基于ResNeXt网络的扰动轨道角动量谱识别

Disturbance Orbital Angular Momentum Spectrum Recognition Based on ResNeXt Network

涡旋波束携带的轨道角动量(OAM)模态在通信容量提高、同时同频多路信息调制等领域具有重要的应用前景,但涡旋波束经复杂介质环境后会造成波束场幅度和相位扰动,进而引起信道串扰、高误码率等问题。基于ResNeXt网络,提出了一种基于实测涡旋波束扰动场的图像,识别扰动场OAM谱分布的方法。以涡旋贝塞尔波束入射玻璃板的实验图像为例,利用所提方法进行OAM谱识别,对于不同入射方向情况下的场幅度图像,通过优化后的ResNeXt网络获得了透射场的OAM谱分布结果,对识别结果进行谱分布重构,并与数值计算结果进行对比,分析误差。结果表明,优化后的ResNeXt网络可以有效地识别出穿过玻璃介质之后的入射角为0°~45°的贝塞尔波束的透射场OAM谱分布,由于谱分布的弥散程度随着入射角度的增大而增大,与理论计算结果相比,主模相对误差亦随角度的增大而增大,但最大不超过22.86%。

Objective Vortex beams carrying orbital angular momentum(OAM)mode have important application prospects in improving communication capacity,multiple-channel information modulation with the same frequency and time.As the vortex beam propagates through complex medium environments,the beam field amplitude and phase may be disturbed,causing channel crosstalk and high bit error rate.Several studies proved that the OAM spectrum disturbance caused by a complex medium environment is one of the key problems that need to be solved in the OAM multiplexing technology.The distribution of the vortex beam’s OAM spectrum can easily be obtained through the numerical method.However,the accurate inversion of the OAM spectrum distribution according to the measured field in the actual measurement system is still worth investigating and discussing.Existing methods for classifying OAM mode mainly focus on the main mode.This study proposes a method for identifying the OAM spectrum distribution of the measured image of the disturbed field using the ResNeXt network.Converting the problem of OAM spectrum distribution to the probability problem discriminates test samples belonging to training samples of each type in convolutional neural network(CNN),and the percentage of the main module and side lobes of the OAM modal can be obtained.Methods By optimizing the ResNeXt network,the fitting function of the OAM spectrum distribution of the vortex beam’s transmission field calculated from the spectrum analysis theory of vortex beams is set as the self-defined loss function of the network.The total loss function of the network L_(total) consists of three parts.L_(1) is the cross-entropy function,which calculates the main model classification loss of the test sample.L_(2)+L_(3)are the loss functions for predicting the OAM spectrum distribution,and the custom loss function is included in L_(2).L_(3) is the cross-entropy function,the same as L_(1).The training samples are the light intensity pattern of a Bessel vortex beam with l=4--12,which does not propagate through the glass medium without aberration.The test samples are the light density diagrams of a Bessel vortex beam with l=4,propagating through an isotropic glass plate with a thickness of 4mm under different incident angles.The optimized ResNeXt network must first test the category of test samples,called the main mode discrimination.Then,it sets the network study according to the preset fitting function of the OAM spectrum distribution(the self-defined loss function)and obtains the probability that test samples belong to training samples in each category,achieving the purpose of reconstructing the OAM spectrum distribution of the beam’s transmission field.Results and Discussions The discriminating results of the OAM spectrum of the Bessel vortex beam’s transmission field are compared with the numerical results based on the ResNeXt network by using a fixed recognition process(Table 1),and light density diagrams of the eighth-order Bessel vortex beam propagate through aglass medium under different incident angles as test samples(Fig.3).Additionally,the relative errors are calculated(Fig.4).Since the diffusion of the OAM spectrum distribution increases with an increase in the incident angle,the main mode loses its dominance when the incident angle increases to a certain degree.The proportion of side lobes exceeds the main mode,and the spectrum distribution’s regularity is weakened.The ResNeXt network’s discriminating error also has an increasing tendency with an increase in the incident angle.However,the maximum relative error does not exceed 22.86%compared with numerical results,and the absolute error of side lobes does not exceed 22.23%(Table 4).There are three main reasons.First,since the Bessel beam has the characteristics of multi-topological charges,its OAM spectrum distribution extends infinitely to both sides with the position of the main mode in the center.However,the training set types are limited and can only be discussed in the main modes.Second,since the regularity of the OAM spectrum distribution of the Bessel vortex beam’s transmission field decreases with an increase in the incident angle,the dispersion becomes more obvious,decreasing the recognition accuracy.Finally,since the OAM spectrum recognition problem is different from the conventional classification problem,the CNN feature of test samples is relatively related to the main mode and weakly related to the side lobes.Although the custom loss function contributes to reducing the error,it cannot determine the recognition result of the network.Thus,the side lobe recognition error is greater than the main mode.Conclusions Based on the ResNeXt network and by introducing self-defined loss function,this study discriminates the OAM spectrum distribution of the Bessel vortex beam’s transmission field,which propagates through the glass medium with an incident angle ranging from 0°~45°,the comparison is made,and the error of the numerical result is analyzed.The results show that the relative error of the main mode increases along with the increase in the wave beam incident angle.However,it does not exceed 22.86%,and the discriminating error of side lobes is bigger than that of the main mode.The proposed method is not limited to the category discrimination of the main mode,but discriminates the percentage of the main mode in the OAM spectrum distribution in detail.This study provides a new idea for the OAM mode discrimination;however,how to improve the discriminating accuracy of side lobes will be the next challenge.