# On the Orbital Angular Momentum Incident Fields in Linearized Microwave Imaging

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Formulation of the Inverse Scattering Problem

## 3. Linear Imaging with OAM Incident Fields

## 4. Numerical Benchmarks

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**A sketch of the adopted multiview-multistatic measurement configuration to probe the region of interest by means of Tx-Rx primary sources (filamentary currents) placed on a circumference $\Gamma $ of radius ${r}_{m}$.

**Figure 2.**Amplitude (not normalized) and phase distribution of the OAM incident fields used to probe the imaging domain with a circular array of V = 36 filamentary currents. (

**a**),(

**d**) $\ell =0$; (

**b**),(

**e**) $\ell =1$; (

**c**),(

**f**) $\ell =11$.

**Figure 3.**Reconstruction of a small weak circular scatterer through the Born approximation. (

**a**) Real and (

**e**) imaginary part of the actual contrast profile; (

**b**) real and (

**f**) imaginary part of the retrieved contrast profile for $\ell =0,\pm [1-18]$, $err=0.2028$ with a cutoff value in the TSVD equal to ${N}_{T}$ = 252; (

**c**) real and (

**g**) imaginary part of the retrieved contrast profile for $\ell =0,\pm [1-3]$, $err=0.2384$ with a cutoff value in the TSVD equal to ${N}_{T}$=142; (

**d**) real and (

**h**) imaginary part of the retrieved contrast profile using $V=M=37$ equispaced filamentary currents $err=0.2020$ with a cutoff value in the TSVD equal to ${N}_{T}$ = 252. The axes of the imaging domain are expressed in background wavelengths.

**Figure 4.**Reconstruction of a two small weak scatterers through the Born approximation. (

**a**) Real and (

**e**) imaginary part of the actual contrast profile; (

**b**) real and (

**f**) imaginary part of the recovered contrast profile for $\ell =0,\pm [1-18]$, $err=0.2241$ with a cutoff value in the TSVD equal to ${N}_{T}$ = 252; (

**c**) real and (

**g**) imaginary part of the recovered contrast profile for $\ell =0,\pm [1-4]$, $err=0.4017$ with a cutoff value in the TSVD equal to ${N}_{T}$ =166; (

**d**) real and (

**h**) imaginary part of the recovered contrast profile for $\ell =\pm [6-11]$ (without the lowest order modes), $err=0.60$ with a cutoff value in the TSVD equal to ${N}_{T}$ = 187. The axes of the imaging domain are expressed in background wavelengths.

**Figure 5.**Reconstruction of a large circular scatterer through the Rytov approximation exploiting OAM fields generated in the far-field (${\underline{r}}_{m}=100$) m and near-field (${\underline{r}}_{m}=9$) m of the imaging domain. The OAM orders used are $\ell =0,\pm [1-35]$. (

**a**) Real and (

**d**) imaginary part of the actual contrast profile; (

**b**) real and (

**e**) imaginary part of the retrieved contrast profile in the far-field measurement configuration, reconstruction $err=0.1108$ with a cutoff value in the TSVD reconstruction ${N}_{T}$ = 1856; (

**c**) real and (

**f**) imaginary part of the retrieved contrast profile in the near-field measurement configuration, reconstruction $err=0.1267$ with a cutoff value in the TSVD reconstruction ${N}_{T}$ = 1557. The axes of the imaging domain are expressed in background wavelengths.

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**MDPI and ACS Style**

Pavone, S.C.; Sorbello, G.; Di Donato, L. On the Orbital Angular Momentum Incident Fields in Linearized Microwave Imaging. *Sensors* **2020**, *20*, 1905.
https://doi.org/10.3390/s20071905

**AMA Style**

Pavone SC, Sorbello G, Di Donato L. On the Orbital Angular Momentum Incident Fields in Linearized Microwave Imaging. *Sensors*. 2020; 20(7):1905.
https://doi.org/10.3390/s20071905

**Chicago/Turabian Style**

Pavone, Santi Concetto, Gino Sorbello, and Loreto Di Donato. 2020. "On the Orbital Angular Momentum Incident Fields in Linearized Microwave Imaging" *Sensors* 20, no. 7: 1905.
https://doi.org/10.3390/s20071905