## 1 Introduction  
Precision optical components have a wide range of applications in many fields. The quality of optical elements directly affects the performance of the whole optical system. Therefore, optical element damage detection has attracted increasing attention. Machine vision provides a reliable real-time detection method [1]. Nonlinear optical imaging can detect important properties such as crystal orientation and boundaries [2]. Laser speckle technology can detect micro vibrating objects [3]. LCs have excellent optical properties and have been used in LC wave plates [4], LC tunable filters [5], LC polarization gratings [6], and variable delay devices [7]. LC has also been proposed for use in optical fiber sensing [8], lasers [9], spectral imaging [10], and other fields. Among these, LC spectral imaging technology achieves spectral imaging with high spatial and spectral resolutions. Owing to their small size, light weight, low power consumption, flexibility, and convenience of use, LCs have attracted attention for research on spectral imaging. We consider whether spectral imaging based on LC can be used in optical component defect detection. The most-used LC spectral imaging technique is based on a liquid crystal tunable filter (LCTF) that can perform continuous spectral tuning by altering the center wavelength of the filter. The Japan Aerospace Exploration Agency (JAXA) was the first organization to research LC spectral imaging [11]. In order to obtain a narrower bandwidth, cascaded LC was used based on a LCTF [12]. Combining the two structures of a Solc filter and a Lyot filter can achieve high efficiency and a narrower full width at half maximum [13]. However, the LCTF requires multiple LC cells to work simultaneously, which leads to defects in the uniformity of the light-passing surface and acquisition time. In addition, the LCTF hasbeen investigated for compressive sensing, which can improve the spectral and spatial resolutions [14]. However, the complex and time-consuming acquisition and calculations were found to be drawbacks. Additionally, the LCTFs used in spectral imaging systems are complicated and use multiple LCs devices with significant costs. The combination of LC and interference spectral imaging technology is another important LC spectral imaging technique. This technique can obtain spectral information on the measured object using the Fourier transform of the interferogram. In double-beam interference, the interferogram is obtained by varying the optical path difference between the coherent beams. Therefore, the birefringence effect of the LCs introduces an optical path difference between the two coherent beams. Interferometric spectral imaging using LC delayers was proposed in 1990 [15]. However, in recent years, owing to the development of high-speed charge-coupled devices (CCDs) [16], and data recording and processing capabilities, LC delayers have become a key component in spectral imaging. By varying the driving voltage of the LC, a series of interferogram images can be recorded. Spectral reconstruction can be realized using the interference spectral imaging theory [17]. However, a short acquisition time and a high spectral resolution cannot be achieved simultaneously. In order to improve the spectral resolution by using multiple reflections to increase the optical path difference, [PERSON] obtained a resolution of 1 nm @ 630 nm [18]. However, this technique cannot be used to obtain two-dimensional spatial data. In addition, [PERSON] et al. proposed dynamically driving a 195-\(\upmu\)m-thick LC with a step voltage, constituting an optical delay line, in combination with a periodic interferometric spectrum to obtain the relationship between the relative delay and the optical path between the two waves [19]. Furthermore, they applied imaging to tilted cholesteric LC structures [20]. A spectral resolution of 130 cm\({}^{-1}\) (6 nm) was achieved at 400-1000 nm in 130 s by using a thicker LC with a fourfold improvement in the spectral resolution [17].