CN106371304A - Safe compressed holographic imaging system and method - Google Patents

Abstract

The invention discloses a safe compressed holographic imaging system. The system comprises the following processes of decomposing a beam of light emitted from a light source into object light and reference light through a light source generating and beam splitting device; obtaining an encrypted object light beam with an object image through an encryption device; obtaining a reference light beam with a host image through a phase modulation device; generating an encrypting and watermarking-superimposed interference hologram through an image generating and watermarking device; collecting interference hologram data through an image collection device and transmitting the interference hologram data to an image reconstruction device; and reconstructing an object image through the image reconstruction device according to the interference hologram data. The interference hologram is recorded by using a three-step phase shift method; image encryption, image watermarking and image compression are simultaneously achieved in an all-optical domain environment; the safety of information in transmission and storage processes is ensured; and an original object image is prevented from being illegally stolen or tampered. The invention further provides a safe compressed holographic imaging method.

Description

Safe compression holographic imaging system and imaging method thereof

Technical Field

The invention relates to the field of image security imaging, in particular to a compression holographic imaging system with security and an imaging method thereof.

Background

In the big data era, information becomes more transparent, and the security problem of the information and the data becomes more and more important. The image security mainly comprises image encryption, image watermarking and the like. The image encryption is to encode the image data itself, make the original image pixel scrambling become secret data to generate the encrypted image, the purpose is not only to generate a visually disordered image, but to apply it as an effective auxiliary measure to the preprocessing and post-processing process of the digital watermarking technology, so as to achieve the purpose of image security transmission. The image watermark is to embed the encrypted image information into a host image, and achieves the purpose of encrypting image data by the watermark under the condition of keeping the original visual information of the host image approximately unchanged, thereby not only ensuring the safety of the information in the transmission and storage process, but also avoiding the attention of a thief, and further realizing the requirement of safe imaging.

Unlike traditional imaging method for recording light intensity distribution of object, the holographic imaging technology records complex amplitude wave of object, i.e. it can record amplitude and phase information of object at the same time to reproduce wave front of object. Therefore, holographic techniques have significant advantages in imaging phase objects and 3D scenes. The compressed sensing technology provides a new direction for the research in the imaging field, and the compressed sensing technology is used for acquiring the non-adaptive linear projection value of the signal far below the Nyquist sampling rate, and accurately reconstructing the original signal by solving an optimization problem, thereby greatly reducing the data volume acquired by the system. This theory therefore provides the possibility of direct compressive sampling of the hologram in the pure optical domain. The optical encryption method also has the characteristics of high-speed operation, multi-dimensional capability and the like. Many new applications based on compressive sensing technology have emerged in the field of holography. With the sparsity of the signal, the encrypted and watermarked objects can be compressed into less data.

In addition, many groups at home and abroad adopt an area array imaging mode such as a charge coupled device (hereinafter referred to as CCD) and the like, and then the compression of a safe image is realized in an electric signal in a digital domain, although the data volume can be well compressed; however, due to the limitation that the CCD needs to sense light through the photodiode, which is sensitive to light, many imaging modes at home and abroad cannot be applied to pure light systems, such as an all-optical network; the characteristics of high speed, high parallelism and the like of an optical system cannot be fully exerted, and the application of the optical system is severely restricted; and the functions of optical image perception, optical image security processing, optical image compression and the like cannot be simultaneously completed in the optical imaging system.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides a safe compression holographic imaging system which can simultaneously realize image encryption, image watermarking and image compression, can ensure the safety of information in the transmission and storage processes and avoid the illegal stealing or tampering of the original object image.

The invention is realized by the following technical scheme: a safe compression holographic imaging system comprises a light source generating and beam splitting device, an encryption device, a phase modulation device, an image generating and watermarking device, an image acquisition device and an image reconstruction device;

the light source generating and beam splitting device is used for splitting one beam of light emitted by the light source into two beams of light, wherein one beam of light is object light irradiating on the object image, and the other beam of light is reference light irradiating on the host image;

the encryption device is used for reflecting the object light to irradiate the object image and encrypting the object light information to obtain an encrypted object light beam carrying the object image;

the phase modulation device is used for irradiating the reference light after phase modulation on a host image to obtain a reference light beam carrying the host image;

the image generation and watermark device is used for receiving an encrypted object light beam carrying an object image and a reference light beam carrying a host image at the same time and generating an interference hologram superposed by encryption and watermark;

the image acquisition device is used for acquiring the interference hologram data and transmitting the interference hologram data to the image reconstruction device;

and the image reconstruction device is used for reconstructing an object image according to the interference hologram data.

Compared with the prior art, the method has the advantages that the interference hologram is recorded by using a three-step phase shift method, the image encryption, the image watermarking and the image compression are simultaneously realized in the all-optical domain environment, the confidentiality is higher, the safety of information in the transmission and storage processes is ensured, the original object image is prevented from being illegally stolen or tampered, and the requirement of safe compression imaging is realized.

Further, the encryption device includes a mirror, a first random phase plate, and a second random phase plate; the reflecting mirror is arranged behind the light source generating and beam splitting device and in front of the object image along the optical path of the object light, and the reflecting mirror is used for reflecting the object light and then irradiating the object light to the object image; arranging the first random phase plate behind an object image; a second random phase plate parallel to the first random phase plate is arranged behind the first random phase plate; after the object light penetrates through the object image, the object light sequentially passes through the first random phase plate and the second random phase plate to obtain an encrypted object light beam carrying the object image; the encrypted object light beam irradiates the image generation and watermarking device again;

according to the fresnel diffraction formula, the encrypted object image represented by the encrypted object light beam is represented by a complex amplitude distribution as:

$\begin{array}{c}{\mathrm{\ψ}}_o(\mathrm{\ξ},\mathrm{\η})=A(\mathrm{\ξ},\mathrm{\η})\exp \left(i\mathrm{\φ}\right(\mathrm{\ξ},\mathrm{\η})\\ ={\mathrm{Frt}}_{z_2}\left\{{\mathrm{Frt}}_{z_1}\right\{K_1\×O(x_0,y_0)\×\exp \[i2\mathrm{\π}\×p(x_0,y_0)\]\}\×\exp \[i2\mathrm{\π}\×q(x_1,y_1)\]\},\end{array}$

wherein, K₁Representing the optical amplitude of the object optical path; o (x)₀,y₀) Is the complex amplitude distribution of the object light at the first random phase plate; exp [ i2 pi.p (x)₀,y₀)]And exp [ i2 π q (x)₁,y₁)]The complex amplitude transmittances of the first random phase plate and the second random phase plate respectively; p (x)₀,y₀) And q (x)₁,y₁) Are all distributed in [0,1 ]]Statistically independent white noise over an interval; frt_ZRepresenting a Fresnel transformation with a diffraction distance Z, the distance between the first random phase plate and the second random phase plate being Z₁The distance between the second random phase plate and the digital micromirror device is Z₂。

Furthermore, the phase modulation device comprises a piezoelectric converter and a second beam splitter, wherein the piezoelectric converter is used for dividing the reference light into three times of phases and then generating the phases of 0 respectively,a pi interference light source; the second beam splitter irradiates the phase-modulated reference light to a host image so as to obtain a reference light beam carrying the host image;

the complex amplitude distribution of the host image represented by the reference light beam can be represented as:

${\mathrm{\ψ}}_h(\mathrm{\ξ},\mathrm{\η};{\mathrm{\φ}}_R)=A_h(\mathrm{\ξ},\mathrm{\η})\exp \[{\mathrm{i\φ}}_h(\mathrm{\ξ},\mathrm{\η})\]\exp \left({\mathrm{i\φ}}_R\right),({\mathrm{\φ}}_R=0,\frac{\mathrm{\π}}{2},\mathrm{\π}),$

further, the image generation and watermarking device comprises a third beam splitter; the third beam splitter receives the reference light beam carrying the host image and the encrypted object light beam carrying the object image at the same time to form coaxial interference light, and superposes the two beams to generate an interference hologram carrying the encrypted and watermarked object image information;

the light intensity value of the interference hologram with the encryption and the watermark superposed is expressed as

I_H(ξ,η；φ_R)

＝|ψ₀(ξ,η)+ψ_h(ξ,η；φ_R)|²

＝A(ξ,η)²+A_h(ξ,η)²

+2A(ξ,η)A_h(ξ,η)cos[φ_h(ξ,η)+φ_R-φ(ξ,η)],

$({\mathrm{\φ}}_R=0,\frac{\mathrm{\π}}{2},\mathrm{\π}),$

Further, the image acquisition device comprises a digital micromirror device, a converging lens and a single photon detector; the digital micromirror device compresses and samples interference hologram data generated by the image generation and watermarking device, converges at one point through the convergent lens and then collects the data through the single photon detector;

the output voltage of the high-sensitivity photodiode of the single-photon detector is expressed as:

whereinRepresenting an m-dimensional pseudo-random measurement matrix on the plane of the digital micromirror device;

this process was repeated M times and the measurement Y obtained was:

Y＝[y₁,y₂,y₃]＝Ψ[I_H1,I_H2,I_H3],

wherein,Ψ∈R^M×Nis a measurement matrix obtained by the digital micromirror device plane, Y ∈ R^M×3Is a measured value, y_k∈R^M×1，I_Hk∈R^N×1。

Further, the image reconstruction device comprises an analog-to-digital conversion module, an image transmission module and an image reconstruction module; the analog-to-digital conversion module is used for converting the analog interference hologram data collected by the image collection device into digital interference hologram data; the image transmission module is used for transmitting the digital interference hologram data to the image reconstruction module; the image reconstruction module is used for reconstructing an original object image by utilizing a two-step iterative contraction algorithm, a Fresnel inverse transformation algorithm and complex amplitude information of a host image according to the digital interference hologram data transmitted by the image transmission device;

the expression for reconstructing the light intensity of the superimposed interference on the digital micromirror device using the compressive sensing algorithm is:

$\begin{array}{ccc}\underset{I_{Hk}}{min}\frac{\mathrm{\μ}}{2}\left|\right|Y_k-\mathrm{\Ψ}{\hat{I}}_{Hk}|{|}_2^2+TV\left({\hat{I}}_{Hk}\right)& s.t.& Y_k={\mathrm{\ΨI}}_{Hk}\end{array},$

wherein, mu is a constant value,is a least squares term whenAnd the associated vector quantization value Y_kIts value is the smallest at the time of coincidence,is a fully variant representation of the signal, specifically the following equation:

$TV\left({\hat{I}}_{Hk}\right)=\underset{adj.i,j}{\mathrm{\Σ}}\left|{\hat{I}}_{Hki}-{\hat{I}}_{Hkj}\right|,)$

the subscripts i, j in this formula denoteAll the pairs of adjacent pixel points are adjacent to each other,is a discrete gradientL of₁And (4) norm.

The phase information φ (ξ) and amplitude information A (ξ) of the encrypted and watermarked object image on the digital micromirror device are as follows:

$A(\mathrm{\ξ},\mathrm{\η})=\frac{{\[{({\hat{I}}_{H1}-{\hat{I}}_{H3})}^2+{(2{\hat{I}}_{H2}-{\hat{I}}_{H1}-{\hat{I}}_{H3})}^2\]}^{1/2}}{4A_h},$

wherein the diffraction profile of the host image is phi_h，A_hThe method is obtained in advance by using a three-step phase shift method under a Mach-Zehnder interferometer;

reconstructing the object image through a Fresnel inverse transformation algorithm, wherein the process is represented as:

wherein IFrt_ZRepresenting the inverse fresnel transform with a diffraction distance Z.

The invention also provides a safe compression holographic imaging method, which comprises the following steps:

step S1: splitting a beam of light emitted by a light source into two beams of light, wherein one beam of light is object light irradiating on an object image, and the other beam of light is reference light irradiating on a host image;

step S2: reflecting and illuminating object light to an object image, and encrypting the object light to obtain an encrypted object light beam carrying the object image;

step S3: respectively performing phase modulation on the reference light for three times and irradiating the reference light on a host image to obtain a reference light beam carrying the host image;

step S4: generating an interference hologram with the superposition of encryption and watermarking according to an encrypted object light beam carrying an object image and a reference light beam carrying a host image;

step S5: interference hologram data is collected and an object image is reconstructed from the digital interference hologram data.

Compared with the prior art, the method has the advantages that the interference hologram is recorded by using a three-step phase shift method, the image encryption, the image watermarking and the image compression are simultaneously realized in the all-optical domain environment, the confidentiality is higher, the safety of information in the transmission and storage processes is ensured, the original object image is prevented from being illegally stolen or tampered, and the requirement of safe compression imaging is realized.

For a better understanding and practice, the invention is described in detail below with reference to the accompanying drawings.

Drawings

FIG. 1 is a functional block diagram of a secure compressed holographic imaging system in an embodiment of the present invention;

FIG. 2 is a schematic diagram of a secure compressed holographic imaging system in an embodiment of the present invention;

FIG. 3 is a flow chart of a secure compressed holographic imaging method in an embodiment of the invention;

FIG. 4 is a flowchart illustrating an embodiment of step S2 shown in FIG. 3;

FIG. 5 is a flowchart illustrating an embodiment of step S5 shown in FIG. 3;

fig. 6 is a diagram of an experimental simulation result of the secure compression holographic imaging method in the embodiment of the present invention.

Detailed Description

Referring to fig. 1 and 2, fig. 1 is a schematic block diagram of a secure compression holographic imaging system in an embodiment of the present invention; FIG. 2 is a schematic diagram of a secure compressed holographic imaging system in an embodiment of the invention. The safe compression holographic imaging system comprises a light source generating and beam splitting device 11, an encryption device 12, a phase modulation device 13, an image generating and watermarking device 14, an image acquisition device 15 and an image reconstruction device 16.

The light source generating and splitting device 11 is configured to split a beam of light emitted by the light source into two beams of light, where one beam of light is object light irradiated on the object image 17, and the other beam of light is reference light irradiated on the host image 18. The encryption device 12 is configured to reflect the object light to the object image 17, and encrypt the object light to obtain an encrypted object light beam carrying the object image 17. The phase modulation device 13 is configured to irradiate the host image 18 with the reference light after phase modulation, so as to obtain a reference light beam carrying the host image 18. The image generating and watermarking device 14 is configured to receive an encrypted object light beam carrying an object image 17 and a reference light beam carrying a host image 18 at the same time, and generate an interference hologram in which the encryption and the watermarking are superimposed. The image collecting device 15 is configured to collect the interference hologram data and transmit the interference hologram data to the image reconstructing device 16. The image reconstruction means 16 are arranged for reconstructing an object image 17 from the interference hologram data.

The light source generating and beam splitting device 11 includes a laser 111, a beam expander 112 and a first beam splitter 113. A beam of linearly polarized laser light emitted from the laser 111 is expanded and collimated by the beam expander 112, and then irradiates the first beam splitter 113. The first beam splitter 113 splits the laser beam into two beams, wherein one beam is the object light irradiated on the object image 17; the other beam is the reference beam that is illuminated on the host image 18.

The encryption device 12 comprises a mirror 121, a first random phase plate 122 and a second random phase plate 123. The mirror 121 is disposed along the object light path after the first beam splitter 113 and before the object image 17, and the mirror 121 is configured to reflect the object light and irradiate the object light to the object image 17. The first random phase plate 122 is disposed behind the object image 17; a second random phase plate 123 is disposed behind and in parallel with the first random phase plate 122. After the object light penetrates through the object image 17, the object light sequentially passes through the first random phase plate 122 and the second random phase plate 123, and an encrypted object light beam carrying the object image 17 is obtained; the encrypted object beam is then directed to the image generating and watermarking device 14. After the object light passes through the reflector 121, the object image 17, the first random phase plate 122 and the second random phase plate 123, an encrypted image of the object image 17 after pixel scrambling can be obtained by using a double random phase encoding technique.

Specifically, it is assumed that the transmittance of the object light irradiated on the object image 17 is O (x)₀,y₀) Then, the encrypted object light beam obtained by passing through the first random phase plate 122 and the second random phase plate 123 can represent the encrypted object image with a complex amplitude distribution as follows:

$\begin{array}{c}{\mathrm{\ψ}}_o(\mathrm{\ξ},\mathrm{\η})=A(\mathrm{\ξ},\mathrm{\η})\exp \left(i\mathrm{\φ}\right(\mathrm{\ξ},\mathrm{\η})\\ ={\mathrm{Frt}}_{z_2}\left\{{\mathrm{Frt}}_{z_1}\right\{K_1\×O(x_0,y_0)\×\exp \[i2\mathrm{\π}\×p(x_0,y_0)\]\}\×\exp \[i2\mathrm{\π}\×q(x_1,y_1)\]\},\end{array}$

the above expression describes information of an encrypted image generated after the object image 17 is encrypted. Wherein, K₁Representing the optical amplitude of the object optical path; exp [ i2 pi.p (x)₀,y₀)]And exp [ i2 π q (x)₁,y₁)]Complex amplitude transmittances of the first random phase plate 122 and the second random phase plate 123, respectively; p (x)₀,y₀) And q (x)₁,y₁) Are all distributed in [0,1 ]]Statistically independent white noise over an interval; frt_ZRepresenting a Fresnel transformation with a diffraction distance Z, the distance between the first random phase plate 122 and the second random phase plate 123 being Z₁The distance between the second random phase plate 123 and the image acquisition device 15 is Z₂。

The phase modulation device 13 comprises a piezoelectric converter 131 and a second beam splitter 132, wherein the piezoelectric converter 131 divides the reference light into three phases for phase modulation, and generates phases of 0 respectively,a pi interference light source; the second beam splitter 132 illuminates the phase-modulated reference light onto the host image 18 to obtain a reference light beam carrying the host image 18.

The complex amplitude distribution of the host image 18 represented by the phase-modulated reference light beam can be expressed as:

${\mathrm{\ψ}}_h(\mathrm{\ξ},\mathrm{\η};{\mathrm{\φ}}_R)=A_h(\mathrm{\ξ},\mathrm{\η})\exp \[{\mathrm{i\φ}}_h(\mathrm{\ξ},\mathrm{\η})\]\exp \left({\mathrm{i\φ}}_R\right),({\mathrm{\φ}}_R=0,\frac{\mathrm{\π}}{2},\mathrm{\π}),$

the above expressions describe the step phase shift phi separately_RInformation of three host images 18 that are phase shifted by 0, pi/2, pi.

The image generation and watermarking device 14 includes a third beam splitter 141. The third beam splitter 141 receives the reference light beam carrying the host image 18 and the encrypted object light beam carrying the object image 17 at the same time to form coaxial interference light, and superimposes the two beams to generate an interference hologram carrying the encrypted and watermarked object image information. In this embodiment, the interference hologram is generated by superimposing the light intensity and the phase of the encrypted object beam and the reference beam serving as the carrier.

The image capturing device 15 includes a digital micromirror device 151, a converging lens 152, and a single photon detector 153. The digital micromirror device 151 compresses and samples the interference hologram data generated by the image generating and watermarking device 14, converges at a point through the converging lens 152, and then collects the data through the single photon detector 153.

The dmd 151 is actually a spatial light modulator that behaves as a random measurement matrix, with the tiny mirrors of the dmd 151 in a particular pseudo-random state, based on limited equidistant compression sensing. The direction of each micro lens is controlled by a random number generator, so that the micro lenses can deflect in two directions of +12 degrees or-12 degrees according to the horizontal direction; wherein the-12 ° deflection corresponding image is not reflected onto the single photon detector 153, appearing as a 0 in the measurement matrix; the +12 ° deflection corresponds to the image being reflected onto the single-photon detector 153, representing a 1 in the measurement matrix; these measurements are calculated as the output voltage.

Specifically, the light intensity values of the three interference holograms superimposed on the plane of the digital micromirror device 151 can be expressed as:

I_H(ξ,η；φ_R)

＝|ψ₀(ξ,η)+ψ_h(ξ,η；φ_R)|²

＝A(ξ,η)²+A_h(ξ,η)²

+2A(ξ,η)A_h(ξ,η)cos[φ_h(ξ,η)+φ_R-φ(ξ,η)],

$({\mathrm{\φ}}_R=0,\frac{\mathrm{\π}}{2},\mathrm{\π}),$

the output voltage of the high-sensitivity photodiode of the single-photon detector 153 is expressed as:

wherein,representing an m-dimensional pseudo-random measurement matrix in the plane of the digital micromirror device 151.

This procedure was repeated M times, resulting in a measurement Y of: y ═ Y₁,y₂,y₃]＝Ψ[I_H1,I_H2,I_H3],

Wherein,Ψ∈R^M×Nis a measurement matrix obtained from the plane of the digital micromirror device, Y ∈ R^M×3Is a measured value, y_k∈R^M×1，I_Hk∈R^N×1。

The image reconstruction apparatus 16 includes an analog-to-digital conversion module 161, an image transmission module 162, and an image reconstruction module 163. The analog-to-digital conversion module 161 is configured to convert the analog interference hologram data collected by the image collection device 15 into digital interference hologram data. The image transmission module 162 is configured to transmit the digital interference hologram data to the image reconstruction module 163. The image reconstruction module 163 is used for reconstructing the object image 17 according to the digital interference hologram data transmitted by the image transmission device.

Further, the image reconstructing module 163 reconstructs three interference holograms on the dmd 151 through an optimization algorithm, thereby reconstructing the object image 17.

Specifically, the interference light intensity is first reconstructed using a two-step iterative shrinkage algorithm (TwIST) by solving the following optimization problem:

$\begin{array}{ccc}\underset{I_{Hk}}{min}\frac{\mathrm{\μ}}{2}\left|\right|Y_k-\mathrm{\Ψ}{\hat{I}}_{Hk}|{|}_2^2+TV\left({\hat{I}}_{Hk}\right)& s.t.& Y_k={\mathrm{\ΨI}}_{Hk}\end{array},$

wherein, mu is a constant value,is a least squares term whenAnd the associated vector quantization value Y_kIts value is the smallest at the time of coincidence,is a fully variant representation of the signal;the subscripts i, j in this formula denoteAll the pairs of adjacent pixel points are adjacent to each other,is a discrete gradientL of₁And (4) norm. To this end, the algorithm has reconstructed three interference holograms on the digital micromirror device 151.

Using the three holograms obtainedThe distance Z between the first random phase plate 122 and the second random phase plate 123₁The distance Z between the second random phase plate 123 and the digital micromirror device 151₂The complex amplitude transmittances of the first random phase plate 122 and the second random phase plate 123 to restore the original object image 17.

Next, the phase information Φ (ξ, η) and the amplitude information a (ξ, η) of the encrypted and watermarked object image are calculated as follows:

$\mathrm{\φ}(\mathrm{\ξ},\mathrm{\η})={\tan }^{-1}\frac{2{\hat{I}}_{H2}-{\hat{I}}_{H1}-{\hat{I}}_{H3}}{{\hat{I}}_{H1}-{\hat{I}}_{H3}}+{\mathrm{\φ}}_h(\mathrm{\ξ},\mathrm{\η}),$

$A(\mathrm{\ξ},\mathrm{\η})=\frac{{\[{({\hat{I}}_{H1}-{\hat{I}}_{H3})}^2+{(2{\hat{I}}_{H2}-{\hat{I}}_{H1}-{\hat{I}}_{H3})}^2\]}^{1/2}}{4A_h},$

wherein the diffraction profile of the host image is phi_h，A_hIs obtained in advance by using a three-step phase shift method under a Mach-Zehnder interferometer.

Finally, the object image 17 is reconstructed by the inverse fresnel transform algorithm, and the process is expressed as follows:

wherein IFrt_ZRepresenting the inverse fresnel transform with a diffraction distance Z.

The secure compressed holographic imaging step is described in detail below:

please refer to fig. 3, which is a flowchart illustrating a secure compression holographic imaging method according to an embodiment of the present invention.

Step S1: one beam of light from the light source is split into two beams of light, one beam of which is the object light illuminating the object image 17 and the other beam of which is the reference light illuminating the host image 18.

Specifically, a laser 111 emits a linearly polarized laser light source; the linearly polarized laser light source is expanded and collimated by the beam expander 112, and then, is irradiated to the first beam splitter 113. The first beam splitter 113 splits the laser beam into two beams, wherein one beam is the object light irradiated on the object image 17; the other beam is the reference beam that is illuminated on the host image 18.

Step S2: the object light is reflected and irradiated to the object image 17 and encrypted to obtain an encrypted object light beam carrying the object image 17.

Please refer to fig. 4, which is a flowchart illustrating an embodiment of step S2 shown in fig. 3.

Step S21: a reflector 121 is arranged in front of the object image 17 along the optical path of the object light, and the object light is reflected by the reflector 121 and then illuminates the object image 17;

step S22: the first random phase plate 122 is disposed behind the object image 17; a second random phase plate 123 is disposed behind and in parallel with the first random phase plate 122; the object light transmitted through the object image 17 passes through the first random phase plate 122 and the second random phase plate 123 in sequence to obtain an encrypted object light beam carrying the object image 17.

After the object light passes through the reflector 121, the object image 17, the first random phase plate 122 and the second random phase plate 123, an encrypted image of the object image 17 after pixel scrambling can be obtained by using a double random phase encoding technique.

It is assumed that the transmittance of the object light irradiated on the object image 17 is O (x)₀,y₀) Then, the encrypted object light beam obtained by passing through the first random phase plate 122 and the second random phase plate 123, whose represented encrypted object image 17, can be represented by a distribution of complex amplitudes as:

$\begin{array}{c}{\mathrm{\ψ}}_o(\mathrm{\ξ},\mathrm{\η})=A(\mathrm{\ξ},\mathrm{\η})\exp \left(i\mathrm{\φ}\right(\mathrm{\ξ},\mathrm{\η})\\ ={\mathrm{Frt}}_{z_2}\left\{{\mathrm{Frt}}_{z_1}\right\{K_1\×O(x_0,y_0)\×\exp \[i2\mathrm{\π}\×p(x_0,y_0)\]\}\×\exp \[i2\mathrm{\π}\×q(x_1,y_1)\]\},\end{array}$

the above expression describes information of an encrypted image generated after the object image 17 is encrypted.

Wherein, K₁Representing the optical amplitude of the object optical path; exp [ i2 pi.p (x)₀,y₀)]And exp [ i2 π q (x)₁,y₁)]Complex amplitude transmittances of the first random phase plate 122 and the second random phase plate 123, respectively; p (x)₀,y₀) And q (x)₁,y₁) Are all distributed in [0,1 ]]Statistically independent white noise over an interval; frt_ZRepresenting a Fresnel transformation with a diffraction distance Z, the distance between the first random phase plate 122 and the second random phase plate 123 being Z₁The distance between the second random phase plate 123 and the digital micro-mirror device 151 is Z₂。

Step S3: the reference light beam carrying the host image 18 is obtained by phase modulating the reference light and illuminating the host image 18.

Specifically, the reference light is phase-modulated three times by the piezoelectric converter 131 to generate phases of 0,a pi interference light source; the second beam splitter 132 illuminates the phase-modulated reference light onto the host image 18 to obtain a reference light beam carrying the host image 18.

The phase modulated reference light beam, representing the complex amplitude distribution of the host image 18, may be represented as:

${\mathrm{\ψ}}_h(\mathrm{\ξ},\mathrm{\η};{\mathrm{\φ}}_R)=A_h(\mathrm{\ξ},\mathrm{\η})\exp \[{\mathrm{i\φ}}_h(\mathrm{\ξ},\mathrm{\η})\]\exp \left({\mathrm{i\φ}}_R\right),({\mathrm{\φ}}_R=0,\frac{\mathrm{\π}}{2},\mathrm{\π}),$

the above expressions describe the step phase shift phi separately_RWith a 0-degree distribution of the total weight of the alloy,information of three host images 18 that are pi-shifted.

Step S4: the encrypted object light beam carrying the object image 17 and the reference light beam carrying the host image 18 are superimposed to generate an interference hologram.

The third beam splitter 141 receives the reference light beam carrying the host image 18 and the encrypted object light beam carrying the object image 17 at the same time to form coaxial interference light, and superimposes the two beams to generate an interference hologram carrying the encrypted and watermarked object image information.

Step S5: interference hologram data is collected and an object image 17 is reconstructed from the digital interference hologram data.

Specifically, the step S5 further includes the following steps:

please refer to fig. 5, which is a flowchart illustrating an embodiment of step S5 shown in fig. 3.

Step S51: compressively sampling the interference hologram data by a digital micromirror device 151;

the superimposed interference hologram is collected at high speed by the digital micromirror device 151, then a measurement matrix on the plane of the digital micromirror device 151 and a random linear measurement value of the interference hologram are calculated to obtain a sample of a compressed hologram, and then a light beam passes through a converging lens 152 and is collected as an analog electric signal by a single photon detector 153.

In this embodiment, the characteristics of the optical control switch of the micromirror unit of the digital micromirror device 151 are utilized to realize the collection and compressive sampling of the superimposed interference hologram information. In this embodiment, the emitted light corresponding to the +12 ° deflection angle of the digital micromirror device 151 is collected by the single photon detector 153 through the converging lens 152.

Specifically, the light intensity values of the three interference holograms superimposed on the plane of the digital micromirror device 151 can be expressed as:

I_H(ξ,η；φ_R)

＝|ψ₀(ξ,η)+ψ_h(ξ,η；φ_R)|²

＝A(ξ,η)²+A_h(ξ,η)²

+2A(ξ,η)A_h(ξ,η)cos[φ_h(ξ,η)+φ_R-φ(ξ,η)],

$({\mathrm{\φ}}_R=0,\frac{\mathrm{\π}}{2},\mathrm{\π}),$

the above expression describes three interference holograms after superposition of the encrypted object light beam carrying the object image 17 and the reference light beam carrying the host image 18. Thus, the object image 17 can be encrypted and watermarked in a plenoptic domain environment using an improved mach-zehnder interferometer.

The output voltage of the high-sensitivity photodiode of the single-photon detector 153 is expressed as:

whereinRepresenting an m-dimensional pseudo-random measurement matrix in the plane of the digital micromirror device 151. This process was repeated M times and the measurement Y obtained was:

Y＝[y₁,y₂,y₃]＝Ψ[I_H1,I_H2,I_H3],

whereinΨ∈R^M×NIs a measurement matrix obtained in the plane of the digital micromirror device 151, Y ∈ R^M×3Is a measured value, y_k∈R^M×1，I_Hk∈R^N×1。

In the above, the acquisition of analog signals and compressive sampling of the superimposed interference hologram information are completed.

Step S52: the compressed hologram is converged by a converging lens 152, single-point detection and photoelectron counting are performed on the compressed hologram data by a single-photon detector, an optical signal is converted into an analog electrical signal, and the analog electrical signal is converted into a digital compressed hologram by an analog-to-digital converter.

Step S53: reconstructing the interference hologram superimposed on the digital micromirror device 151 using a compressed sensing algorithm according to the digital compressed hologram; and reconstructing an original object image 17 by utilizing a Fresnel inverse transformation algorithm, complex amplitude information of the host image 18 and an electrical or optical method.

In this embodiment, the superimposed interference hologram on the digital micromirror device 151 is reconstructed using a two-step iterative shrinkage algorithm (TWIST).

The interference light intensity is reconstructed using a two-step iterative shrinkage algorithm (TwinT) by solving the following optimization problem:

$\begin{array}{ccc}\underset{I_{Hk}}{min}\frac{\mathrm{\μ}}{2}\left|\right|Y_k-\mathrm{\Ψ}{\hat{I}}_{Hk}|{|}_2^2+TV\left({\hat{I}}_{Hk}\right)& s.t.& Y_k={\mathrm{\ΨI}}_{Hk}\end{array},$

wherein, mu is a constant value,is a least squares term whenAnd the associated vector quantization value Y_kIts value is the smallest at the time of coincidence,is a fully variant representation of the signal, specifically the following equation:

$TV\left({\hat{I}}_{Hk}\right)=\underset{adj.i,j}{\mathrm{\Σ}}\left|{\hat{I}}_{Hki}-{\hat{I}}_{Hkj}\right|,)$

in this formula the indices i, j denoteAll the pairs of adjacent pixel points are adjacent to each other,is a discrete gradientL of₁And (4) norm.

To this end, the algorithm has reconstructed three interference holograms on the digital micromirror device 151.

Using the three holograms obtainedThe distance Z between the first random phase plate 122 and the second random phase plate 123₁The distance Z between the second random phase plate 123 and the digital micromirror device 151₂The complex amplitude transmittances of the first random phase plate 122 and the second random phase plate 123 to restore the original object image 17.

Specifically, the phase information Φ (ξ, η) and the amplitude information a (ξ, η) of the encrypted and watermarked object image are calculated as follows:

$\mathrm{\φ}(\mathrm{\ξ},\mathrm{\η})={\tan }^{-1}\frac{2{\hat{I}}_{H2}-{\hat{I}}_{H1}-{\hat{I}}_{H3}}{{\hat{I}}_{H1}-{\hat{I}}_{H3}}+{\mathrm{\φ}}_h(\mathrm{\ξ},\mathrm{\η}),$

$A(\mathrm{\ξ},\mathrm{\η})=\frac{{\[{({\hat{I}}_{H1}-{\hat{I}}_{H3})}^2+{(2{\hat{I}}_{H2}-{\hat{I}}_{H1}-{\hat{I}}_{H3})}^2\]}^{1/2}}{4A_h},$

wherein the diffraction profile of the host image is phi_h，A_hThe method is obtained in advance by using a three-step phase shift method under a Mach-Zehnder interferometer.

Reconstructing the object image 17 by using an inverse fresnel transform algorithm, wherein the process is represented as follows:

wherein IFrt_ZRepresenting the inverse fresnel transform with a diffraction distance Z.

Please refer to fig. 6, which is a diagram illustrating an experimental simulation result of a secure compression holographic imaging method according to an embodiment of the present invention.

In the experiment, the wavelength of the helium-neon laser was 632.8nm, the amplitude ratio of the object light and the reference light was 0.000001:1, and the distance Z between the first random phase plate 122 and the second random phase plate 123 was₁0.1m, the distance Z between the second random phase plate 123 and the digital micromirror device 151₂0.2m, diffraction distance Z of host image 18₃In the simulation experiment, 256 × 256 ×.2% of measurement data of an encrypted watermark image is used for image reconstruction, and accurate recovery of the object image 17 can be realized by using compressed data of the encrypted watermark image in combination with correct passwords and optical system parameters.

Compared with the prior art, the method has the advantages that the interference hologram is recorded by using a three-step phase shift method, the image encryption, the image watermarking and the image compression are simultaneously realized in the all-optical domain environment, the confidentiality is higher, the safety of information in the transmission and storage processes is ensured, the original object image is prevented from being illegally stolen or tampered, and the requirement of safe compression imaging is realized.

The present invention is not limited to the above-described embodiments, and various modifications and variations of the present invention are intended to be included within the scope of the claims and the equivalent technology of the present invention if they do not depart from the spirit and scope of the present invention.

Claims (10)

1. A safe compression holographic imaging system is characterized by comprising a light source generating and beam splitting device, an encryption device, a phase modulation device, an image generating and watermarking device, an image acquisition device and an image reconstruction device;

the light source generating and beam splitting device is used for splitting one beam of light emitted by the light source into two beams of light, wherein one beam of light is object light irradiating on the object image, and the other beam of light is reference light irradiating on the host image;

the encryption device is used for reflecting the object light to irradiate the object image and encrypting the object light information to obtain an encrypted object light beam carrying the object image;

the phase modulation device is used for irradiating the reference light after phase modulation on a host image to obtain a reference light beam carrying the host image;

the image generation and watermark device is used for receiving an encrypted object light beam carrying an object image and a reference light beam carrying a host image at the same time and generating an interference hologram superposed by encryption and watermark;

the image acquisition device is used for acquiring the interference hologram data and transmitting the interference hologram data to the image reconstruction device;

and the image reconstruction device is used for reconstructing an object image according to the interference hologram data.

2. The secure compressed holographic imaging system of claim 1, wherein the encryption device comprises a mirror, a first random phase plate, and a second random phase plate; the reflecting mirror is arranged behind the light source generating and beam splitting device and in front of the object image along the optical path of the object light, and the reflecting mirror is used for reflecting the object light and then irradiating the object light to the object image; arranging the first random phase plate behind an object image; a second random phase plate parallel to the first random phase plate is arranged behind the first random phase plate; after the object light penetrates through the object image, the object light sequentially passes through the first random phase plate and the second random phase plate to obtain an encrypted object light beam carrying the object image; the encrypted object light beam irradiates the image generation and watermarking device again;

according to the fresnel diffraction formula, the encrypted object image represented by the encrypted object light beam is represented by a complex amplitude distribution as:

$\begin{array}{c}{\mathrm{\ψ}}_o(\mathrm{\ξ},\mathrm{\η})=A(\mathrm{\ξ},\mathrm{\η})\exp \left(i\mathrm{\φ}\right(\mathrm{\ξ},\mathrm{\η})\\ ={\mathrm{Frt}}_{z_2}\left\{{\mathrm{Frt}}_{z_1}\left\{K_1\×O\left(x_0,y_0\right)\×\exp \[i2\mathrm{\π}\×p\left(x_0,y_0\right)\]\right\}\×\exp \[i2\mathrm{\π}\×q\left(x_1,y_1\right)\]\right\},\end{array}$

wherein, K₁Light flux of objectThe optical amplitude of the path; o (x)₀,y₀) Is the complex amplitude distribution of the object light at the first random phase plate; exp [ i2 pi.p (x)₀,y₀)]And exp [ i2 π q (x)₁,y₁)]The complex amplitude transmittances of the first random phase plate and the second random phase plate respectively; p (x)₀,y₀) And q (x)₁,y₁) Are all distributed in [0,1 ]]Statistically independent white noise over an interval; frt_ZRepresenting a Fresnel transformation with a diffraction distance Z, the distance between the first random phase plate and the second random phase plate being Z₁The distance between the second random phase plate and the image acquisition device is Z₂。

3. The secure compression holographic imaging system of claim 2, wherein the phase modulation device comprises a piezoelectric transformer and a second beam splitter, wherein the piezoelectric transformer phase modulates the reference light three times to generate phases of three timesThe interference light source of (1); the second beam splitter irradiates the phase-modulated reference light to a host image so as to obtain a reference light beam carrying the host image;

the complex amplitude distribution of the host image represented by the reference light beam can be represented as:

${\mathrm{\ψ}}_h(\mathrm{\ξ},\mathrm{\η};{\mathrm{\φ}}_R)=A_h(\mathrm{\ξ},\mathrm{\η})\exp \[{\mathrm{i\φ}}_h(\mathrm{\ξ},\mathrm{\η})\]\exp \left({\mathrm{i\φ}}_R\right),({\mathrm{\φ}}_R=0,\frac{\mathrm{\π}}{2},\mathrm{\π}),$

4. a secure compressed holographic imaging system according to claim 3, wherein said image generation and watermarking device comprises a third beam splitter; the third beam splitter receives the reference light beam carrying the host image and the encrypted object light beam carrying the object image at the same time to form coaxial interference light, and superposes the two beams to generate an interference hologram carrying the encrypted and watermarked object image information;

the light intensity value of the interference hologram with the encryption and the watermark superposed is expressed as

I_H(ξ,η；φ_R)

＝|ψ₀(ξ,η)+ψ_h(ξ,η；φ_R)|²

＝A(ξ,η)²+A_h(ξ,η)²

+2A(ξ,η)A_h(ξ,η)cos[φ_h(ξ,η)+φ_R-φ(ξ,η)],

$({\mathrm{\φ}}_R=0,\frac{\mathrm{\π}}{2},\mathrm{\π}),$

5. The secure compressed holographic imaging system of claim 4, in which the image acquisition device comprises a digital micromirror device, a converging lens, and a single photon detector; the digital micromirror device compresses and samples interference hologram data generated by the image generation and watermarking device, converges at one point through the convergent lens and then collects the data through the single photon detector;

the output voltage of the high-sensitivity photodiode of the single-photon detector is expressed as:

whereinRepresenting an m-dimensional pseudo-random measurement matrix on the plane of the digital micromirror device;

this process was repeated M times and the measurement Y obtained was:

Y＝[y₁,y₂,y₃]＝Ψ[I_H1,I_H2,I_H3],

wherein,Ψ∈R^M×Nis a measurement matrix obtained by the digital micromirror device plane, Y ∈ R^M×3Is a measured value, y_k∈R^M×1，I_Hk∈R^N×1。

6. The secure compressed holographic imaging system of claim 5, wherein the image reconstruction means comprises an analog-to-digital conversion module, an image transmission module, and an image reconstruction module; the analog-to-digital conversion module is used for converting the analog interference hologram data collected by the image collection device into digital interference hologram data; the image transmission module is used for transmitting the digital interference hologram data to the image reconstruction module; the image reconstruction module is used for reconstructing an original object image by utilizing a two-step iterative contraction algorithm, a Fresnel inverse transformation algorithm and complex amplitude information of a host image according to the digital interference hologram data transmitted by the image transmission device;

the expression for reconstructing the light intensity of the superimposed interference on the digital micromirror device using the compressive sensing algorithm is:

$\begin{array}{ccc}\underset{I_{Hk}}{\min }\frac{\mathrm{\μ}}{2}\left|\right|Y_k-\mathrm{\Ψ}{\hat{I}}_{Hk}|{|}_2^2+TV\left({\hat{I}}_{Hk}\right)& s.t.& Y_k={\mathrm{\ΨI}}_{Hk}\end{array},$

wherein, mu is a constant value,is a least squares term whenAnd the associated vector quantization value Y_kIts value is the smallest at the time of coincidence,is a fully variant representation of the signal, specifically the following equation:

$TV\left({\hat{I}}_{Hk}\right)=\underset{adj.i,j}{\Σ}|{\hat{I}}_{Hki}-{\hat{I}}_{Hkj}|,)$

in this formulaThe indices i, j denoteAll the pairs of adjacent pixel points are adjacent to each other,is a discrete gradientL of₁And (4) norm.

The phase information φ (ξ) and amplitude information A (ξ) of the encrypted and watermarked object image on the digital micromirror device are as follows:

$A(\mathrm{\ξ},\mathrm{\η})=\frac{{\[{({\hat{I}}_{H1}-{\hat{I}}_{H3})}^2+{(2{\hat{I}}_{H2}-{\hat{I}}_{H1}-{\hat{I}}_{H3})}^2\]}^{1/2}}{4A_h},$

wherein the diffraction profile of the host image is phi_h，A_hThe method is obtained in advance by using a three-step phase shift method under a Mach-Zehnder interferometer;

reconstructing the object image through a Fresnel inverse transformation algorithm, wherein the process is represented as:

wherein IFrt_ZRepresenting the inverse fresnel transform with a diffraction distance Z.

7. A secure compressed holographic imaging method, comprising the steps of:

step S1: splitting a beam of light emitted by a light source into two beams of light, wherein one beam of light is object light irradiating on an object image, and the other beam of light is reference light irradiating on a host image;

step S2: reflecting and illuminating object light to an object image, and encrypting the object light to obtain an encrypted object light beam carrying the object image;

step S3: respectively performing phase modulation on the reference light for three times and irradiating the reference light on a host image to obtain a reference light beam carrying the host image;

step S4: generating an interference hologram with the superposition of encryption and watermarking according to an encrypted object light beam carrying an object image and a reference light beam carrying a host image;

step S5: interference hologram data is collected and an object image is reconstructed from the digital interference hologram data.

8. The secure compressed holographic imaging method of claim 7, further comprising, in step S2, the steps of:

step S21: a reflector is arranged in front of the object image along the optical path of the object light, and the object light is reflected by the reflector and then irradiates the object image;

step S22: arranging the first random phase plate behind an object image; a second random phase plate parallel to the first random phase plate is arranged behind the first random phase plate; and the object light which penetrates through the object image passes through the first random phase plate and the second random phase plate in sequence to obtain an encrypted object light beam carrying the object image.

9. The secure compressed holographic imaging method of claim 8, further comprising, in step S5, the steps of:

step S51: compressively sampling the interference hologram data by a digital micromirror device;

step S52: after the compressed hologram is converged by a converging lens, single-point detection and photoelectron counting are carried out on an optical signal of the compressed hologram through a single-photon detector, the optical signal is converted into an analog electric signal, and the analog electric signal is converted into a digital signal through an analog-to-digital converter;

step S53: reconstructing the interference hologram superposed on the digital micromirror device by using a compressed sensing algorithm according to the digital compressed hologram; and reconstructing an original object image by utilizing a Fresnel inverse transformation algorithm, complex amplitude information of the host image and an electrical or optical method.

10. A secure compression holographic imaging method of claim 9,

in the step S2, in step S2,

according to the fresnel diffraction formula, the encrypted object image represented by the encrypted object light beam is represented by a complex amplitude distribution as:

$\begin{array}{c}{\mathrm{\ψ}}_o\left(\mathrm{\ξ},\mathrm{\η}\right)=A\left(\mathrm{\ξ},\mathrm{\η}\right)\exp (i\mathrm{\φ}\left(\mathrm{\ξ},\mathrm{\η}\right)\\ ={\mathrm{Frt}}_{z_2}\left\{{\mathrm{Frt}}_{z_1}\left\{K_1\×O\left(x_0,y_0\right)\×\exp \[i2\mathrm{\π}\×p\left(x_0,y_0\right)\]\right\}\×\exp \[i2\mathrm{\π}\×q\left(x_1,y_1\right)\]\right\},\end{array}$

wherein, K₁Representing the optical amplitude of the object optical path; o (x)₀,y₀) Is the complex amplitude distribution of the object light at the first random phase plate; exp [ i2 pi.p (x)₀,y₀)]And exp [ i2 π q (x)₁,y₁)]The complex amplitude transmittances of the first random phase plate and the second random phase plate respectively; p (x)₀,y₀) And q (x)₁,y₁) Are all distributed in [0,1 ]]Statistically independent white noise over an interval; frt_ZRepresenting a Fresnel transformation with a diffraction distance Z, the distance between the first random phase plate and the second random phase plate being Z₁The distance between the second random phase plate and the digital micromirror device is Z₂；

In the step S3, in step S3,

the complex amplitude distribution of the host image represented by the reference light beam can be represented as:

${\mathrm{\ψ}}_h(\mathrm{\ξ},\mathrm{\η};{\mathrm{\φ}}_R)=A_h(\mathrm{\ξ},\mathrm{\η})\exp \[{\mathrm{i\φ}}_h(\mathrm{\ξ},\mathrm{\η})\]\exp \left({\mathrm{i\φ}}_R\right),({\mathrm{\φ}}_R=0,\frac{\mathrm{\π}}{2},\mathrm{\π}),$

in the step S4, in step S4,

the light intensity value of the interference hologram with the encryption and the watermark superposed is expressed as

I_H(ξ,η；φ_R)

＝|ψ₀(ξ,η)+ψ_h(ξ,η；φ_R)|²

＝A(ξ,η)²+A_h(ξ,η)²

+2A(ξ,η)A_h(ξ,η)cos[φ_h(ξ,η)+φ_R-φ(ξ,η)],

$({\mathrm{\φ}}_R=0,\frac{\mathrm{\π}}{2},\mathrm{\π}),$

In the step S5, in step S5,

the output voltage of the high-sensitivity photodiode of the single-photon detector is expressed as:

whereinRepresenting an m-dimensional pseudo-random measurement matrix on the plane of the digital micromirror device;

this process was repeated M times and the measurement Y obtained was:

Y＝[y₁,y₂,y₃]＝Ψ[I_H1,I_H2,I_H3],

wherein,Ψ∈R^M×Nis a measurement matrix obtained by the digital micromirror device plane, Y ∈ R^M×3Is a measured value, y_k∈R^M×1，I_Hk∈R^N×1；

The expression of the light intensity for reconstructing the superimposed interference on the digital micromirror device by using a compressed sensing algorithm is as follows:

$\begin{array}{ccc}\underset{I_{Hk}}{\min }\frac{\mathrm{\μ}}{2}\left|\right|Y_k-\mathrm{\Ψ}{\hat{I}}_{Hk}|{|}_2^2+TV\left({\hat{I}}_{Hk}\right)& s.t.& Y_k={\mathrm{\ΨI}}_{Hk}\end{array},$

wherein, mu is a constant value,is a least squares term whenAnd the associated vector quantization value Y_kIts value is the smallest at the time of coincidence,is a fully variant representation of the signal, specifically the following equation:

$TV\left({\hat{I}}_{Hk}\right)=\underset{adj.i,j}{\Σ}|{\hat{I}}_{Hki}-{\hat{I}}_{Hkj}|,)$

the subscripts i, j in this formula denoteAll the pairs of adjacent pixel points are adjacent to each other,is a discrete gradientL of₁And (4) norm.

The phase information φ (ξ) and amplitude information A (ξ) of the encrypted and watermarked object image on the digital micromirror device are as follows:

$A(\mathrm{\ξ},\mathrm{\η})=\frac{{\[{({\hat{I}}_{H1}-{\hat{I}}_{H3})}^2+{(2{\hat{I}}_{H2}-{\hat{I}}_{H1}-{\hat{I}}_{H3})}^2\]}^{1/2}}{4A_h},$

wherein the diffraction profile of the host image is phi_h，A_hThe method is obtained in advance by using a three-step phase shift method under a Mach-Zehnder interferometer; reconstructing the object image through a Fresnel inverse transformation algorithm, wherein the process is represented as:

wherein IFrt_ZRepresenting the inverse fresnel transform with a diffraction distance Z.