practical color matching approach for color computer-generated holography

638 JOURNAL OF DISPLAY TECHNOLOGY, VOL. 9, NO. 8, AUGUST 2013

Practical Color Matching Approach for ColorComputer-Generated Holography

Yile Shi, Hui Wang, Yong Li, Lihong Ma, and Qiong Wu

Abstract—A color matching method for improving the colorreproduction quality of color computer-generated holography(CCGH) is proposed. It is found that the amplitude of objectwave in CCGH is related with object’s color quantity in com-puter display colorimetric system, three primary wavelengthsof CCGH and spectral distribution of illuminant source. Thus,this paper presents the conversion relationship between colorquantity in computer display colorimetric system and amplitudeof object wave in CCGH, which can improve the color qualityof holographic image. In order to demonstrate the effectivenessof the proposed method, two experiments are conducted. TheCCGH targets are respectively two-dimensional (2D) color object,three-dimensional (3D) gray and color mixed object. The exper-imental results demonstrate that the proposed color matchingmethod of CCGH is effective. It has practical applications in bothstatic and real-time dynamic holographic display, especially inhigh quality CCGH display.

Index Terms—Computer-generated holography (CGH), colorholography, colorimetry, holographic display.

I. INTRODUCTION

T HREE-DIMENSIONAL (3D) display based on com-puter-generated holography (CGH) attracts special

attention in both academia and industry for its flexible wave-front reconstruction ability, which has become the researchfocus of optics domain [1]–[3]. It is well-known that colorcomputer-generated holography (CCGH) is a more attractivepractical holographic display technique. Researchers havemade some significant research achievements both in staticand dynamic color 3D display based on CGH in recent years[4]–[6].For practical CCGH, one of the goals is to obtain a 3D image

in true color as closely as possible to the color object on com-puter monitor (CRT or LCD). There have been many papers de-voted to the wavelength selection for optimizing the color re-production of CCGH, but fewer researches have been done onhow to match the amplitude of three primary color object waveduring CCGH in order to improve the color quality of holo-graphic image. Pierre St-Hilaire and Stephen A. Benton havecombined three primary wavelengths lasers and acousto-optic

Manuscript received October 08, 2012; revised February 18, 2013; acceptedApril 09, 2013. Date of publication May 03, 2013; date of current version Au-gust 07, 2013. This work was supported by National Natural Science Foun-dation of China under Grant 61205012, the Natural Science Foundations ofZhejiang Provincial of China under Grant LQ12F05002 and by the Innovationteam project supported by Zhejiang Normal University, Jinhua, China. (Corre-sponding author: H. Wang)The authors are with the Institute of Information Optics, Zhejiang Normal

University, Jinhua 321004, China, and also with Province Key Laboratory ofOptical Information Detection and Holographic Display, Zhejiang Normal Uni-versity, Jinhua, 321004, China (e-mail: [email protected]).Digital Object Identifier 10.1109/JDT.2013.2258323

modulator (AOM) to display color 3D images. They advisedthat the gamut encircle by three primary calculated wavelengthsshould be larger than that obtained from a conventional colormonitor. Therefore, the color holographic display system canreproduce most of the colors on color monitor [7]. Takeshi Ya-maguchi, Gen Okabe and Hiroshi Yoshikawa have proposeda color 3D display technique with white light-emitting diode(LED) and liquid crystal on silicon (LCOS). They indicatedthat the color of holographic image turned to blue is due tothe spectral distribution of LED [8]. However, none of themhas proposed an effective approach that can optimize the colorquality of holographic image. In addition, many studies havebeen published in the last few years about the CCGH displaytechnique, which just mentioned that the color object from com-puter was decomposed into RGB components and three primaryobject waves are encoded into hologram during CCGH [9]–[11].However, they have not established the relationship betweenamplitude of object wave and RGB components. So far, colormatchingmethod of digital color image is used for CCGHby de-fault. For example, the RGB components proportion of a whitedigital image is . Therefore, the amplitudeproportion of three primary colors of object waves for the whiteobject in CCGH is considered as .By using this method, there exists great color difference be-tween holographic image and digital color image, which maybe still acceptable in some cases because of the color constancyof human eyes. Obviously, it is not the correct color matchingmethod for CCGH, which has prevented practical applicationof CCGH especially in some occasions that requires high colorreproduction quality such as color information preservation ofcultural assets and valuable artware by holography, holographicdisplay of portrait, real-existing objects and so on [5], [12], [13].Thus, an appropriate color matchingmethod is indispensable forimproving the color reproduction quality of holographic imageof CCGH.In this paper, the conversion relationship between color

quantity in computer display and CCGH colorimetric systemis established based on color matching and transfer theory.At the same time, isochromatic transfer relationship betweencolor quantity in CCGH colorimetric system and amplitude ofthree primary color object waves in CCGH is given. To confirmour proposed novel color matching approach for CCGH, twoexperiments are conducted. The CCGH targets are respectivelytwo-dimensional (2D) color object, three-dimensional (3D)gray and color mixed object. The experimental results anddiscussions are given in Section III.

II. COLOR MATCHING APPROACH FOR CCGH

It is well known that color information in CCGH is alwayscomes from a digital color image, which can be acquired

1551-319X © 2013 IEEE

SHI et al.: PRACTICAL COLOR MATCHING APPROACH FOR CCGH 639

from virtual 3D modeling or real-existing object capturing [5],[13]. The color transfer process is determined by the RGBcolorimetric system of computer monitor, such as PAL-RGBand NTSC-RGB systems. However, holographic imaging isbased on diffraction. The color of holographic image mainlydepends on amplitude of three primary color object waves,spatial frequency of hologram and spectral power distributionof illumination source. Ideal color reconstruction of CCGHmeans that the color of holographic image is as close to that ofthe digital image as possible. This paper attempts to proposea color matching method for CCGH, which can improve thecolor quality of holographic image.The color information for CCGH is from computer dis-

play colorimetric system in which three primary colors aredetermined by phosphor chromaticity coordinates of CRT orthe back-light and color filter spectral characteristics of LCD.The three primary colors are not spectral color. However,three primary colors of CCGH must be spectral color becausewe need to use spectral color to encode hologram. The colorreproduction characteristics of CCGH colorimetric systemis determined by the three primary calculated wavelengths.The color reproduction characteristics of CCGH colorimetricsystem is different from that of computer display colorimetricsystem. Assuming an arbitrary digital color image whose coloris C, and its color quantity in computer display colorimetricsystem is . It means that the mixed color is C in thecondition of in computer display colori-metric system. However, color quantity in CCGHcolorimetric system cannot be mixed into color C. Thus, ourfirst work is to establish the conversion relationship betweencomputer display and CCGH colorimetric system with the helpof CIE 1931-XYZ colorimetric system. Conversion from

to XYZ tristimulus values is given by [14]

(1)

where is the color transfer matrix, which is determined by thechromaticity of three primary colors of monitor and referencewhite. The common color system of monitor is PAL-RGB orNTSC-RGB. There chromaticity coordinates of three primarycolors and reference white are given, thus we can obtain thecolor transfer matrix by color matching

(2)

If the three primary wavelengths in CCGH are given, thechromaticity coordinates of three primary colors of CCGH col-orimetric system is also determined. Supposing that the colorquantity of CCGH colorimetric system is . The con-version from XYZ to can be expressed by

(3)

where is the color transfer matrix, which is determined bythe chromaticity coordinates of three primary color of CCGHcolorimetric system and reference white. Combing (1) and (3)gives the following transformation from totristimulus values

(4)

By the above conversion, we can obtain the color quantity, which represent C in CCGH colorimetric system.

The physical quantity of object light field in computer-gener-ated holography (CGH) must be amplitude or complex ampli-tude because the CGH forming process is essentially a digital-ized physical process. Thus, we need to establish the conversionbetween amplitude of object light field and .Assuming color quantity of C in CCGH colorimetric system

is , which are proportional to light intensity of threeprimary colors object light. The amplitude of three primarycolor object light is can be expressed by

(5)

coefficients , , and are calibration factors, whichdepends on three primary calculated wavelengths and spectralpower distribution of illuminant source. Assuming the threeprimary calculated wavelengths of CCGH are , theCGH fabrication process is ideal, the color of reconstructedimage is only depend on three spectral colors of illumi-nant source whose wavelengths are . The relativepower of illuminant source at are respectively

and . Assuming the color of object iswhite, the color quantity in computer colorimetric systemare . By using (4), we can obtain thecolor quantity of white in CCGH colorimetric system are

. The light intensity of three primarycolors light is

. The luminance of three primary colors lightis

is luminosity function. Therefore, thecalibration factors are

(6)

Assuming the chromaticity coordinates of three primarycolors light whose wavelengths are are

. Their luminance are , , and. Therefore, their color quantity can be calculated by

(7)


Fig. 1. 2D color object.

Assuming the color quantity of reference white is, the color matching equation of white light

can be expressed by

(8)

Thus, can be obtained by solving (8)

(9)

where are

(10)

By combing (4) and (5), we can obtain the amplitude of threeprimary object waves for CCGH. In order to demonstrate theeffectiveness of our proposed color matching method, two ex-periments will be conducted in the following sections.

III. EXPERIMENTS AND DISCUSSION

A simple and typical 2D color object from PAL-RGB colori-metric system is selected as the experimental target shown inFig. 1.In order tomatch asmuch color as PAL-RGBmonitor can dis-

play, the gamut of CCGH colorimetric system should be largerthan gamut of PAL-RGB colorimetric system. Therefore, wecan chose main wavelengths of PAL-RGB colorimetric systemas three primary calculated wavelengths of CCGH. They are re-spectively nm, nm and nm. Thegamut of the two colorimetric systems is shown in Fig. 2.A halogen light source is chosen as an illuminant source

(PHILIPS, 12 V, 50 W, 36 ) to reconstruct hologram. The rela-tive spectral power distribution of the halogen is shown in Fig. 3(Tested by Ocean Optics-USB4000 Fiber Optic Spectrometer).The power proportion at the three calculated wavelengths isthat .

TABLE ICOLOR QUANTITY AND AMPLITUDE OF OBJECT LIGHT OF COLOR OBJECT

Based on the approach described in Section II, the conversionrelationships between color quantity and amplitude of objectlight is described by the following expression:

(11)where the color quantity in CCGH is

(12)

The color object shown in Fig. 1 contains seven color regions.Their original color quantity in computer display colorimetricsystem and the corresponding object light amplitude are givenin Table I.The experimental processes are illustrated as follows. Firstly,

color quantity of object is obtained from the digitalimage. Secondly, the color quantity can be convertedto by (12), then the amplitude of object light field

are obtained by employing (11). Thirdly, theCGCRH algorithm is used to encode the color object lightwhose amplitude are [5]. The width of slit,viewing distance and reference incidence angle are respectively3 mm, 350 mm and 11.2 . Finally, the digital rainbow holo-gram is direct written on holographic recording material by aself-made CGH auto-microfilming system [5], [15]. The colorrainbow hologram that can be reconstructed by white light isobtained after processing the exposed hologram plate. In orderto demonstrate the effectiveness of the proposed color matchingmethod for CCGH, an experiment with conventional method isalso performed. We calculate the color hologram whose ampli-tude of object light isand other conditions of the experiment are the same as theformer experiment. The two holograms are illuminated by thehalogen simultaneously. A CCD camera (Canon EOS 550D)with a slit ( mm) in front of the camera lens takes theholographic images. The experimental results are respectivelyshown in Fig. 4(a) and in (b).By comparing the two images with Fig. 1, we can easily find

that Fig. 4(a) is more similar to the object than Fig. 4(b). In addi-tion, we can compare the holographic images with object quan-titatively by using CIEDE 2000. Firstly, mean value of corre-sponding color region of Fig. 4(a) and (b) are calculated, whichis considered as color quantity of each color region. Secondly,color quantity of each color region is converted into XYZ by(1). Thirdly, color difference between object and holographic


Fig. 2. Gamut of PAL-RGB color monitor and CCGH colorimetric system in CIE chromaticity diagram.

Fig. 3. Relative spectral power distribution of illuminant source.

Fig. 4. Color holographic images. (a) Use the color matching method to cali-brate the amplitude of object light. (b) Use as amplitudeof object light.

images are calculated by using CIEDE2000. The correspondingstatistics are given in Table II.The mean value of color difference between Figs. 4(a) and

1 is , which means that the color differencebetween holographic image and the object has fallen by 21.9%than the conventional method.From the above experimental results, we can draw the con-

clusion that the proposed method is feasible for 2D color object.However, we still do not know whether the color matchingmethod is feasible for grayscale object or color 3D object.

TABLE IICOLOR QUANTITY OF IMAGES AND COLOR DIFFERENCE BETWEEN IMAGES

AND OBJECT

Therefore, we try to use a gray and color mixed 3D object asthe CCGH target. The experimental process, parameters settingof CCGH, holographic image capturing method are the same asthe above experiment. The original object and its holographicimages in different viewpoints are shown in Fig. 5. The colorof holographic images can represent the original color objecttruthfully.The color difference calculated by CIEDE2000 is given in

Table III.The above two experiments demonstrate that the proposed

color matching method of CCGH is feasible. The saturationof holographic images is slightly lower than the object itself.The main reason of this phenomenon is that the spectrum ofthree primary colors will broaden during reconstruction. Ac-tually, color rainbow hologram contains three monochromaticrainbow holograms. Therefore, three parallel rainbow spec-trums whose relative positions are stagger will be reproducedwhile color rainbow hologram is illuminated by white light[16]. From Tables I and II, we can see that the color difference


Fig. 5. Image of gray and color mixed 3D object and its holographic images.(a) Object in computer display colorimetric system. (b) Left holographic image.(c) Front holographic image. (d) Right holographic image.

TABLE IIICOLOR QUANTITY OF OBJECT AND COLOR DIFFERENCE BETWEEN IMAGE

AND OBJECT

of blue object is quite large. In addition, the color differenceof the proposed method is larger than conventional method.Seemingly, the color matching method is an ineffective way toblue object. The reason is that the modulation transfer functionof CGH-microfilming system is not a constant, which is muchlower in high frequency than in low frequency. The diffractionefficiency of three monochromatic rainbow holograms is dif-ferent. The diffraction efficiency of rainbow hologram of blueobject is low. Therefore, the calibration factor may not feasibleto blue object.The rainbow spectrum will become wider while the refer-

ence light incident angle increase and the spectrum that can betaken by eye will narrow down. It means that the saturation ofeach three reconstructed primary colors will be close to spec-tral color. Thus, the color difference between color samples andtheir holographic images will decrease when the reference lightincident angle becomes larger. In addition, the color qualityof blue object will be improved when the modulation transferfunction of auto-microfilming system is enhanced. However, thespatial frequency will increase when the reference light incidentangle is larger. When the physical size of CGH is determined,the higher spatial frequency of CGH indicates that the calcu-lation amount is greater. Moreover, it requires a higher resolu-tion CGH auto-microfilming system for direct writing. The spa-tial resolution of our self-made CGH auto-microfilming systemis 440 lp/mm, so we cannot increase the reference light inci-dent angle blindly. In fact, this technique will soon be improvedwhen our next generation system whose spatial resolution will

achieve 1500 lp/mm is completed. It is hoped that the color sat-uration of holographic image will be almost the same as its orig-inal color object.

IV. CONCLUSION

In conclusion, in this paper, a color matching method forimproving the color reproduction quality in CCGH is proposed,and two experiments are given. By using the proposed colormatching method, the color of holographic images will befaithful. As a potential color display technique, the practicaluse of CCGH is just at its beginning. Our research may providetheoretical and technique basis for practical use of CCGH andresearch for minimizing color difference in CCGH.

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Yile-Shi was born in 1984. He received the B.S. andM.S. degree in physics and optics from ZhejiangNormal University, Jinhua, China, in 2007 and 2010,respectively, and is currently working toward thePh.D. degree in optical engineering from the Insti-tute of Information Optical Engineering, SoochowUniversity, Suzhou, China.His recent research interests include CGH-

based three-dimensional display technique andcolorimetry.

Hui-Wang was born in 1958. He received the M.S.degree in optics from Hangzhou University of Chinain 1986, and the Ph.D. degree in optics from SichuanUniversity of China in 1993.He is a Professor of Optics at the institute of infor-

mation optics, Zhejiang Normal University, Jinhua,China. Also, he is currently a vice-president of Zhe-jiang Normal University. He haswrittenmore than 50papers, and holdsmore than 10 registered patents. Hismajor interests are holographic display, digital holo-graphic microscopy and micro structure design and

fabrication.Dr. Wang is a director of Chinese Optical Society.

practical color matching approach for color computer-generated holography

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