ARTICLE IN PRESS

Optics and Lasers in Engineering 48 (2010) 69–74

Contents lists available at ScienceDirect

Optics and Lasers in Engineering

0143-81

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/optlaseng

Quality of images decrypted from in-line holographic encryption of images

Siriwat Soontaranon, Joewono Widjaja �

Institute of Science, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand

a r t i c l e i n f o

Article history:

Received 1 May 2009

Received in revised form

13 July 2009

Accepted 20 July 2009Available online 8 August 2009

Keywords:

Holographic image encryption

Quality of decrypted image

In-line holography

Background noise removal

66/$ - see front matter & 2009 Elsevier Ltd. A

016/j.optlaseng.2009.07.013

esponding author. Tel.: +66 44 224194; fax: +

ail address: widjaja@sut.ac.th (J. Widjaja).

a b s t r a c t

We investigate quality of images decrypted from in-line holograms recorded with a random phase mask

placed behind an input image. High- and low-contrast fingerprint images are used as test scenes. The

simulation results show that due to multiple convolution processes and a limitation of the CCD sensor

resolution, quality of decrypted images is sensitive to spatial separations between the input image, the

phase mask and the hologram. We propose a new method for improving quality of decrypted images by

using background noise removal. It is found that in comparison with high-contrast input, the low-

contrast image is more robust to distortion caused by the encryption–decryption process.

& 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Recently, much research has been devoted to digital-opticalimage encryption by using holographic technique. The reason forthis interest is that holographic recording process can beconsidered as an encryption of an object wave by using areference wave as a key. An image of the object can be decryptedprovided a correct reference wave is used to read out hologram. Inorder to improve security, holographic encryptions that use arandom phase mask placed behind the object transparency as anadditional key were proposed [1,2]. Since the phase of the objectwave is now randomized, two keys that are the correct referencewave and the phase mask must be used for decryption ofhologram. Recently, security improvement of holographic encryp-tion by using gyrator transform has been reported [3].

Owing to flexibility of setting recording distance and resolu-tion limitation of CCD sensor, Fresnel holography using Mach–Zehnder interferometer have been widely employed for thisencryption. Based on this approach one arm of the interferometeris used to carry object wave, while the other arm is for a referencewave. The object wave is randomized by placing the phase maskat a distance behind the image. The encrypted image is thenholographically recorded by using a CCD sensor. In order toeliminate twin image problem of the in-line holography, phase ofthe reference wave was retarded according to a phase shiftingholography [4]. Thus, the encrypted images are represented asdigital Fresnel holograms recorded with four phase-shiftedreference waves. To retrieve the original image, the object

ll rights reserved.

66 44 224185.

wavefront is numerically calculated. It is worth mentioning thatin order to have successful decryption, we need not only therandom phase mask, however, the locations of the object and thephase mask with respect to the recording plane must also becorrect as well. Due to a large degree of freedom of the employedphase mask, security of the encrypted information can bemaximized.

In this work, we study the quality of the decrypted image fromthe holographic encryption technique [1] through computersimulations. To our best knowledge quality of the decryptedimage obtained by using the correct decryption keys has not beeninvestigated. This study employs high- and low-contrast finger-print images as test scenes. Quality of the decrypted images isquantitatively measured by using a peak signal to noise ratio(PSNR).

2. In-line holographic encryption

Let us consider holographic image encryption by usingMach–Zehnder interferometer as shown in Fig. 1 [1]. In theupper arm of the interferometer, a real object with an amplitudetransmittance function f(x1, y1) is placed at a distance z1 in front ofthe random phase mask P(x2, y2) ¼ exp[if(x2, y2)] with therecording distance is z2. The lower arm carries a plane referencewave whose relative phase is shifted by p radian through the useof a phase retarder for four subsequent recordings of holograms.

According to Fresnel diffraction integral [5], the complexamplitude of a diffracted object wave at the hologram plane canbe mathematically expressed as

Oðx3; y3Þ ¼ f½f ðx3; y3Þ � hz1ðx3; y3Þ�Pðx3; y3Þg � hðz2�z1Þðx3; y3Þ; ð1Þ

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where � denotes the 2-D convolution operation, while theimpulse response of propagation through free space is defined by

hzðx3; y3Þ ¼ejkz

jlzexp

jk

2zðx2

3 þ y23Þ

� �: ð2Þ

The first convolution in Eq. (1) represents the effect ofdiffraction of the object at the distance z1. The diffracted waveis subsequently randomized by multiplying with the phase mask.The last convolution corresponds to the diffraction of therandomized object information at the hologram plane where aCCD sensor is placed.

In the numerical reconstruction process, each hologram isilluminated by its corresponding phase-shifted reference wave.The addition of four reconstructed waves gives [4]

Wðx3; y3Þ ¼ 4Rðx3; y3ÞOðx3; y3Þ; ð3Þ

where R(x3, y3) is the plane reference wave. This equation showsthat the result is proportional to the desired information of the

Laser

beam

Phase retartder

BS1

BS2

M1

M2

Input imagef(x1,y1)

HologramI(x3,y3)

Randomphase mask

P(x2,y2)

z1

z2

Fig. 1. Schematic diagram of Mach–Zehnder interferometer for recording the

phase-shifted holograms, where M and BS stand for mirror and beam splitter,

respectively.

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Fig. 2. (a) High-contrast and (b) low-contra

object wave O(x3, y3). The real image that is the conjugate of theobject wave can be retrieved as

f̂ ðx4; y4Þ ¼ f½W�ðx4; y4Þ � hðz02�z01Þðx4; y4Þ�P

0ðx4; y4Þg � hz01 ðx4; y4Þ:

ð4Þ

This mathematical computation corresponds to the reversepropagation of the object wave from the hologram plane back tothe original image plane in the upper arm of the interferometer inFig. 1. If the decrypting phase mask P0(x4, y4), the location z01 andz02 of each plane are the same as those used in the encryptionprocess, Eq. (4) reduces to

f̂ ðx4; y4Þ ¼ 4Rðx4; y4Þf�ðx4; y4Þ: ð5Þ

Since f(x4, y4) is real, the presence of its conjugate in Eq. (5)ensures that the original image can be decrypted from thehologram.

3. Quality of decrypted images

In this work, the holographic encryption was simulated byusing Matlab 7.5 running on Windows XP 64 bits operatingsystem installed onto a personal computer with Intel E6750processor having the speed of 2.66 GHz and 4 GB of RAM. Theinput plane, the phase mask and the CCD sensor had the sameresolution of 1920�1440 pixels. In order to determine the qualityof the decrypted image, high- and low-contrast fingerprintpatterns shown in Fig. 2(a) and (b), respectively, were employedas test images. They had the same size of 240�380 pixels. Theinput image was constructed by embedding the fingerprintpattern into a transparent input plane.

Fig. 3 shows the random function f(x, y) generated fromGaussian white noise having mean and variance of p and 0.01,respectively. The pixels of the function f(x, y) were grouped intoblocks of 40� 40 pixels. Phase values were randomly variedbetween 0–2p from block to block. The random phase mask wasgenerated by computing P(x, y) ¼ exp[if(x, y)]. The hologramswere obtained by interfering the phase-shifted plane referencewave and the object wave given by Eq. (1). Finally, the decryption

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was performed in accordance with Eq. (4). The quality of thedecrypted image was then measured by calculating the PSNRfrom [6]

PSNR ¼ 10 log101

mn

Xm�1

i¼0

Xn�1

j¼0

ff ðxij; yijÞ � f̂ ðxij; yijÞg2

f 2maxðx; yÞ

24

35�1

; ð6Þ

where m and n are the number of pixels in the horizontal and thevertical directions of the image, while fmax represents themaximum attainable grey scale value in the image pixels. f(x, y)and f̂(x, y) are the original and the decrypted images, respectively.

11

3.1. High-contrast input

Fig. 4(a) shows the whole area of the decrypted high-contrastimage obtained from the hologram recorded at the distancez2 ¼ 7 cm, while the phase mask was located at z1 ¼ 1 cm. Theenlarged central area of the decrypted fingerprint is shown inFig. 4(b). It is obvious that quality of the decrypted image is verylow, because the desired fingerprint image is buried in strongnoise. Our study found that this noise is a result of thepropagation of the randomized wave through a distance z2�z1.

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Fig. 3. Random phase function f(x, y).

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Fig. 4. (a) Decrypted image and (b) its enlargement at the fingerprint area fo

The impulse response associated with this short propagationcontains very high-frequency components. Due to a limitedresolution of the CCD sensor, an under sampling process occurs.According to the convolution property, the decryption given by Eq.(4) can be mathematically rewritten as

f̂ ¼ f½f½f � � h�z1�P�g � h�ðz2�z1Þ

� hðz02�z01Þ�P0g � hz01 : ð7Þ

In an ideal case, the convolution of hðz2�z1Þ with its conjugatethat is equivalent to an autocorrelation operation gives a sincfunction that appears in the center of Fig. 5, instead of a deltafunction. However, as the consequence of the under samplingeffect, the autocorrelation output also contains unwanted sincfunctions which appear symmetrically with respect to the desiredone in the center. The position of the unwanted sinc function isdetermined by the frequency content of the under sampledimpulse response. When the randomized signal corresponding tothe operation inside the inner curly bracket of Eq. (7) is convolvedwith the array of sinc functions, the signal is replicated. As thereplications overlap, the decryption output is distorted. Thus, the

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r the high contrast fingerprint encrypted with z1 ¼1 cm and z2 ¼ 7 cm.

-0.5

0

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3.5x10

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Am

plitu

de (

a.u.

)

Fig. 5. Distorted delta function resulted from an autocorrelation of the under

sampled impulse response.

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PSN

R

with backgroundwithout background

1 2 3 4 5 6

z1 (cm)

Fig. 7. PSNRs of the decrypted high-contrast fingerprint as a function of distance z1

for the recording distance z2 ¼ 7 cm.

S. Soontaranon, J. Widjaja / Optics and Lasers in Engineering 48 (2010) 69–7472

effect of the phase randomization cannot be completely canceledwhen this resultant convolution is further multiplied with thedecrypting phase mask P0. The result appears as a noisebackground of the decrypted image.

This similar distortion also occurs when hz1is convolved with

its conjugate. However, since the size of the fingerprint is smallerthan that of the phase mask, the distortion caused by overlappingof the replicated fingerprint images is less severe. This effect willbe clearly seen after the distortion from the phase mask isremoved.

In order to reduce the distortion caused by the phase mask, theencryption and decryption of a transparent image were performedusing the same phase mask placed at the same distances z1 and z2.As a result, the resultant decrypted image gives a similarbackground noise as that of the decrypted image of thefingerprint. The noise is then removed by subtracting the resultantdecryption of the transparent image from that of the fingerprintimage. The whole decrypted image after the background noiseremoval is shown in Fig. 6(a). In this figure, the fingerprint imageappears at the center is of principal interest. Its enlarged image isshown in Fig. 6(b). In comparison with Fig. 4, it is clear thatthe distortion caused by the phase mask can be significantlyreduced. From these two figures, it is also apparent that multiplefingerprint patterns are produced. Since they overlap each other,the desired fingerprint is distorted. This is a result of the undersampling of the impulse response hz1

as discussed in thepreceding paragraph. The locations of the unwanted fingerprintpatterns correspond to the positions of the redundant sincfunctions of the autocorrelation of hz1

.In order to quantify quality of the decrypted image, the PSNR

of the desired fingerprint image shown in Fig. 6(b) is calculated.Fig. 7 plots the PSNRs as a function of the distance z1 for therecording distance z2 ¼ 7 cm. The cross and the circle symbolsrepresent the PSNRs with and without the background noise,respectively. It can be seen that the background noise removalimproves significantly quality of the decrypted images, because itsPSNR is higher. As a consequence of the under sampled impulseresponse hz1

; the PSNRs fluctuate as a function of the separation z1.Furthermore, the decryption process can be regarded as

the convolution of two autocorrelation signals h�z1� hz1

andh�ðz2�z1Þ

�hðz2�z1Þ. The previous discussion reveals that eachautocorrelation signal does not give only single sinc function,but also unwanted array of sinc functions as well. Note that sinc

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Fig. 6. (a) Decrypted image and (b) its enlargement at the fingerprint area for the high

noise removal.

function has bipolar amplitude. When this convolution output issubsequently convolved by the fingerprint image, the negativeamplitude of the convolution output distorts the resultant imageassociated with the positive amplitude. Since the convolutionoperation is performed by calculating overlapping area of twosignals, the convolution of two identical sinc functions produceslarger amplitude than that of dissimilar ones. When the distance2z1 ¼ z2, the two impulse response are the same hz1

¼ hðz2�z1Þ.Their autocorrelations produce two identical sinc functions.Accordingly, the image distortion at this distance is higher thanthose at the distance 2z1az2. This can be clearly seen from Fig. 7where the PSNRs at z1 ¼ 3.5 cm is the lowest.

3.2. Low-contrast input

We also examined the quality of decrypted images from theencrypted low-contrast fingerprint shown in Fig. 2(b). Fig. 8(a)and (b) show the resultant image decryption with the removal of

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-contrast fingerprint encrypted with z1 ¼1 cm and z2 ¼ 7 cm after the background

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the background noise and its enlarged image from the centralarea, respectively. Like high-contrast input, multiple productionsof fingerprint patterns also occur.

The PSNRs for the recording distance z2 ¼ 7 cm are plotted inFig. 9. The same symbols are used to represent PSNRs with andwithout the background noise. The background removal methodgives obviously higher PSNRs. This verifies the effectiveness of theproposed method for improving the quality of the decryptedimages. In a similar fashion with the high-contrast fingerprint, it isapparent that PSNRs fluctuate as a function of the separation z1

and its value is the lowest when the phase mask is placed in themiddle between the input and the hologram plane or 2z1 ¼ z2. It isinteresting to note that PSNRs of the low-contrast fingerprint arehigher than those of the high-contrast one. This is because thewave diffracted from the low-contrast image has loweramplitude. Any distortion occurred to the wave during theencryption–decryption process is thus smaller than that of thehigh-contrast image. As the distortion is smaller, higher PSNR isachieved from the low-contrast fingerprint.

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R

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Fig. 9. PSNRs of the decrypted low-contrast fingerprint as a function of distance z1

for the recording distance z2 ¼ 7 cm.

4. Conclusions

We have investigated quantitatively the quality of imagesdecrypted from the in-line holographic encryption by measuringthe PSNR. The high- and low-contrast fingerprint images are usedas the test scenes. The simulation results show that the decryptedimage is generally buried in strong background noise caused bythe phase mask.

To solve this problem, we have proposed and verified thebackground noise removal method which is done by encryptinginformation of the phase mask. Its decrypted informationis then subtracted from the decrypted information of thefingerprint.

Although quality of the decrypted images can be significantlyimproved, it is found that the PSNRs fluctuate as a function of theposition z1 of the phase mask. This is because: first, theencryption–decryption process is mathematically equivalent tothe convolutions of the input fingerprint and two autocorrelationsof the free-space impulse response. Instead of a delta function,each autocorrelation gives sinc function which is bipolar innature. The negative part of the sinc function distorts thedecrypted image. Second, the limited resolution of the CCD sensor

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Fig. 8. (a) Decrypted image and (b) its enlargement at the fingerprint area for the low

noise removal.

causes the aliasing problem. The autocorrelation of the undersampled impulse response does not give only single sinc function,but a set of unwanted sinc functions as well. As a result, thedesired fingerprint image is overlapped by the unwanted ones.Therefore, when the phase mask is located at the middle of therecording distance the two impulse responses becomes identicalsuch that hz1

¼ hðz2�z1Þ. As the result, the image distortion is thelargest. Finally, since the low-contrast image has lower amplitudethat the high-contrast image, the distortions of the decrypted low-contrast fingerprint is also smaller.

Acknowledgement

The financial support from the Commission on Higher Educa-tion through the postdoctoral research fellowship (2006) isacknowledged.

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[3] Li H, Image encryption based on gyrator transform and two-step phase-shifting interferometry. Opt Lasers Eng 2009;47:45–50.

[4] Songcan L, Brian K, Mark AN. Wave front reconstruction bymeans of phase-shifting digital in-line holography. Opt Commun 2000;173:155–160.

[5] Goodman JW. Introduction to Fourier optics, 2nd ed.. New York: McGraw-Hill;1996.

[6] Shuyu Y, Xiaoxi Z, Sunanda M. Performance of lossy compression algorithmfrom statistical and perceptual metrics. In: Proceedings of the12th IEEE symposium on computer-based medical systems. 1999.p. 242–7.