@phdthesis{oai:niigata-u.repo.nii.ac.jp:02000952,
 author = {Zhang, Kaining},
 month = {2023-04-24, 2023-04-24},
 note = {Spectral resolved interferometer (SRI) has a broadband light source and a spectrum analyzer (SPA). The interference signal produced by the SPA is roughly expressed by cos(2πvL), where v is wavenumber and L is an optical path difference (OPD) between an object surface and an reference surface. When L is large, a high-resolution SPA is needed. A SPA with a wavelength resolution higher than about 0.05 nm is required to measure a large thickness more than a few millimeters. In this thesis a new method is proposed to measure a large thickness of glass plate by using a SPA with a low-resolution of 0.5 nm and a piezo electric transducer (PZT) stage with a positioning accuracy of 10 nm. The position of a reference surface in the SRI of Michelson type is adjusted by the PZT stage to generate a small OPD. Thus, the interference signal can be detected with the low-resolution SPA. There are two ways to extract the OPD L from the detected interference signal. One way is that L is obtained from a position of maximum amplitude in Fourier transform of the interference signal. The other way is that L is obtained from the spectral phase 2πvL which is extracted through Fourier transform and frequency filtering. When the object is a glass plate, OPD L is a function of wavenumber v due to the phase refractive index n(v) of a glass plate. This phenomenon is called "dispersion effect". OPD L cannot be exactly obtained from a position of the maximum amplitude because of a strong dispersion effect when thickness T of a glass plate is large. On the other hand, OPD L can be exactly obtained from the spectral phase because L is directly related with the spectral phase and the dispersion effect produces only nonlinear component in the spectral phase. Hence, in this thesis spectral phase is utilized to measure thickness T and refractive index n(v).There is another dispersion effect caused by a beam splitter cube whose two sides do not have the same length. In order to eliminate this dispersion effect and measure thickness T, different optical configurations of the SRI are formed by using another fixed reference surface in the object arm or a compensation glass (CG) plate in the reference arm. Different spectral phases are detected with different positions of the reference surface in the different optical configurations. Thickness T can be measured from many detected spectral phases. Measurement of phase refractive index of a glass plate can be achieved by using the SRI and the measurement method in the thickness measurement. The following three different measurements are described in this thesis. (1) Large thickness measurement of glass plate whose refractive index is not known. Amplitude distribution in Fourier transform of an interference signal produced by a rear surface of glass plate has a large spread width due to the dispersion effect of the glass plate. The position of the reference surface is adjusted so that the interference signal having a small OPD can be detected with the low-resolution SPA. Another reference surface is fixed in the object arm. Four different optical configurations are used with four different positions of the reference surface. From the four different spectral phases a spectral phase without containing the refractive index of glass plate is derived. The thickness of the glass plate can be measured from the slope of this spectral phase distribution. In experiments, it was confirmed that the detected position of maximum amplitude in Fourier transform of the interference signal agreed with the theoretical one. A small measurement error of 50 nm was achieved in measuring 1 mm thickness of a glass plate. (2) More larger thickness measurement of glass plate using a compensation glass whose refractive index is known. In order to reduce the large spread width in the amplitude distribution caused by the dispersion effect of a larger thickness, a compensation glass (CG) plate is employed. Thickness larger than one millimeter can be measured by using the CG. A spectral phase is detected from the interference signal generated from the front surface of a glass plate and a reference surface. After putting the CG into the reference arm, another spectral phase is detected from an interference signal generated from the rear surface of the glass plate and the reference surface. A detected spectral phase is obtained from these two spectral phases. By comparing the nonlinear component of the detected spectral phase with a theoretical one, the difference in thickness between the glass plate and the CG can be obtained. Thickness of the glass plate can be measured from this thickness difference and a linear component of the detected spectral phase. In experiments, measurement errors were less than 800 nm and 2 µm for 1 mm and 5 mm thickness glass plates, respectively. (3) Phase refractive index measurement of glass plate together with thickness measurement. Phase refractive index is an important property of optical material. The SRI and the measurement method in the thickness measurement are applied for measurement of phase refractive index. Object was a quartz glass plate with 20 µm thickness. By combining the three spectral phases detected in two different configurations, thickness of the quartz glass was measured with an error less than 6 nm. The refractive index is obtained from one of the three spectral phases. It is required to determine 2π phase ambiguity existing in the spectral phase distribution for the refractive index measurement. This determination is carried out by fitting the spectral phase distribution with fitting functions based on Cauchy dispersion formula. Phase refractive index distribution of the quartz glass plate could be measured with an error less than 0.0005 from the measured thickness, the determined 2π phase ambiguity, and the spectral phase distribution., 新大院博(工)第533号},
 school = {新潟大学, Niigata University},
 title = {Research on measurement of thickness and refractive index of glass plates with a spectrally resolved interferometer},
 year = {}
}