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An optical encryption of three-dimensional (3D) object with digital holography was implemented. In the process of encryption, two holograms involved recording key information and 3D object were obtained. In the process of decryption, the 3D object was reconstructed from the two holograms by extracting the object and key information, followed by multiplication of the two holograms and inverse Fresnel transform numerically. The robustness of the method was also tested for different occlusions attacks and Gaussian noises. The results showed that the method was able to encrypt and decrypt the 3D object while being robust under different occlusions attacks and Gaussian noises.

Optical encryption is applied in numerous engineering fields for its competitive efficiency, parallel processing capability, and superior information storage capacity [

Optical digital holographic encryption technique was developed and popularized recently owning to its advantages of conveniences of data recording, transmission, and processing [

In this research, an encryption of tangible 3D object was proposed. In this new method, two separate off-axis Fresnel holograms were recorded. The first hologram involved recording the 3D object and encryption key, and the second hologram only recorded encryption key. Following the hologram recording, encrypted information of 3D object and encryption key was extracted by the filtering out of zeroth-order information and conjugate information in frequency domain. Similarly, for second hologram, encrypted information of encryption key was extracted through filtering out of zeroth-order information and conjugate information in frequency domain. Multiplication of the first and the conjugate of second extracted information was performed, which followed by inverse Fourier transform to get the 3D object wave on the hologram plane. The Fresnel transform was then used for reconstructing decrypted images in the object domain. Furthermore, the decrypted images with different diffractive distances were also obtained. For reducing the effects of speckle noises on reconstructed images, a speckle noise suppression method was applied by averaging multiple reconstructed images. The robustness of the method was tested against occlusion and noise attacks.

The encryption process contains two optical paths. The first optical path is used to record a digital hologram I_{E} with 3D object and encryption keys of two random phase masks shown in _{1}. One beam passes through the random phase mask (RPM_{2}), acting as a reference

wave, which is placed on the front focal plane of lens L_{4}. The combination of lens L_{3} and L_{4} with same focus length consists of a 4f optical system. The other beam illuminates the 3D object after being reflected by M_{3}. The reflected wave from the 3D object, acting as a object wave, passes through the random phase mask (RPM_{1}) which is placed on the front focal plane of lens L_{1}. The combination of L_{1} and L_{2} is also a 4f system. The hologram I_{E}, which is thus an interference pattern formed by the reference wave and the object wave superim-

position. The object can be treated as a two-dimensional image at different distances _{1} [_{1} and RPM_{2}, respectively. The hologram I_{E} captured by CCD can be written in below:

where _{1} [_{1} and RPM_{2}.

The second optical path is to record a digital hologram of the encryption key I_{M} shown in _{2} and the object wave passing through RPM_{1}. This hologram contains the information of encryption key, which can be expressed with:

where _{1} and RPM_{2}.

In order to extract the encrypted information of 3D object and encryption key, zeroth, first order and conjugate of the hologram in frequency domain have to be separated. As such, the reference beam was slightly inclined planar wave for the separation of them. Following the separation, the two recorded holograms were Fourier transformed to extract the third term on the right hand side of Equation (1) and the fourth term on the right-hand side of Equation (2) [

When the

The experimental system is shown in _{1} and L_{2} is 30 cm and the focal length of L_{3} and L_{4} is 40 cm. RPM is random phase mask, which was made from glass corroded by hydrofluoric acid. The 3D object is located at an approximate distance d from the RPM_{1} in the object wave.

In the experiments, the encrypted target object consists of two dices. The size of the dice in this experiment is 5 mm × 5 mm × 5 mm, with distance between them is 70 mm. A CCD (4M180MCL) camera which recorded hologram with resolution of 2048 × 2048, pixel size of

The reconstructed image quality was degraded by speckle noise [

where M is the number of independently captured holograms.

In order to obtain the independent holograms, the diffusing screen was moved continuously perpendicular to the optical axis of a CCD sensor for 15 times and thus 15 uncorrelated holograms are able to be captured by CCD.

The occlusion attacks often exist in data transfer process. For this, the simulation of occlusion attacks was conducted for both I_{E} and I_{M} holograms. Within the simulation, the occlusion area is the length of the hologram and the width of the occlusion is selected as shown in

The robustness of encryption of decryption against Gaussian noise was also validated for both the hologram I_{E} and I_{M}. A computer simulated Gaussian noise is used as shown in

The intensities of holograms

The reconstructed images at different distances are shown in

The results of robustness against occlusion and noise attacks are presented below. Correlation coefficient (CC) was used to evaluate the decrypted image quality between the reconstructed images without occlusion attacks and the reconstructed images with occlusion attacks.

With speckle noises, the results of reconstructed objects with 70% and 90% occluded

With speckle noises, the reconstructed object from with Gaussian noise of mean 0 and variance 0.0015, mean 0 and variance 0.002 in

A tangible 3D object information encryption and decryption method was proposed in this research. The encryption process started at recording encrypted 3D object and key holograms. Multiplication of the first and the conjugate of second extracted information from the holograms was performed, which followed by inverse Fourier transform to get the 3D object wave on the hologram plane. The Fresnel transform was then used for reconstructing decrypted images. The robustness of the method was tested against occlusion attacks and Gaussian noises.

Results showed that the 3D objects were successfully encrypted, decrypted, and reconstructed. The speckle noise reduction is evident through the multiple images superposition method. The 3D object can also be reconstructed at different diffraction distances. Additionally, the proposed method is also robust against occlusion attacks and Gaussian noise pollution.

In distinction from the previous research, a tangible 3D object was utilized for encryption and decryption. Only two holograms are needed for encryption, whereas the previous research often involved using multiple

holograms. Additionally, this method encrypts both object and reference light wave, which can possibly increase the security of the encryption. Potentially, the results of this research can find its applications in real 3D encryption and decryption.

Limitations also exist in this study. The proposed method is still not able to be used to encrypt large 3D object due to the limited resolution of CCD camera used for recording holograms. Furthermore, we have not yet analyzed the 3D coordinates of the objects, which can be investigated in the future.

This work was supported by National Natural Science Foundation of China (No. 61377010)

YinghongLiu,WeiminJin,XinYang,DiWu,HongboZhang, (2015) A Robust Optical Encryption Method for Three-Dimensional Object Based on the Fresnel Transform. Optics and Photonics Journal,05,313-319. doi: 10.4236/opj.2015.511029