As an important branch of quantum science, quantum optical communication has gained a lot of attention and investment in scientific research worldwide due to its advantages of high security and good physical confidentiality. In free-space quantum optical communication, the maintenance and detection of the beacon rotation angle between the transmitter and receiver of the beacon light is the key to ensure the success of quantum optical communication in the free-space motion platform. How to obtain the rotation angle of the beacon light transmitter on the moving platform and effectively use the limited optical link to obtain the attitude information of the target is one of the difficult technologies for low-cost mobile quantum optical communication in the future. The existing techniques for measuring the rotation angle of beacon light are limited by a variety of factors such as the large error of the measurement system caused by the construction of hardware equipment and the limited range of angle measurement, and the debugging of parameters in the angle calculation method using adaptive iteration has a large impact on the experimental results. In this paper, by streamlining the optical path design, an optical method of deviation self-compensation is proposed. A combined beacon beam is obtained using red (R), green (G) and blue (B) three-color light carrying different polarization angle information. The concepts of difference and ratio are introduced to construct the parameter β to calculate the three-color light intensity. Finally, the θ-β relation between the beacon rotation angle θ and the characteristic parameter β is established. In this way, we decouple the measurement of the rotational attitude angle of the platform. To some extent, the scheme we propose can reduce the interference error introduced by the environment, expand the application scenario of beacon rotation angle measurement, and achieve the design goal of the system.

In this paper, the red, green and blue combined beacon light adjusted by 0°, 45° and -45° polarizer start biases is designed to carry the rotational attitude angle information of the carrier platform. After the free-space transmission, the combined beacon light is decoupled by the ground receiving system and the three-color light intensity value of the beacon light is obtained at the receiving end using three photodetectors. The schematic diagram of the measurement system is shown in Fig. 1. The data processing flow of this measurement system involving four main steps (Fig. 6). The system performs RGB three-channel measurement on the carrier platform, and three sets of raw data will be obtained. First, the raw data need to be filtered to remove the noise in the measurement process and to be normalized to eliminate the influence of the magnitude on the values. In the next step, the magnitude relationship between the three-color light intensity values can be used to initially determine the range of the object rotation angle. Further, the characteristic parameter β is constructed according to the difference and ratio of the three-color light intensity values, and the calculation process of β is represented in Fig. 4 to establish the θ-β relation curve between the beacon light rotation angle θ and the characteristic parameter β. In this way, fine angle results are obtained, realizing the measurement and calculation process from light intensity value to rotation angle.

According to Malus law, the light intensity model of the scheme is established as shown in Eqs. (4)-(6). The θ-β relation curve under ideal condition is shown in Fig. 7. To test the applicability of the curves, the RGB ensemble beacon optical rotational attitude decoupling measurement system was established, and multiple measurements were performed at different distances both in the laboratory and outdoors. The experimental results (Figs. 10 and 11) are consistent with the theoretical values in the measurement range of 0°-90°. In the positions of θ=22°, 23°, 24°, 67°, 68°, there are relatively large errors in the experimental values, and the accuracy of the remaining parts is relatively high, with the error no more than 0.0012. This error contains two meanings. One is the randomness of the measurement results, caused by the background light, air pressure, temperature and other random factors at the time of measurement. This kind of error is generally small. The other comes from the phase deviation among three channels, which is caused by the optical path structure and optical devices and will lead to the false β calculation results. This kind of error will impact the measurement results more substantially than the former. We conducted a detailed error analysis of the theoretical values and measurement results, and the error characteristic indices are shown in Table 2. The spatial attitude angle accuracy of the beacon can be 0.05°, with 3σ of 0.5° under indoor conditions and 1° under outdoor conditions. In summary, the overall average error of the experimental system is low, and the consistency between the experimental results and the theoretical results is high, indicating that the proposed scheme is practical and feasible.

The method is based on the red (R), green (G), and blue (B) ensemble beacon light with specified starting angle of polarization to decouple the rotational attitude angle of a space motion platform. The idea of difference and ratio is introduced, and the correlation curves are constructed to provide intuitive numerical results for the application of polarized light to rotational attitude angle decoupling. The stable and high accuracy measurement results are maintained in the experiments of different measurement environments. The accuracy of the beacon spatial attitude angle can be up to 0.05°, with 3σ of 0.5° under indoor conditions and 1° under outdoor conditions. The error indices of the measurement results under different measurement conditions are calculated to verify the feasibility of the optical decoupled rotational attitude angle of the RGB ensemble beacon. The method has little dependence on environmental stability, low complexity of the measurement device, and light burden of experimental data calculation. The current measurement system still needs to be improved in terms of phase compensation, which can improve the resolution of the measurement and the error correction effects to meet the requirements of higher precision dynamic measurement.