## 1 Introduction  
Transparent film, as an important industrial component, is widely used in modern optics, semiconductors, displays, and other related scientific and technological fields [1; 2; 3]. The thickness of thin films produced by physical or chemical deposition methods is directly related to the optical properties, barrier performance, and tensile properties of subsequent applications [4; 5; 6]. However, multiple production factors such as emission characteristics, preparation environment, relative position placement, and surface shape of the plated parts, might result in uneven thickness distribution, which ultimately affects the product quality [7; 8; 9]. Online film thickness monitoring is thus particularly important for predicting application effects, modifying process parameters, and improving product quality. Limited by the irregular production environment and cost, there is an urgent need for a fast, accurate, and robust online film thickness measurement system. Non-contact techniques, such as ultrasonic, ray, terahertz, and optical methods, can be used for online film thickness measurement. Ultrasonic-based technology detects the thickness of a material by accurately measuring the time of ultrasonic wave propagation. Commonly used for oil film thickness monitoring, ultrasonic-based thickness measurement technology features a wide measurement range but suffers from low detection accuracy [10; 11; 12]. Ray radiation technology obtains the film thickness by detecting the attenuation of the ray intensity after penetrating the object. Despite that the ray radiation methods demonstrate the capacity for high-precision real-time film thickness measurement, the radioactive sources are expensive and highly hazardous [13; 14; 15]. Terahertz time-domain spectroscopy (THz-TDS) utilizes the time-of-flight (TOF) and resonance frequencies to acquire the thickness of the films. THz-TDS is commonly used for thickness measurement of non-transparent coatings [16; 17; 18]. The flaws of the two methods render them unsuitable for online thickness measurement in film production. Among various optics-based methods for thickness measurement, including optical reflection contrast (ORC), spectroscopic ellipsometry (SE), structured illumination microscopy (SIM), chromatic confocal, optical interferometry, and spectral interferometry, ORC is based on the film thickness calculation by capturing the reflectance at certain specific wavelengths with a simple optical configuration. However, for materials with high absorbance, the detectable thickness range is limited to tens of nanometers due to the saturation of the reflected signal with increasing thickness [4; 19]. SE is a non-destructive, noncontact, and non-invasive optical technique that is based on the change in the polarization state of light as it is reflected obliquely from a thin film sample. Despite the capacities of spectroscopic ellipsometry for measuring the thickness, reflectance, and refractive index of thin films from sub-micron to nanometer scale [20; 21], the application of the technique is limited by additional measurement time, a small thickness measuring range, and a complicated structure. SIM can obtain the surface profiles and film thickness by detecting the peaks of the modulation depth response curves [22; 23]. It can detect micrometer-thick films but cannot be used for industrial inspection due to its slow detection speed. Chromatic confocal microscopy converts the axial position of the film surface into spectral information through a confocal pinhole in front of the spectrometer; hence, the measurable thickness range is restricted by spectral bandwidth and resolution [24]. Based on the principle of optical interferometry, laser interferometry [25], white light interferometry [26], and differential interferometry [27] have been developed to achieve nanometer thickness measurement accuracy in the millimeter measurement range. The industrial applications of these methods are also constrained by the high cost and strict requirements of environmental conditions.