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Enhancing efficacy in laser projection by four wavelength combination ∗ Ian Wallhead, Roberto Ocanã and Paula Quinza´ AIDO, Instituto Tecnolo´gico de O´ptica, C/Nicolás Copérnico, 7-13, Parque Tecnolo´gico, 46980 Paterna, Valencia, Spain ∗ Corresponding author: [email protected], [email protected] Inthisletterwepresentanovelstudyaboutthecombinationoffourlaserwavelengthsinorderto maximize both color gamut and efficacy to producethecolor white. Firstly, an analytic method to calculateefficacyasfunctionofbothfourlaserwavelengthsandfourlaserpowersisderived. Secondly we provide a new way to present theresults by providing the diagram efficacy vs color gamut area that summarizes the performance of any wavelength combination for projection purposes. The 3 results indicate that the maximal efficacy for the D65 white is only achievable by using a suitable 1 0 combination of both laser power ratios and wavelengths. 2 PACSnumbers: n a J Mobile projection devices (usually known as picopro- dard Colorimetric Observer “whenever correlation with 8 jectors) should be designed to maximize their luminous visualcolormatchingoffieldsofangularsubtensegreater 1 ◦ efficacy. This is for two main reasons. Firstly, being ei- than about 4 at the eye of the observer is desired”. It ther stand alone devices or embedded in other products, hasalsobeennotedintheliteraturethatintheoptimiza- ] s they are likely to be powered by battery, and lifetime tion of the efficacy of a 3-wavelengthprojectorthere is a c an important factor [1]. Secondly, the increasing use of trade-offwiththecolorgamut[2]. Forthisreason,inthis i pt lasers to project images calls for a consideration of eye study we comparethe efficacy withthe colorgamutarea o safety issues [2]. The brightness of the projected im- aspresentedontheCIE1976UCS(uniformchromaticity . age may be limited by the Class II accessible emission scale) diagram. s c limit. There is reasonto believe that current laser beam The tristimulus values (X, Y and Z) are determined i s scanning picoprojectortechnologyis alreadyclose to the from the color matching functions, x(λ), y(λ), and z(λ), y powerceilingbasedoneyesafetylimits[3]. Consequently, ofa givenilluminantspectralpowerdistributionP(λ) as h it would be desirable to improve luminous efficacy to in- follows: p [ crease the output luminous flux for the same eye-safe ∞ 1 optical power limit. Gn =Z0 P(λ)gn(λ)dλ, (1) The relationship between the choice of laser wave- v 9 lengths and the resulting luminous efficacy has been dis- where Gn and gn(λ) represent the sequences (X,Y,Z) 1 cussedintheliterature[4–6]. Herewepresenttheoppor- and(x(λ),y(λ),z(λ))respectively. Forthecaseofathree 3 tunity to increase luminous efficacy by adding a fourth wavelength combination if we define a matrix M as 4 laserwavelength. Usually,thethreeprimarywavelengths . 1 ofalaserdisplayofferawidecolorgamutandsotheem- x(λr) x(λg) x(λb) 0 phasis in this study has been to maximize the safe lumi- M=y(λr) y(λg) y(λb) , (2) 3 1 nous flux whilst maintaining the gamut, rather than in- z(λr) z(λg) z(λb)  creasingthegamut. Utilizationofadditionalwavelengths : v the powerofred, greenandblue laserscanbe calculated orcolorsindisplay andilluminationapplicationsis how- i by X evernotnew. Reasonsforaddingoneormoreadditional r colorshavetraditionallybeenforimprovedgamutand/or P (λ)=M−1W, (3) a improved brightness and have usually applied to liquid rgb crystal display applications. Brown et al. [7] have dis- wherethevectorWcontainsthex, y andz chromaticity cussedaddingawhitepixeltothered,greenandbluepix- coordinates of white D65 point, and λ the wavelengths els ofan LCD display to increase the brightness ofa dis- λ , λ , and λ . In the framework of the CIE 1964 10◦ r g b play. Sharp has recently launched a four-color television color-matching functions, the coordinates x, y and z are with claims of increased brightness and color gamut [8]. 0.31382, 0.331 and 0.35518 respectively. P describes rgb Here we present a study of the choices of four laser theuniquesolutionofthecombinationofrelativepowers wavelengthstooptimizeluminousefficacyfortheprojec- of the red, green and blue wavelengths to produce D65 tionoftheCIEstandardilluminantD65(daylightwhite). white. Forafour-wavelengthcombinationthereisnosin- Sincethisisadisplayapplication,thebasisforcolormix- glesolution. Thecombinationoffourcolorsisdependent ◦ ingcalculationsisthesetof1964,10 CIEcolormatching on the relative power of the fourth wavelength. As will functions [9]. The CIE recommends the use of the color- be demonstrated this fourth wavelength is consistently matchingfunctionsoftheCIE1964SupplementaryStan- found to be in the yellow region and so is represented 2 as λ . To calculate the four color combination we first y define a new vector W˜ : 4x ′ u = (10) 3+12y−2x x −P x(λ ) w y y W˜ =y −P y(λ )  (4) w y y 9y ′ z −P z(λ ) v = (11)  w y y  3+12y−2x Expression 3 can be now rewritten in terms of W˜ for the case of a four wavelength combination as follows: P (λ,λ ,P )=M−1W˜ (5) rgb y y In the former expression, P depends on P and λ as rgb y y well. If we redefine λ as the four-dimensionalvector [λ , r λ , λ , λ ], the powervectorcontainingthe contribution g b y of all laser sources might be written as follows: P= P (λ,P ), P (λ,P ), P (λ,P ), P (6) r y g y b y y (cid:2) (cid:3) Since the combination of colors is in terms of relative powerswearbitrarilychoosetodefinethepowersofeach wavelength with respect to the blue wavelength. Hence, wedefine a new powervectorP˜ asP/P . Thus, ifvalues b for the components red, green, blue and yellow of the vector λ and the ratio P /P are selected, expression 5 y b FIG. 1: Left part: CIE 1931 chart. Right part: CIE 1976 provides a unique result for the ratios P /P and P /P . r b g b chart. In both graphs, achievable color gamuts by the DCI The total power normalized by P is b andHDTVinputsignals havebeenplotted. Dashedlinecor- responds to the optimal solution found here using the laser P P P P˜ = r + g +1+ y (7) wavelengths 630 nm,520 nm, 441 nm and 563 nm t P P P b b b The color gamut area can be considered as a tri- In the same way, using the values Pr/Pb, Pg/Pb and angle formed by the coordinates (u′,v′), (u′,v′) and Py/Pb, a normalized flux L˜t can be obtained. So, the (u′,v′) of the red, green and blue lasrersr respegctigvely if b b efficacy is λ ≥ 520 nm. As fig. 1 shows, the yellow coordinates g are in this case almost on the line formed by the green L˜ L E = t = t (8) andredcoordinatesandthereforethecontributionofthe ff P˜t Pt yellowlasertothe formationofa morecomplexareacan be neglected for more simplicity. Thus, under this ap- Thismethodallowsustocalculatethe efficacybychoos- proximation the color gamut area (A) is: ing the relative power of the yellow source with respect to the blue source. 1 A= [u′(v′ −v′)+u′(v′ −v′)+u′(v′ −v′)] (12) Since the CIE 1976 chromaticity diagram is known to 2 b r g g b r r g b be perceptively relatively linear [10] it is appropriate to In order to obtain solutions that could be of practi- quantify the extent of the color gamut as the enclosed cal interest and that can be compared with current dis- area as represented on this plot [5]. In doing so any play devices, we have selected wavelength ranges that trade-off between efficacy and gamut can be evaluated. try to cover the most important signal inputs, i.e. DCI To do this, we firstly have to calculate the x, y and z and HDTV signal inputs plotted in fig. 1 [11, 12]. In coordinatesforeachlaserwavelength. Thesecoordinates this way, a laser projector could display the color spec- can be obtained from the following expression: trum managed by these inputs. The selected wave- g = Gn , (9) length ranges are as follows: 600 nm ≤ λr ≤ 630 nm, n 3n=1Gn 520 nm ≤ λg ≤ 550 nm, 440 nm ≤ λb ≤ 470 nm and P 560 nm≤λy ≤590 nm. where g representone element of the sequence (x,y,z). Fig. 2 contains the positive solutions of over 21 mil- n ′ ′ From this set of coordinates, the u and v of the CIE lion calculations of equation (5) at the above specified 1976 chart are obtained as follows: wavelength ranges and several power ratios P /P . The y b 3 has to be understood to be the maximum efficacy with which the color white (D65 point) can be projected by any combination of illumination sources. The shape of the areas shown in fig. 2 depends on the wavelengthranges used. In fact, if we decrease the color gamut area by using other wavelength ranges closer to ′ ′ theD65whitepointintheu,v space,theefficacywould increaseuptothemaximumvalueof∼455lm/W butat the cost of the color gamut area limiting the capability for obtaining different colors. In conclusion,we havederiveda formulationthat per- mits to calculate the best combination of four wavelengths and powersfor laser projectionmaximizing both color gamut area and efficacy of the D65 white point. Theresultsshowthatthe maximalefficacyprojectedus- FIG. 2: Efficacy of the white point D65 as function of the ing the most common video input signals can be only colorgamut areafordifferentratiosoftheyellowlaser power achieved by adding a fourth laser wavelength. Combi- to the blue laser power. The big isolated circle denotes the nation of three laser wavelengths would produce less ef- commercial projector described in thetext. ficacy at suitable color gamuts for projection. The best selection of wavelengthsand powers in this frameworkis found at the wavelengths 630 nm, 520 nm, 441 nm and efficacy-gamut trade-off of a three color mix is clear. As 563nmforthe red,green,blue andyellowlasersandthe the power of the fourth wavelength is increased the effi- power ratio P /P = 1.8 that would produce an efficacy cacyofthe white point D65increasesatthe wavelengths y b of 449.7 lm/W when forming a D65 white. These con- studied. If we choose a figure of merit of the prod- clusions and results represent a guideline for the future uct of efficacy and color gamut area, the most optimum value occurs at P /P = 1.8, P /P = 9 × 10−3 and development of picoprojectors and cinema projectors in y b r b P /P =7×10−3 and at the wavelengths 630 nm of the which particular emphasis is placed on the use of high g b laserpowertoincreaseluminousfluxanditsimplications red laser, 520 nm of the green laser, 441 nm of the blue in safety regulations. laser and 563 nm of the yellow laser which produce an efficacy of 449.7 lm/W. Since the power needed for the formation of D65 white with the red and green laser is negligible,thecalculationresultsindicatethatthischoice forbothoptimumefficacyandcolorgamutareaismainly [1] K. V. Chellappan, E. Erden, and H. Urey, “Laser-based obtained with the contributions of the blue and yellow displays: a review” Appl.Opt.49, F79 (2010) ′ ′ laser. In the u, v space this means that the chromatic- [2] I.Wallhead,R.OcanãandP.Quinza´,“Designingalaser ity coordinate of the D65 white point is on the straight scanning projector. Part 2: laser safety related issues”, lineformedbythebluelaserandyellowlasercoordinates. Appl. Opt.Vol. 51, 5619 (2012) Note that the red and green wavelengths can be consid- [3] E. Buckley, “Eye-safety analysis of current laser-based scanned-beamprojectionsystems,”J.Soc.Inf.Disp.,18, eredinthedevelopedmethodasfreevariablesaswelland 944 (2010). therefore are obtained as the best optimum wavelengths [4] I.Wallhead,R.OcanãandP.Quinza´,“Designingalaser which together with the blue wavelength maximize the scanningpicoprojector. Part1: characteristicsoftheop- color gamut area in expression 12. ticaldisplayingsystemandcolor-management-relatedis- By comparison, a commercially available three-color sues”, Appl.Opt. Vol.51, 4803 (2012) picoprojector (Microvision Show WX [13]) with wave- [5] E. Buckley,“Laser wavelength choices for pico-projector applications”, J. Disp. Technol. 7, pp.402, (2011). lengths of 442 nm, 532 nm and 642 nm has an efficacy [6] Optimal colors for a laser pico-beamer, Willem Hoving, of 254 lm/W. The performance of this device has been USPatentApplicationPublication,US2009/0003390A1, plotted in fig. 2 by means of the coordinates of the effi- Jan 1, 2009. cacyandcolorgamutarea. An additionofa yellowlaser [7] C.H. Brown Elliott, T.L. Credelle, and M.F. Higgins, at 564 nm (Py =1.76Pb) would increase the efficacy by “Addinga white subpixel,”J. Soc. Inf. Disp.26, (2005). 77% to 451 lm/W. [8] http://www.aquos-world.com/usen/product/4_color_innovation.htm [9] Publication CIE No. 15.2 (1986), Colorimetry, Second Oneadditionalpointisworthmentioning. Fig.2shows edition,Commission Internationaledel’Eclairage (CIE), that there is a very distinct upper limit to the efficacy CentralBureauoftheCIE,Vienna,Austria.ISBN3900 of any color mix. This occurs at ∼ 455 lm/W. Insofar 734 00 3 as the photopic curve presents the maximum efficacy for [10] Colorimetry: Understanding the CIE System, Jnos a single wavelength (683 lm/W at 555 nm), 455 lm/W Schanda(Editor), Wiley, 2007 4 [11] http://www.itu.int/rec/R-REC-BT.709-5-200204-I/e [13] http://www.microvision.com/showwx/pdfs/showwx_userguide.pdf [12] SMPTE ST 431-1:2006 D-Cinema Quality - Screen Lu- minance Level, Chromaticity and Uniformity.