# Surface Depth-Mapping of Material via the Transport-of-Intensity Equation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{−1}—operators of direct and inverse Fourier transforms, respectively; k

_{x,y}= 2πν

_{x,y}—frequency coefficients, ν

_{x,y}—frequency grids.

## 3. Experimental Demonstration

_{1/e}≈ 0.6 μm. Ablation was performed in a single-pulse mode, with the energy per pulse being E = 450 nJ.

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**SEM-images of the crater under study: (

**a**) in the focusing plane; (

**b**) displaced by 50 μm; (

**c**) displaced by 100 μm.

**Figure 4.**2D crater images retrieved using TIE for different conditions: (

**a**,

**d**) no boundary conditions; (

**b**,

**e**) Neumann boundary conditions; (

**c**,

**f**) Dirichlet boundary conditions.

**Figure 5.**2D crater images retrieved using TIE from digitally processed SEM-images: (

**a**,

**d**) no boundary conditions; (

**b**,

**e**) Neumann boundary conditions; (

**c**,

**f**) Dirichlet boundary conditions.

**Figure 6.**RMSE between depth maps obtained by AFM and SEM for: (

**a**) no boundary conditions; (

**b**) Neumann boundary conditions; (

**c**) Dirichlet boundary conditions.

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**MDPI and ACS Style**

Stsepuro, N.; Kovalev, M.; Krasin, G.; Podlesnykh, I.; Gulina, Y.; Kudryashov, S.
Surface Depth-Mapping of Material via the Transport-of-Intensity Equation. *Photonics* **2022**, *9*, 815.
https://doi.org/10.3390/photonics9110815

**AMA Style**

Stsepuro N, Kovalev M, Krasin G, Podlesnykh I, Gulina Y, Kudryashov S.
Surface Depth-Mapping of Material via the Transport-of-Intensity Equation. *Photonics*. 2022; 9(11):815.
https://doi.org/10.3390/photonics9110815

**Chicago/Turabian Style**

Stsepuro, Nikita, Michael Kovalev, George Krasin, Ivan Podlesnykh, Yulia Gulina, and Sergey Kudryashov.
2022. "Surface Depth-Mapping of Material via the Transport-of-Intensity Equation" *Photonics* 9, no. 11: 815.
https://doi.org/10.3390/photonics9110815