Diffractive parameric colors

$Page 1: Diffractive parameric colors$
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Orava et al. Vol. 25, No. 12 /December 2008 /J. Opt. Soc. Am. A 2901

Diffractive parameric colors

Joni Orava,1,* Noora Heikkila,1 Timo Jaaskelainen,1 and Jussi Parkkinen2

1Department of Mathematics and Physics, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland2Department of Computer Science, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland

*Corresponding author: [email protected]

Received March 13, 2008; revised September 18, 2008; accepted September 21, 2008;posted September 25, 2008 (Doc. ID 93833); published November 4, 2008

A method of producing inkless parameric color pairs is studied. In this method, colors are formed additivelyusing diffraction gratings with differing grating periods as primary colors. Gratings with different grating pe-riods reflect different spectral radiance peaks of a fluorescent lamp to the desired viewing angle, according tothe grating equation. Four spectral peaks of a 4000 K fluorescent lamp—red, green, cyan, and blue—are usedas the primary colors. The colors are mixed additively by fixing the relative areas of different grating periodsinside a pixel. With four primary colors it is possible to mix certain colors with different triplets of primarycolors. Thus, it is theoretically possible to produce metameric colors. In this study, three parameric color pairsare fabricated using electron beam lithography, electroplating, and hot embossing. The radiance spectra of thecolor pairs are measured by spectroradiometer from hot-embossed plastic samples. The CIELAB �Eab andCIEDE2000 color differences between radiance spectra of the color pairs are calculated. The CIEDE2000 colordifferences of color pairs are between 2.6 and 7.2 units in reference viewing conditions. The effects of viewingangle and different light sources are also evaluated. It is found that both the viewing angle and the light sourcehave very strong influences on the color differences of the color pairs. © 2008 Optical Society of America

OCIS codes: 330.1690, 330.1730, 050.1950, 050.1970.

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. INTRODUCTIONtheory of using reflective diffraction gratings for addi-

ive color mixing has been published recently by our team1,2]. The theory shows a way to inkless printing with aery large gamut. The spectral radiance peaks of the illu-ination, for example, fluorescent lamps or LEDs, are

sed as primary colors, which are then reflected to de-ired viewing angles by diffraction gratings.

The period of the diffraction grating will determine theavelength that is reflected to a viewing angle, according

o the grating Eq. (1) [3]:

n sin��r� = n sin��i� +m�

d, �1�

here n is the refractive index of the medium, �i is thengle of incidence, �r is the angle of reflection (viewingngle), m is the diffraction order, � is the wavelengthsed, and d is the grating period. Usually the −1st diffrac-ion order is used.

With one wavelength, only monochromatic colors cane represented. If different grating periods are mixed ad-itively in a pixel, a plurality of wavelengths will be re-ecting to the viewing angle. Thus, polychromatic colorsan be reflected to a viewing angle (Fig. 1). In Fig. 1, dr,g, and db illustrate different grating periods.If a fixed set of grating periods, i.e., primary colors, is

sed, a certain gamut of colors can be reflected to a pre-etermined viewing angle with reasonable accuracy [2].sually, only three different primary colors are needed to

epresent a certain color. However, if the radiance spec-rum of a light source has more than three peaks, thenore primary colors can be used. This allows not only a

arger gamut, but also the possibility of using different

1084-7529/08/122901-7/$15.00 © 2

riplets of primary colors to create the same color. In thisarticular case, two colors with the same CIE 1931 coloroordinates have different radiance spectra. Thus, theyorm a metameric pair [4]. The general definition of

etamerism by Judd and Wyszecki is as follows:‘Metameric objects are objects that, when illuminated by

given reference illuminant, reflect stimuli of differentpectral power distributions that produce the same colornder the same viewing conditions’’ [5], p. 26. (See also

6]) If the color sensation between the objects is approxi-ately the same, the term “paramerism” is used [7].Recently a method of producing illumination-

ndependent colors by diffractive optics has been accom-lished [8]. In that study, the tristimulus values remainhe same with two different light sources. In our study, onhe other hand, color pairs are designed to have the sameIE 1931 color coordinates only with certain illuminationnd viewing conditions.Several security applications using metamerism in

ome form have been reported [9,10]. Our method offerseveral benefits compared with the present metameric se-urity features that are based on inks with different spec-ral behavior. First, a change of the illumination will in-rease the color difference between metameric orarameric colors more than when using inks, because ofhe usually wider reflectance peaks of inks compared withhose of diffraction gratings. The utilization of gratingslso allows very strong angular paramerism. Only alight change in viewing angle will increase the color dif-erence of a parameric pair strongly. Another benefit of us-ng diffraction gratings as security features is their com-lexity. Counterfeiting of gratings is both much moreifficult and much more expensive than in the case of ink-ased metameric security features.

008 Optical Society of America

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Fig. 2. Radiance spectrum of a 4000 K fluorescent lamp.

Fig. 3. Measured radiance spectra of the primary colors.

2902 J. Opt. Soc. Am. A/Vol. 25, No. 12 /December 2008 Orava et al.

. EXPERIMENTALhree color pairs were designed using the four primaryolors of our earlier study [2]. Also the type of the lightource was that same, a 4000 K fluorescent lamp. The ra-iance spectrum of a 4000 K fluorescent lamp is shown inig. 2. The measured radiance spectra and the propertiesf the primary colors are shown in Fig. 3 and Table 1, re-pectively.

There are four different variations of three primaryamuts when four primary colors R, G, C, B (red, green,yan, and blue, respectively) are used. The possible varia-ions are RGC, RGB, RCB, and GCB. Three target colorairs were chosen from different areas of the gamut (Fig.). Each color pair can be produced by two different trip-ets at a time. The colors were intentionally chosen fromhe central parts of the gamuts, because the amount ofhe third primary color would be very small in the edgerea of a gamut. In that case the spectra of a color pairould be almost the same, which would not be convenienthen the definition of metamerism or paramerism is con-

idered. The properties of the designed color pairs arehown in Table 2. The computation method for relativeroportions of the primary colors is presented in [1,2].The master plate with six 5 mm�5 mm gratings was

abricated using electron beam lithography. The profilesf the gratings were binary with a fill factor of one. Thelastic sample was manufactured using electroplatingnd hot embossing. The detailed method is described in11–13].

The gratings were divided into 50 �m�50 �m pixels,ach being filled with a certain proportion of primaryratings according to Table 2. A schematic drawing and acanning electron microscope (SEM) image of a pixel arehown in Figs. 5 and 6, respectively.

The spectra of three color pairs were measured by spec-roradiometer using the setup of Fig. 7. The type of spec-roradiometer was PR-705 with 1

4° aperture. The distancerom sample to illumination was approximately 1.0 m,nd the measuring distance was 0.5 m. The viewing angleas varied from 26° in 2° steps to 34°.

. RESULTS AND DISCUSSIONhe radiance spectra of the color pairs at a viewing anglef 30.0° are shown in Fig. 8. When comparing the reflec-ance spectra of the color pairs, it can be seen that theyiffer strongly. Both the combinations of reflectance peaksnd the heights of the corresponding peaks are different.hus, from that point of view the definition of metamer-

sm is strongly supported, considering that the CIE 1931olor coordinates are the same.

Primary Gratingsa

Grating Depth��m�

Viewing Angle(deg) x y

0.14 30.0 0.663 0.3330.14 30.0 0.277 0.7100.14 30.0 0.075 0.2580.14 30.0 0.169 0.017

Table 1. Properties of the

rimary ColorPeak Wavelength

��m�Grating Period

��m�

Red 0.614 1.230Green 0.546 1.100Cyan 0.488 0.98Blue 0.436 0.875

aIllumination angle is 0° for all primary colors.

ig. 1. Different colors reflecting from diffraction gratings tohe same angle.

400 450 500 550 600 650 700 7500

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The CIE 1931 chromaticity values, CIELAB values,nd �Eab and �EDE2000 color differences of three colorairs are listed in Table 3. Theoretical values are the tar-et values, and measured values are computed from theeasured spectra. �Eab color difference has been consid-

red as a rather good metamerism index in the literature5]. However, the CIELAB �Eab values are not compa-able with each other in different regions of the colorpace. Especially in a high-chroma region of the colorpace, the CIELAB �Eab color difference formula will giveoo large values. Therefore, the color differences are alsoomputed using the CIEDE2000 color difference formula.efinitions of CIELAB �Eab and CIEDE2000 �EDE2000

olor difference formulas can be found in [4,14,15].Table 3 shows that �Eab and CIEDE2000 color differ-

nces within color pairs are between 6.8–9.5 and 2.6–7.2,espectively. A large difference between �Eab andEDE2000 color difference values can be seen, especiallyith blue and purple samples, which have higher chromaalues. These values can be considered to be quite high,specially when remembering that an average observeran perceive color differences as small as 0.5 �Eab, de-ending on the chromaticity of a sample [14,15]. Thus, theolor pairs are parameric, not metameric. However, with

Table 2. Properties o

Color

Relative Areas of Primary Gratings insid

Red Green Cyan

Blue RCB 0.038 0 0.795Blue GCB 0 0.046 0.443Beige RGB 0.171 0.203 0Beige RGC 0.239 0.119 0.642urple RGB 0.133 0.069 0urple RCB 0.189 0 0.528

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

x

y

C

G

R

B

Blue pair

Beige pair

Purple pair

ig. 4. Different gamuts with four primary colors and theoreti-al xy values of color pairs.

any cross-media metameric systems the �Eab color dif-erences between metameric pairs (or those supposed toe metameric) are of the same level. It must be noted alsohat observer variability in metameric color matches cane very large, with cross-media color matching at even 19Eab units [16].The viewing angle dependence of the color pairs can be

een in Figs. 9 and 10, where a minor change in the view-ng angle has a very strong influence on the color match-ng. It can also be seen from Figs. 9 and 10 that the blueair is less dependent on viewing angle than the beigend purple pairs. That can be explained, at least partially,y the fact that the blue pair has relatively greater pro-ortions of short grating periods than the other pairs. Itan be easily seen from the grating Eq. (1) that themaller the grating period d, the smaller is the change inavelength � as the viewing angle �r is changed. Also the

act that only invisible wavelengths exist below violetavelengths ��380 nm� affects the angular dependence.The color pairs were also measured with another light

ource, a 6500 K fluorescent lamp. Its radiance spectrare shown in Fig. 11. The spectral characteristics areuite similar between the illuminants. The peaks are athe same wavelengths, although their relative heights areifferent. One main difference is that the 6500 K lampas a continuous part in its spectrum. The measuringetup was the same as with 4000 K illumination. CIE931 chromaticity values, CIELAB values, and color dif-erences (�Eab and �EDE2000) of three color pairs with the500 K illuminant are shown in Table 4. The CIE 1931hromaticity values of the color pairs at the viewing anglef 30° are shown in Fig. 12.

Color Pairs in Fig. 4

el Theoretical CIE 1931 Chromaticity Values

Blue x y Y

0.167 0.150 0.200 27.40.314 0.150 0.200 27.40.267 0.350 0.400 78.10 0.350 0.400 78.10.503 0.300 0.200 22.90.283 0.300 0.200 22.9

ig. 5. Schematic drawing of a pixel; the gray lines representrating lines.

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Table 4 and Fig. 12 show also that a change in illumi-ant affects the color matching strongly, although thepectral characteristics of the illuminants are not greatlyifferent. As with angular dependence, also in this casehe change in color difference was the smallest in the blueolor pair. A blue color pair still matches at some levelompared with the other color pairs, the CIEDE2000 colorifference being 6.3, almost three times larger than withhe 4000 K illuminant. For the beige and purple colorairs, there is no match at any level. One reason for themaller change in color matching with the blue color pairs that the human visual system has lower sensitivity inhe blue end of the visual spectrum [4].

It must be noted that the accuracy of color matching be-ween color pairs is dependent on fabrication accuracy.or example, a change in grating period of �1% of wouldause 0.3° change in output angle of a primary color. Fur-hermore, it is very important that the profiles of the dif-raction gratings be the same as with primary gratings.

ig. 6. SEM image from the beige RGC pixel: (a) RGC pixel; (b)reater magnification of the RGC pixel. Green periods �1.10 �m�re on central area.

Fig. 7. Measuring setup.

he depth and shape of the grating profile affect stronglyhe relative diffraction efficiencies of primary gratingsnd therefore the accuracy of color mixing [1]. The elec-ron beam and electroplating processes have good repeat-

(a)

(b)

(c)

ig. 8. Radiance spectra of the color pairs at 30° viewing angle:a) blue color pair; (b) beige color pair; (c) purple color pair.

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Table 3. CIE 1931 Chromaticity Values, CIELAB Values, and �Eab Color Differences of Three Color Pairs atViewing Angle of 30°

Luminance

x y Y �cd/m2 sr� L* a* b* �Eab �EDE2000

Measured white 0.387 0.389 100.0 63.9 100.0 0.0 0.0Theoretical blue 0.150 0.200 27.4 17.5 59.3 −29.3 −101.4

Blue RCB 0.152 0.193 30.6 19.5 62.2 −25.1 −108.66.8 2.6

Blue GCB 0.157 0.187 29.4 18.8 61.1 −18.4 −109.6Theoretical beige 0.350 0.400 78.1 49.9 90.8 −19.4 −5.1

Beige RGB 0.369 0.388 74.6 47.7 89.2 −6.9 −5.38.1 7.2

Beige RGC 0.382 0.388 85.8 54.8 94.2 −1.6 −1.9Theoretical purple 0.300 0.200 35.8 22.9 66.4 52.0 −89.7

Purple RGB 0.320 0.201 32.1 20.5 63.5 57.7 −82.89.5 4.0

Purple RCB 0.307 0.205 29.5 18.8 61.2 48.7 −80.8

(a)

(c)

(e)

(b)

(d)

ig. 9. xy values of the color pairs in CIE 1931 chromaticity diagram at different viewing angles with 4000 K illumination: (a) 26°; (b)8°; (c) 30°; (d) 32°; (e) 34°.

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bility, but the hot embossing process can change the pro-les drastically, if quality control is not sufficiently high

17,18].A digital photograph was taken of the plastic sample at

30° viewing angle with 4000 K illuminant (Fig. 13). It isasily seen from the image that color pairs do not appearo match. However, as shown in Table 3, the CIELABolor differences of the pairs are below 10 for all threeairs. One reason for the obvious color difference in eacholor pair is that a digital camera does not accurately rep-esent human metameric pairs. This is quite obvioushen noting that the spectral responses of a digital cam-ra are different from the CIE 1931 color matching func-ions [19]. Furthermore, the blue color pair is out of aRGB gamut. Also the overall color errors of digital cam-ras generally can be quite large, over 10 �Eab units [20].

. CONCLUSIONSthree-pair set of diffractive parameric color samples

as designed, fabricated, measured, and analyzed. It wasound that the performance at the designed angle was atpromising level, the CIEDE2000 color differences of the

airs being between 2.6 and 7.2 �Eab units. However, theethod should be further developed to permit fabrication

f metameric color pairs. The angular dependence on the

Table 4. CIE 1931 Chromaticity Values, CIELAB Vwith 6500 K Illumina

x y Y �cd

Measured white 0.3231 0.3348 100.0Blue RCB 0.145 0.083 20.1Blue GCB 0.147 0.087 15.8Beige RGB 0.334 0.397 55.1Beige RGC 0.252 0.228 70.2Purple RGB 0.289 0.202 29.2Purple RCB 0.221 0.134 27.1

26 27 28 29 30 31 32 33 340

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20

30

40

50

60

70

80

90∆E

DE

2000

viewing angle (deg)

blue pairbeige pairpurple pair

ig. 10. CIEDE2000 color differences of the color pairs at dif-erent viewing angles.

atching of color pairs was found to be very strong. A mi-or change in viewing angle increased the color differenceetween samples strongly.

, and �Eab Color Differences of Three Color PairsViewing Angle of 30°

Luminance

� L* a* b* �Eab �EDE2000

100.0 0.0 0.052.7 65.0 −128.8

18.8 6.346.8 55.7 −113.679.1 −18.5 21.1

85.5 45.787.1 20.4 −54.661.0 46.5 −46.8

38.7 11.959.0 57.5 −83.8

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Fig. 11. Radiance spectra of 6500 K fluorescent lamp.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

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blue RCBblue GCBbeige RGBbeige RGCpurple RGBpurple RCBtheoretical blue 4000Ktheoretical beige 4000Ktheoretical purple 4000K

ig. 12. xy values of the color pairs in CIE 1931 chromaticityiagram with 6500 K illumination and viewing angle of 30°.

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The existence of metamerism with different lightources was also studied. It was found that paramerism,t least, diminishes strongly when the illuminant ishanged.

This kind of technology could be used, for example, inecurity and authenticity markings. A suitable viewingevice should be provided with this kind of application.he strong angular dependence makes counterfeitinguch harder than in the case of conventional printedetameric security markings.

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7. American Society for Testing and Materials, E284-08,“Standard terminology of appearance,” (ASTM Committee

Fig. 13. Digital photograph of the color pairs at 30° v

on Standards, 2008), pp 15, 16.

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2. P. Rai-Choudhury, ed., Handbook of Microlithography,Micromachining and Microfabrication, Vol. 2 (SPIE, 1997).

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angle. From the left: blue, beige, and purple samples.
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Diffractive parameric colors