几何量的测量在科学研究、精密制造和空间定位等领域均有着广阔的应用。光学干涉测量方法是目前最常用、也是精度最高的测量几何量的方法。一般情况下，光学干涉测量方法直接获得的不是几何量，而是光程，需要补偿物质折射率才能获得几何量，因此折射率的补偿精度最终决定了几何量的测量精度。近年来，光学频率梳的出现对精密测量领域产生了革命性的推进。因此，本文结合光频梳色散干涉测量方法，研究了固体平板折射率直接测量方法和空气折射率自修正补偿方法。首先，本文研究了光频梳色散干涉理论模型，分析了光谱仪分辨率对色散干涉方法的影响，提出了光谱干涉对比度与光程差和光谱仪分辨率之间的理论关系，解释了一定光谱测量分辨率下，色散干涉方法的相干范围。同时提出了修正因子用于补偿由于光谱仪分辨率导致的干涉光谱相位偏移系统误差，可在较低光谱测量分辨率条件下提高基于光频梳的色散干涉方法的测量精度。其次，本文提出了一种基于光频梳色散干涉的固体平板折射率和几何厚度同时测量方法。该方法利用光束在固体平板前后表面的来回反射光实现折射率和几何厚度的同时测量。相比于传统的单点扫描系统，该方法通过一维线光源扫描待测样品，提高测量速度。为了提高厚度的测量范围，本文利用增大光束尺寸的方法提高自制光谱仪的分辨率。该方法最终折射率的测量精度为4.0×10-4，几何厚度的测量精度为50 nm。再次，针对空气折射率修正，本文提出了一种多波长自修正方法，研究了这种多波长方法的理论模型，根据理论模型提出了精度优化方向。该方法通过高非线性光纤扩宽光频梳光谱，利用色散干涉方法同时测量多个波长处的光程值，直接通过多波长光程值和修正系数完成空气折射率自修正，最终修正精度为3.5×10-7。在潮湿不稳定的环境下，多波长方法的空气折射率修正精度要优于传统的双波长方法。最后，本文在群相双波长空气折射率自修正方面进行了探索，理论分析表明该方法可以克服传统双波长方法无法适用于潮湿空气的缺陷。并进一步提出实验构想，利用色散干涉测量某一波长群折射率对应的光程量，利用外差干涉精确测量另一特定波长相折射率对应的光程量。

Precise geometrical length measurement plays an important role in scientific research, space missions, precision manufacture, space location and other fields. Optical interference measurement method is the most widely used and the most accurate method in the filed of geometrical length measurement. Usually, optical interference measurement method directly obtains the optical length, not the geometrical length. To calculate the geometrical length, refractive index should be corrected, therefore the accuracy of refractive index correction finally determines the accuracy of geometrical length measurement. In recent years, the development of optical frequency comb (OFC) has started a new chapter for high-precision measurement technology. This dissertation proposes the solid refractive index measurement and air refractive index correction based on dispersive interferometry of optical frequency comb.At first, we propose a theoretical model to analyze the influence of spectral resolution, which can explain the relationship between the interference contrast of the interference spectrum and the variation in the measured distance with the resolution of a spectrometer. It can also be used to compensate for the systematic error caused by the resolution of the spectrometer. This method improves the accuracy of dispersive interferometry of optical frequency comb.Then, this dissertation presents a method to measure the wafer thickness and refractive index simultaneously by dispersive interferometry of optical frequency comb. This method employs the fundamental transmission beam and echo reflected beam to realize thickness and refractive index measurement simultaneously. The field of view can cover a line ranging which improve the measurement speed. Meanwhile, the resolution of the self-made spectrometer is improved by increasing the size of the beam, and the measurement range of the thickness is increased. The accuracy of refractive index measurement is 5×10-4, and the accuracy of thickness measurement is 50 nm.Furthermore, we propose a multi-color method for the self-correction of air refractive index based on dispersive interferometry of optical frequency comb. This method can be applied to correct air refractive index for long-distance measurements in moist air. Optical lengths of multi-wavelength are obtained simultaneously by dispersive interferometry of optical frequency comb. We broaden the optical spectrum by the high nonlinear optical fiber. By applying the multi-color method, correction of air refractive index with an uncertainty of 3.5×10-7 is achieved.Finally, this dissertation proposes a group-phase two-color method of air refractive index correction which can be used in moist and unstable air environment. This method is achieved by using the phase refractive index of one color by heterodyne interference of OFC and the group refractive index of another color by dispersive interferometry of OFC for the correction of air refractive index. In this chapter, a method to calculate the effective center wavelength of wide spectrum heterodyne interference signal was explored though both simulation and experiment.