# Double-Sided Terahertz Imaging of Multilayered Glass Fiber-Reinforced Polymer

## Abstract

**:**

## 1. Introduction

- non-contact measurement in reflection and transmission arrangement;
- non-ionizing nature;
- inner structure and spectral information is obtainable; and
- fraction of a millimeter resolution.

- low power of THz emitters;
- low speed of examination (need of raster scanning in case of VNA and TDS solutions);
- restriction to nonconductive materials (because of high frequency and skin effect); and
- high cost of VNA and TDS solutions.

## 2. Materials and Methods

#### 2.1. Pulsed Terahertz Measuring System

#### 2.2. Proposed Algorithm

**H**is the convolution matrix,

**I**is the identity matrix, λ is the regularization parameter, s

_{m}is the measured signal, and g

_{m}is the deconvolved signal—reflectivity profile of material.

_{CH1}and w

_{CH2}were calculated as an envelope based on the signal obtained using the analytical model (presented in Section 2.3). This step is shown in Figure 7. The utilized model enabled the calculation of the waveform reflected from a given multi-layered structure if an incident wave is in the form of a wideband Gaussian pulse. In order to obtain analytical form of weighting function the following approximation was utilized:

_{CHk}(t) is the weighting function of given channel k = 1 or 2, and p

_{i}, q

_{i}are the approximation coefficients.

_{cmb}(t) is the combined signal, w

_{nCH1}(t) and w

_{nCH2}(t) are the weighting functions normalized to the 〈0;1〉 range, associated with channel one and two, respectively, and g

_{mCH1}(t) and g

_{mCH2}(t) are the deconvolved signal of channel one and two, respectively. The reconstructed signal g

_{cmb}(t) in the vicinity of the FSR pulse is calculated mainly based on g

_{mCH1}(t), and close to the BSR pulse based on g

_{mCH2}(t). The signal from channel two was multiplied by −1 and time-reversed (−g

_{mCH2}(−t)). This operation enabled obtaining the same polarization of FSR, BSR, and defect-caused pulses, thus, constructive interference is possible. The combined signal in case of measurements will be presented in Section 3. Finally, the obtained signal contains high amplitude pulses caused by material-air interfaces (FSR and BSR). The signal caused by layers reflections is symmetrical—the highest values are close to FSR/BSR. Even in the center of whole material response—where the signal is weakest—its amplitude is noticeably higher than in the case of the raw signal (obtained for single-side inspection).

#### 2.3. Analytical Model

_{i}and b

_{i}are forward- and backward-traveling wave amplitudes in each layer in the case of the considered frequency. For cascade connections of n sections (layers) we have the following equation [41,42]:

_{n}

_{+1}= 0)—we have:

_{1}for a given frequency f based on the incident field amplitude c

_{1}and the selected chain matrix elements. A block scheme of the reflected pulse calculation algorithm is presented in Figure 8b. Incident Gaussian pulse is transformed to frequency domain, where the analytical model (Equation (5)) is applied for each harmonics. After calculation of reflected wave b

_{1}(f), the result is transformed back to the time domain. The incident pulse and its spectrum, as well as the reflected pulse, are presented in Figure 8c,d, respectively. One can observe the similarity of the obtained signal with the measured one presented in Figure 6. It consists of FSR and BSR pulses, as well as the exponentially-attenuated layer reflection pulse.

## 3. Results and Discussion

_{mCH1}(t) and −g

_{mCH2}(−t) obtained using the proposed double-sided inspection and signal processing are presented in Figure 10. One can observe constructive interference of FSR

_{CH1}–BSR

_{CH2}, FSR

_{CH2}–BSR

_{CH1}and defect/layer reflection pulses, respectively. Similarly, B-scan signals obtained during a single line scan along the sample are presented in Figure 11 (deconvolved) and Figure 12 (channel 2 signal time-reversed). In each case BSR pulse has smaller amplitude and frequency content in comparison with FSR pulse. This is caused by attenuation of the pulse energy during propagation through multilayered structures and defocusing. As mentioned before, layers’ reflection pulses (in the case of layers close to back surfaces) are blurred, as well. Based on Figure 12, one can see that g

_{mCH1}(t) and g

_{mCH2}(−t) signals contain complementary information about the layers.

## 4. Conclusions

_{nCH1}(t) and w

_{nCH2}(t) can be calculated based on approximation Equation (2) and measured signal, without application of analytical model. It is possible, because the character of the layer reflection response (exponential decay) is similar in the case of all multilayered materials as long as there is one type of layer within the whole thickness.

_{mCH1}and g

_{mCH2}signals. Additionally visible layer response (Figure 6) can be attenuated before reaching the central area of the material cross-section. In this case, in the center of the combined signal g

_{cmb}(t) the amplitude and SNR are very low.

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Utilized pulsed terahertz imaging system: (

**a**) photo; and (

**b**) simplified scheme; Tr—photoconductive transmitter, Rx—photoconductive receiver, OUT—object under test, Fl—focusing lens, B—beam splitter, PCA—photoconductive antenna.

**Figure 3.**Geometries utilized in composite materials evaluation using pulsed terahertz imaging: (

**a**) transmission setup; (

**b**) reflection “V” setup; (

**c**) reflection setup with beam splitter; and (

**d**) proposed geometry-double-sided measurement using reflection setup.

**Figure 4.**Interaction of the Gaussian pulse with single dielectric layer; results of the 1D FDTD simulation for various time instances.

**Figure 5.**Signals acquired in case of inspection of layered composite material (basalt fiber-reinforced) consisting of six layers: (

**a**) A-scan; and (

**b**) B-scan; FSR-front surface reflection, BSR—back surface reflection.

**Figure 6.**Signals acquired in the case of the inspection of the layered composite material (glass fiber-reinforced) consisting of 30 layers: (

**a**) A-scan; and (

**b**) B-scan.

**Figure 8.**Analytical model: (

**a**) cascade connection of multiple layers; (

**b**) block scheme of reflected signal calculation; (

**c**) time domain excitation signal (and its spectrum) in the form of a wideband Gaussian pulse; and (

**d**) the signal obtained using the analytical model for reflection arrangement (and its spectrum).

**Figure 9.**Photo of the multilayered polymer composite structure subjected to stress resulting in multiple delaminations.

**Figure 10.**Exemplary results of double-sided pulsed THz measurements for given (x,y) position (signal from channel 2 was multiplied by −1 and time-reversed according to the proposed algorithm).

**Figure 11.**Exemplary B-scan signals obtained using double-sided inspection of a composite sample subjected to stress: (

**a**) deconvolved channel 1 signal g

_{mCH1}(t,x); and (

**b**) deconvolved channel 2 signal g

_{mCH2}(t,x).

**Figure 12.**B-scan signals prepared for weighted summing: (

**a**) deconvolved channel 1 signal g

_{mCH1}(t,x); and (

**b**) time reversed channel 2 signal g

_{mCH2}(−t,x).

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**MDPI and ACS Style**

Lopato, P. Double-Sided Terahertz Imaging of Multilayered Glass Fiber-Reinforced Polymer. *Appl. Sci.* **2017**, *7*, 661.
https://doi.org/10.3390/app7070661

**AMA Style**

Lopato P. Double-Sided Terahertz Imaging of Multilayered Glass Fiber-Reinforced Polymer. *Applied Sciences*. 2017; 7(7):661.
https://doi.org/10.3390/app7070661

**Chicago/Turabian Style**

Lopato, Przemyslaw. 2017. "Double-Sided Terahertz Imaging of Multilayered Glass Fiber-Reinforced Polymer" *Applied Sciences* 7, no. 7: 661.
https://doi.org/10.3390/app7070661