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Multiplexcodingforreal-timeopticalimageprocessing

DATASETinPROCEEDINGSOFSPIE-THEINTERNATIONALSOCIETYFOROPTICALENGINEERING·SEPTEMBER2011

ImpactFactor:0.2·DOI:10.1117/12.899570

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Multiplex coding for real-time optical image processing

S. Elwardi *a,b, B.-E. Benkelfatb, M. Zghala

aUniversity of Carthage, Engineering School of Communication of Tunis (Sup’Com), Cirta’Com Laboratory, Ghazala Technopark, 2083, Ariana, Tunisia

bInstitut Télécom; Télécom SudParis SAMOVAR UMR INT-CNRS 5157; 9 rue Charles Fourier 91011 Evry Cedex, France

ABSTRACT

The latest developments in optical image processing for security, compression and cryptography require parallel real time processing and multiplexing. In this paper, we propose the application of the well-know “coherence modulation of light” technique for real-time encoding and decoding of signals which can be useful for optical image processing. This method uses the coherence properties of broadband sources for encoding signals onto light beams. One major asset of this approach, compared to other conventional optical modulation methods, is an original multiplex coding of several signals through a single light beam. We achieve simultaneous real-time all optical image processing of analog two-dimensional signals and suggest a set of new criteria, based on mean square error, signal to noise ratio and peak to peak signal to noise, to improve the quality of the decoding image as function of the optical path difference and the coherence length of the source.

Keywords: Coherence multiplexing, optical image processing, birefringence

1. INTRODUCTION The latest developments in optical image processing for security, compression and cryptography require parallel real time processing and multiplexing. In this domain, several method based mainly on the VanderLugt type optical correlator1,2 and the standard architecture of a joint-transform correlator (JTC)3 has been proposed. Coherence modulation of broadband light source has found many applications in the last decade including optical communications and optical sensing4,5. In this paper, we report the application of coherence modulation of light in two-dimensional real-time multi-channel processing. The method can be used for a higher number of input signals. This technique, which uses the path difference multiplexing technique, has been considered as an attractive alternative for transmitting simultaneously N channels6. Furthermore, it has been also proposed in optical sensing7 and data processing domains such as faster matrix-vector, matrix-matrix products8. The coherence modulation of light (also called path-difference modulation) consists in encoding a signal on a light beam as an optical delay larger than its coherence length ωπ Δ= clc 2 , (with Δω: linewidth of the source expressed in angular frequency and c: velocity of light in vacuum). This opens the way to the use of broadband sources in systems that thought to be restricted to quasi-monochromatic light. The different signals to be processed are encoded by two-dimensional spatial coherence modulators (S-CM’s) set in cascade and illuminated by a single light beam. Each S-CM, which consists of a liquid crystal spatial light modulator and a birefringent plate placed between two polarizers, introduces an optical delay greater than the coherence time of the light source. Delays are chosen to minimize the channel cross talk. The decoding module is formed by a birefringent plate Qr tuned to the one used in the S-CM and set between two polarizers. The remained of this paper is organized as follow, in the second section; we present the principle of operation of the architecture. Furthermore, a theoretical validation will be established for encoding and decoding images. In the next section, simulation results are then presented and discussed. Finally, we suggest a set of new criteria, based on mean square error, signal to noise ratio and peak to peak signal to noise, to improve the quality of the decoding image as function of the ratio between the optical path-difference introduced.

*Sonia.elwardi@supcom.rnu.tn; phone (216) 71 857 000; fax (216) 71 856 829; http://www.supcom.mincom.tn

Optical Design and Engineering IV, edited by Laurent Mazuray, Rolf Wartmann, Andrew Wood, Jean-Luc M. Tissot, Jeffrey M. Raynor, Proc. of SPIE Vol. 8167, 81671Y · © 2011 SPIE · CCC code: 0277-786X/11/$18 · doi: 10.1117/12.899570

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2. PRINCIPLE OF COHERENCE MULTIPLEXING TECHNIQUE The principle of operation is illustrated by a classical imaging system using achromatic lenses. The input image ( )yxf , is encoded by two-dimensional spatial coherence modulator (S-CM) set in input plane and illuminated by a plane wave with a short coherence length lc. The S-CM (also called encoding module) consists of a liquid crystal spatial light modulator (SLM), which is used to display the input image, and a birefringent plate Q placed between two polarizers oriented at an angle of 45° to fast and slow axes of Q. The decoding module (DM) is composed by a birefringent plate Qr tuned to the one used in the SCM and with its fast and slow axes at 45° to the polarizing directions of the polarizers. The S-CM works as a two-wave interferometer and introduces, for each pixel of the image (x,y), an optical delay between light fields given by,

),(),( 0 yxyx δ+Δ=Δ (1)

where Δ0 is the static optical delay introduced by the birefringent plate Q. The latter is chosen so that its delay is greater than the coherence length lc of the source. The second term in (1) is spatial-varying optical delay induced electro-optically by the SLM. It’s proportional locally to the amplitude transmittance of input image.

cyxneyxfKyx ),(),(),( ∂⋅

=⋅=δ (2)

where K is a constant related to SLM, ( )yxn ,∂ is the birefringence of the liquid crystal which is dependent on the applied voltage and e is the thickness of the liquid crystal cell. The S-CM behaves as a two-wave interferometer whose spectral-transmission curve is of the form “ ( )yx,2cos1 Δ+ πσ ”, where σ is the wave number. After decoding operation, which performed by a decoding module (DM) (P-Qr-A), the total energy on the CCD camera placed on the output image plane is shown to be directly proportional to input image. This method can be generalized to coherence multiplexing schemes. In the multiplexing stage, each S-CM is formed by a liquid crystal SLM and an appropriate birefringent plate set between two polarizers. The input signals ( )yxf ,1 and ( )yxf ,2 are displayed, respectively, on the SLM1 and SLM2. Each S-CM introduces an optical delay given, respectively, by:

( ) ( )yxyx ,, 1011 δ+Δ=Δ and ( ) ( )yxyx ,, 2022 δ+Δ=Δ (3)

where Δ01 and Δ02 are the static delays exhibited by S-CM1 and S-CM2, respectively. In general, in order to provide the minimum cross talk, the ratio between the continuous optical delays Δ01 and Δ02 must be correctly chosen. We define R the ratio between the Δ01 and Δ02. The decoding module DM is formed by a birefringent plate which is matched to those used in the spatial-coherence modulators. The energy, at the output of the multiplexed encoding system, is expressed as:

( ) ( ) ( )( ) ( )( )yxcyxcPE ,2cos1,2cos141

2010 Δ+Δ+= σπσπσσ (4)

where ( )σP is the power-spectrum, expressed in wave number σ = 1/λ, of the broadband light source centered at 0σ . So, the detected energy at the output of the decoding module is written as,

( ) ( ) ( )( ) ( )( )( )dd cyxcyxcPE Δ+Δ+Δ+= 02010 2cos1,2cos1,2cos141 σπσπσπσσ (5)

In that case, the intensity detected by the CCD as function of the variable optical delay is expressed as:

( )∫Δ=σ

σσ dEI d (6)

where the integral is taken over the spectral range Δσ of the source.

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0,00000,00

0,05

0,10

0,15

0,20

0,25

ΔdΔ2

Det

ecte

d in

tens

ityOptical delay (s)

I(Δd,t)

Δ1

Figure 1 Evolution of the intensity at the output of receiving interferometer for a multiplexing coherence scheme

Fig. 1 shows the detected intensity as a function of the optical delay dΔ introduced at the decoding module. It consists of five fringe packets centered at Δd = 0, 1Δ , 2Δ , Δ1 - Δ2, and Δ1 + Δ2. In order to obtain a detected energy proportional to f1(x,y) (respectively f2(x,y)), the optical delay introduced by the receiving interferometer must be adjusted to the fixed optical delay 4001 λ+Δ (respectively 4002 λ+Δ ). Then the signal provides by the CCD is proportional to f1(x,y) (respectively f2(x,y)).

3. NUMERICAL RESULTS AND DISCUSSION In order to validate the approach of the encoding and the decoding images, we carried out some simulations using a system powered by a broadband light source with a coherence length mlc μ20= , Figure 3 shows the input images displayed, respectively, on the first and the second SLM. Measurement criteria are required to assess the performance of the proposed method9. The first criterion, we opted for, is the mean square error (MSE) and is given by eq. (7). The second used criterion is the signal to noise ratio (SNR) which is expressed in eq. (8). Finally, the third criterion is the peak-to-peak signal to noise ratio (PSNR) and it is defined by the eq. (9).

( ) ( )2

1 12 ,,1 ∑∑

= =

−=N

i

N

jdecorig jiIjiI

NMSE (7)

( ) ( )( )⎟⎟⎠

⎞⎜⎜⎝

⎛=

decorig

origdecorig IIMSE

IVARIISNR

,log10, 10 (8)

( ) ( )⎟⎟⎠⎞

⎜⎜⎝

⎛=

decorigdecorig IIMSE

pIIPSNR,

log10,2

10 (9)

where p is the maximum value in one pixel; Iorig (i,j) is the intensity of the (i,j) pixel of the original image; Idec(i,j) is the intensity of the (i,j) pixel of the image obtained after decoding; VAR(Iorig) is the variance of the original image Iorig. Figure 2 illustrates the input images used in the input plane. We used the known images “clown” and “lena”. Figure 3 and fig. 4 present, respectively, the numerical results of the decoding of the first and the second images encoded with coherence modulation of light for different ratio 0201 ΔΔ=R , R = 1, 1.2 and 1.5. We can show that for R ≤ 1.5 a crosstalk appears in the decoding images. When R ≥ 1.5, no crosstalk is detected at the output plane.

Fig. 5 shows the evaluation of the decoding image 1 and image 2 as function of the ratio R. It illustrates the variation of the SNR, the PSNR and the MSE. We note that the PSNR and SNR increase with the R ratio. Also, we note that the MSE decrease with R. When we decode the first image “clown” and from R = 1.5 the output decoding image is practical identical to the original image of figure 3 (a). But, in the case of decoding the second image “lena”, R = 2 introduces a

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crosstalk due to the interference between image 1 and image 2. So, it is suggested to do not choose R = 2 in this configuration of multiplexed coherence modulation. This result proves the importance of the choice of the ratio R between the optical path differences, to reduce crosstalk between signals.

(a) (b)

Figure 2 Input images (original images), (a): ( )yxf ,1 , (b): ( )yxf ,2

(a) (b) (c)

Figure. 3 Decoding process of the first image (image 1) versus the ratio R; (a) R=1, (b) R=1.2, (c): R=1.5

(a) (b) (c)

Figure 4 Decoding process of the second image (image 2) versus the ratio R; (a) R=1, (b) R=1.2, (c): R=1.5

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1,0 1,5 2,0 2,5 3,0 3,5

-10

0

10

20

30

40

50

60

70

SN

R( d

B)

R

image 2 image1

1,0 1,5 2,0 2,5 3,0 3,5

0

10

20

30

40

50

60

70

80

90

PSN

R (d

B)

R

image2 image1

(a) (b)

1,0 1,5 2,0 2,5 3,0 3,5-0,0002

0,0000

0,0002

0,0004

0,0006

0,0008

0,0010

0,0012

0,0014

MS

E

R

image 2 image 1

(c)

Fig.5 Evaluation of decoding image 1 and image 2 as function of the ratio R; (a): Variation of the SNR, (b): PSNR, (c): MSE

4. CONCLUSION We have described a novel application of the coherence multiplexing technique (also called path-difference multiplexing) for 2-D optical signal processing. We have performed a theoretical and numerical study for encoding and decoding images by coherence multiplexing system. The decoding image quality is compared for different ration R. We have also evaluated the performance of the system for different criterion, mean square error MSE, signal to noise ratio SNR and peak to peak signal to noise PSNR as function of R. We can conclude that for decoding image, we can take R ≥ 1.5. In this case, perfectly image is decoded.

REFERENCES

[1] A. Vanderlugt, “Signal detection by complex filtering”, IEEE Trans. Inf. Theory, IT10, 139 (1964). [2] A. Vanderlugt, “Optical signal processing”, chap.5, Wiley Series in Pure and Applied Optics, N.Y (1992). [3] G. S. Pati, G. Unnikrishnan and K. Singh, “Multichannel image addition and subtraction using joint-transform correlator architecture,” Optics Communications, vol. 150, 33-37 (1998).

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[4] J. P. Goedgebuer, R. Ferrière, B.-E. Benkelfat, “An acousto-optic correlator working by coherence modulation of light,” Opt. Com., 103, 245 - 253 (1993). [5] J. P Goedgebuer, H. Porte, P. Mollier, “Coherence modulation and correlation of stochastic light fields,” J. Phys. III, 3, 1413 - 1443 (1993). [6] J. Hauden, H. Porte, J. -P. Goedgebuer, J. Abiven, C. Gibassier, C. Gutierrez-Martinez, “Demonstration of single source bidirectional fibre link using polarisation insensitive LiNBO3 integrated coherence modulators,” IEEE JLT. 14, 1630 (1996). [7] Gutierrez-Martinez, C. Santos-Aguilar, J., “Electric Field Sensing Scheme Based on Matched LiNbO3 Electro-Optic Retarders,” IEEE TIM. 57, 1630 (2008). [8] R. Giust, J.-P. Goedgebuer, and N. Butterlin, “A digital processor formed by cascaded spatial light modulators,” Opt. Comm., vol. 181, 279–285 (2000). [9] A. Alkholidi, A. Alfalou, H. Hamam, “A new approach for optical colored image compression using the JPEG standards,” Signal Processing, vol. 87, 569 – 583 (2007).

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