基于主成分分析法的高性能波长计研究与实现

波长探测作为科学技术中的一个基本工具，在分析化学、生物传感和光学通信等众多领域具有重要作用。从多模光纤信号传输理论出发，在绝热、准直模型中建立基于模式干涉效应的强度干涉图像理论；实验测量时，在光纤尾端引入缓变（斜率约为0.01）锥形区域设计，保证收集到侧面辐射信号的同时，也近似满足理论模型和数值仿真结果。在搭建的显微共焦成像系统中，连续扫描窄带激光器进行干涉图像存储，经过区域选取、向量拼接以及奇异值分解等步骤得到由器件特性决定的校样矩阵。波长的探测过程共分为两个步骤：在工作带宽内纳米量级粗略扫描光波长得到粗略校准矩阵，一维待测信号强度图像与之进行内积相关性运算后，选取数值最高的波长值作为预估波长单元；在此基础上精细扫描得到精细校样矩阵，选取三个最大主成分并定义与波长欧氏距离最小值确定最终探测波长。采用内积相关性运算联合主成分分析法不仅可以将波长探测分辨率提高到20 pm、准确率达到96.7%，探测效率较其他光谱重建算法提高50倍。实验证实该波长计工作范围至少为400～700 nm，器件尺寸仅为π×(20 μm)2×0.5 mm。该器件在高性能、便携式和低成本方面较同类器件有较大提升，在光谱重建效率也集成了高效算法，能够广泛应用于光纤传输系统的波长实时探测。

Research and Implementation of High-Performance Wavemeter Based on Principle Component Analysis

As an essential tool in science and technology, wavelength detection plays a vital role in analytical chemistry, bio-sensing and optical communication. The traditional spectrometers based on dispersing components or resonant cavities greatly suffer from bulky size, high power consumption and fabrication imperfection. With the rapid development of micro processing, novel types of high-performance and portable spectrometers emerged, and the pursuit of pushing the performance to limit remains unsettled. Based on the signal transmission theory in multimode fiber, the intensity interference patterns are resulting from the mode interference effect were established in adiabatic and collimated model. In the experimental measurement, the tapered region with a slowly varying slope (about 0.01) was introduced near the end of the fiber to ensure that the side radiation signal could be collected. To estimate the number of modes supported in different structures, both the theoretical and numerical simulations are consistent with the experimental tendency. Using the confocal microscope system we made, the interference patterns are stored by continuous scanning a narrow-band laser. The calibration matrix corresponding to the device’s unique characteristics is obtained by region selection, vector splicing and singular value decomposition. The following wavelength detection process can be divided into two steps: the rough calibration matrix within the working bandwidth is obtained after the rough scanning of the wavelength in 1nm scale, and the wavelength units with the non-zero value are selected as the target after inner product correlation operation with the degraded one-dimensional signal intensity vector. This initial procedure provides the criterion of optimizing the structural parameters. On this basis, fine scanning is performed to obtain the refine calibration matrix. The three largest principal components are selected and defined as the final detected wavelength based on the minimum Euclidean distance. The inner product correlation operation combined with the principal component analysis can improve the wavelength detection resolution to 20 pm with the accuracy rate of 96.7%. The detection efficiency is fifty times higher than other nonlinear spectral reconstruction algorithms reported. The experimental results show that the working bandwidth is at least from 400 to 700 nm, and the device size is only π×(20 μm)2×0.5 mm. The practical feasibility and photon detection are also investigated, considering its further application. Compared with its counterparts, this device has a significant improvement in high performance, portability and low cost, it also integrates with an efficient algorithm in wavelength detection procedures. Both device and theory could be widely used in real-time wavelength detection of optical fiber transmission systems.