Accurate beacon positioning method for satellite-to-ground optical communication

Qiang Wang; Ling Tong; Siyuan Yu; Liying Tan; Jing Ma

doi:10.1364/OE.25.030996

1. Introduction

With the potential advantages of a large capacity, high data rate, less mass, less power consumption, small antennas, less volume and low probability of intercept, laser satellite communication has become an important research topic [1–5]. In laser optical communication, the primary task is to determine the exact position of the laser spot, aiming to rapidly acquire beacon light and establish a reliable and stable laser communication link. Therefore, study of the locating algorithm of the beacon for improving the locating accuracy, is of great significance [6]. In order to quickly establish a stable communication link, a receiving probe with high sensitivity detection capability is required. CCD (Charge Coupled Device) is used as a detector in optical communication terminals, but some factors, such as nonlinear photoelectric conversion, dark background of the detectors (caused by the bias voltage of the circuit), read out noise (introduced by the detector circuit), and signal photon noise (caused by random fluctuations of the incident light photon signals) [7], largely influence the locating accuracy of the beacon. By analyzing the causes and distribution characteristics of the various noises, Ref [7] reached a conclusion that the noise interferences and the centroid’s positional standard deviation can be reduced effectively when the threshold is the mean value plus three times the standard deviation of noise. In addition, there are a variety of external factors, such as processing and alignment errors of optical elements [8], background light interferences, and turbulence of the communication channels, that affect the laser spot received by detectors and result in a very uneven distribution of light intensity or even a breaking of the laser spot. Therefore, these factors seriously affect the accuracy of acquisition, and thereby, affect the stability and reliability of satellite optical communication systems [9]. Ref [9] proposed a reconstructive geometric-centroid algorithm, which can effectively reduce the impacts of atmospheric turbulence on laser spot locating in satellite optical communication. The common algorithm is the gray centroid algorithm which is used for computing the location of the beacon in optical communication [10-11].

In recent years, although semiconductor technology and optical component technology has developed rapidly, the hardware is complex and very costly. This paper focuses on using a software-based approach to process the imaging spots of a detector, with the aim to improve the accuracy of acquisition and tracking. Although gray centroid algorithm is commonly used for computing the location of beacon in optical communication, atmospheric turbulence degrades its accuracy. In order to solve this problem, this paper proposes a new algorithm that considers the characteristics of the beacon completely, and thereby improves the locating accuracy of the beacon. Compared with the conventional methods, we propose the method for accurate beacon positioning considering the complexity and real-time performance and the influencing factors that the proposed algorithm tends to address are background noise and atmospheric turbulence. If the new method is applied in satellite-to ground optical communication systems, atmospheric turbulence should be considered. We design a long distance laser transmission experiment (11.16 km) for examining the performance of the new approach. The influence of vertical link atmospheric channel for laser transmission is less than that of the 10 km horizontal link atmospheric channel [12], and hence the horizontal laser communication link is used to validate the new method described in this paper to guarantee the feasibility of the approach for satellite-ground laser communication.

This paper analyzes different characteristics of the existing locating algorithm and presents a novel locating algorithm. The basic principle of this approach is introduced in Section 2. The specific process and numerical simulation are described in Section 3. An 11.16 km bi-directional free space optical link experiment to verify the proposed approach is described in Section 4, and Section 5 presents the conclusions.

2. Basic principle

2.1 Basic principle of the gray centroid algorithm

In satellite optical communication systems, the gray centroid algorithm is usually used to calculate the center position of the beacon. This algorithm takes gray values as weights. We suppose that the size of the spot image is $M \times N$ , and $f_{i j}$ represents the gray values of the pixel in the ith row and jth column. In the digital processor, the values are integers. The centroid of the beacon is calculated by the following formula [13]:

x_{c} = \frac{\sum_{i = 1}^{M} \sum_{j = 1}^{N} i \times f_{i j}}{\sum_{i = 1}^{M} \sum_{j = 1}^{N} f_{i j}}, y_{c} = \frac{\sum_{i = 1}^{M} \sum_{j = 1}^{N} j \times f_{i j}}{\sum_{i = 1}^{M} \sum_{j = 1}^{N} f_{i j}}

The processing of the centroid algorithm is simple and only requires a small amount of computation, but is easily influenced by the variation of the gray distribution and is susceptible to image noise. For an even distribution and high SNR (signal-to-noise ratio) images [14], the gray centroid algorithm can yield high positional accuracy [14].

2.2 Basic principle of the new algorithm

Here we only consider the receiving condition of the single aperture. In the ideal case, the beacon light beam forms a central symmetry around the laser spot in the optical communication terminal detector [15]. The influencing factors that the proposed algorithm tends to address are background noise and atmospheric turbulence. The effects of the influencing factors on different pixels are different. We suppose that the size of the spot image is $M \times N$ , and $f_{i j}$ represents gray values of the pixel in the ith row and jth column. In the horizontal direction, we regard $f_{i j}$ as the center, the three gray values to the left of center are $f_{i j - 3}$ , $f_{i j - 2}$ , $f_{i j - 1}$ _, and the three gray values to the right are $f_{i j + 1}$ , $f_{i j + 2}$ , $f_{i j + 3}$ . These seven points form a set of data (D7). Secondly, the seven points are fitted by a least squares quadratic curve. We select seven points for fitting curve considering the computation complexity and real-time feature. The absolute value of the correlation coefficient between the fitting curve and the original curve is $R_{i j}$ , which indicates the difference between the fitting curve and the original curve. The discrete matrix R consists of all the correlation coefficients $R_{i j}$ ( $1 \leq i \leq M$ , $1 \leq j \leq N$ ). $R_{i j}$ is expressed by:

R_{ij} = {(\frac{\sum_{i = 1}^{7} K_{m}^{2}}{\sum_{m = 1}^{7} K_{m}^{2} - \sum_{m = 1}^{7} {(K_{m} - P_{m})}^{2}})}^{\frac{1}{2}}

where

K_{m}

(m = 1,…7) are the gray values which belong to this set (D7), and

P_{m}

(m = 1,…7) are the values of this fitting curve for set (D7).

Finally, we take correlation coefficients as weights and incorporate them into Eq. (3). The horizontal centroid $x_{r}$ is calculated as:

x_{r} = \frac{\sum_{i = 1}^{M} \sum_{j = 1}^{N} i \times R_{i j}}{\sum_{i = 1}^{M} \sum_{j = 1}^{N} R_{i j}}

Similarly, the vertical centroid $y_{r}$ is calculated using Eq. (4) according to the above algorithm. The specific flow chart is shown in Fig. 1.

Fig. 1 Flow chart of the new algorithm.

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y_{r} = \frac{\sum_{i = 1}^{M} \sum_{j = 1}^{N} j \times R_{i j}}{\sum_{i = 1}^{M} \sum_{j = 1}^{N} R_{i j}}

In terms of the boundary points, namely, j = 1, there is no point to its left. Accordingly, we get $f_{i j - 3}$ , $f_{i j - 2}$ , $f_{i j - 1}$ based on cubic interpolation. Afterwards, $r_{i 1}$ is calculated. Similarly, the problems of boundary points in the vertical direction are solved. The algorithm mentioned above is associated with the neighborhood interior points. When the gray value of a certain point in a laser spot changes significantly, the correlation coefficient of the point becomes smaller. Therefore, the algorithm, which takes correlation coefficients as weights for determining the centroid, can effectively decrease noise.

3. Simulation

3.1 Simulations for the ideal light spot

To examine the accuracy of the algorithm described in the previous section, the laser spot of the optical communication terminal is simulated with MATLAB. The laser wavelength is 800 nm, the focal length of the telescope is 0.56 m and the size of the laser spot is 101 × 101 pixels (the pixel size of CCD is 6.7μm). The simulation image is shown in Fig. 2. The light intensity distribution is shown in Fig. 3.

Fig. 2 The gray-scale image.

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Fig. 3 Light intensity distribution.

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Three laser spot images whose centers are known were generated by MATLAB. The centroids of the laser spots are at (51, 51). With a reasonable threshold, the centroids are obtained using the traditional centroid algorithm and the new algorithm proposed in this paper. The simulation results are shown in Table 1.

Table 1. Simulation results of the laser spots

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3.2 Simulation of the laser spot with noise

As mentioned in Section 2.2, the algorithm which takes correlation coefficients as weights for determining the centroid, can effectively decrease noise. In order to verify this opinion, different densities of impulse noise are added to the ideal spot via MATLAB software. The image, with added impulse noise density of 0.01, is presented in Fig. 4 and Fig. 5.

Fig. 4 The image with impulse noise.

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Fig. 5 The gray-scale image with impulse noise.

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The definition of centoid error of single frame is that the difference between the ideal centroid position and the computation centroid position. The ideal centroid position is computed with no noise. Due to the randomness of the noise, the images of 10 frames, which add the same density noise, were generated. The average centroid error is the average results of 10 frames. We then calculated the average errors of the centroids with the result shown in Fig. 6. As can be seen from Fig. 6, the average centroid errors of the new algorithm are obviously less than that of the gray centroid algorithm. With the increase of the density of the noise, the locating accuracy of the laser spots decreases. For instance, when the noise density is 0.025, the error for the centroid algorithm is greater than 2 pixels. However, the corresponding value for the new algorithm is only 0.7 pixels. Thus, the accuracy of the centroid computation has been improved by 65% by using the new algorithm.

Fig. 6 Average centroid errors with different algorithms.

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4. Experiment

4.1 Near-field experiment

To illustrate the effectiveness of the new algorithm, a near field experiment was established in the laboratory.

The experiment setup is composed of a transmitting terminal and a receiving terminal, as shown in Fig. 7. The distance between the transmitter and receiver is 10 m, and the receiver tracks the laser light from the transmitter.

Fig. 7 The experimental setup.

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During the experiment, we attempted to reduce the interferences of background light as quickly as possible. Finally, the data were collected and processed by the receiver.

We use safety goggles for protecting our eyes from being burned by the laser. In addition, the optical link is higher than most of buildings near the optical path and beam directions are adjusted so that the laser cannot injure other residents’ eyes. So this experiment is very safe.

The centroid of the laser is calculated by the centroid algorithm and the new algorithm, respectively. The receiving terminal tracks the centroid of the laser. The higher the positioning accuracy, the smaller the tracking error. The tracking errors with the two algorithms are shown in Fig. 8. Photographs of the terminals are shown in Figs. 9(a) and 9(b).

Fig. 8 Tracking error with different algorithms in near field experiment.

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Fig. 9 Transmitting and receiving devices.

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From the experimental results, the average tracking error with the new algorithm is 1.11 μrad, and that with the centroid algorithm is 1.63 μrad. The tracking error with the new algorithm is less than that of the centroid algorithm, and the locating accuracy with the new algorithm is higher.

4.2 Long distance laser transmission experiment

As mentioned in Section 2.2, the new algorithm can effectively decrease noise. Similarly, this algorithm can effectively reduce the influence of atmospheric turbulence on the beacon.

In August 2015, an 11.16 km bi-directional free space optical link experiment was established to examine the performance of the new algorithm. The light source was a semiconductor laser, with a wavelength of 800 nm, and a power of 100 mw. The focal length of the receiving telescope was 560 mm and the receiving diameter was 80 mm. The divergence angle of transmitting device is 100μrad, and the aperture of transmitting device is 120mm.After propagating through the reflector, the incident light was focused on the photosensitive surface of the CMOS detector. Afterwards, the data are collected. The experimental configuration consists of two of the same transmitting terminals and two of the same receiving terminals as used in the previous experiment. The experimental setups are shown in Figs. 9(a) and 9(b).

Passing through the atmospheric turbulence, distorted laser spots were obtained. The gray-scale image and the light intensity distribution are shown in Figs. 10(a) and 10(b), respectively.

Fig. 10 Light intensity distribution through atmospheric turbulence and the corresponding gray-scale image.

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In order to compare the performance of the different algorithms in the same environment, we used two laser link systems in parallel, each using different methods, in order to guarantee the same outfield conditions. We consider the errors induced by the individual performance differences of different systems, and the errors have been calibrated in the laboratory. The errors are less than 1 μrad, and therefore, individual performance differences of the two experimental systems have negligible impact on the tracking error.

Figure 11 shows the tracking errors with the two algorithms.

Fig. 11 Tracking error with different algorithms in far field experiment.

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For the long distance, C_n² is given by [16],

C_{n}^{2} \approx \frac{σ_{α}^{2}}{1.093 {zD}^{- 1 / 3}}

where C_n² is the refractive-index structure parameter, D is the diameter of the receiving aperture, z is the link distance and

σ_{α}^{2}

is the variance of angle of arrival.

A comparison of the results and experimental condition is presented in Table 2. The tracking error with the new algorithm is less than that with the centroid algorithm. Thus, we can see that the locating precision for the beacon using the new algorithm is higher than that using the centroid algorithm in long distance laser transmission, and the locating accuracy increases by 50% over that of the conventional centroid algorithm.

Table 2. Comparison results of two different algorithms

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5. Summary

This paper reports on improvement in locating the beacon in satellite optical communication through the use of a new algorithm, which takes correlation coefficients as weights for computing the centroid of the beacon. Simulation results illustrate that the new algorithm can accurately calculate the centroid of the laser spots. Compared with the conventional gray centroid algorithm, the new algorithm can effectively inhibit the impulse noise interferences.

To examine the feasibility of the new algorithm, an 11.16 km bi-directional free space optical link experiment was established. The results show that the new algorithm can accurately calculate the centroid of the laser spots. For the distorted laser spots propagating through atmospheric turbulence, the experimental results show that this new algorithm is able to improve the positional accuracy of the beacon compared with the traditional centroid algorithm, and hence the tracking performance of the optical communication system was greatly improved by using the new algorithm.

Funding

National Natural Science Foundation of China (NSFC) (11404082,61503096, 11504068,61401279); Fundamental Research Funds for the Central Universities of Harbin Institute of Technology(AUGA5710058015); Advance research Fund for National Key Laboratory of Tunable Laser Technology (6142406030204).

Acknowledgments

The authors are grateful to Free Space Optical Communication Technology Research Center of Harbin Institute of Technology.

References and links

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Laser spots	The gray centroid algorithm	The new algorithm
1	(51.00, 51.00)	(51.00, 51.00)
2	(51.00, 51.00)	(51.00, 51.00)
3	(51.00, 51.00)	(51.00, 51.00)

	MAX (μrad)	AVERAGE (μrad)	Experimental condition
Tracking error with centroid algorithm	9.6	5.8	C_n² = 1.3 × 10⁻¹⁴m^-2/3
Tracking error with new algorithm	4.8	2.5	C_n² = 1.3 × 10⁻¹⁴m^-2/3

Laser spots	The gray centroid algorithm	The new algorithm
1	(51.00, 51.00)	(51.00, 51.00)
2	(51.00, 51.00)	(51.00, 51.00)
3	(51.00, 51.00)	(51.00, 51.00)

	MAX (μrad)	AVERAGE (μrad)	Experimental condition
Tracking error with centroid algorithm	9.6	5.8	C_n² = 1.3 × 10⁻¹⁴m^-2/3
Tracking error with new algorithm	4.8	2.5	C_n² = 1.3 × 10⁻¹⁴m^-2/3

Accurate beacon positioning method for satellite-to-ground optical communication

Abstract

1. Introduction

2. Basic principle

2.1 Basic principle of the gray centroid algorithm

2.2 Basic principle of the new algorithm

3. Simulation

3.1 Simulations for the ideal light spot

3.2 Simulation of the laser spot with noise

4. Experiment

4.1 Near-field experiment

4.2 Long distance laser transmission experiment

5. Summary

Funding

Acknowledgments

References and links

Cited By

Figures (11)

Tables (2)

Equations (5)

Optics Express