## 1 Introduction  
In recent years, with the maturity and development of high-precision spectroscopic technology, the precise measurement of the hyperfine structure (HFS) of alkali metal atoms and related physical constants has been a topic of concern in the fields of atomic physics, laser spectroscopy, and precision measurement [1; 2]. To reduce the Doppler broadening effect, two-photon Doppler-free spectroscopy [3] and electromagnetically-induced transparency (EIT) [4] have been used for precise measurements. The hyperfine splitting interval of the excited state of alkali metal atoms can be measured and the corresponding hyperfine interaction constants can be further derived with high precision. The hyperfine structure of atoms resulting from electron-nuclear interactions provides structural information about the nuclear and electronic structure of the atoms [5]. There is a further problem with parity nonconservation (PNC) [6; 7]. PNC is sensitively dependent on the overlap of the nuclear and electronic wave functions [8], which is related to an accurate atomic structure. As the hyperfine structure can be accurately measured, we can improve the accuracy of measurements to explain the relevant physical measurements and calculations [9; 10]. [PERSON] et al. [11] recently studied the calculation of the nuclear spin-independent parity violating the electric dipole transition amplitude and constraints on new physics from an improved calculation of parity violation in Cs. On the other hand, another challenging problem which arises in this domain, as highlighted by [PERSON] et al. [12], is that the polarizability of the \(6p\) state is consistent with the experimental values, but the lifetime is inconsistent with the experimental values of the \(5d\) state. The polarizability and the lifetime are also closely related to the calculation of the dipole matrix element [10; 13]. In order to analyze the origin of this inconsistency, it is necessary to continue studying the structural properties of \(nd\) states. [PERSON] et al. [14], who studied the feasibility of measuring PNC amplitudes in the dipole-forbidden transitions of cesium (Cs) atoms, was hampered by the difficulty of the strong correlation effects. Therefore, research related to the \(nd\) state and the precise measurement of hyperfine structures play an important role in fundamental physics, such as atomic frequency calibration, construction of quantum theoretical models, laser cooling and trapping, and isotope identification [15; 16; 17; 18; 19]. Although many groups carried out theoretical and experimental studies on the atomic hyperfine structure, there were few precise measurements of the hyperfine interaction constants, especially for the \(nd\) state. Considering the complexity of their internal electronic cloud's structure and strong correlation effects [14], the calculation results of different theoretical models differ greatly. In order to verify the theoretical model of the \(nd\) state, it is urgent to accurately measure the hyperfine-level structure of the \(nd\) state experimentally. In 1995, [PERSON] et al. [20] measured the hyperfine interaction constant of the \({}^{85}\)Rb \(4p^{6}5d\)\({}^{2}\)D\({}_{5/2}\) state by using optical double resonance spectroscopy and performed frequency calibration using an acousto-optic modulator (AOM). [PERSON] et al. [21] conducted experimental and theoretical research on the polarizability and hyperfine interaction constants of Cs atoms in the \(d\) state, and the experimental values of the hyperfine interaction constants were obtained from the energy-level crossover signal of the \(nd\) state. On the basis of the atomic coherence effect of a \(5p^{6}6s\)\({}^{2}\)S\({}_{1/2}\)-\(5p^{6}6p\)\({}^{2}\)P\({}_{3/2}\)-\(5p^{6}8s\)\({}^{2}\)S\({}_{1/2}\) system in a Cs atomic cell at room temperature, [PERSON] et al.