1 December 1998

Ž .Optics Communications 157 1998 23–26

Recognition of color patternsusing a photorefractive LiNbO :Fe crystal3

Qian Sun, Yudong Li, Jingjun Xu, Xinzheng Zhang, Guoquan Zhang, Simin Liu,Guangyin Zhang 1

Institute of Photonics, College of Physics, Nankai UniÕersity, Tianjin 300071, China

Received 26 June 1998; revised 20 August 1998; accepted 24 August 1998

Abstract

In this paper, we used a LiNbO :Fe crystal to produce a matched spatial filter and realize recognition of color patterns.3

Our method is simple and sensitive to variation of the shape and color distribution of the color patterns. q 1998 ElsevierScience B.V. All rights reserved.

Keywords: Recognition of color patterns; LiNbO :Fe crystal; Matched spatial filter; Photorefractive3

Pattern recognition is a very important optical process.It can be used to realize machine vision, automatic controland other important applications. Using monochromaticlight, we can distinguish patterns with different shapes.When objects have the same outline, the recognition capa-bility is not satisfactory. In this case, we should check thecolor distributions of the objects, i.e. we should utilizecolor pattern recognition. There are two methods to recog-nize color patterns. The first method is based on the BGR

w xmodel 1,2 and it needs a two-dimensional color CCD.The high price and the limited resolution of the two-di-mensional color CCD impede its practice. The second one

w xis by using color image correlation 3–6 . The difficultyfor this method is producing a matched spatial filter for therecognized patterns. It is simple to record holograms fordifferent wavelength components of the recognized patternin common holographic media, e.g. photographic plate.But during the developing and the fixing precession ofholograms, the thickness of the holographic media alwayschanges. Although the thickness variation can be mini-mized by carefully adjusting the conditions for developingand fixing, the variation has unfortunately no repeatability.

1 E-mail: zhanggy@sun.nankai.edu.cn

Photorefractive crystals are widely used in optical andphotonics techniques such as in hologram recording andself-phase-conjugation. In this paper, we realized colorpattern recognition using a photorefractive LiNbO :Fe3

crystal to produce a matched spatial filter. When twocoherent monochromatic light interfere in a photorefractive

Ž .crystal, charges electrons andror holes in the crystal arephoto-excited. After migration and retraption of thecharges, there is a spatial electric field in the crystal.Arising from the electro-optical effect, the refractive indexof the crystal is modulated and a volume phase hologram

w xbuilds up 7 . When we record holograms in a photorefrac-tive crystal, the crystal need not to be developed and fixed.The thickness of the crystal does not change. The holo-grams have long lifetime and do not attenuate in dampenvironment. So our method is more practical.

For the sake of simplicity, we studied the recognition ofpatterns just containing two color components, red andblue. Our experimental setup is shown in Fig. 1. A colorpattern placed at the front focal plane of an achromaticFourier transform lens L was illuminated by a collimated1

uniform blue light coming from an Argon laser and acollimated uniform red light coming from a He-Ne laser.The focal length of the lens is 13.456 cm. The wavelengthsof the blue and the red light are l s488 nm and l sb r

0030-4018r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved.Ž .PII: S0030-4018 98 00472-6

( )Q. Sun et al.rOptics Communications 157 1998 23–2624

Fig. 1. Experimental setup. CP, color pattern. L, lens. LN, LiNbO :Fe crystal. C, C-axis of the crystal. S, screen. BR, blue reference beam.3

RR, red reference beam.

632.8 nm respectively. The light amplitude distribution ofthe transmitted beam behind the input plane can be writtenas

s x , y sb x , y ,l qr x , y ,l , 1Ž . Ž .Ž . Ž .b r

Ž . Ž .where b x, y,l and r x, y,l are the blue and redb r

components of the amplitude transmissions of the colorpattern respectively. The light distribution at the back focalplane of lens L is1

S u ,Õ sB u ,Õ qR u ,Õ , 2Ž . Ž . Ž . Ž .Ž .where u,Õ represents the spatial coordinate system of the

Ž . Ž .Fourier plane, B u,Õ and R u,Õ are the color FourierŽ . Ž .spectra of b x, y,l and r x, y,l respectively. Ab r

LiNbO :Fe crystal was placed at the back focal plane of3

the transform lens. The thickness of the crystal is 2.0 mmand the crystal is 0.1 wt% doped. Besides the Fourier

Ž .transform S u,Õ , the crystal was illuminated simultane-Ž .ously by a uniform red plane wave red reference beam

Ž .and a uniform blue plane wave blue reference beamwhich came from the same Argon laser and the sameHe-Ne laser respectively. The incident angles of the blueand the red wave u and u were 308 and 408 in the airb r

respectively. Because the blue light is incoherent with thered light, the light distribution in the LiNbO :Fe crystal3

can be described as2

I u ,Õ s P exp yik Pr qB u ,ÕŽ . Ž .Ž .b b

2q P exp yik Pr qR u ,Õ . 3Ž . Ž .Ž .r r

Here P and P denote the amplitude of the blue and theb r

red reference beams. k and k denote the wave vector ofb r

the blue and the red reference beams. Under illuminationof the interference pattern, the refractive index of theLiNbO :Fe crystal is spatially modulated and a phase3

hologram builds up. Then we get a matched spatial filterŽ . Ž .for the color pattern s x, y . According to Eq. 3 , the

interference pattern can be regarded as simple superimpo-sition of an interference pattern produced by the light andanother pattern produced by the red light. So the phase

hologram can be regarded as the superimposition of aŽphase hologram written by blue light referred as hologram

.B below and a phase hologram written by red lightŽ .referred as hologram R below .

The variation of refractive index in the LiNbO :Fe3

crystal is proportional to the incident intensity and is veryw xsmall, i.e. it is far smaller than pr2 7 . So the transmis-

sion of the crystal can be written astAexp ib I s1q ib I , 4Ž . Ž .where b is a constant decided by the parameters of thephotorefractive crystal.

XŽ . XŽ .When a new color pattern s x, y sb x, y,l qbXŽ .r x, y,l is placed at the front focal plane of lens L , itsr 1

XŽ . XŽ . XŽ .Fourier transform S u,Õ sB u,Õ qR u,Õ illuminatesthe crystal. Hologram B and hologram R in the crystal will

XŽ .diffract S u,Õ . The diffraction is decided by the factorŽ .ib I in Eq. 4 . The thickness of the LiNbO :Fe crystal, 2.03

mm, is very large. So only when incident light is at theBragg angle of a hologram in the crystal, it can bediffracted by the hologram. In our setup, the red lightdeviates far from the Bragg angle of hologram B, sohologram B just diffracts incident blue light. Based on thesame reason, hologram R just diffracts the red light. So the

XŽ .transmission of S u,Õ through the crystal can be ex-pressed as

2 XI A P exp yik Pr qB u ,Õ BŽ .Ž .t b b2 Xq P exp yik Pr qR u ,Õ R . 5Ž . Ž .Ž .r r

ŽI is transformed by an achromatic lens L fs13.456t 2.cm placed after the crystal. The intensity distribution on

the screen placed at the focal plane of L can be written as2

I sFTy1 IŽ .s t2 X X X

)A P b qbmb wb qb xqd , y wbŽ .b b2X X X

) )qb xyd , y mb x , y q P r qrmr wrŽ .Ž .b r

qrX xqd , y wrqrX xyd , y mr ) x , y .Ž .Ž . Ž .r r

6Ž .

( )Q. Sun et al.rOptics Communications 157 1998 23–26 25

Here d s f sinu , d s f sinu , w denotes convolutionb b r r

product, m denotes cross correlation. According to theŽ .fourth and eighth factors in Eq. 6 , we can observe on the

screen at the back focal plane of L a blue correlation spot2Ž .centered at d ,0 which is produced by the blue compo-b

Ž . XŽ .nent of patterns s x, y and s x, y and a red correlationŽ .spot centered at d ,0 which is produced by the redr

Ž . XŽ .component of s x, y and s x, y . Through measurementof the red and the blue correlation spot, we can testwhether the incident pattern is the same as the patternstored in the photorefractive crystal or not.

Our method is sensitive to the shape and the colorvariations of the input patterns. If the input pattern hasdifferent shape andror color distribution, the blue androrthe red correlation spots will diminish and the intensitywill decrease, even to be zero.

In our experiment, we stored a color pattern composedby two red numbers, ‘‘1’’ and ‘‘2’’, and two blue num-bers, ‘‘3’’ and ‘‘4’’ in the LiNbO :Fe crystal to form the3

matched spatial filter. The black-and-white photograph ofthe color pattern and its self-correlation spot on the screenis shown in Fig. 2. The left correlation spot is red and theright one is blue. The two correlation spots are round andbright. We illuminated the LiNbO :Fe crystal by color3

patterns which have different shapes and the same colordistribution as the one we stored in the crystal. The red andthe blue correlation spots are too weak to be observed. Oneof these patterns contains two red numbers, ‘‘0’’ and ‘‘1’’,and two blue numbers, ‘‘2’’ and ‘‘3’’. Fig. 3 shows theblack-and-white photograph of this color pattern and itscorrelation spots.

Furthermore, we check the sensitivity of our method tothe color variation. In our experiment, we input five colorpatterns into the matched spatial filter sequentially. Thepatterns are all composed by the same four numbers, ‘‘1’’,‘‘2’’, ‘‘3’’ and ‘‘4’’. But the color distributions of the fivepatterns are different. The four numbers in pattern A areall red. In pattern B, ‘‘4’’ is blue and the other threenumbers are red. In pattern C, ‘‘1’’ and ‘‘2’’ are red,whereby ‘‘3’’ and ‘‘4’’ are blue. In pattern D, only ‘‘1’’ isred and the other three numbers are blue. In pattern E, thefour numbers are blue. There is just one pattern, pattern C,which is the same as the pattern stored in the crystal. The

Fig. 2. Black-and-white photograph of the color pattern ‘‘1234’’and its self-correlation spot.

Fig. 3. Black-and-white photograph of the color pattern ‘‘0123’’and its correlation spot.

intensities of the blue and the red correlation spots for thefive patterns are listed in Table 1. In Table 1, we take theintensity of the blue and the red correlation spots forpattern C as units. We can see that, when the colordistribution of an input color pattern differs from the onestored in the LiNbO :Fe crystal, at least one of the two3

correlation spots becomes weak. By measuring the intensi-ties of the two correlation spots, we can investigate whetherthe shape and the color distribution of a color pattern areall the same as the shape and the distribution of the patternstored in matched spatial filter.

The photorefractive sensitivity of LiNbO :Fe crystal is3

different at different wavelengths. It induces variation ofthe diffraction efficiency of the hologram recorded in thecrystal with the wavelength of the recording waves. In ourmethod, we do not care how much is the diffractionefficiency. We only need to compare the intensities of thered and the blue self-correlation spots of the pattern storedin the LiNbO :Fe crystal with the intensities of the two3

correlation spots of the recognized pattern. So the inhomo-geneity in photorefractive sensitivity does not influencepattern recognition in our method. If the diffraction effi-ciency of the hologram is too small, it is difficult to detectthe correlation spot and the signal to noise ratio is low.Fortunately, the diffraction efficiency of LiNbO :Fe is3

quite large in the visible wave band.In summary, we introduce the application of the pho-

torefractive crystal in the color pattern recognition. Ourmethod is simple and practical. It is sensitive not only tothe shape but also to the color distribution of the inputpattern. In this paper we just use two types of light withdifferent wavelengths to produce a matched spatial filter.

Table 1Intensities of the red and the blue correlation spots for pattern A,B, C, D and E

A B C D E

Intensity of the red 1.10 1.05 1.00 0.51 0.00correlation spotIntensity of the blue 0.00 0.48 1.00 1.04 1.08correlation spot

( )Q. Sun et al.rOptics Communications 157 1998 23–2626

Many holograms can be superimposed at the same positionw xof a LiNbO :Fe crystal 7 . Using more types of light with3

different wavelengths to illuminate a color pattern andrecord holograms in a photorefractive crystal, more colorcomponents of the input pattern can be checked. In thisway, the recognition exactness of our method will begreatly improved. Furthermore, we can store many colorpatterns in one photorefractive crystal to save the price ofthe recognition system.

Acknowledgements

This research is financially supported by the NationalŽ .Science Foundation of China No. 19734004 , the Key

Research Project in Climbing Program from the StateScience and Technology Commission of China, the Na-

Ž .tional Advanced Materials Committee of China NAMCC ,and the Funding for excellent young researchers fromNational Education Committee of China.

References

w x1 M.S. Millan, M. Corbalian, J. Romero, M.J. Yzuel, OpticsŽ .Lett. 20 1995 1722.

w x2 I. Moreno, V. Kober, V. Lashin, J. Campos, L.P. Yaroslavsky,Ž .M.J. Yzuel, Optics Lett. 21 1996 498.

w x Ž .3 S.K. Case, Appl. Optics 18 1979 1890.w x Ž .4 Y. Ishii, K. Murata, Optics Lett. 7 1982 230.w x Ž .5 F.T.S. Yu, T.H. Chao, Appl. Phys. B 32 1983 1.w x6 Z.Q. Wang, C.M. Cartwright, C. Souter, W.A. Gillespie,

Ž .Appl. Optics 32 1993 715.w x7 P. Gunter, J. Huignard, Topic of Applied Physics, Photorefrac-¨

tive Materials and Their Application, Springer, 1988.