Floating volumetric image formation using adihedral corner reflector array deviceDaisuke Miyazaki,*Noboru Hirano,13 Yuki Maeda,Siori Yamamoto,Takaaki Mukai,'and Satoshi Maekawa?'Graduate School of Engineering,Osaka City University,3-3-139 Sugimoto,Sumiyoshi-ku,Osaka 558-8585,Japan2National Institute of Information and Communications Technology,2-2-2 Hikaridai,Seika-cho,Soraku-gun,Kyoto 619-0289,JapanBRicoh Company,Ltd.810,Simo-imaizumi,Ebina-shi,Kanagawa 243-0460,Japan*Corresponding author:miyazaki@elec.eng.osaka-cu.ac.jpReceived 20 August 2012;revised 14 October 2012;accepted 14 October 2012;posted 15 October 2012(Doc.ID 174608);published 28 November 2012A volumetric display system using an optical imaging device consisting of numerous dihedral comerreflectors placed perpendicular to the surface of a metal plate is proposed.Image formation by thedihedral corner reflector array (DCRA)is free from distortion and focal length.In the proposedvolumetric display system,a two-dimensional real image is moved by a mirror scanner to scan a three-dimensional(3D)space.Cross-sectional images of a 3D object are displayed in accordance with the posi-tion of the image plane.A volumetric image is observed as a stack of the cross-sectional images.The use ofthe DCRA brings compact system configuration and volumetric real image generation with very low distortion.An experimental volumetric display system including a DCRA,a galvanometer mirror,and adigital micro-mirror device was constructed to verifythe proposed method.A volumetric image consisting0 CIS code8:230.3990,120.2040,100.6890.1.IntroductionA volumetric display is one of promising true 3DThree-dimensional (3D)display is a promising tech-display technologies [1-5].A volumetric display sys-nology for a next-generation visual interface,whichtem arranges light spots in a volume to form a 3Dprovides intuitive understanding of a 3D image.3Dimage by scanning the 3D space with a light spotdisplay systems based on binocular parallax usingor a two-dimensional(2D)image.We have proposedspecial glasses or lenticular sheets are commerciallythe principle of a volumetric display,in which anavailable.These displays,however,do not satisfyinclined optical real image is moved in lateral direc-all physiological factors for stereoscopic vision,suchtions perpendicular to an optical axis using a mirroras accommodation and binocular convergencescanner [6-11].In the previous papers,we reportedAlthough holography is one of the true 3D displayvolumetric display systems using concave mirrors fortechniques that can satisfy all the criteria foroptical real image formation [10].One of the pro-stereoscopic vision,the realization of a practicalblems of the experimental volumetric display sys-holographic display is difficult even by using state-tems was the distortion of a 3D image caused byof-the-art technologies.optical aberrations.Another problem is bulkinessof the optical systems.Recently,a dihedral comer reflector array(DCRA),which is an array of micro mirrors,has been devel-1559-128X/13/01A281-09815.00/0oped as a novel optical imaging element [12-15].This2013 Optical Society of Americadevice forms a real image of an object placed at the1 January 2013/Vol.52,No.1 APPLIED OPTICSA281opposite side of the device by converging optical rayspassing through a mirror hole is directed to the retro-reflected by the micro mirrors.The imaging positiondirection for the directional components parallel tois plane symmetric with respect to the device surface.the device surface,based on the principle of a cornerRemarkable features of this device compared withreflector as shown in Fig.1(a).The directional com-conventional optical elements such as lenses andponent perpendicular to the device surface does notconcave mirrors are that it has no focal length andchange by the device as shown in Fig.1(b).Conse-that it is theoretically free from distortion.Thesequently,a light ray reflecting twice in a mirror holefeatures are useful to achieve compact systemtravels the plane-symmetric path for the incidentconfiguration and low-distortion imaging for alight path with respect to the device surface.volumetric display.When multiple light rays diverging from a point lightIn this paper,we propose a volumetric display sys-source pass through a DCRA with double reflection,tem based on a real image formation using a DCRA.every ray converges onto a point,which is located atA 2D image formed by a DCRA is moved at highplane-symmetric position for the point light sourcespeed by a mirror scanner to generate a volumetricwith respect to the device surface as shown inimage.We constructed a volumetric display systemFig.1(c).This relation is held for every point lightusing a DCRA,a digital micro-mirror device (DMD)source at each arbitrary position of an object.Thus,and a galvanometric mirror scanner to verify oura DCRA can form a 3D real image that is plane-proposed method.symmetric for the object with respect to the devicesurface.2.Imaging Device Based on Dihedral Corner ReflectorAn optical imaging element based on a DCRA hasArrayseveral features that are different from ordinaryA DCRA is a transmissive micro-mirror device for op-imaging elements,such as a lens and a concave mir-tical imaging [12-15].A DCRA can be fabricated byror.An optical imaging system including a DCRAdoes not have focal length or optical axis.Thus,specular walls,on a metal plate as shown in Fig.1.the imaging position is free from a focal point,andTwo adjacent internal walls of each hole constitute athe magnification is unity regardless of the imagingminute dihedral corner reflector.Incident light into aposition.A DCRA does not have curved surfaces ormirror hole is reflected by the internal adjacent wallsrefractive surfaces,so theoretically,it does nottwo times and passes through the device.A light rayoptical distortion.Point light sourceReal image ofand its real imagePoint light sourcethe light source■Dihedral comer reflector array(b)Real image ofthe light sourceDihedral corner reflector arrayFig.1.(Color online)Schematic diagram of light rays passing through a DCRA:(a)top view,(b)side view,and (c)angular view.A282APPLIED OPTICS/Vol.52,No.1 /1 January 2013A high-precision fabrication for flat and specularwalls in every mirror hole is required to achieve finemirror holeimaging by a DCRA device.We fabricated a mastermold consisting of an array of micropillars from acopper baseplate by the nano-precision-machiningtechnique.The surface roughness of each sidewallof the pillars was less than 10 nm.A negative copyof the master mold was fabricated by nickel electro-forming,and the copper master mold was dissolved.The DCRA was fabricated within a circle area oftop view180 mm diameter on a nickel plate of 150 um thick-ness.Each side of the square aperture of each holewas 150 jm and the interval between adjacent holeswas210μm.An observation angle is restricted by the light in-cident angle that enables the light to be reflectedtwice by adjacent mirrors in each mirror hole.Theoptimum incident elevation angle 00 from the devicesurface,which enables maximum light transmissionside viewas shown in Fig.2,is obtained byFig.3.Schematic diagram of incident light with minimum inci-dent angle for double reflection in a mirror hole on a DCRA.Inci-ddent light with an angle less than cannot reflect twice on theadjacent walls in a mirror hole.The minimum incident elevation angle 0min accepta-directions.Light transmissivity for double reflectionble for light transmission with double reflection isin mirror holes decreases as the light path deviatesshown in Fig.3 and calculated byfrom the optimum angle.The change of light trans-missivity for any angle is simulated in Maekawa et al.d(2)[12].The optimum incident elevation angle 0p35 deg and the minimum incident elevation angle0min =19 deg for the DCRA fabricated for thisThe maximum incident elevation angle 0max,isresearch.90 deg.Acceptable incident angle in the directionImaging resolution of a DCRA is mainly deter-parallel to the DCRA surface is 45 deg from themined by the aperture size of the mirror holes andbisector of a dihedral corner reflector for boththe fabrication accuracy of micro mirrors.On the ba-sis of geometrical optics,the image of a point lightsource formed with a DCRA is a light spot that ismirror holedouble the size of a mirror hole aperture regardlessof the imaging distance.For this reason,the sizereduction of mirror holes is preferable to obtain ahigh-imaging resolution.The diffraction effect atthe aperture of each mirror hole,however,decreasesimaging resolution as the size of the mirror is re-duced and as the distance of the image from the de-vice is increased.Therefore,optimization of the sizetop viewof the mirror holes should be investigated by consid-ering both the geometric and diffraction effect.light spreadside viewFig.2.Schematic diagram of incident light with optimum inci-dent angle Bop to maximize the quantity of light passing througha mirror hole on a DCRA.1 January 2013/Vol.52,No.1 APPLIED OPTICSA283