It is a radical but pressing problem to measure the group refractive index of dispersive material both accurately and rapidly in optical engineering field. In this paper, a white-light spectral interferometric system employing a fiber-optic spectrometer is developed for solving this problem. The system takes advantage of the characteristic of fiber-optic spectrometer which can get all the interferometric information by a single shot image without any mechanical scanning.Compared with the traditional windowed Fourier transform, a wavelet transform algorithm is used to directly extract the group delay rather than the phase from the interferogram. Therefore, the new method can provide a simple and fast solution, while still maintaining high accuracy. Based on this white-light Michelson interferometric system, fused silica and BK7 glass samples are measured respectively and the results agree well with the theoretical values over a broad spectral range. At the end of this paper, different mirror positions are used to verify the repeatability of our method.%对群折射率的精确而快速测量是光学工程领域一个基础而又亟需解决的难题,本文提出了一套光谱型迈克尔逊白光干涉系统的解决方案.该系统充分利用了微型光纤光谱仪一次测量便可获得所有干涉信息的特点,无需机械扫描装置,具有结构简单和测量快速的优点.与传统的窗口傅里叶变换算法相比,本文采用小波变换直接从干涉信号的小波脊中提取群延迟,减小了由相位求导得到群延迟过程中引入的误差放大效应,进而提高了群折射率的测量精度.基于此迈克尔逊白光干涉系统,在不同干涉位置处对两块不同厚度的石英和BK7玻璃进行了测量,实验结果表明此方法在宽光谱范围内具有较高的测量精度和良好的重复性.
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