# Evaluation of the Number of Degrees of Freedom of the Field Scattered by a 3D Geometry

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## Abstract

**:**

## 1. Introduction

## 2. The Statement of the Problem

## 3. NDF Evaluation for the Surface of a Cube

## 4. The Optimal Number of Incident Plane Waves

## 5. Application to Microwave Tomography of Dielectric Object

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## References

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**Figure 10.**The domain spanned by (

**a**) four incident plane waves, (

**b**) six incident plane waves, and (

**c**) eight incident plane waves in the spectral domain for a planar ID.

**Figure 11.**Comparison of the behavior of the normalized singular values for different numbers of impinging plane waves for a single XY face ID.

**Figure 13.**Comparison of the behavior of the normalized singular values for different numbers of impinging plane waves for two parallel XY faces.

**Figure 14.**Comparison of the behavior of the normalized singular values for different numbers of impinging plane waves for the L shape ID.

**Figure 15.**Comparison of the behavior of the normalized singular values for different numbers of impinging plane waves for all sides of a cube ID.

**Figure 17.**Comparison of the behavior of the normalized singular values for three scenarios for a XY face.

**Figure 18.**Reconstructed images of a dielectric the scatterer within a planar ID for three scenarios from: (

**a**) sufficiently large of impinging plane waves, (

**b**) plane waves belonging to the same plane as the object, and (

**c**) form eight plane waves belonging to a different plane.

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**MDPI and ACS Style**

Sekehravani, E.A.; Leone, G.; Pierri, R.
Evaluation of the Number of Degrees of Freedom of the Field Scattered by a 3D Geometry. *Sensors* **2023**, *23*, 4056.
https://doi.org/10.3390/s23084056

**AMA Style**

Sekehravani EA, Leone G, Pierri R.
Evaluation of the Number of Degrees of Freedom of the Field Scattered by a 3D Geometry. *Sensors*. 2023; 23(8):4056.
https://doi.org/10.3390/s23084056

**Chicago/Turabian Style**

Sekehravani, Ehsan Akbari, Giovanni Leone, and Rocco Pierri.
2023. "Evaluation of the Number of Degrees of Freedom of the Field Scattered by a 3D Geometry" *Sensors* 23, no. 8: 4056.
https://doi.org/10.3390/s23084056