# A Miniaturized and Fast System for Thin Film Thickness Measurement
## 1 Introduction  
Transparent film, as an important industrial component, is widely used in modern optics, microelectronics, optical engineering, and other related scientific and technological fields. Various films produced by physical or chemical deposition methods can use interference effects to change optical properties, such as antireflection, filtering, and polarization. Meanwhile, their protection characteristics such as high-temperature resistance, corrosion, and abrasion play a decisive role in the quality of optical instruments in the fields of communication, display, storage, etc. [1,2] However, film preparation is affected by process parameters such as emission characteristics, relative position placement, and surface shape of the plated parts, resulting in uneven thickness distribution, which affects the barrier performance and tensile properties of subsequent applications [3]. Therefore, the measurement and evaluation of film thickness are particularly important in the production process, especially for the thickness measurement of micron-grade industrial films. Limited by the irregular industrial environment, there is an urgent need for a fast, stable, and robust high-resolution film thickness measurement system. Based on the characteristics of light absorption, reflection, and polarization, the optical measurement methods of film thickness can be divided into spectrophotometry [4,5], ellipsometry [6, 7, 8], interferometry [9, 10, 11], and multiple compound methods [12, 13, 14]. Although the measurement methods based on ellipsometry and interferometry have high resolution and accuracy, the disadvantages of large system size, high price, and strict environmental conditions do not meet the rapid and stable application requirement of industrial measurement. The spectrophotometry is more widely used dueto its simplicity and portability. Spectral reflectometry is an effective means to detect the thickness of the weakly absorbing film in spectrophotometry. Reflectometry has less affection than transmittance by extinction coefficient [15] and can realize the compound assembly of the signal transmitter and receiver due to optical fiber technology, thus avoiding the alignment problem. The film thickness calculation methods based on the reflection spectrum can be subdivided into the envelope method [5], the full-spectrum fitting method [16], the turning point fitting method, etc. The above methods all use the reflectivity curve as the medium to obtain the film thickness indirectly. Therefore, the system is required to have a high stability light source or a high-precision reference sample. Second, these methods depend greatly on the reflectivity model, which means that non-ideal signals containing noise in actual measurements are prone to distortion. Among them, the envelope method, fitting the upper and lower envelope by the extreme points of the reflectivity curve, is easily affected by the baseline drift under temperature changes; for the full spectrum fitting method, the period and amplitude of the full-spectrum reflectance spectrum are matched at the same time, which may lead to over-fitting and low matching efficiency; only a very few wavelength data with an odd multiple of the optical thickness \(\uplambda\)4 is used in the turning point fitting method. The effective data segment needs to be selected manually, which makes it difficult to achieve automatic measurement. According to the current research on thin-film thickness measurement, the existing methods still have disadvantages such as poor robustness, low efficiency, and high cost, which cannot meet the needs of industrial-grade rapid and stable measurement. Therefore, this paper built a miniaturized and rapid film thickness measurement system based on the principle of film low-coherence interference and confocal spectral imaging. A novel algorithm named phase power spectrum (PPS) analysis was proposed to calculate the film thickness by solving the power spectral density of the phase term.