Method for measuring atmospheric coherence length of a free-space optical communication link

Abstract

This invention discloses a method for measuring the atmospheric coherence length of a free-space optical communication link. The method includes: firstly, within the framework of Kolmogorov's atmospheric turbulence theory, expressing the time average of the variance of the optical signal wavefront phase fluctuation caused by atmospheric turbulence in the free-space optical communication link using the time average of the phase structure function; then, establishing an analytical expression for the relationship between the time average of the variance of the optical signal wavefront phase fluctuation and the atmospheric coherence length based on the relationship between the phase structure function and the atmospheric coherence length, thereby indirectly measuring the atmospheric coherence length using the information on the optical signal wavefront phase fluctuation caused by atmospheric turbulence in the free-space optical communication link.

Description

Technical Field

[0001] This invention belongs to the field of free-space optical communication, and specifically relates to a measurement of atmospheric coherence length of a free-space optical communication link. Background Technology

[0002] Traditional radio communication systems suffer from problems such as susceptibility to interference, limited bandwidth, high power consumption, and frequency licensing issues. Free-space optical communication, also known as wireless optical communication, is not subject to these limitations. Due to the high directivity of the laser beam and its small divergence angle, it offers high security. Compared to valuable radio spectrum resources, optical frequency bands can be used without licenses. Another advantage of free-space optical communication is that the required terminals are more compact and consume less power than radio communication systems. Furthermore, free-space optical communication can be deployed and put into operation within hours. These advantages make free-space optical communication a highly promising communication method. However, free-space optical communication systems are not only affected by the system equipment itself, but their communication links are also affected by atmospheric turbulence. Under the combined effects of temperature differences, humidity gradients, and wind, atmospheric turbulence forms in the free-space channel. Atmospheric turbulence causes perturbations in the atmospheric refractive index. When optical signals propagate in free-space channels, their wavefront phase is distorted due to the influence of atmospheric turbulence. Over a transmission distance, this phase fluctuation can significantly degrade the performance of free-space optical communication, especially for free-space communication systems using multi-level modulation formats, where it can significantly increase the system's bit error rate. Atmospheric coherence length characterizes the degree of wavefront phase fluctuation of optical signals and is one of the important parameters reflecting the impact of atmospheric turbulence on free-space optical communication. Therefore, high-precision measurement of atmospheric coherence length can provide important technical support for the performance evaluation and optimization design of free-space optical communication systems.

[0003] Current methods for measuring atmospheric coherence length include temperature pulsation, laser scintillation, radar measurement, differential imaging, and slope difference. However, these methods all have certain drawbacks. Temperature pulsation meters can only be installed on low-altitude iron towers and cannot measure the atmospheric coherence length of optical links above the tower; laser scintillation meters are only suitable for measuring the atmospheric coherence length of relatively short optical links on the ground at the kilometer level; radar measurement is only suitable for measuring the atmospheric coherence length of fixed-point terminals, and its measurement equipment is cumbersome to install and very expensive. Differential imaging systems are small, low-cost, easy to install, and have long measurement distances, but this method can only statistically analyze the motion of the centroids of two sub-aperture spots at a fixed location, resulting in a very long measurement time for atmospheric coherence length. The Shack-Hartman sensor in the slope difference method causes noise, aliasing, and modal cross-coupling, which severely reduces the accuracy of atmospheric coherence length.

[0004] In summary, existing methods for measuring atmospheric coherence length all have certain limitations and limited accuracy. Summary of the Invention

[0005] The purpose of this invention is to solve the aforementioned technical problems. Therefore, this patent proposes a method for indirectly measuring atmospheric coherence length using wavefront phase fluctuation information of optical signals. The proposed method is simple to operate, has high measurement accuracy, and effectively avoids the aforementioned shortcomings.

[0006] The technical solution adopted by this invention to solve its technical problem is:

[0007] A method for measuring the atmospheric coherence length of a free-space optical communication link includes the following steps:

[0008] (1) Within the framework of Kolmogorov's atmospheric turbulence theory, a functional relationship is established between the time average of the variance of the optical signal wavefront phase fluctuation caused by atmospheric turbulence and the time average of the phase structure function in a free-space optical communication link. Then, using the relationship between atmospheric coherence length and phase structure function, an analytical expression for the time average of the variance of the optical signal wavefront phase fluctuation and the atmospheric coherence length is further established.

[0009]

[0010] Where r0 represents the atmospheric coherence length, R is the receiver aperture radius, and κ... l =3.3 / l inner ,κ o =2π / L outer , l inner L represents the internal scale factor of atmospheric turbulence. outer This represents the external scale factor of atmospheric turbulence, <σ 2 (R,t)> represents the average value of the phase fluctuation variance over time.

[0011] (2) The existing commonly used optical signal wavefront phase extraction method is used to obtain the optical signal wavefront phase fluctuation information caused by atmospheric turbulence, and the time average value of the phase fluctuation variance is calculated using the optical signal wavefront phase fluctuation information.

[0012] (3) Based on the established analytical expression of the time average of the phase fluctuation variance of the optical signal wavefront and the atmospheric coherence length, the value of the atmospheric coherence length can be calculated using the calculated time average of the phase fluctuation variance.

[0013] This invention employs a wavefront phase structure function pump spectrum model within the framework of Kolmogorov's atmospheric turbulence theory to characterize the statistical regularity of wavefront phase fluctuations in optical signals caused by atmospheric turbulence. This model incorporates both internal and external scale factors of atmospheric turbulence, exhibiting a sharp bulge at high spatial frequencies, which closely matches experimental data. Therefore, the wavefront phase structure function pump spectrum model describes the statistical regularity of wavefront phase fluctuations in actual free-space optical communication links. By substituting the wavefront phase structure function pump spectrum model into the functional relationship between the time average of phase fluctuation variance and the time average of the phase structure function, and performing algebraic operations and simplification, a high-precision measurement of atmospheric coherence length is achieved. The invention also includes a process flow for measuring and obtaining atmospheric coherence length values ​​consistent with actual free-space optical communication links.

[0014] This invention further discloses a method for measuring the atmospheric coherence length of a free-space optical communication link. This method is simple to operate and has high measurement accuracy, and can be used for performance evaluation and optimization design of free-space optical communication systems. Experimental results show that the method proposed in this invention can be used for high-precision measurement of the atmospheric coherence length of practical free-space optical communication links.

[0015] This invention mainly addresses the operational limitations and limited measurement accuracy of existing atmospheric coherence length measurement methods. It focuses on the wavefront phase fluctuations of optical signals caused by atmospheric turbulence in free-space optical communication links. The main challenge lies in obtaining the analytical expression of the time average of the variance of the wavefront phase fluctuations of optical signals as a function of atmospheric coherence length.

[0016] The atmospheric coherence length measurement method for free-space optical communication links disclosed in this invention has the following advantages compared with existing technologies:

[0017] (1) By establishing a functional analytical expression for the time average of the phase fluctuation variance of the optical signal wavefront and the atmospheric coherence length, the measurement of atmospheric coherence length is greatly simplified and the measurement accuracy of atmospheric coherence length is improved.

[0018] (2) By adopting the wavefront phase structure function pump spectrum model under the Kolmogorov atmospheric turbulence theory framework, the atmospheric coherence length measurement value that matches the actual free space optical communication link is obtained. Attached Figure Description

[0019] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0020] Figure 1This is a flowchart of the atmospheric coherence length measurement method for free-space optical communication links according to an embodiment of the present invention;

[0021] Figure 2 This is a comparison chart of the numerical calculation results and the function analytical expression calculation results of the atmospheric coherence length measurement method for free space optical communication links described in this embodiment of the invention;

[0022] Figure 3 This is a comparison chart of atmospheric coherence length measurements based on the phase structure function Kolmogorov spectral model and the pump spectral model for the free-space optical communication link measurement method described in this embodiment of the invention. Detailed Implementation

[0023] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0024] Appendix Figure 1 This is a flowchart of the atmospheric coherence length measurement method for free-space optical communication links proposed in this invention. Figure 2 Based on the appendix Figure 1 A comparison chart shows the numerical calculation results of the functional expression for the atmospheric coherence length of the free-space optical communication link, derived theoretically in Step 1, and its calculation results using the analytical expression. (See attached...) Figure 2 As can be seen, the calculated results of the functional expression and its analytical expression are basically consistent, with negligible differences, indicating the accuracy of the analytical expression of the atmospheric coherence length function. (Appendix) Figure 3 This is a comparison chart of atmospheric coherence length measurements based on the phase structure function pump spectrum model and the Kolmogorov spectrum model. (See attached...) Figure 3 As can be seen, the calculated atmospheric coherence length based on the Kolmogorov spectral model is significantly greater than that based on the pump spectral model. Since the Kolmogorov spectral model does not include the internal and external scale factors of atmospheric turbulence, it cannot characterize real atmospheric turbulence. In contrast, the pump spectral model includes both internal and external scale factors of atmospheric turbulence, best matching real-world atmospheric turbulence. Therefore, the atmospheric coherence length measurement method based on the phase structure function pump spectral model is suitable for practical free-space optical communication links. (See Appendix...) Figure 1 As can be seen from the above, the implementation method of the present invention is achieved through the following steps:

[0025] Step 1: Within the framework of Kolmogorov's atmospheric turbulence theory, establish the functional relationship between the variance of the optical signal wavefront phase fluctuations and the phase structure function caused by atmospheric turbulence. Then, adopt the pump spectrum model of the phase structure function that best matches the actual free-space optical communication link, and express this model in terms of atmospheric coherence length. Finally, establish the analytical expression of the time average of the variance of the optical signal wavefront phase fluctuations and the atmospheric coherence length r0.

[0026] To facilitate obtaining information on the phase fluctuations of the optical signal wavefront caused by atmospheric turbulence, a plane wave is used as a reference. According to Kolmogorov's theory of atmospheric turbulence, atmospheric turbulence is statistically homogeneous and isotropic in both space and time, and also satisfies ergodicity. Therefore, after transmission through a free-space channel, the phase structure function of the optical signal wavefront can be expressed as the time statistical average of the phase difference between two points on the wavefront.

[0027] D Φ (r) = <[Φ(r,t)-Φ(0,t)] 2 >, (1)

[0028] Where r represents the distance between two points in the wavefront space, t represents time, Φ(0,t) and Φ(r,t) represent the phase at the origin and at a distance r from the origin, respectively, and the operators < and > represent time statistical averages.

[0029] The instantaneous phase fluctuation variance of the optical signal on the circular aperture of the receiver can be expressed in polar coordinates as:

[0030]

[0031] Where R is the aperture radius of the receiver, and ψ represents the polar angle. Taking the time statistical averages of both sides of formula (2), we obtain the functional relationship between the time average of the phase fluctuation variance of the optical signal wavefront and the time average of the phase structure function. According to Kolmogorov's theory of atmospheric turbulence, atmospheric turbulence has isotropic properties; therefore, the time average of the phase fluctuation variance is equal to the spatial average of the phase structure function, i.e.

[0032]

[0033] There are two commonly used theoretical models for the phase structure function (PSF). One is the Kolmogorov spectral model, which has the simplest mathematical expression, but it does not match actual free-space optical communication links at high and low spatial frequencies. The other is the pump spectral model, whose mathematical expression is complex, incorporating the internal and external scale factors of atmospheric turbulence, and exhibiting a sharp bulge at high spatial frequencies, which closely matches experimental data. Therefore, the pump spectral model of the PSF describes the statistical law of wavefront phase fluctuations caused by real atmospheric turbulence and best matches actual free-space optical communication links. The pump spectral model of the PSF, which includes atmospheric coherence length, is as follows:

[0034]

[0035] Among them, κ l =3.3 / l inner ,κ o =2π / L outer , l inner L represents the internal scale factor of atmospheric turbulence. outer Γ(·) represents the atmospheric turbulence external scale factor, Γ(·) represents the gamma function; 1F1(·) represents the first-order convergence hypergeometry function, and r0 represents the atmospheric coherence length. Substituting the phase structure function pump spectrum model in formula (4) into formula (3), and through algebraic calculation, the time average of the phase fluctuation variance of the optical signal wavefront <σ 2 The analytical expression of the function (R,t)> between the atmospheric coherence length r0 and the given expression.

[0036]

[0037] According to formula (5), the atmospheric coherence length of the free-space optical communication link can be calculated from the time average of the variance of the phase fluctuation of the optical signal wavefront.

[0038]

[0039] Step 2: Obtain the wavefront phase information of the optical signal caused by atmospheric turbulence using wavefront phase extraction methods. Mature and commonly used methods include the Shack-Hartman sensor wavefront phase reconstruction method and the Gerchberg-Saxton phase extraction method. After obtaining the wavefront phase information of the optical signal, calculate the time average of the phase fluctuation variance.

[0040] Step 3: Substitute the calculated time average of the phase fluctuation variance of the optical signal wavefront into formula (6) to obtain the atmospheric coherence length of the free space optical communication link.

[0041] For example, the simulation parameters are shown in Tables 1 and 2.

[0042] Table 1 Simulation Parameters

[0043]

[0044] Table 2 Simulation Parameters

[0045]

[0046] Figure 2 The numerical calculation results of the atmospheric coherence length function expression formula (3) and the analytical expression formula (6) are presented based on the simulation parameters shown in Table 1. As can be seen from the figure, by selecting multiple average values ​​of phase fluctuation variance that correspond to actual free-space optical communication links, the numerical calculation results of formula (3) and formula (6) are basically consistent, with negligible differences. This demonstrates the accuracy of the analytical expression of the wavefront phase fluctuation variance time average of the optical signal and the atmospheric coherence length. This analytical expression is simple in form and provides a convenient and highly accurate measurement of the atmospheric coherence length of free-space optical communication links.

[0047] Figure 3 The calculation results of the atmospheric coherence length function analytical expressions for the pump spectrum model based on the phase structure function and the Kolmogorov spectrum model are presented based on the simulation parameters shown in Table 2. As can be seen from the figure, the atmospheric coherence length of the free-space optical communication link gradually decreases as the time-averaged variance of the optical signal wavefront phase fluctuation decreases, while the atmospheric coherence length based on the Kolmogorov spectrum model is significantly larger than that based on the pump spectrum model. This is because the Kolmogorov spectrum model is only valid within the inertial range and does not include the internal and external scale factors of atmospheric turbulence; therefore, it cannot characterize the real atmospheric turbulence. The pump spectrum model, on the other hand, includes the internal and external scale factors of atmospheric turbulence, exhibiting a sharp bulge at high spatial frequencies, which best matches the actual free-space optical communication link. Therefore, the atmospheric coherence length measurement method based on the pump spectrum model using the phase structure function has higher accuracy, and the measurement results best match the actual free-space optical communication link.

[0048] It should be noted that the embodiments described above are not intended to limit the present invention in any way, and all modifications made based on the technical essence of the present invention shall still fall within the scope of the present invention.

Claims

1. A method of measuring the atmospheric coherence length of a free-space optical communication link, characterized by, Includes the following steps: S1: Within the framework of Kolmogorov's atmospheric turbulence theory, a functional relationship is established between the time average of the variance of the optical signal wavefront phase fluctuation caused by atmospheric turbulence and the time average of the phase structure function. Then, using the relationship between atmospheric coherence length and the phase structure function, an analytical expression for the time average of the variance of the optical signal wavefront phase fluctuation and the atmospheric coherence length is further established. Where r0 represents the atmospheric coherence length, and R is the receiver aperture radius. , This represents the internal scale factor of atmospheric turbulence. This represents the external scale factor of atmospheric turbulence. This represents the average value of the phase fluctuation variance over time, where t represents time. S2: The optical signal wavefront phase extraction method is used to obtain the optical signal wavefront phase fluctuation information caused by atmospheric turbulence, and the time average value of the phase fluctuation variance is calculated using the optical signal wavefront phase fluctuation information. S3: Based on the established analytical expression of the time average of the phase fluctuation variance of the optical signal wavefront and the atmospheric coherence length, the atmospheric coherence length can be calculated by obtaining the calculated time average of the phase fluctuation variance.

2. The measuring method of claim 1, characterized in that, The time average is taken for both the wavefront phase fluctuation variance and the phase structure function of the optical signal.

3. The method of measuring of claim 1, wherein, The wavefront phase structure function of the optical signal adopts the pump spectrum model that best matches the actual free-space optical communication link.

4. The method of measuring of claim 1, wherein, The wavefront phase structure function of an optical signal includes the atmospheric coherence length.

5. The measurement method according to claim 1, characterized in that, Based on the pump spectrum model of the phase structure function that includes atmospheric coherence length, an analytical expression is established for the time average of the variance of the wavefront phase fluctuation of the optical signal caused by atmospheric turbulence and the atmospheric coherence length.

6. The method of measuring of claim 1, wherein, Also includes: The implementation method is used to output a high-precision atmospheric coherence length value that matches the actual free-space optical communication link.

7. The method of measuring of claim 1, wherein, Applications in performance evaluation and optimization design of free-space optical communication systems.

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