Invited PaperTransmissive Optical Imaging Device with Micromirror ArraySatoshi Maekawa,Kouichi Nitta and Osamu Matoba"National Institute of Information and Communications Technology,3-5 Hikaridai,Seika-cho,Soraku-gun,Kyoto,Japan;Kobe University,1-1 Rokkodai-cho,Nada-ku,Kobe,JapanABSTRACTWe propose a new imaging optics called the Transmissive Mirror Device (TMD).It consists of numerous micro-mirrors placed perpendicular to the surface of a fat,thin metal plate.The micro-mirror array is implementedby the inner walls of minute square holes,which are densely pitted on the device.The basic mode of operationis based on two reflections by a pair of adjacent mutually perpendicular mirrors,i.e.,a dihedral corner reflector.Although the principal of operation is based on reflection by mirrors,the device is also transmissive and deflectslight.Since this imaging system forms a real image at a plane symmetric point,the depth of the 3D image isinverted.Its optical defects are low optical transmittance and stray light caused by non-reflected light and thatreflected once.We manufactured the device experimentally with nano-precision machining technology and alsoevaluated it.Keywords:transmissive mirror device,dihedral corner reflector array,mirror image,real image,reflectionsymmetry1.INTRODUCTIONThere are some basic imaging optics that can form a real image,such as a convex lens,a concave mirror,anddiffraction optics (a Fresnel lens).Although the convex and Fresnel lenses involve transmissive refractive optics,and the concave mirror involves reflective optics,these optics form images based on the same optical principles.These have an optical axis and a specific focal length.Moving an object closer to the optics,the real imageforms farther from it and is magnified.In contrast,imaging optics can form 3D-images without distortion.Anexample of this is a plane mirror.Because the images are formed at a plane-symmetric position,they are mirrorimages and have unit magnification and are free from distortion.Moreover,their structure is homogeneous andthere is no optical axis or specific focal length.However,as a plane mirror can only form virtual images,theworld in the mirror is treated as a fantasy.!There are already imaging optics forming erect real images with unitmagnification when images are limited to 2D.For example,there are systems that are based on the lens arrayof the Graded Index Lens (GRIN),2 Roof Mirror Lens Array (RMLA),3 and the stacking of various micro-lensarrays.4.5 These have been applied to the facsimiles and copiers that are widely used today.The basic optics responsible for imaging,such as that of the convex lens,concave mirror,and plane mirror,has been understood since the pre-Christian era.The convex lens and the concave mirror are a pair of imagingoptics,which are based on the same optical principles but have a different light path,refraction,or reflection.However,no pair of imaging optics has so far existed for the plane mirror,which forms a real mirror image.Thatis,if there were an imaging optics forming a real mirror image,it could fill in the lost pieces from basic imagingoptics missing since the time of the ancients.The authors of this paper propose a new imaging optics forming a real mirror image with the use of micro-mirrors.We called this imaging optics a Transmissive Mirror Device (TMD).Section 2 of this paper presents itsstructure and some of its operation modes.Section 3 discusses its characteristics,such as transmittance,straylight,and image quality,as well as providing some applications.Further author information:(Send correspondence to S.M.)K.N.:E-mail:nitta@kobe-u.ac.jp,Telephone:+81 (0)78 803 6236O.M.:E-mail:matobaakobe-u.ac.jp,Telephone:+81 (0)78 803 6235Three-Dimensional TV,Video,and Display V,edited by Bahram Javidi,Fumio Okano,Jung-Young SonPoc.ofSP1EVol.6392.63920E,(2006)·0277-786X/06/s15·doi:10.1117/12.690574Proc.of SPIE Vol.6392 63920E-1Downloaded From:http://proceedings.spiedigitallibrary.org/on 09/19/2015 Terms of Use:http://spiedigitallibrary .org/ss/Terms OfUse.aspxMicromirrors(dihedral corner reflector)Figure 1.Overview of TMD structure.Small dihedral corner reflectors that consist of two perpendicular micro-mirrorsare aligned densely on a metal plate.Each micromirror is also perpendicular to the device surface.Dihedral cornerreflectors can be produced from the internal walls of the square through holes.2.FUNDAMENTAL CONCEPTSThe structure of the proposed imaging optics,TMD,is shown in Figure 1.It consists of many micro dihedralcorner reflectors.Each one has two perpendicular micro-mirrors,which are also perpendicular to the device'ssurface.A simple approach to fabrication is to produce micro square holes whose internal walls are specular.After this,these holes will be called mirror holes.The mirror holes are punctured through the device,and lightpasses through each after being reflected by its internal specular walls.As the mirror holes are very small,thelight is divided into many thin rays after passing through the TMD.The TMD's resolusion is determined by thegranularity of the division.Resolution can be improved by finely dividing according to the geometrical optics,but fine division will actually deteriorate resolution because of diffraction.Many optical devices using micro-mirrors have been proposed,such as DMD6 and GLV,7 which have beenmanufactured with MEMS technology.Although these are active control devices,the TMD is passive.Inaddition,the function of DMD and GLV is switching,but TMD's function is imaging.As the arrangement ofthe micro-mirrors in DMD and GLV is parallel to the device surfaces in manufacturing,polishing the mirrorsis easy.However,since TMD's micro-mirrors must be exactly perpendicular to the device surface,polishing isimpossible and more advanced manufacturing technology is needed.2.1.Operation ModeSince the TMD is a transmissive imaging optics,the light rays transmit to the other side of the device via mirrorholes.There are some operation modes that have a different number of reflections in a mirror hole.These aredirect,i.e.,non-reflection,single-reflection,double-reflection,and multi-reflection modes,in which the light raysare reflected more than three times.Operation as a dihedral corner reflector corresponds to the double-reflectionmode.To form a mirror real image,operation with the other modes creates stray light,so these modes must besuppressed.The image in the direct mode is the same as that through the grid.Although the multi-reflectionmode is too complex to analyze within the space limitations of this paper,it can be suppressed by variouscountermeasures.Proc.of SPIE Vol.6392 63920E-2Downloaded From:http://proceedings.spiedigitallibrary.org/on 09/19/2015 Terms of Use:http://spiedigitallibrary.org/ss/TermsOfUse.aspxLine BLine AFigure 2.Schematic of single-reflection mode.S is a point light source.The light reflected by the micro-mirrors in lineA converges to point A as a virtual image.The light reflected by the micro-mirrors in line B converges to point B as areal image.2.1.1.Single-reflection modeThis section discusses the single-reflection mode.The light rays in this mode are reflected once when passingthrough a mirror hole.Figure 2 explains operation with the single-reflection mode.We will discuss the two mirror groups in LinesA and B separately when this operation mode is analyzed.Only mirrors that face the right,which are left-sidemirrors in the mirror holes,are considered here.The mirrors in Line A can be considered as one long dividedmirror,and the light from point light source S forms virtual image A,which is a mirror image of S.The mirrorsin Line B have a common perpendicular,and the light rays reflected by the micro-mirrors travel along theaxisymmetiric paths about the perpendicular.Therefore,all the reflected light rays pass through common pointB,which is the axisymmetric point of S.As a result,if observed from the point on the extension of line segmentAB,extraordinarily,both points,i.e.,virtual image A and real image B,can be observed simultaneously.Ofthe bundles of rays that enter the pupil,rays that line up vertically create real image B,and rays that line uphorizontally create virtual image A.The movement of the viewpoint is considered next.When moving the viewpoint parallel to Line A(B),thelight passing through point A(B)can be observed continuously.Therefore,the image of point light source S isobserved as localized at point A(B).Therefore,the different direction of movement of the viewpoint changes theimage position,above or behind the device.In relation to binocular disparity instead of the movement of theviewpoint,if both eyes are placed along Line A(B),image A(B)can be observed.In addition,because the images obtained by adjacent line mirror groups are focused on a slightly slippedposition,aberration occurs and the image is blurred even if it is from a point light source.2.1.2.Double-reflection modeThe double-reflection mode is discussed in this section,in which the light rays are reflected twice when passingthrough a mirror hole.In this case,reflection by two adjacent micro-mirrors is considered,which constitute aProc.of SPIE Vol.6392 63920E-3Downloaded From:http://proceedings.spiedigitallibrary.org/on 09/19/2015 Terms of Use:http://spiedigitallibrary .org/ss/Terms OfUse.aspx