Optimal optical path difference of an asymmetric common-path coherent-dispersion spectrometer

Optical path difference (OPD) is a very significant parameter in the asymmetric common-path coherent-dispersion spectrometer (CODES), which directly determines the performance of the CODES. In order to improve the performance of the instrument as much as possible, a temperature-compensated optimal optical path difference (TOOPD) method is proposed. The method does not only consider the influence of temperature change on the OPD but also effectively solves the problem that the optimal OPD cannot be obtained simultaneously at different wavelengths. Taking the spectral line with a Gaussian-type power spectral density distribution as a representative, the relational expression between the OPD and the visibility of interference fringes formed by the CODES is derived for the stellar absorption/emission line. Further, the optimal OPD is deduced according to the efficiency function, and the relationship between the optimal OPD and wavelength is analyzed. Then, based on the materials' dispersion characteristics, different optical materials are combined and added to the interferometer's reflected and transmitted optical path to implement the optimal OPD at different wavelengths, thereby improving the detection precision. Meanwhile, the materials whose refractive index negatively changes with temperature are selected to reduce or even offset the temperature impact on OPD, and hence the system's stability is improved and further improves the detection precision. Under certain input conditions, the material combination that approximates the optimal OPD is performed within the range of 0.66-0.9 µm. The simulation results show that the maximal difference between the optimal OPD obtained by the efficiency function and the OPD produced by the material combination is 0.733 mm for the absorption line and 1.122 mm for the emission line, which is reduced by 1 time compared with only one material. The influence of temperature on the OPD can be reduced by 2-3 orders of magnitude by material combination, which greatly ameliorates the stability of the whole spectrometer. Hence, the TOOPD method provides a new idea for further improving the high-precision radial velocity detection of the asymmetric common-path CODES.