1. National Key Laboratory on Vacuum Technology and Physics, Lanzhou Institute of Physics, Lanzhou 730010, China
2. Key Laboratory of Spectral Imaging Technology, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi'an 710119, China
Abstract：With the quantization transformation of traditional metrology standards, quantum vacuum metrology technology based on optical methods has been developed. Combining the quantum vacuum metrology technology based on optical interference and spatial heterodyne interference spectroscopy, this paper proposes a new method for measuring gas pressure using refractive index. The two-arm passages of the spatial heterodyne interferometer are set as closed chambers that can be evacuated and de-aerated. When the gas pressure in the chamber changes, the refractive index of the gas changes accordingly. The change in refractive index changes the propagation path of light in the two arms, causing changes in the spatial frequency, phase and other characteristics of the interference fringes, from which the gas pressure can be inverted. In this paper, based on the analysis of the influence of refractive index on the grating diffraction angle, the optical path difference is calculated to obtain the theoretical expression of spatial heterodyne interference fringes containing refractive index. Through theoretical analysis, it is obvious that the change in refractive index brings about the drift of the Littrow wavelength of the interferometer, thereby causing the change of the spatial frequency and phase of the fringes. Then, numerical simulation is carried out based on the theoretical expression. When the air pressure changes from 0 ATM to 1 ATM, the maximum changes of the sampling fringe period and phase are 6.21 periods and 19.50 rad, respectively. An optical model is established with the same parameters for ray tracing simulation, and the simulated interference pattern is inverted with the same Fourier method. The changes of the fringe period and phase under the same air pressure change in the inversion result are very close to the numerical simulation, with a difference of only 5.6×10-3 periods and 0.014 8 rad, which verifies the theoretical expression of spatial heterodyne interference fringes with refractive index effect in this paper, and illustrates the feasibility of refractive index inversion and gas pressure calculation based on this theory. Finally, two methods of changing Littrow wavelength and increasing optical path difference scanning range to further improve phase response sensitivity are discussed, and simulations of changing grating diffraction order and increasing optical path difference offset are carried out. In the simulation, compared with the first-order diffraction, changing the order can increase the diffraction order by times, and increasing the offset of 1 mm compared with the symmetrical structure also improves the phase response by 27.65%, which proves that the feasibility of using spatial heterodyne interferometer for gas pressure measurement can be further improved after optimized design.
Key words：Spatial heterodyne spectroscopy; Vacuum measurement; Refractivity index
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