空间光调制器的应用

DOI 10.1007/s11141-015-9547-8

Radiophysics and Quantum Electronics,Vol.57,Nos.8–9,January,2015

(Russian Original Vol.57,Nos.8–9,August–September,2014)

APPLICATION OF THE PHASE LIGHT MODULATOR IN THE IMAGE OPTICAL ENCRYPTION SCHEME WITH SPATIALLY INCOHERENT ILLUMINATION

A.P.Bondareva,N.N.Evtikhiev,V.V.Krasnov,?

and S.N.Starikov UDC004.932.4+004.942

+535.42+535.8

We describe application of the phase liquid-crystal spatial light modulator HoloEyePLUTOVIS

as an encoding element in the image optical encryption scheme with spatially incoherent illumi-

nation.Optical encryption and numerical decryption of test images were conducted.The results

of experiments demonstrate the e?ciency of the constructed optical encryption scheme.

1.INTRODUCTION

Currently,we are witnessing the existence and intense development of the optical encryption meth-ods characterized by a high speed,simultaneous multichannel processing,and the absence of concomitant radiation in the radio-frequency band.Encryption systems in spatially coherent monochromatic light are widespread.One of the best-known systems uses the double random-phase encryption[1–5].In this case, encryption is performed in monochromatic spatially coherent light using two random phase masks.Appli-cation of random phase masks as two-dimensional encoding keys leads to the fact that such systems have a high cryptographic strength.However,because of the need to record phase,such systems require holo-graphic methods of recording and,correspondingly,complex optical schemes.Moreover,the use of random phase masks leads to a poor-quality encryption of images.

To simplify the encryption schemes and improve the decryption quality,one can pass from spatially coherent to spatially incoherent radiation.In this case,recording of the encrypted image is no longer required and the holographic recording scheme becomes unnecessary.The encryption is performed by transmission of monochromatic spatially incoherent radiation from the encrypted object through a di?ractive optical element,resulting in the formation of an intensity distribution described by the object image convolution with a point spread function,namely,an impulse response of the di?ractive optical element in intensity[6, 7].This intensity distribution is the encrypted image recorded by a matrix photosensor.

The fundamental possibility of optical encryption in incoherent light was demonstrated in[8],but using a random phase mask as the encoding di?ractive optical element precluded the achievement of an acceptable decryption quality.This is because the point spread function of a random phase mask is virtually unlimited in space and signi?cantly exceeds the size of the encrypted image.As a result,the photosensor records only the central part of the encrypted image,which leads to distortions of the decrypted image.To solve this problem,we suggest that the encoding element is not used as a random phase mask,but as a di?ractive optical element having a given spatially limited point spread function,with length smaller than the size of the encrypted image.

?vitally.krasnov@mail.ru

National Nuclear Research University(NNRU),Moscow,Russia.Translated from Izvestiya Vysshikh Ucheb-nykh Zavedenii,Radio?zika,Vol.57,No.8–9,pp.693–701,August–September2014.Original article submitted November11,2013;accepted March31,2014.

0033-8443/15/5708-0619c 2015Springer Science+Business Media New York619

Fig.1.Block diagram of optical encryption using a di?ractive optical element.

The scheme of the encryption process is given in Fig.1.The object is illuminated by spatially inco-herent monochromatic light.When the radiation passes through a di?ractive optical element,an intensity distribution g,which corresponds to the colvolution of the image of object f and the point spread function h of the di?ractive optical element,is formed in the photosensor plane.The recorded image g is the encrypted image of object f and the point spread function h is the encoding key.

As a di?ractive optical element,the Fourier holograms are often used.However,the fact that the holograms have several di?raction orders impedes using them in optical numerical systems since the required encoding point spread function can be formed only in one di?raction order.An alternative application of holograms is the use of such synthesized phase di?ractive elements as phase-only synthetic holograms[9], which form a single di?raction order that contains the required point spread function[10].

Since the encryption is performed through a convolution,a bound is imposed on the distribution h of the Fourier spectrum amplitude of the encoding key.The spectrum of the key should overlap the spectrum of the encrypted image f;otherwise,losses of information of the encrypted image at the spatial frequencies not covered by the spectrum of the key are unavoidable in the encryption.The Fourier spectrum of a perfect key should not contain small amplitudes compared with the average level to avoid losses of information in the encryption.

The main requirement for the encoding systems is that the encoding key can be changed for each portion of encrypted information.This limits the possibility of using statistical encoding elements.To implement the encryption system with a dynamically varied encoding key,for mapping of the di?ractive optical element it is expedient to use spatio-temporal light modulators[11]by which the element can be changed at a rate of tens of hertz or more.

This encryption scheme was proposed and tested by us in[12].The experimental results obtained in that paper demonstrated the insu?cient degree of hiding of information in the encrypted images.In this regard,the present work aims at determining the reasons,their elimination,and performing experiments on optical encryption in spatially incoherent light by using a liquid-crystal spatial light modulator to form the encoding point spread function.

The paper is organized as follows.In Sec.2,we describe the experimental setup.In Sec.3,we give the results of seeking and eliminating the reasons for the insu?cient degree of hiding of information.In Sec.4,we give a description and the results of the experiments.The main?ndings are formulated in the Conclusions.

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Fig.2.Scheme of the experimental setup for optical encryption of images in spatially incoherent light based in a phase liquid-crystal spatial light modulator.

2.EXPERIMENTAL SETUP FOR OPTICAL ENCRYPTION WITH SPATIALLY INCOHERENT

ILLUMINATION AND THE ABILITY TO DYNAMICALLY CHANGE THE ENCODING KEY

The optical encryption scheme capable of dynamically changing the key was experimentally imple-mented by the temporal integration method[12,13],which was employed in,e.g.,incoherent acousto-optical correlators[14–16].The idea of the method is as follows.We record an image of the object moving along some encoding trajectory,which gives rise to an image described by the convolution of the image of the object and the encoding trajectory.Mathematically,this process of encoding of the image f by the discrete trajectory h can be described as follows:

g(i,j)=

i

k=1

j

l=1

f(k,l)h(i?k,j?l).(1)

Here,g(i,j)is the brightness of an image pixel at the point with the coordinates i and j,h(i?k,j?l)is the value of the element(i?k,j?l)of the matrix of a trajectory with the coordinates i?k and j?l; the quantity h characterizes the time of?nding the image at this point on the trajectory.The trajectory h forms the encoding point spread function of the optical system by analogy with the point spread function of the di?ractive optical element and the encoding key.

The scheme of the experimental setup for optical image encryption in spatially incoherent light based on a phase liquid-crystal spatial light modulator(SLM),which we proposed in[12],is shown in Fig.2.The radiation of a He–Ne laser(wavelength0.63μm)is collimated by lenses L1and L2.Rotating opal di?user (ROD)breaks the spatial coherence of the radiation.The encoded scene is located in the front focal plane of lens L3.The liquid-crystal spatial light modulator HoloEyePLUTOVIS,which consists of1920×1080pixels with sizes8×8μm,is able to output256levels of the phase and is located in the rear focal plane of lens L3. Polarizers P and A are oriented so as to ensure the correct operation of the phase modulator.Lens L4forms an image of the encoded scene on the photosencor of the monochrome camera MegaPlus II ES11000with a 4008×2672pixel resolution,a10-bit analogue-to-digital converter,and the maximum signal-to-noise ratio equal to140.The modulator generates a sequence of alternating phase gratings with a sawtooth pro?le. Changing the modulator-mapped grating(changing their period and orientation)during the frame record

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Fig.3.Image encryption:before(a)and after(b)the decrease in temporal?uctuations of the modulator phase shift.

leads to the movement of the scene image on the camera photosensor.As a result,the image recorded by the camera corresponds to the convolution of the scene image and the encoding trajectory.

3.ANALYSIS AND ELIMINATION OF THE REASONS FOR THE INSUFFICIENT

DEGREE OF HIDING OF INFORMATION ON ENCRYPTED IMAGES

The analysis has shown that the insu?cient degree of hiding of information in the encrypted images was due to signi?cant temporal?uctuations of the phase shift during the frame mapping in the light mod-ulator[17,18].As a result of these?uctuations,besides the desired?rst di?raction order,the undesirable zero order was observed during the formation of each point of the point spread function.According to the measurement results,the intensity of the latter made up one-fourth of the intensity of the?rst order. Correspondingly,in the encoding point spread function used in the experiments and composed of30points, the total intensity of the zero order was about a factor of eight greater than the intensity of the other points. As a result,the recorded image can be represented as the sum of the encrypted image proper,formed by the design point spread function without the zero order,and the original non-encrypted image with brightness a factor of eight greater than the brightness of the?rst term.This is exactly the reason for the insu?cient degree of hiding of information in the resulting encrypted image.The result of encryption in described conditions is given in Fig.3a.The original image stands up against the background of the encrypted one.

To decrease the temporal?uctuations of the phase shift,we replaced the standard address con?gu-ration of the control voltage in the light modulator by the con?guration we received from the producer by request.According to the measurements,changing the con?guration reduced the maximum amplitude of ?uctuations almost fourfold,from0.48πto0.13π.

As a result,we managed to increase two times the intensity ratio of the?rst and the zero di?raction orders,from4.0to8.0.This made it possible to improve fundamentally the quality of hiding of information in the encrypted images.This was demonstrated in Fig.3:while previously the original text stood up against the background of the encrypted one(see Fig.3a),only a small number of individual characters are identi?ed after the decrease in temporal?uctuations of the phase shift of the liquid-crystal spatial light modulator in the encrypted image(see Fig.3b).The further decrease in?uctuations can be achieved by using synchronization tools[18].

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Fig.4.Optical encryption of the grayscale scene

image:image of the scene to be encrypted (a ),

encoding point spread function (b )and encrypted

scene image (c ).

4.EXPERIMENTS ON OPTICAL ENCRYPTION AND NUMERICAL DECRYPTION OF IMAGES

To demonstrate encryption by the implemented setup,we used two types of images,namely,grayscale and binary line images.In the experiments we used images with linear sizes in a range of 700to 1500pixels of the photosensor.The linear size of the encoding point spread function made up one-third of the size of the encrypted images and was chosen to hide information and provide the subsequent decryption.

An example of optical encryption of the grayscale scene image by the implemented setup is shown in Fig.4.The encrypted grayscale image occupied a region of 800×780pixels on the camera photosensor.The encoding point spread function comprised 30points located on a ?eld of 251×296samples and occupied a region of 342×403pixels.Correspondingly,the encrypted image occupied a region of 1141×1382pixels.The information content in the encrypted image was visually lost,as was expected.

Image decryption was performed numerically by the inverse ?ltering method with Tikhonov’s reg-ularization [19].The result of numerical decryption of the grayscale scene image presented in Fig.4c is given in Fig.5a .This image,decrypted with regularization parameter equal to 10?2,is visually the best in the group of images decrypted with di?erent parameters of the image regularization.Normalized standard deviation of decrypted image from the original can serve as the measure of quality of decrypted image [20].

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Fig.5.Numerical decryption of the grayscale scene image (Fig.3c ):(a )is the image decrypted with regulariza-tion parameter equal to 10?2and (b )is the dependence of the normalized standard deviation δon Tikhonov’s regularization parameter α.

Fig.6.Optical encryption of a fragment of text:

(a )is the image of the text,(b )is the encoding

point spread function,and (c )is the encrypted im-

age of the text.

The dependence of the normalized standard deviation of decrypted images on Tikhonov’s regularization parameter is given in Fig.5b .Despite the noisiness,the decrypted image is con?dently identi?ed.

An example of optical encryption of the image of a fragment of text is given in Fig.6.The encrypted 624

Fig.7.Numerical encryption of the image of a fragment of text:(a)is the decrypted image with the minimum normalized standard deviation from the original and(b)is the dependence of the normalized standard deviation δon Tikhonov’s regularization parameterα.

image of a fragment of text occupied a region of1104×864pixels on the camera photosensor.We used the same encoding point spread function as in the previous case.Correspondingly,the encrypted image occupied a region of1445×1266pixels.Although a small number of individual characters are identi?ed in the encrypted image,the encrypted text can de?nitely not be read.

The result of numerical decryption of the image of a fragment of text(Fig.6c)is given in Fig.7a. This image,decrypted with regularization parameter equal to10?4,has the minimum normalized standard deviation on the original and is visually the best in the group of images decrypted with di?erent regularization parameters.The dependence of the normalized standard deviation on Tikhonov’s regularization parameter is presented in Fig.7b.The decrypted image of a fragment of text is con?dently read.

The quality of encryption was determined by the number of nonzero points of the encoding point spread function.Due to the limited exposure of the camera,the number of points of the encoding trajectory was limited to30,which not always was su?cient for a complete hiding of encrypted information.The noise observed in the decrypted images was stipulated,?rst of all,by notable temporal?uctuations of the phase shift and residual nonlinear dependence of the phase shift on the level of the signal supplied.This has led to the appearance of higher di?raction orders going beyond the region of record of encrypted image.

5.CONCLUSIONS

The scheme of optical decryption of images in spatially incoherent light based on a phase liquid-crystal spatial light modulator capable of dynamically changing the encoding key has been experimentally implemented.The temporal integration technique was employed to generate the encoding point spread function.Due to a fourfold decrease in the temporal?uctuations of the phase shift in the modulator(from 0.48πto0.13π),we reduced by two times the intensity of the zero di?raction order in the encoding point spread function.This ensured a su?cient degree of hiding of information in the optically encrypted images. In the optical encryption experiments,the linear size of the encoding point transfer function made up about one-third of the size of the encrypted images and was chosen to provide hiding of information and enable the subsequent numerical decryption.The decrypted text images are identi?ed with the corresponding originals. The results of the experiments con?rm the e?ciency of the implemented encryption scheme with spatially incoherent illumination and the ability to dynamically change the encrypting key.

The noise observed in the decrypted images are stipulated,?rst of all,by notable temporal?uctuations of the phase shift in the light modulator.For the further decrease in?uctuations and,therefore,improvement

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of the encryption quality one should use synchronization of the modulator and radiation source or the recording camera.

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