Terahertz Thickness Measurement Based on Stochastic Optimization Algorithm
ZHANG Hong-zhen1, 2, HE Ming-xia1, 2*, SHI Li-li3, WANG Peng-fei1, 2
1. State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China
2. School of Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin 300072, China
3. Research Institute of Superconductor Electronics (RISE), School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
Abstract：The coating is an indispensable process in automobile, marine, aerospace manufacturing and other industries. Reasonable film thickness is not only conducive to the stability of painting quality but also conducive to saving paint and reducing painting cost. With the advent of industrial 4.0 era, it is an inevitable trend to realize online, non-contact, non-destructive and high-precision detection. Compared with traditional measurement methods, THz thickness measurement method could perform the non-contact online measurement. However, when the optical thickness of the sample is small, terahertz reflection pulses will overlap in the time domain, and it is impossible to obtain the exact flight time directly from the peak position of the pulses. In order to solve this problem, a thickness measurement method based on reflective terahertz time domain spectroscopy system and the stochastic optimization algorithm are proposed. A multivariate regression model of the terahertz reflection pulses is established. With the application of the Differential Evolution algorithm, the thickness of the sample is calculated automatically. The convergence of the differential evolution algorithm was verified by calculating the results from the same time-domain signal several times. The measurement error introduced by the angle error between the normal direction of the substrate and the direction of terahertz probe is also evaluated. In addition, the feasibility of time-of-flight (TOF) method for measuring the thickness of each layer in multi-layer structure samples is studied. The measurement results show that the calculated results of Differential Evolution algorithm are stable. The uncertainty of thicknesses of zinc dipping paint, black paint and base paint are 0.22 μm(223.87 μm), 0.05 μm(54.18 μm) and 0.08 μm(284.95 μm), respectively. The uncertainty of refractive indexes is 0.004(3.967), 0.002(2.091) and 0.001(1.769), respectively. For zinc dipping paint, angle error of 1° leads to a measurement error of 0.073. Due to the existence of multiple reflection effects, although the method can find the flight time of each reflection pulse in the terahertz measurement signal of many layers of samples, it is impossible to distinguish which reflection interface the reflection pulse comes from, so that the thickness of each layer coating cannot be solved. The analysis shows that the thickness measurement method based on the time-of-flight principle is simple and easy, and the thickness of the single-layer sample can be measured more accurately, which is not sensitive to the angle error. When expanding to the measurement of multi-layer samples, the method has greater limitations. It is impossible to distinguish multiple reflection pulses in the time domain, and is not feasible to calculate the thickness of each layer.
Key words：Terahertz spectroscopy; Time of flight; Differential evolution algorithm
张洪桢，何明霞，石粒力，王鹏騛. 随机优化算法应用于太赫兹测厚方法的研究[J]. 光谱学与光谱分析, 2020, 40(10): 3066-3070.
ZHANG Hong-zhen, HE Ming-xia, SHI Li-li, WANG Peng-fei. Terahertz Thickness Measurement Based on Stochastic Optimization Algorithm. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2020, 40(10): 3066-3070.
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