可调谐高精度光学分数阶傅里叶变换器基础研究

Fractional Fourier transform plays an important role in the application of non-stationary signal analysis and processing. Nevertheless, the implement method in digital domain spends enormous expenditure on computing, and is confronted with the bottleneck of achieving high-accuracy digitization of wideband signals. In recent years, the implementation of fractional Fourier transform in analog domain with the assistance of lightwave, which utilizes its characteristics of broadband and high speed, is regarded as a potential technique to solve the above-mentioned problems. In order to overcome the issues of low resolution and fixed order in the existing optical fractional Fourier transformers, a new method to achieve a large equivalent dispersion with a free tunable scale is proposed based on a frequency-shift optical loop in this project. Using this method, a tunable optical fractional Fourier transformer with a high resolution is realized. The research content of this project can be summarized as follows. Firstly, the realization mechanism and method of a large equivalent dispersion with a free tunable scale in a frequency-shift optical loop will be researched. Then, the realization mechanism of an optical fractional Fourier transformer based on a frequency-shift-optical loop will be researched, and its characteristics will be analyzed. Finally, the experiment application of a tunable optical fractional Fourier transform with a high resolution in real-time signal analysis and processing will be researched. The research will be carried out in full-scale, including theoretical analysis, numerical simulation and experiment verification, which is expected to promote the development of the optical real-time signal processing.

分数阶傅里叶变换在非平稳信号的分析和处理中具有非常重要的应用。然而，数字域实现方法存在庞大的计算开销和宽带高精度数字化瓶颈问题。目前，利用光波的宽带、高速特性在模拟域实现信号的分数阶傅里叶变换是避免上述问题的潜在技术途径。为了解决现有光学分数阶傅里叶变换器分辨率较低且阶数固定的问题，本项目提出了一种基于移频光环路实现宽范围可调谐等效大色散的方法，并利用该方法实现阶数可调谐的高精度光学分数阶傅里叶变换器。项目拟从理论分析、数值仿真和实验验证等方面，研究移频光环路的宽范围可调谐等效大色散实现机理及方法，研究基于移频光环路的光学分数阶傅里叶变换器实现机理和特性，研究可调谐高精度光学分数阶傅里叶变换器在实时信号分析和处理中的实验应用等，期望促进光学模拟信号实时处理的发展。

本项目针对宽带无线通信、先进雷达、电子侦察等民用和国防领域对宽带微波信号实时处理的亟需，围绕基于光学色散的模拟信号处理技术开展研究工作，重点研究了基于光学移频环路等效大色散的分数阶傅里叶变换、基于色散啁啾补偿超短光脉冲采样的宽带微波信号测频和基于色散傅里叶变换的光学时间拉伸模数转换，突破了连续可调谐的等效大群速度色散实现、色散功率代价导致的数字化模拟带宽受限等关键理论问题，掌握了实时高精度大范围的微波频率和啁啾率测量，以及宽带微波信号高速线性化模数转换等关键技术，形成了一套实现宽带微波信号实时处理的方法。对于基于光学移频环路的分数阶傅里叶变换器，建立了完整的理论模型；提出了基于三路自由光谱范围互质的高精度大范围微波信号频率和啁啾率测量方案，并进行了仿真和实验验证；提出了基于频域基频判据的微波信号啁啾率测量方法，以提高系统的抗噪声特性，同时降低系统对光电探测器和测量仪器的模拟带宽需求，并完成了验证。针对基于色散啁啾补偿超短光脉冲的测频，建立了理论模型，设计并搭建了重复频率可调的超短光脉冲源；提出了采用三通道重复频率互质的超短光脉冲源进行光采样，实现宽带多频率微波信号的高精度频率测量，并进行了实验验证。针对基于色散傅里叶变换的光学时间拉伸模数转换器，建立了全套理论模型，提出了采用互补单边带调制结构结合数字域补偿算法的宽带线性化光学模数转换方案，同时抑制了载波包络和调制非线性导致的失真，并解决了色散功率代价导致的模拟带宽受限的问题，完成了实验验证。项目的研究成果对于基于光学色散的模拟信号处理具有参考价值。

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