 12, without installing the compound-eye receiving antenna.
(3) The optical power was measured at distances of 1, 3, and 5 m. The continuously measured data was recorded by the optical power meter for a duration of 1 hour.
(4) The single-layered compound-eye receiving antenna was installed at the position of the compound-eye receiving antenna shown in Fig. 12, and step (3) was repeated.
(5) The single-layered compound-eye receiving antenna was replaced by the double-layered compound-eye receiving antenna, and step (3) was repeated.
(6) While installing the double-layered compound-eye receiving antenna, the optical-power measuring instrument was replaced by the photoelectric detector, and an oscilloscope was used to read the output waveform.

The experimental measurements were carried out according to the above steps, and the results are shown in Figs. 13 and 14. The beam alignment error caused by mechanical jitter and gravity sinking makes the received power attenuate with the increase of measurement time.

Fig. 13. Optical power measurements at different receivers for transmission distances of 1, 3, and 5 m.

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Fig. 14. Oscilloscope readout of the waveform at (a) transmitter (b) using double-layered fly-eye-lens receiver with distance = 1 m. (c) using double-layered fly-eye-lens receiver with distance = 3 m. (d) using double-layered fly-eye-lens receiver with distance = 5 m.

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4.4 Analysis of results

We used numerical simulation software to theoretically calculate the optical power of the fly-eye lens using Eq. (16) and compared the theoretical data with the experimental data. It is more intuitive to see the difference in the optical power received by the receiving end in the three states: no compound-eye receiving antenna, single-layered compound-eye receiving antenna, and double-layered compound-eye receiving antenna. The experimental environment was still water; therefore, the influence of turbulent flow was not considered. The numerically calculated parameters were consistent with the experimentally designed data: P₀= 500 µW, D_t= 38 mm, D_r= 100 mm, σ_r²= 10^–10∼10^–13, η_t= 0.82, c(λ) = 0.151 m^-1, B = 150 MHz, T = 290, R = 50 Ω, and β = 20°. The results are shown in Table 7, where the theoretical data and is the average value of the collected experimental data (P_r represents the theoretical data, and P_e represents the experimental data).

Table 7. Theoretical data and experimental data^a

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The solid line in Fig. 15 is the curve fitted using the experimental data, and the dotted line is that fitted after calculation using the compound-eye-structured light-power equation; these three sets of curves all agree with the exponential decay trend. It can be observed from the Fig. 15 that when the transmission distance is constant, the power value received by the double-layered fly-eye lens is higher than that of the single-layered fly-eye lens.

Fig. 15. Theoretical and experimental curves.

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Combined with the experimental data in Table 7, the bit-error rate of the system receiving end was calculated and analyzed using Eq. (14), and the bit error rate at the receiving end of the single- and double-layered fly-eye lenses as a function of the transmission distance were generated, as shown in Fig. 16.

Fig. 16. Bit-error rate at the receiving end of two fly-eye lenses at 1, 3, and 5 m.

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As shown in Fig. 16, the bit-error rate of the single-layered fly-eye lens system is higher than that of the double-layered counterpart under different transmission distances. By comparing the three sets of data in Table 7, it can be seen that the maximum deviation between the measured data and the theoretical data is 1.3%. This may be because tap water was used in the experiments, and salt was added to simulate seawater, leading to a large discrepancy with the composition of real seawater. Therefore, some gaps are within an acceptable range. Combining Table 7 and Fig. 16, it can be seen that when the transmission distance was 1, 3, and 5 m, the optical power values received by the double-layered compound-eye system were 72%, 65%, and 60% higher, respectively, than those of the single-layered system, which is consistent with the conclusion that the optical simulation data increased by 70%. The experimental results, theoretical results, and optical simulation results are basically consistent. In summary, the double-layered fly-eye lens designed in this study has a good superposition of light intensity, improves the optical power received by the receiving end, and reduces the bit-error rate.

5. Conclusions

For underwater optical wireless communication applications, a transmission model of an LED light source was established. The single-layered, curved fly-eye lens and double-layered, curved, fly-eye-lens systems were analyzed from the theoretical point of view, and Zemax software was used for modelling and ray-tracing analysis. The insertion loss of the compound eye lens increased with the increase of the incident angle of the light source. The power values of the two models converged on the surface of the detector and were compared and analyzed; the double-layered fly-eye-lens optical receiving system exhibited a 70% increase in the received optical power compared with the single-layered counterpart. An experimental device was built to measure the receiving efficiency of the underwater blue-green LED communication system, and the optical power of the receiving end in the three states of the receiving antenna (i.e., without fly-eye lens, receiving antenna with single-layered fly-eye lens, and receiving antenna with double-layered fly-eye lens) were measured and compared. The experimental results show that when the transmission distance is 1, 3, and 5 m, the optical power received by the double-layered compound-eye system increases by 72%, 65%, and 60%, respectively, compared with the single-layered system. The experimental results verify the accuracy of the theoretical analysis and simulation design. Therefore, the double-layered compound-eye receiving antenna provides a feasible solution for increasing the distance of underwater optical wireless communication. Future research will focus on improving the transmission performance of this communication system using channel-equalization technology.

Funding

Key Industry Innovation Chain of Shaanxi (2017ZDCXL-GY-06-01); Xi’an Science and Technology Innovation Guidance Project of China (201805030YD8CG14(12)); Scientific Research Program of Education Department of Shaanxi Province of China (18JK0341).

Acknowledgments

The authors would like to thank Jiali Wu for suggestions with writing process. We would also like to express our sincerer gratitude to the anonymous reviewers for their valuable feedback.

Disclosures

The authors declare no conflicts of interest.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Attenuation coefficient (m^–1)	α(λ)	β(λ)	c(λ)
Pure sea water	0.053	0.003	0.056
Clear sea water	0.114	0.037	0.151
Offshore sea water	0.179	0.219	0.398
Turbid sea water	0.295	1.875	2.17

Object Type	Source	Compound-Eye Lens	Detector Rectangle
Diameter/mm	–	5	6
Position/mm	–5	0	4.5
Thickness/mm	–	1	–
Material	–	BK7	–

incident angle (°)	0°	5°	10°	15°	20°
incident power to the fly-eye lens (W)	4.29×10⁻⁵	4.29×10⁻⁵	4.29×10⁻⁵	4.29×10⁻⁵	4.29×10⁻⁵
active area detector power (W)	1.80×10⁻⁵	1.74×10⁻⁵	1.67×10⁻⁵	1.47×10⁻⁵	1.36×10⁻⁵
insertion loss (dB)	3.77	3.92	4.10	4.65	4.99

Object Type	Source	Compound-Eye Lens	Convergent Lens	Detector Rectangle
Diameter/mm	–	5	3	6
Position/mm	5	0	5	10.5
Thickness/mm	–	1	2.2	–
Material	–	BK7	BK7	–

incident angle (°)	0°	5°	10°	15°	20°
incident power to the fly-eye-lens (W)	4.29×10⁻⁵	4.29×10⁻⁵	4.29×10⁻⁵	4.29×10⁻⁵	4.29×10⁻⁵
active area detector power (W)	3.09×10⁻⁵	2.89×10⁻⁵	2.16×10⁻⁵	2.05×10⁻⁵	1.54×10⁻⁵
insertion loss (dB)	1.43	1.72	2.98	3.21	4.45

Underwater blue-green LED communication using a double-layered, curved compound-eye optical system

Abstract

1. Introduction

2. Transmission model of the LED light source in water

3. Structural design and analysis of fly-eye lens optical receiving antenna

3.1 Lens array structure of fly-eye lens receiving antenna

3.2 Evaluation indicators

3.2.1 Optical efficiency

3.2.2 Bit-error rate

3.3 Received optical power of fly-eye lens

3.4 Design and simulation analysis of optical receiving antenna with curved fly-eye lens

3.4.1 Optical design

3.4.2 Single-layered fly-eye-lens optical simulations

3.4.3 Double-layered fly-eye-lens optical simulations

4. Experiment

4.1 Double-layered fly-eye-lens optical receiving antenna structure design

4.2 Insertion loss measurement

4.3 Experimental design

4.4 Analysis of results

5. Conclusions

Funding

Acknowledgments

Disclosures

Data availability

References

Data availability

Cited By

Figures (16)

Tables (7)

Equations (21)

Optics Express

incident angle (°)	0°	5°	10°	15°	20°
incident power to the fly-eye lens (W)	4.89×10⁻⁵	4.89×10⁻⁵	4.89×10⁻⁵	4.89×10⁻⁵	4.89×10⁻⁵
active area detector power (W)	3.1×10⁻⁵	2.77×10⁻⁵	2.17×10⁻⁵	1.97×10⁻⁵	1.69×10⁻⁵
insertion loss (dB)	1.97	2.47	3.52	3.95	4.61

Distance (m)	No fly-eye lens (µw)	Single-layered fly eye (µw)	Double-layered fly eye (µw)	Double-layered to single-layered lift ratio	Deviation
1	P_r =4.771	P_r =17.855	P_r =30.762	72%	0.7%
1	P_e =3.765	P_e =16.457	P_e =28.431	72.7%	0.7%
3	P_r =0.048	P_r =1.012	P_r =1.683	66.3%	1.3%
3	P_e =0.052	P_e =1.049	P_e =1.731	65%	1.3%
5	P_r =0.014	P_r =0.303	P_r =0.485	60.05%	0.05%
5	P_e =0.018	P_e =0.378	P_e =0.605	60%	0.05%