Low-noise and fast three-dimensional information encryption based on the double-phase method


A low-noise and fast optical encryption method for three-dimensional (3-D) information using the double-phase method is proposed. First, the 3-D information is encoded into a phase-only hologram (POH) by the angular-spectrum diffraction and the double-phase method. Second, the chaotic random phase mask (CRPM) is generated by the hybrid logical map and the iterative chaotic map with infinite collapses map to modulate the POH and obtain the ciphertext. As the secret key, the CRPM cannot only improve the secret key space of the scheme but also achieve the purpose of scrambling and hiding 3-D information. Third, the background noise of the decrypted image is successfully reduced by the cross-shaped filter, which is designed for the first time based on the POH spectrum distribution. The proposed scheme has successfully improved the encryption speed of the 3-D information and the quality of the reconstructed images. Numerical simulation and optical results show the effectiveness and feasibility of the proposed encryption scheme.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11


  1. 1.

    Hennelly, B., Sheridan, J.T.: Optical image encryption by random shifting in fractional Fourier domains. Opt. Lett. 28, 269–271 (2003)

    ADS  Article  Google Scholar 

  2. 2.

    Chen, L.F., Zhao, D.M.: Optical image encryption based on fractional wavelet transform. Opt. Commun. 254, 361–367 (2005)

    ADS  Article  Google Scholar 

  3. 3.

    Singh, N., Sinha, A.: Optical image encryption using fractional Fourier transform and chaos. Opt. Laser Eng. 46, 117–123 (2008)

    Article  Google Scholar 

  4. 4.

    Tao, R., Lang, J., Wang, Y.: Optical image encryption based on the multiple-parameter fractional Fourier transform. Opt. Lett. 33, 581–583 (2008)

    ADS  Article  Google Scholar 

  5. 5.

    Chen, W., Chen, X.D., Sheppard, C.J.R.: Optical image encryption based on coherent diffractive imaging using multiple wavelengths. Opt. Commun. 285, 225–228 (2012)

    ADS  Article  Google Scholar 

  6. 6.

    Liu, Q., Wang, Y., Wang, J., Wang, Q.H.: Optical image encryption using chaos-based compressed sensing and phase-shifting interference in fractional wavelet domain. Opt. Rev. 25, 46–55 (2018)

    Article  Google Scholar 

  7. 7.

    Ren, G.H., Han, J.A., Fu, J.H., Shan, M.G.: Asymmetric multiple-image interference cryptosystem using discrete cosine transform and conditional decomposition. Opt. Rev. 27, 1–8 (2020)

    Article  Google Scholar 

  8. 8.

    Refregier, P., Javidi, B.: Optical-image encryption based on input plane and Fourier plane random encoding. Opt. Lett. 20, 767–769 (1995)

    ADS  Article  Google Scholar 

  9. 9.

    Zhou, N.R., Liu, X.B., Zhang, Y., Yang, Y.X.: Image encryption scheme based on fractional Mellin transform and phase retrieval technique in fractional Fourier domain. Opt. Laser Technol. 47, 341–346 (2013)

    ADS  Article  Google Scholar 

  10. 10.

    Wang, X.G., Chen, W., Chen, X.D.: Fractional Fourier domain optical image hiding using phase retrieval algorithm based on iterative nonlinear double random phase encoding. Opt. Express 22, 22981–22995 (2014)

    ADS  Article  Google Scholar 

  11. 11.

    Chen, X.D., Wang, Y., Wang, J., Wang, Q.H.: Asymmetric color cryptosystem based on compressed sensing and equal modulus decomposition in discrete fractional random transform domain. Opt. Laser Eng. 121, 143–149 (2019)

    Article  Google Scholar 

  12. 12.

    Ren, G.H., Han, J.A., Fu, J.H., Shan, M.G.: Asymmetric image encryption using phase-truncated discrete multiple-parameter fractional Fourier transform. Opt. Rev. 25, 701–707 (2018)

    Article  Google Scholar 

  13. 13.

    Chen, W., Chen, X.D., Sheppard, C.J.R.: Optical color-image encryption and synthesis using coherent diffractive imaging in the Fresnel domain. Opt. Express 20, 3853–3865 (2012)

    ADS  Article  Google Scholar 

  14. 14.

    Huang, J.J., Hwang, H.E., Chen, C.Y., Chen, C.M.: Lensless multiple-image optical encryption based on improved phase retrieval algorithm. Appl. Opt. 51, 2388–2394 (2012)

    ADS  Article  Google Scholar 

  15. 15.

    Rajput, S.K., Nishchal, N.K.: Fresnel domain nonlinear optical image encryption scheme based on Gerchberg-Saxton phase-retrieval algorithm. Appl. Opt. 53, 418–425 (2014)

    ADS  Article  Google Scholar 

  16. 16.

    Liu, Z.J., Guo, Q., Xu, L., Ahmad, M.A., Liu, S.T.: Double image encryption by using iterative random binary encoding in gyrator domains. Opt. Express 18, 12033–12043 (2010)

    ADS  Article  Google Scholar 

  17. 17.

    Liu, Z.J., Xu, L., Lin, C., Liu, S.T.: Image encryption by encoding with a nonuniform optical beam in gyrator transform domains. Appl. Opt. 49, 5632–5637 (2010)

    ADS  Article  Google Scholar 

  18. 18.

    Singh, H., Yadav, A.K., Vashisth, S., Singh, K.: Fully phase image encryption using double random-structured phase masks in gyrator domain. Appl. Opt. 53, 6472–6481 (2014)

    ADS  Article  Google Scholar 

  19. 19.

    Hong, K., Yeom, J., Jang, C., Hong, J., Lee, B.: Full-color lens-array holographic optical element for three-dimensional optical see-through augmented reality. Opt. Lett. 39, 127–130 (2014)

    ADS  Article  Google Scholar 

  20. 20.

    Li, X.W., Lee, I.K.: Modified computational integral imaging-based double image encryption using fractional Fourier transform. Opt. Laser Eng. 66, 112–121 (2015)

    Article  Google Scholar 

  21. 21.

    Kong, D.Z., Cao, L.C., Jin, G.F., Javidi, B.: Three-dimensional scene encryption and display based on computer-generated holograms. Appl. Opt. 55, 8296–8300 (2016)

    ADS  Article  Google Scholar 

  22. 22.

    Frauel, Y., Naughton, T.J., Matoba, O., Tajahuerce, E., Javidi, B.: Three-dimensional imaging and processing using computational holographic imaging. Proc. IEEE 94, 636–653 (2006)

    Article  Google Scholar 

  23. 23.

    Mehra, I., Singh, K., Agarwal, A.K., Gopinathan, U., Nishchal, N.K.: Encrypting digital hologram of three-dimensional object using diffractive imaging. J. Opt. 17, 035707 (2015)

    ADS  Article  Google Scholar 

  24. 24.

    Kim, H., Kim, D.H., Lee, Y.H.: Encryption of digital hologram of 3-D object by virtual optics. Opt. Express 12, 4912–4921 (2004)

    ADS  Article  Google Scholar 

  25. 25.

    Alfalou, A., Brosseau, C.: Implementing compression and encryption of phase-shifting digital holograms for three-dimensional object reconstruction. Opt. Commun. 307, 67–72 (2013)

    ADS  Article  Google Scholar 

  26. 26.

    Shiu, M.T., Chew, Y.K., Chan, H.T., Wong, X.Y., Chang, C.C.: Three-dimensional information encryption and anticounterfeiting using digital holography. Appl. Opt. 54, A84–A88 (2015)

    Article  Google Scholar 

  27. 27.

    Wang, Y., Liu, Q., Wang, J., Wang, Q.H.: Optical encryption of multiple three-dimensional objects based on multiple interferences and single-pixel digital holography. Chin. Phys. B 27, 034202 (2018)

    ADS  Article  Google Scholar 

  28. 28.

    Muniraj, I., Kim, B., Lee, B.G.: Encryption and volumetric 3D object reconstruction using multispectral computational integral imaging. Appl. Opt. 53, G25–G32 (2014)

    Article  Google Scholar 

  29. 29.

    Xiao-Wei, L., Arum-Sulgi, C., In-Kwon, L., Sung-Jin, C., Seok-Tae, K.: Three-dimensional object encoding approach using computer-generated integral imaging and random phase encoding. Appl. Mech. Mater. 764–765, 970–974 (2015)

    Google Scholar 

  30. 30.

    Kong, D.Z., Shen, X.J., Cao, L.C., Zhang, H., Zong, S., Jin, G.F.: Three-dimensional information hierarchical encryption based on computer-generated holograms. Opt. Commun. 380, 387–393 (2016)

    ADS  Article  Google Scholar 

  31. 31.

    Zhao, Y., Cao, L.C., Zhang, H., Kong, D.Z., Jin, G.F.: Accurate calculation of computer-generated holograms using angular-spectrum layer-oriented method. Opt. Express 23, 25440–25449 (2015)

    ADS  Article  Google Scholar 

  32. 32.

    Pang, H., Wang, J.Z., Cao, A., Zhang, M., Shi, L.F., Deng, Q.L.: Accurate hologram generation using layer-based method and iterative Fourier transform algorithm. IEEE Photonics J. 9, 2200108 (2017)

    Google Scholar 

  33. 33.

    Tsang, P.W.M.: Single-random-phase holographic encryption of images. Opt. Laser Eng. 89, 22–28 (2017)

    Article  Google Scholar 

  34. 34.

    Tsang, P.W.M., Poon, T.C.: Novel method for converting digital Fresnel hologram to phase-only hologram based on bidirectional error diffusion. Opt. Express 21, 23680–23686 (2013)

    ADS  Article  Google Scholar 

  35. 35.

    Chang, K.M., Chen, C., Wang, J., Wang, Q.H.: Improved single-random-phase holographic encryption using double-phase method. Opt. Commun. 443, 19–25 (2019)

    ADS  Article  Google Scholar 

  36. 36.

    Mendoza-Yero, O., Minguez-Vega, G., Lancis, J.: Encoding complex fields by using a phase-only optical element. Opt. Lett. 39, 1740–1743 (2014)

    ADS  Article  Google Scholar 

  37. 37.

    Qi, Y.J., Chang, C.L., Xia, J.: Speckleless holographic display by complex modulation based on double-phase method. Opt. Express 24, 30368–30378 (2016)

    ADS  Article  Google Scholar 

  38. 38.

    Kim, Y.K., Lee, J.S., Won, Y.H.: Low-noise high-efficiency double-phase hologram by multiplying a weight factor. Opt. Lett. 44, 3649–3652 (2019)

    ADS  Article  Google Scholar 

Download references


This work is supported by the National Natural Science Foundation of China (NSFC) under Grant U1933132. Chengdu Science and Technology Program (2019-GH02-00070-HZ).

Author information



Corresponding author

Correspondence to Jun Wang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Wang, X., Chang, K., Chen, C. et al. Low-noise and fast three-dimensional information encryption based on the double-phase method. Opt Rev 28, 190–198 (2021). https://doi.org/10.1007/s10043-021-00649-5

Download citation


  • Three-dimensional encryption
  • Double-phase method
  • Phase-only hologram