Abstract

Optical voice encryption based on digital holography (DH), which uses the double random phase encoding (DRPE) in the Fourier transform domain, has been proposed [Opt. Lett. 42, 4619 (2017) [CrossRef]  ]. In the present work, we propose optical voice encryption in other optical domains such as fractional Fourier, Fresnel, and gyrator transform, which convert input information into different mixed space-frequency domains. We also analyze the recording conditions of human voice and some security aspects of the scheme. An optical setup based on off-axis DH is used to record the time-series of holograms, and these holograms can visualize the sound wave propagation. Then, the different encryption domains in double random phase encoding (DRPE) are used to encrypt voice information with enhanced security. With the numerical reconstruction and decryption procedure of DRPE with all correct keys and correct orders of optical domains, the original voice information can be retrieved. The extension of voice encryption in different domains will enhance the security level and analysis of recording, and security aspects will explore the possibilities and challenges of the optical voice encryption scheme. We present simulation results for encryption of an experimentally recorded human voice in various domains.

© 2019 Optical Society of America

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References

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2018 (3)

2017 (4)

A. Yan, Y. Wei, Z. Hu, J. Zhang, P. W. M. Tsang, and T. C. Poon, “Optical cryptography with biometrics for multi-depth objects,” Sci. Rep. 7, 12933 (2017).
[Crossref]

S. K. Rajput and O. Matoba, “Optical voice encryption based on digital holography,” Opt. Lett. 42, 4619–4622 (2017).
[Crossref]

S. K. Rajput and N. K. Nishchal, “Optical double image security scheme based on random fractional Fourier domain phase encoding and phase-retrieval algorithm,” Opt. Commun. 388, 38–46 (2017).
[Crossref]

S. K. Rajput and N. K. Nishchal, “Optical asymmetric cryptosystem based on photon counting and phase-truncated Fresnel transforms,” J. Mod. Opt. 64, 878–886 (2017).
[Crossref]

2016 (5)

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

K. Ishikawa, K. Yatabe, N. Chitanont, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, and M. Yoshii, “High-speed imaging of sound using parallel phase-shifting interferometry,” Opt. Express 24, 12922–12932(2016).
[Crossref]

G. Verma and A. Sinha, “Digital holographic based cancellable biometric for personal authentication,” J. Opt. 18, 055705 (2016).
[Crossref]

G. Verma and A. Sinha, “Securing information using optically generated biometric keys,” J. Opt. 18, 115701 (2016).
[Crossref]

K. Falaggis, A. H. R. Andrade, J. G. G. Luna, C. G. Ojeda, and R. Porras-Aguilar, “Optical encryption with protection against Dirac delta and plain signal attacks,” Opt. Lett. 41, 4787–4790 (2016).
[Crossref]

2015 (4)

2014 (2)

S. Liu, C. Guo, and J. T. Sheridan, “A review of optical image encryption techniques,” Opt. Lasers Eng. 57, 327–342 (2014).
[Crossref]

O. Matoba, H. Inokuchi, K. Nitta, and Y. Awatsuji, “Optical voice recorder by off-axis digital holography,” Opt. Lett. 39, 6549–6552 (2014).
[Crossref]

2013 (2)

R. C. Johnson, W. J. Scheirer, and T. E. Boult, “Secure voice-based authentication for mobile devices: vaulted voice verification,” Proc. SPIE 8712, 87120P (2013).
[Crossref]

Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38, 1425–1427 (2013).
[Crossref]

2012 (2)

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on phase retrieval combined with three-dimensional particle-like distribution,” J. Opt. 14, 075402 (2012).
[Crossref]

A. Torras-Rosell and S. Barrera-Figueroa, “Sound field reconstruction using acousto-optic tomography,” J. Acoust. Soc. Am. 131, 3786–3793 (2012).
[Crossref]

2010 (3)

2009 (2)

N. Singh and A. Sinha, “Gyrator transform-based optical image encryption, using chaos,” Opt. Lasers Eng. 47, 539–546 (2009).
[Crossref]

O. Matoba, T. Nomura, E. Perez-Cabre, M. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

2008 (1)

2007 (2)

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Applications of gyrator transform for image processing,” Opt. Commun. 278, 279–284 (2007).
[Crossref]

T. Nomura and B. Javidi, “Object recognition by use of polarimetric phase-shifting digital holography,” Opt. Lett. 32, 2146–2148(2007).
[Crossref]

2004 (1)

2003 (2)

2000 (2)

1999 (1)

1995 (1)

1994 (1)

Alfalou, A.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

A. Alfalou and C. Brosseau, “Dual encryption scheme of images using polarized light,” Opt. Lett. 35, 2185–2187 (2010).
[Crossref]

Alieva, T.

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Applications of gyrator transform for image processing,” Opt. Commun. 278, 279–284 (2007).
[Crossref]

Andrade, A. H. R.

Awatsuji, Y.

S. K. Rajput, O. Matoba, and Y. Awatsuji, “Characteristics of vibration frequency measurement based on sound field imaging by digital holography,” OSA Contin. 1, 200–212 (2018).
[Crossref]

O. Matoba, H. Inokuchi, K. Nitta, and Y. Awatsuji, “Optical voice recorder by off-axis digital holography,” Opt. Lett. 39, 6549–6552 (2014).
[Crossref]

Barrera, J. F.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Barrera-Figueroa, S.

A. Torras-Rosell and S. Barrera-Figueroa, “Sound field reconstruction using acousto-optic tomography,” J. Acoust. Soc. Am. 131, 3786–3793 (2012).
[Crossref]

Belmeguenai, A.

A. Belmeguenai, K. Mansouri, and M. Lashab, “Speech encryption using stream Cipher,” Br. J. Appl. Sci. Technol. 8, 107–125 (2015).
[Crossref]

Boult, T. E.

R. C. Johnson, W. J. Scheirer, and T. E. Boult, “Secure voice-based authentication for mobile devices: vaulted voice verification,” Proc. SPIE 8712, 87120P (2013).
[Crossref]

Brosseau, C.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

A. Alfalou and C. Brosseau, “Dual encryption scheme of images using polarized light,” Opt. Lett. 35, 2185–2187 (2010).
[Crossref]

Calvo, M. L.

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Applications of gyrator transform for image processing,” Opt. Commun. 278, 279–284 (2007).
[Crossref]

Carnicer, A.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Chen, W.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on phase retrieval combined with three-dimensional particle-like distribution,” J. Opt. 14, 075402 (2012).
[Crossref]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).
[Crossref]

Chen, X.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on phase retrieval combined with three-dimensional particle-like distribution,” J. Opt. 14, 075402 (2012).
[Crossref]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).
[Crossref]

Chitanont, N.

Falaggis, K.

Gao, Q.

Guo, C.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

S. Liu, C. Guo, and J. T. Sheridan, “A review of optical image encryption techniques,” Opt. Lasers Eng. 57, 327–342 (2014).
[Crossref]

He, W.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

C. Zhang, W. He, J. Wu, and X. Peng, “Optical cryptosystem based on phase-truncated Fresnel diffraction and transport of intensity equation,” Opt. Express 23, 8845–8854 (2015).
[Crossref]

Hennelly, B.

Hu, Z.

A. Yan, Y. Wei, Z. Hu, J. Zhang, P. W. M. Tsang, and T. C. Poon, “Optical cryptography with biometrics for multi-depth objects,” Sci. Rep. 7, 12933 (2017).
[Crossref]

Ikeda, Y.

Inokuchi, H.

Ishikawa, K.

Javidi, B.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

O. Matoba, T. Nomura, E. Perez-Cabre, M. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

T. Nomura and B. Javidi, “Object recognition by use of polarimetric phase-shifting digital holography,” Opt. Lett. 32, 2146–2148(2007).
[Crossref]

O. Matoba and B. Javidi, “Secure three-dimensional data transmission and display,” Appl. Opt. 43, 2285–2291 (2004).
[Crossref]

S. Kishk and B. Javidi, “Watermarking of three-dimensional objects by digital holography,” Opt. Lett. 28, 167–169 (2003).
[Crossref]

B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25, 28–30 (2000).
[Crossref]

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24, 762–764 (1999).
[Crossref]

P. Refregier and B. Javidi, “Optical image encryption based on input plane encoding and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
[Crossref]

B. Javidi, Optical and Digital Techniques for Information Security (Springer, 2005).

Johnson, R. C.

R. C. Johnson, W. J. Scheirer, and T. E. Boult, “Secure voice-based authentication for mobile devices: vaulted voice verification,” Proc. SPIE 8712, 87120P (2013).
[Crossref]

Joseph, J.

Jueptner, W.

U. Schnars and W. Jueptner, Digital Holography; Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).

Juvells, I.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Keshavarzi, P.

Kishk, S.

Kumar, D.

Lancis, J.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Lashab, M.

A. Belmeguenai, K. Mansouri, and M. Lashab, “Speech encryption using stream Cipher,” Br. J. Appl. Sci. Technol. 8, 107–125 (2015).
[Crossref]

Li, H.

Li, T.

Liu, S.

S. Liu, C. Guo, and J. T. Sheridan, “A review of optical image encryption techniques,” Opt. Lasers Eng. 57, 327–342 (2014).
[Crossref]

Lokberg, O.

Luna, J. G. G.

Mansouri, K.

A. Belmeguenai, K. Mansouri, and M. Lashab, “Speech encryption using stream Cipher,” Br. J. Appl. Sci. Technol. 8, 107–125 (2015).
[Crossref]

Markman, A.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Matoba, O.

Matsumoto, T.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Millan, M.

O. Matoba, T. Nomura, E. Perez-Cabre, M. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

Millan, M. S.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Mosk, A. P.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Mozaffari, S.

Naruse, M.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Nishchal, N. K.

S. K. Rajput and N. K. Nishchal, “Optical double image security scheme based on random fractional Fourier domain phase encoding and phase-retrieval algorithm,” Opt. Commun. 388, 38–46 (2017).
[Crossref]

S. K. Rajput and N. K. Nishchal, “Optical asymmetric cryptosystem based on photon counting and phase-truncated Fresnel transforms,” J. Mod. Opt. 64, 878–886 (2017).
[Crossref]

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

S. K. Rajput, D. Kumar, and N. K. Nishchal, “Photon counting imaging and phase mask multiplexing for multiple image authentication and hologram security,” Appl. Opt. 54, 1657–1666 (2015).
[Crossref]

Nitta, K.

Niwa, H.

Nomura, T.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

O. Matoba, T. Nomura, E. Perez-Cabre, M. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

T. Nomura and B. Javidi, “Object recognition by use of polarimetric phase-shifting digital holography,” Opt. Lett. 32, 2146–2148(2007).
[Crossref]

B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25, 28–30 (2000).
[Crossref]

Oikawa, Y.

Ojeda, C. G.

Onuma, T.

Peng, X.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

C. Zhang, W. He, J. Wu, and X. Peng, “Optical cryptosystem based on phase-truncated Fresnel diffraction and transport of intensity equation,” Opt. Express 23, 8845–8854 (2015).
[Crossref]

W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35, 118–120 (2010).
[Crossref]

Perez-Cabre, E.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

O. Matoba, T. Nomura, E. Perez-Cabre, M. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

Pinkse, P. W. H.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Poon, T. C.

A. Yan, Y. Wei, Z. Hu, J. Zhang, P. W. M. Tsang, and T. C. Poon, “Optical cryptography with biometrics for multi-depth objects,” Sci. Rep. 7, 12933 (2017).
[Crossref]

Porras-Aguilar, R.

Qin, W.

Rajput, S. K.

S. K. Rajput, O. Matoba, and Y. Awatsuji, “Characteristics of vibration frequency measurement based on sound field imaging by digital holography,” OSA Contin. 1, 200–212 (2018).
[Crossref]

S. K. Rajput and N. K. Nishchal, “Optical asymmetric cryptosystem based on photon counting and phase-truncated Fresnel transforms,” J. Mod. Opt. 64, 878–886 (2017).
[Crossref]

S. K. Rajput and N. K. Nishchal, “Optical double image security scheme based on random fractional Fourier domain phase encoding and phase-retrieval algorithm,” Opt. Commun. 388, 38–46 (2017).
[Crossref]

S. K. Rajput and O. Matoba, “Optical voice encryption based on digital holography,” Opt. Lett. 42, 4619–4622 (2017).
[Crossref]

S. K. Rajput, D. Kumar, and N. K. Nishchal, “Photon counting imaging and phase mask multiplexing for multiple image authentication and hologram security,” Appl. Opt. 54, 1657–1666 (2015).
[Crossref]

Ramirez, J. F. B.

Refregier, P.

Rivenson, Y.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Rodrigo, J. A.

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Applications of gyrator transform for image processing,” Opt. Commun. 278, 279–284 (2007).
[Crossref]

Scheirer, W. J.

R. C. Johnson, W. J. Scheirer, and T. E. Boult, “Secure voice-based authentication for mobile devices: vaulted voice verification,” Proc. SPIE 8712, 87120P (2013).
[Crossref]

Schnars, U.

U. Schnars and W. Jueptner, Digital Holography; Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).

Sheppard, C. J. R.

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on phase retrieval combined with three-dimensional particle-like distribution,” J. Opt. 14, 075402 (2012).
[Crossref]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).
[Crossref]

Sheridan, J. T.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

S. Liu, C. Guo, and J. T. Sheridan, “A review of optical image encryption techniques,” Opt. Lasers Eng. 57, 327–342 (2014).
[Crossref]

B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. 28, 269–271 (2003).
[Crossref]

Shi, Y.

Singh, K.

Singh, N.

N. Singh and A. Sinha, “Gyrator transform-based optical image encryption, using chaos,” Opt. Lasers Eng. 47, 539–546 (2009).
[Crossref]

Sinha, A.

G. Verma and A. Sinha, “Digital holographic based cancellable biometric for personal authentication,” J. Opt. 18, 055705 (2016).
[Crossref]

G. Verma and A. Sinha, “Securing information using optically generated biometric keys,” J. Opt. 18, 115701 (2016).
[Crossref]

N. Singh and A. Sinha, “Gyrator transform-based optical image encryption, using chaos,” Opt. Lasers Eng. 47, 539–546 (2009).
[Crossref]

Situ, G.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Stern, A.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Taheri, M.

Tajahuerce, E.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Tanigawa, R.

Torras-Rosell, A.

A. Torras-Rosell and S. Barrera-Figueroa, “Sound field reconstruction using acousto-optic tomography,” J. Acoust. Soc. Am. 131, 3786–3793 (2012).
[Crossref]

Torroba, R.

A. V. Zea, J. F. B. Ramirez, and R. Torroba, “Optimized random phase encryption,” Opt. Lett. 43, 3558–3561 (2018).
[Crossref]

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Tsang, P. W. M.

A. Yan, Y. Wei, Z. Hu, J. Zhang, P. W. M. Tsang, and T. C. Poon, “Optical cryptography with biometrics for multi-depth objects,” Sci. Rep. 7, 12933 (2017).
[Crossref]

Unnikrishnan, G.

Verma, G.

G. Verma and A. Sinha, “Securing information using optically generated biometric keys,” J. Opt. 18, 115701 (2016).
[Crossref]

G. Verma and A. Sinha, “Digital holographic based cancellable biometric for personal authentication,” J. Opt. 18, 055705 (2016).
[Crossref]

Wang, B.

Wang, Y.

Wei, Y.

A. Yan, Y. Wei, Z. Hu, J. Zhang, P. W. M. Tsang, and T. C. Poon, “Optical cryptography with biometrics for multi-depth objects,” Sci. Rep. 7, 12933 (2017).
[Crossref]

Wu, J.

Yamaguchi, M.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Yan, A.

A. Yan, Y. Wei, Z. Hu, J. Zhang, P. W. M. Tsang, and T. C. Poon, “Optical cryptography with biometrics for multi-depth objects,” Sci. Rep. 7, 12933 (2017).
[Crossref]

Yatabe, K.

Yoshii, M.

Zea, A. V.

Zhang, C.

Zhang, J.

A. Yan, Y. Wei, Z. Hu, J. Zhang, P. W. M. Tsang, and T. C. Poon, “Optical cryptography with biometrics for multi-depth objects,” Sci. Rep. 7, 12933 (2017).
[Crossref]

Zhang, S.

Zhang, Y.

Appl. Opt. (3)

Br. J. Appl. Sci. Technol. (1)

A. Belmeguenai, K. Mansouri, and M. Lashab, “Speech encryption using stream Cipher,” Br. J. Appl. Sci. Technol. 8, 107–125 (2015).
[Crossref]

J. Acoust. Soc. Am. (1)

A. Torras-Rosell and S. Barrera-Figueroa, “Sound field reconstruction using acousto-optic tomography,” J. Acoust. Soc. Am. 131, 3786–3793 (2012).
[Crossref]

J. Mod. Opt. (1)

S. K. Rajput and N. K. Nishchal, “Optical asymmetric cryptosystem based on photon counting and phase-truncated Fresnel transforms,” J. Mod. Opt. 64, 878–886 (2017).
[Crossref]

J. Opt. (4)

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on phase retrieval combined with three-dimensional particle-like distribution,” J. Opt. 14, 075402 (2012).
[Crossref]

G. Verma and A. Sinha, “Digital holographic based cancellable biometric for personal authentication,” J. Opt. 18, 055705 (2016).
[Crossref]

G. Verma and A. Sinha, “Securing information using optically generated biometric keys,” J. Opt. 18, 115701 (2016).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

S. K. Rajput and N. K. Nishchal, “Optical double image security scheme based on random fractional Fourier domain phase encoding and phase-retrieval algorithm,” Opt. Commun. 388, 38–46 (2017).
[Crossref]

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Applications of gyrator transform for image processing,” Opt. Commun. 278, 279–284 (2007).
[Crossref]

Opt. Express (2)

Opt. Lasers Eng. (2)

N. Singh and A. Sinha, “Gyrator transform-based optical image encryption, using chaos,” Opt. Lasers Eng. 47, 539–546 (2009).
[Crossref]

S. Liu, C. Guo, and J. T. Sheridan, “A review of optical image encryption techniques,” Opt. Lasers Eng. 57, 327–342 (2014).
[Crossref]

Opt. Lett. (17)

S. Kishk and B. Javidi, “Watermarking of three-dimensional objects by digital holography,” Opt. Lett. 28, 167–169 (2003).
[Crossref]

B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. 28, 269–271 (2003).
[Crossref]

B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25, 28–30 (2000).
[Crossref]

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887–889 (2000).
[Crossref]

P. Refregier and B. Javidi, “Optical image encryption based on input plane encoding and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
[Crossref]

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24, 762–764 (1999).
[Crossref]

T. Nomura and B. Javidi, “Object recognition by use of polarimetric phase-shifting digital holography,” Opt. Lett. 32, 2146–2148(2007).
[Crossref]

Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33, 2443–2445 (2008).
[Crossref]

W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35, 118–120 (2010).
[Crossref]

A. Alfalou and C. Brosseau, “Dual encryption scheme of images using polarized light,” Opt. Lett. 35, 2185–2187 (2010).
[Crossref]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).
[Crossref]

Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38, 1425–1427 (2013).
[Crossref]

O. Matoba, H. Inokuchi, K. Nitta, and Y. Awatsuji, “Optical voice recorder by off-axis digital holography,” Opt. Lett. 39, 6549–6552 (2014).
[Crossref]

K. Falaggis, A. H. R. Andrade, J. G. G. Luna, C. G. Ojeda, and R. Porras-Aguilar, “Optical encryption with protection against Dirac delta and plain signal attacks,” Opt. Lett. 41, 4787–4790 (2016).
[Crossref]

S. K. Rajput and O. Matoba, “Optical voice encryption based on digital holography,” Opt. Lett. 42, 4619–4622 (2017).
[Crossref]

K. Ishikawa, R. Tanigawa, K. Yatabe, Y. Oikawa, T. Onuma, and H. Niwa, “Simultaneous imaging of flow and sound using high-speed parallel phase-shifting interferometry,” Opt. Lett. 43, 991–994 (2018).
[Crossref]

A. V. Zea, J. F. B. Ramirez, and R. Torroba, “Optimized random phase encryption,” Opt. Lett. 43, 3558–3561 (2018).
[Crossref]

OSA Contin. (1)

S. K. Rajput, O. Matoba, and Y. Awatsuji, “Characteristics of vibration frequency measurement based on sound field imaging by digital holography,” OSA Contin. 1, 200–212 (2018).
[Crossref]

Proc. IEEE (1)

O. Matoba, T. Nomura, E. Perez-Cabre, M. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

Proc. SPIE (1)

R. C. Johnson, W. J. Scheirer, and T. E. Boult, “Secure voice-based authentication for mobile devices: vaulted voice verification,” Proc. SPIE 8712, 87120P (2013).
[Crossref]

Sci. Rep. (1)

A. Yan, Y. Wei, Z. Hu, J. Zhang, P. W. M. Tsang, and T. C. Poon, “Optical cryptography with biometrics for multi-depth objects,” Sci. Rep. 7, 12933 (2017).
[Crossref]

Other (2)

B. Javidi, Optical and Digital Techniques for Information Security (Springer, 2005).

U. Schnars and W. Jueptner, Digital Holography; Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).

Supplementary Material (13)

NameDescription
» Visualization 1       For complete information corresponding to Fig. 5(d), see Visualization 1
» Visualization 2       For complete information corresponding to Fig. 6(b), see Visualization 2
» Visualization 3       For complete information corresponding to Fig. 6(d), see Visualization 3
» Visualization 4       For complete information corresponding to Fig. 7(d), see Visualization 4
» Visualization 5       For complete information corresponding to Fig. 8(b), see Visualization 5
» Visualization 6       For complete information corresponding to Fig. 9(b), see Visualization 6
» Visualization 7       For complete information corresponding to Fig. 9(d), see Visualization 7
» Visualization 8       For complete information corresponding to Fig. 10(d), see Visualization 8.mp4
» Visualization 9       For complete information corresponding to Fig. 11(a), see Visualization 9
» Visualization 10       For complete information corresponding to Fig. 11(b), see Visualization 10
» Visualization 11       For complete information corresponding to Fig. 12(d), see Visualization 11
» Visualization 12       For complete information corresponding to Fig. 13(a), see Visualization 12
» Visualization 13       For complete information corresponding to Fig. 13(b), see Visualization 13

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Figures (15)

Fig. 1.
Fig. 1. Voice recording and encryption scheme based on DH. M, mirror; L, lens; PH, pin hole; PC, personal computer; BS, beam splitter; IS, image sensor. Optical encryption can be implemented using DRPE in various domains.
Fig. 2.
Fig. 2. Optical setup of DRPE in FRT domain. IP, input plane; FP, fractional plane; L, lens; OP, output plane; IS, image sensor. d1 and d2 are the fractional distances.
Fig. 3.
Fig. 3. Optical setup of DRPE in FrT domain. IP, input plane; FSP, free-space propagation; OP, output plane; IS, image sensor. d is the free-space propagation distance.
Fig. 4.
Fig. 4. Optical setup of DRPE in GT domain. IP, input plane; GT, gyrator transform; OP, output plane; IS, image sensor. L1 is the generalized lens, which is a combination of cylindrical lenses.
Fig. 5.
Fig. 5. Voice recording results. (a) Recorded hologram. (b) Reconstructed phase image. (c) Plot of phase versus time. (d) Spectrogram. For complete information, see Visualization 1.
Fig. 6.
Fig. 6. Voice recording results at different distances. (a) Plot of phase versus time at distance of 1 mm. (b) Spectrogram corresponding to (a). (c) Plot of phase versus time at distance of 115 mm. (d) Spectrogram corresponding to (c). For complete information corresponding to Fig. (b) and (d), see Visualization 2 and Visualization 3, respectively.
Fig. 7.
Fig. 7. Optical voice encryption results in FRT domain. (a) Encrypted hologram. (b) Reconstructed phase image from encrypted hologram. (c) Plot of phase versus time. (d) Spectrogram. For complete information, see Visualization 4.
Fig. 8.
Fig. 8. Decryption results in FRT domain with all correct keys. (a) Plot of phase versus time with all correct keys and (b) spectrogram corresponding to (a). For complete information, see Visualization 5.
Fig. 9.
Fig. 9. Decryption results in FRT domain with wrong keys. (a) Plot of phase versus time with wrong RPM. (b) Spectrogram corresponding to (a). (c) Plot of phase versus time with wrong fractional orders. (d) Spectrogram corresponding to (c). For complete information corresponding to Figs. (b) and (d), see Visualization 6 and Visualization 7, respectively.
Fig. 10.
Fig. 10. Optical voice encryption results in FrT domain. (a) Encrypted hologram. (b) Reconstructed phase image from encrypted hologram. (c) Plot of phase versus time. (d) Spectrogram. For complete information, see Visualization 8.
Fig. 11.
Fig. 11. Decryption results in FrT domain. (a) Spectrogram obtained after use of all correct keys. (b) Spectrogram obtained after use of wrong Fresnel distances. For complete information corresponding to (a) and (b), see Visualization 9 and Visualization 10, respectively.
Fig. 12.
Fig. 12. Optical voice encryption results in GT domain. (a) Encrypted hologram. (b) Reconstructed phase image from encrypted hologram. (c) Plot of phase versus time. (d) Spectrogram. For complete information, see Visualization 11.
Fig. 13.
Fig. 13. Decryption results in GT domain. (a) Spectrogram obtained after use of all correct keys. (b) Spectrogram obtained after use of wrong gyrator parameter. For complete information corresponding to (a) and (b), see Visualization 12 and Visualization 13, respectively.
Fig. 14.
Fig. 14. MSE analysis. (a) Plot of MSE versus number of samples when all correct keys are used. (b) Plot of MSE versus number of samples when wrong RPM is used. (c) Plot of MSE versus number of samples when wrong orders are used.
Fig. 15.
Fig. 15. Correlation analysis. (a) Plot of CC versus number of samples when all correct keys are used. (b) Plot of CC versus number of samples when wrong orders are used.

Equations (13)

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n=(n01)(1+PP0)1/γ+1,
n=1+(n01)(1+PP0γ)=n0+PP0γ(n01)nn0=PP0γ(n01)=Δn.
h(x,y)=|O(x,y)|2+|R(x,y)|2+O*(x,y)R(x,y)+O(x,y)R*(x,y),
O(x,y)=|O(x,y)|exp(ip(x,y))=|O(x,y)|exp(i2π[n0+Δn(x,y)]dλ).
E(ξ,η)=OT2{OT1[h(x,y)×R1(x,y)]×R2(u,v)},
fFRTa(u,v)=Kh(x,y)×exp[jπx2+y2+u2+v2tanα2jπxyuvsinα]dxdy,
fFrT(u,v)=exp{i×2π×zλ}iλzh(x,y)×exp[iπλz((xu)2+(yv)2)]dxdy,
fGT(u,v)=h(x,y)|sinβ|×exp[i2π(xy+uv)cosβ(xv+yu)sinβ]dxdy.
hd(x,y)=IOT1{IOT2[E(ξ,η)]×R2*(u,v)}×R1*(x,y),
A(ξ,η,z)=A(ξ,η,0)×exp[i2πzλ1(λξ)2(λη)2].
p(x,y)=angle{IFT[A(ξ,η,z)]}.
MSE=x=0N1y=0N1{h(x,y)hd(x,y)}2N×N.
CC=Cov[h(x,y)hd(x,y)]σh×σhd,

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