# Non-Destructive Imaging of Defects Using Non-Cooperative 5G Millimeter-Wave Signals

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## Abstract

**:**

## 1. Introduction

#### Interferometry Fundamentals

## 2. Materials and Methods

**x**) of the image

**x**, which can be written as

**x**[32]. In this way, we can deblur the image while also achieving denoising at the same time.

## 3. Results

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

HPBW | Half-Power Beamwidth |

FOV | Field of View |

LO | Local Oscillator |

PSF | Point-Spread Function |

IFT | Inverse Fourier Transform |

QAM | Quadrature Amplitude Modulation |

TV | Total Variation |

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**Figure 1.**Non-destructive millimeter-wave inspection of defects by capturing transmission of existing millimeter-wave signals through the materials of interest. The signals are captured using a millimeter-wave interferometric antenna array with image reconstruction taking place through Fourier processing.

**Figure 2.**(

**a**) Array layout of a 24-element asymmetric Y-shaped array. (

**b**) Sampling function $S(u,v)$, which is the result of the cross-correlations between all antenna locations and shows the spatial frequency coverage. (

**c**) Point-spread function (PSF), which shows the synthesized beam in the spatial domain. As interferometric imaging is a Fourier imaging method, the PSF is usually calculated as an inverse Fourier transform of $S(u,v)$.

**Figure 3.**Block diagram of the 24-element millimeter-wave interferometric imaging array, which is capturing the third-party signals of opportunity (shown with blue and red). Quadrature down conversion is implemented using the same 19 GHz local oscillator in all channels. The in-phase and quadrature signals are digitized and processed on the host computer.

**Figure 4.**Photograph of the 38 GHz interferometric imaging array setup. The 24-element millimeter-wave antenna array is shown with red.

**Figure 5.**Summary of the digital image reconstruction implementation. The signals of opportunity that are getting transmitted through the defects are captured in time domain, and the algorithm digitally reconstructs the defect shape, shown with the “E”-shaped target.

**Figure 6.**Experimental setup that shows two millimeter-wave transmitters, and the aluminum-tape-covered target with a slit opening that is used to emulate defects.

**Figure 7.**(

**a**) Foam board covered in aluminum tape with a square opening used as the transmission target. (

**b**) Experimental image reconstruction of the target square opening. (

**c**) One-dimensional slices along $sin\theta sin\varphi $ = 0 (

**top**) and $sin\theta cos\varphi $ = 0 (

**bottom**).

**Figure 8.**(

**a**) Foam board covered in aluminum foil with a slit used as the transmission target. (

**b**) Experimental image reconstruction of the slit. (

**c**) One-dimensional slices along $sin\theta sin\varphi $ = 0 (

**top**) and $sin\theta cos\varphi $ = 0 (

**bottom**).

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**MDPI and ACS Style**

Vakalis, S.; Colon-Berrios, J.R.; Chen, D.; Nanzer, J.A.
Non-Destructive Imaging of Defects Using Non-Cooperative 5G Millimeter-Wave Signals. *Sensors* **2023**, *23*, 6421.
https://doi.org/10.3390/s23146421

**AMA Style**

Vakalis S, Colon-Berrios JR, Chen D, Nanzer JA.
Non-Destructive Imaging of Defects Using Non-Cooperative 5G Millimeter-Wave Signals. *Sensors*. 2023; 23(14):6421.
https://doi.org/10.3390/s23146421

**Chicago/Turabian Style**

Vakalis, Stavros, Jorge R. Colon-Berrios, Daniel Chen, and Jeffrey A. Nanzer.
2023. "Non-Destructive Imaging of Defects Using Non-Cooperative 5G Millimeter-Wave Signals" *Sensors* 23, no. 14: 6421.
https://doi.org/10.3390/s23146421