# Optical Image Encryption Using a Nonlinear Joint Transform Correlator and the Collins Diffraction Transform

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## Abstract

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## 1. Introduction

## 2. Collins Diffraction Transform (CDT)

## 3. Optical Image Encryption System Based on a Nonlinear JTC Architecture in the Collins Diffraction Domain

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic representation of the optical setup. The part I is the encryption system based on a nonlinear joint transform correlator (JTC) architecture in the Collins diffraction domain (CDD) and the part II is the decryption system composed by an two successive Collins diffraction transforms (CDTs).

**Figure 2.**(

**a**) Original image to encrypt $f\left(x\right)$. (

**b**) Random distribution image $n\left(x\right)$ of the random phase mask (RPM) $h\left(x\right)$. (

**c**) Encrypted image ${e}_{M}\left(u\right)$ for the security keys $\lambda =543$ nm, $l=50$ mm and the RPM $h\left(x\right)$.

**Figure 3.**(

**a**) Absolute value of the output plane for the decryption system with the right values of the security keys $\lambda $, l and the RPM $h\left(x\right)$. (

**b**) Magnified region of Figure 3a centred at coordinate $x={x}_{0}$ which is the decrypted image $\tilde{f}\left(x\right)$. Decrypted images when: (

**c**) the security key of the decryption system given by the RPM $h\left(x\right)$ is different from the RPM $h\left(x\right)$ used in the encryption system and (

**d**) an incorrect wavelength of $\lambda $ = 575 nm is used in the decryption system.

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**MDPI and ACS Style**

Vilardy O., J.M.; Perez, R.A.; Torres M., C.O.
Optical Image Encryption Using a Nonlinear Joint Transform Correlator and the Collins Diffraction Transform. *Photonics* **2019**, *6*, 115.
https://doi.org/10.3390/photonics6040115

**AMA Style**

Vilardy O. JM, Perez RA, Torres M. CO.
Optical Image Encryption Using a Nonlinear Joint Transform Correlator and the Collins Diffraction Transform. *Photonics*. 2019; 6(4):115.
https://doi.org/10.3390/photonics6040115

**Chicago/Turabian Style**

Vilardy O., Juan M., Ronal A. Perez, and Cesar O. Torres M.
2019. "Optical Image Encryption Using a Nonlinear Joint Transform Correlator and the Collins Diffraction Transform" *Photonics* 6, no. 4: 115.
https://doi.org/10.3390/photonics6040115