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Single Random Phase Encoding Based on Fractional Fourier Transform

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Tutor: YangHu
School: Shanxi Normal University
Course: Optics
Keywords: Fractional Fourier transform,Random phase mask,Double random phase encoding,Sing
CLC: TP309.7
Type: Master's thesis
Year:  2014
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Application of optical technology in the field of information security can be traced back to the earliest in the1980s, American Banknote Holographic company used Holographic anti-counterfeiting technology to make the credit card. Because the Holographic images can be rapidly replicated in quantity and cost less, and people can observe directly through the eye and identify authenticity, the rainbow Holographic anti-counterfeiting technology is widely used in the field of security and daily life. However, due to the development of photoelectric technology and image processing technology, holographic images become vulnerable to imitation; rainbow holographic anti-counterfeiting technology faced severe challenges. In1995, Bahram Javidi, Philippe and Refregier introduced the concept of double random phase in optical image encryption, and proposed the double random phase encoding technique, hence the prelude that used the random phase mask to realize image encryption has been opened. With the further research on encryption technology, people successively proposed double random phase encoding theory based on fractional Fourier transform, anamorphic fractional Fourier transform and theory of optical image encryption based on Fresnel domain, but the single random phase encoding theory has not yetbeen systematic introduced.At first this paper introduces the basic theory of spatial filtering,and applies the random phase mask to filter system. The paperintroduces encryption and decryption process in detail based on twosystems----Fourier transform of double random phase encodingsystem and Fourier transform of single random phase encodingsystem, illustrates their physical mechanism, compares two kinds ofencryption methods, and analyzes their advantages anddisadvantages. Because of the situation that it is difficult toaccurately get the focal length of the lens and accurately implementin practice for Fourier transform, the paper puts forward singlerandom phase encoding based on the structure of fractional Fouriertransform; according to the similar characteristics of the sphericalwave phase distribution and phase distribution of phase mask, thepaper puts forward the single random phase encoding in the conditionof spherical wave illumination. The encryption method not only canobtain the same encryption effect with the double random phaseencoding, but also can reduce the system optical element, simplifythe optical path of the system setting, reduce light energy losses inthe practice and the influence of coherent noise. The paper expoundsthe encryption and decryption process of the single random phaseencoding in the condition of plane wave illumination and sphericalwave illumination, respectively presents the complex amplitudedistribution of encryption images which are obtained by two kinds ofencryption methods, analyzes the results of decrypted in detail, andcontrasts the two kinds of encryption methods from the key, the type of incident light, the security of the encryption system. At last, thispaper uses computer to simulate experiment for verifying thefeasibility and safety of two kinds of encryption theory and analyzesthe effect and significance of keys in the decrypting process.
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