Inline multilayer thickness sensing by using terahertz time-domain spectroscopy in reflection geometry

Abstract

We present a novel approach to determine the individual layer thickness in a dielectric multilayer sample using pulsed terahertz spectroscopy in reflection geometry. In a first step, the optical parameters of each layer have to be determined. Based on these parameters, we simulate the reflected THz-pulse from the multilayer system and compare it to the measurement. A genetic algorithm is used to determine the best agreement between simulation and measurement by varying the thickness of each layer

Precise Determination of Thicknesses of Multilayer Polyethylene Composite Materials by Terahertz Time-Domain Spectroscopy

“…Due to the complexity resulting from this partial superposition of pulses, the waveform reflected from the multilayer structure with the refractive index of ith layer (N i =n i +iκ (i= 1…k)) was simulated using the TMM [22]. The structure is surrounded from both sides by air with the complex refraction index (N 0 =N k+1 =1).…”

“…Krimi et al have recently proposed a time-domain fitting procedure for a structure composed of few thin layers of different thickness, useful in inspection of automotive paints [22]. This approach is based on the transfer matrix method (TMM) and requires prior knowledge of the material parameters to determine the thicknesses of the layers.…”

“…Here, the algorithm presented in [22] was adapted to a composite sample composed of about 200 layers with a quasi-binary profile of the refractive index, which means that values of the refractive index for subsequent layers are as follows: n+Δn 1 , n−Δn 2 , n+Δn 3 ,…, respectively; n>>Δn i and Δn 1 ≈Δn 2 ≈Δn 3 …. The optimization of both parameters, i.e., the refractive index and the thickness for each layer independently, would be computationally demanding.…”

“…The optimization of both parameters, i.e., the refractive index and the thickness for each layer independently, would be computationally demanding. Therefore, Krimi's algorithm [22] was improved in such a manner that calculations were extended to the optimization of thicknesses of all 200 layers. We assume Δn 1 =Δn 2 =Δn 3 =Δn and Δn was in general optimized for the whole sample.…”

“…We assume Δn 1 =Δn 2 =Δn 3 =Δn and Δn was in general optimized for the whole sample. Due to the larger number of layers and thus more degrees of freedom for the optimization algorithm, it is very difficult to apply directly the optimization approach proposed in [22]. For each layer, the search interval was about 60 μm.…”