Abstract:
Provided herein is a method for fabricating an array. A plurality of insulating media are formed having a plurality of wavelength and polarizing elements embedded therein at an angle relative to the surfaces of the media, such that the spacing between elements halves for each different medium. A phase shifter arrangement is also formed such that a portion of conductive material is disposed on a surface of the insulating media in registry with every other element in each of the media, and other portion of conductive material disposed on another surface overlapping said elements. A phase shifting material is disposed over at least said every other element. The media are stacked such that the topmost insulating medium has two elements, and each succeeding medium has twice as many elements as a preceding medium.

Description:
RELATED APPLICATIONS 
   This application is a Divisional of U.S. patent application Ser. No. 08/784,440 entitled Flat Panel Display and Method of Manufacture filed Jan. 16, 1997, now issued U.S. Pat. No. 6,680,758. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates generally to display devices for beam steering and scanning and, more particularly, to flat panel display devices for beam steering and scanning which are electronic in character and which further incorporate logic trees which are designed to steer electromagnetic energy so that both transmission losses and the number of energizing sources of an imaging array are minimized. The devices include a multi-stage imaging array made up of a plurality of stacked logic trees so arranged that each stage of each logic tree includes active steering elements which access twice as many like steering elements and associated passive steering elements in each succeeding stage. The active and passive elements incorporate cholesteric liquid crystal (CLC) elements which are polarization sensitive disposed within them at an angle of 45°. The active elements include variable half-wave retarders which, under control of a programmable pulsed source change the polarization of incident energy on CLC elements and provide a scanned line of electromagnetic energy to the imaging cells disposed at the output of each logic tree. In such an arrangement, array transmission losses are minimized and one source of electromagnetic energy per logic tree is required. 
   In another arrangement using a similar imaging array, transmission losses are reduced over prior art input arrangements and the number of sources of electromagnetic energy is reduced to one. Using an input logic tree, fed from a single laser and arranged perpendicularly to the array logic trees, the imaging cells of the input logic tree act as inputs to the stacked logic trees of the imaging array. In this way, a scanned line is delivered from each imaging cell of the input logic tree to the first active element of an associated array logic tree. From there, under control of a programmable pulsed generator, portions of the scanned line are directed to the output imaging cells of each of the array logic trees. Two-dimensional images are built up in this way by activating the imaging cells of each array logic tree in succession. Three dimensional images may be obtained using an approach similar to that just described by interleaving stereo displaced images from a 3-D camera at the output imaging cells of an imaging array by activating the first and every other logic tree of an array with one image and the second and every other logic tree with a stereo displaced image. Glasses which respond to a different polarization for each eye are required to produce the 3-D effect. 
   The present invention also relates to a method of fabricating the above described imaging arrays by slicing stacked alternating layers of insulating material and CLC material. To the extent that a final imaging array requires that each logic tree have twice as many CLC elements per stage as a preceding stage after the first stage, the number of CLC element per stage may doubled by halving the spacing between CLC elements during fabrication. This is accomplished by halving the thickness of the insulation disposed between layers of CLC material after setting the initial spacing between CLC layers which are to be used as the first stage of a logic tree. After producing layers of a given thickness by slicing at a 45° angle, transparent metallic ground planes are formed. Then, using photolithographic and etching techniques, electrodes are formed over every other CLC element. A spacer element is then fixed to the periphery of each layer and the resulting volume is filled with a phase shifter material. The resulting stages are then stacked using as many as required to form an imaging array with a desired number of imaging cells. Stacking the stages, which are slices containing differently spaced CLC elements automatically provides the logic trees which deliver scanned line to the output imaging cells. The method uses mass-production techniques and results in an inexpensive, flat-panel display. 
   2. Description of the Prior Art 
   Generally, there are two well-known techniques for the steering and scanning of light beams. One is electromechanical and the other is acousto-optical. Both techniques have severe limitations. One such limitation is that arrangements incorporating these techniques require a large volume due to the small angel through which the light beam can be deflected. Thus, if it is desired to scan a length B, the deflection arrangement has to be positioned a distance, A, providing an A/B ration larger than 1. 
   All known systems require an A/B ratio larger than 1 and to the extent that the arrangement of the present application can provide A/B ratios which are very much less than 1, the resulting structure may also be characterized as a flat-panel display. In the known scanning approaches, scanning speed is relatively sluggish due to the use of electromechanical or electro-acoustic elements. Because such devices are eliminated in the scanning arrangement of the present application, scanning speeds in the microsecond range are achievable. 
   U.S. Pat. No. 4,670,744 filed Mar. 14, 1985 and issued Jun. 2, 1987 in the name of T. Buzak incorporates variable optical retarders and liquid crystal chiral cells. This reference takes advantage of the reflective and transmissive characteristics of chiral cells as well as the ability of variable optical retarders to convert one circular polarization to the other circular polarization. However, when a beam containing image information is projected along a given path in which the chiral cells and retarders are disposed, the beam remains in that given path or is retroreflected along the same path. Opposed to this, the arrangements of the present application while they all incorporate the reflection-transmission characteristics of chiral cells, they all incorporate an ability to divert the reflected beams into other paths. To the extent that the Buzak reference seek to provide a three-dimensional display, all the images reflected must lie in a plane parallel to the planes of the chiral cells. Otherwise distortion and degradation of the reflected images would occur due to the required lateral displacement of the chiral cells. In other words, to provide the desired result, no diversion of the beam in the Buzak reference can be tolerated. 
   U.S. Pat. No. 5,221,982, filed Jul. 5, 1991 and issued on Jun. 22, 1993 to S. M. Faris is entitled Polarizing Wavelength Separator. The patent relates to a polarizing wavelength separating optical element in the form of a flat panel which causes each of a plurality of polychromatic optical beams from a source, entering at one surface and transmitted to another surface, to be converted, with high conversion efficiency, into circularly polarized, spectrally and spatially separated beams. The element is made of a periodic array of cells; each of the latter incorporating a plurality of subcells. One subcell functions as a broadband reflector, while each of the remaining subcells acts as a polarizing, wavelength selective reflector. Each subcell comprises a plurality of layers which are bonded together at their surfaces and are oriented at a 45° angle relative to the horizontal surfaces of the panel. In each subcell, the plurality of layers comprise two cholesteric liquid crystal, CLC films, which reflect at a selected wavelength, at least one optical retarder and clear substrates which provide mechanical support. The thicknesses of the supporting substrates are designed to cause the beams transmitted through the element to be spatially separated by appropriate distances. 
   In the reference, all the elements utilized in the panel are passive in character which constrain beams of electromagnetic energy into paths which are fixed for all time. In contradistinction to this, the present application, with it electronically controllable retarders, provides paths for electromagnetic energy which can be changed from instant-to-instant taking advantage of both the transmissive and reflective capabilities of CLC elements. The combination of a circularly polarized input with controllable retarders and associated CLC elements in the present invention provides the ability to scan a beam from point to point in a panel-like display or to steer a beam it can emanate from any location on an array of imaging cells. Strictly passive arrays with their fixed paths cannot achieve these results. 
   U.S. Pat. No. 5,459,591, filed Mar. 9, 1994 and issued Oct. 17, 1995 to S. M. Faris relates to beam steering and scanning devices which utilize an imaging cell which incorporates a solid-state cholesteric liquid crystal (CLC) element, an electronically controlled, variable half-wave retarder and a source of circularly polarized light. The CLC element is disposed to an angle (45°) relative to the path along which light from the source is projected and is designed to reflect, at a given wavelength, one circular polarization of light and transmit the other. Using this characteristic, light of one polarization or the other is presented to the variable retarder and depending on whether or not it is actuated, light is either diverted into another orthogonal path or remains in the original path. If another similar imaging cell is disposed in the orthogonal path, light incident on that cell can also be diverted into yet another path or transmitted along the orthogonal path under control of a half-wave retarders associated with said another imaging cells. By arranging a plurality of imaging cells in the form of an array and accessing each row of the cells of the array with a column of similar imaging cells and by selectively activating half-wave retarders associated with each of the cells, monochromatic or polychromatic light from a single source or multiple sources may be steered to a selected cell and reflected from its associated CLC element or elements. Utilizing successive cells in the array and causing reflection of a modulated beam or beams provides a frame in the manner of the usual TV set which is viewed by the eyes as an integrated picture. Successive frames, of course, provide the usual moving images. 
   SUMMARY OF THE INVENTION 
   The present invention relates to beam steering and scanning devices which utilize cholesteric liquid crystal (CLC) elements arranged in branches to form a logic tree. Each branch comprises an active and passive CLC element; the former further comprising a half-wave retarder and an electrode and the latter only the CLC element. Each succeeding branch contains twice as many branches as a preceding branch and, by activating active CLC element electrodes under control of a programmable pulsed source, inputs applied to the first stage of a logic tree are delivered as a scanned line of electromagnetic energy or light to the imaging cells of the last stage of the logic tree. By stacking identical logic trees with a laser source for each tree, a flat panel imaging array or display device is formed in which the transmission losses are minimized. 
   Using a similar imaging array, transmission losses may be further reduced by using a logic tree the outputs of which act as inputs to the imaging array where formerly a plurality of lasers were required. By positioning an input logic tree perpendicularly to the similar logic trees of the imaging array, a single source of energy provides an output at each of its imaging cells which acts as an input to an associated logic tree of the imaging array. 2-D and 3-D images are provided by applying modulation to lasers from standard T.V. cameras and cameras designed to provide stereo displaced images respectively. In the array which provides 3-D images, an image and a stereo displaced image are interleaved to provide the desired images each of which has a different circular polarization. 
   The present invention also relates to a method of fabricating structures which provide the above described features. Since all the stages of a logic tree differ only in the number of branches they contain, it was recognized that light beams, for example, applied from a laser beam could pass through a number of stages with minimum dispersion and maintain its original position even though relatively large structures are used to control its position. This recognition permitted the use of CLC elements, electrodes and half-wave retarder material which need not be divided into discrete elements in each logic tree. Thus, each CLC element, each electrode and each retarder material may extend from top-to-bottom or from side-to-side in each stage of an imaging array. 
   Stages are fabricated by slicing layers of insulating material and CLC material at an angle of 45°. The thickness of the insulating material controls the spacing between the resulting CLC elements. Transparent layers, such as indium tin oxide are formed on both sides of the layer or layers containing spaced CLC elements. Using photolithographic techniques, one side is masked and etched to form an electrode over every other CLC element. A spacer element fixed to the periphery of each layer where the electrodes have been etched forms a volume into which half-wave retarder material is introduced in liquid form. In this way, stages containing two, four, eight, sixteen, CLC elements and so on have been massed produced. The stages are then stacked so that each stage contains twice as many CLC elements as a preceding stage forming logic trees the imaging cells of which form an array. 
   The above described arrangements and their fabrication technique provide flat panel displays which substantially reduce transmission losses and the number of energizing sources. These features combined with a novel and inexpensive manufacturing technique are able to deliver a flat panel display which requires neither a vacuum envelope nor unacceptable high voltages. 
   It is, therefore, an object of the present invention to provide an imaging array which has reduced transmission losses compared to prior art arrays. 
   Another object is to provide an imaging array which reduces transmission losses while simultaneously reducing the electromagnetic source requirement to one source. 
   Still another object is to provide an improved flat panel display which is capable of providing both 2-D and 3-D images. 
   Still another object is to provide a method of fabricating flat panel display which is inexpensive and conducive to mass-production techniques. 
   The foregoing objects and features of the present invention will become apparent from the following more detailed description of preferred embodiments taken in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic drawing of a logic tree of active and passive Cholesteric Liquid Crystal (CLC) elements so arranged that a single input to a first stage of the logic tree may be delivered to any one of the outputs of the last stage of the logic tree. 
       FIG. 2  is a schematic diagram of a logic tree similar to that shown in  FIG. 1  which shows that the polarization of CLC members may be varied to produce outputs having polarizations different from those shown in FIG.  1 . 
       FIG. 3  is an orthographic projection of eight logic trees positioned one atop the other which, in accordance with the present invention, provide 64 outputs using one source of electromagnetic radiation per logic tree. 
       FIG. 4  is an orthographic projection similar to  FIG. 3  except that, instead of a plurality of sources of electromagnetic radiation, only a single source of radiation in combination with a logic tree like that shown in FIG.  1  and disposed perpendicularly to the stacked logic trees of  FIG. 3  is required. 
       FIG. 5  is an orthographic projection of an imaging array and its associated electronics which, in conjunction with viewing glasses and stereo displaced images, provides a 3-D display. 
       FIG. 6  is an orthographic, cut-away projection of a plurality of layers of insulating material like SiO 2  and a plurality of layers of CLC material interleaved with the layers of insulating material. The interleaved layers are sliced at an angle of 45°. 
       FIG. 7  is a cross-sectional view of a layer of insulating material in which CLC members are disposed at an angle of 45° and are spaced apart by a distance t. 
       FIG. 8  is a cross-sectional view of a layer of insulating material in which CLC members are disposed at an angle of 45° and is similar to  FIG. 7  except that the CLC members are spaced apart by a distance t/2. 
       FIG. 9  is a cross-sectional view similar to that shown in  FIG. 7  except that the CLC members are spaced apart by a distance t/4. 
       FIG. 10  is a cross-sectional, orthographic projection of an insulation layer with CLC members disposed at an angle of 45° therein like that shown in FIG.  8  and further includes a ground plane disposed on the bottom thereof. 
       FIG. 11  is a cross-sectional orthographic projection similar to  FIG. 10  except that it further includes electrodes disposed over every other CLC member. 
       FIG. 12  is a cross-sectional view similar to that shown in  FIG. 11  further including a spacer disposed around the periphery of the layer of insulation material with the resulting enclosed volume filled with a phase-shifter material in liquid form. 
       FIG. 13  is a top view of a logic tree made up of layers like those shown in  FIGS. 7-12  after they have been stacked and aligned to form an array like those shown in  FIGS. 4 ,  5 . 
   

   DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
   Referring now to  FIG. 1 , there is shown a schematic drawing of a logic tree of active and passive Cholesteric Liquid Crystal (CLC) elements which are so arranged and controlled that a single input to a first stage of the logic tree may be delivered to any one of the outputs of the last stage of the logic tree by appropriately switching electronically controlled half-wave retarders associated with the active CLC elements of the logic tree. By programming the switching of the half-wave retarders of each stage of the logic tree, a laser input to the first stage of the logic tree may, for example, provide a scanned version of the input at the outputs of the last stage of the logic tree. The application of the logic tree as a scanner will be described in detail in what follows. It will also become clear that the same embodiment has other applications. 
   Considering  FIG. 1  in more detail, logic tree  1  is shown consisting of a plurality of stages labeled STAGE  1 -STAGE  4  wherein each stage includes one or more branches each of which consists of an active and passive CLC element. Thus, STAGE  1  consists of a branch  2  which, in turn, includes active CLC element  18  and passive CLC element  19 . STAGE  2  consists of branches  3 ,  4 ; the former including active CLC element  21  and passive CLC element  22  while the latter includes active CLC element  23  and passive CLC element  24 . STAGE  3  consists of four branches  5 - 8  each of the branches consisting of active and passive CLC elements  31 ,  33 ,  35 ,  37  and  32 ,  34 ,  36 ,  38 , respectively. Similarly, STAGE  4  consists of eight branches  9 - 16  each of these branches including active and passive CLC elements  41 ,  43 ,  45 ,  47 ,  49 ,  51 ,  53 ,  55  and  42 ,  44 ,  46 ,  48 ,  50 ,  52 ,  54 , and  56 , respectively, just like the previously mentioned branches. At this point, it should be appreciated that many more stages may be added to tree  1  with each succeeding stages having twice as many branches as the preceding stage. Using this approach, STAGE  4  in  FIG. 1  has 2 n-1  branches wherein n is the stage number. Thus, STAGE  4  has 2 4-1  or eight branches. Since each branch has two CLC elements, each stage has 2 n  elements and, for STAGE  4 , sixteen elements. Thus, STAGE  10 , for example, would have 2 10  or 1024 CLC elements providing one light output per element or 1024 outputs. 
   Since  FIG. 1  is representative of the way logic tree  1  operates regardless of the number of stages, only four stages have been incorporated to clearly demonstrate how such a logic tree may be used to provide a scanned light output from a plurality of elements which are activated by an input from a single source of electromagnetic energy. 
   Before describing the operation of  FIG. 1 , it should be understood that the active CLC elements of each branch in  FIG. 1  do not depart from similar active elements shown in FIG. 1 of U.S. Pat. No. 5,459,591 entitled “Electromagnetic Energy Beam Steering Devices” in the name of S. M. Faris, which is hereby incorporated by reference. The passive CLC elements of the present invention differ from the active CLC elements in that the passive CLC elements do not incorporate an electronically controlled, variable half-wave retarder or π-cell. Thus, each branch of logic tree  1  as represented by branch  2  of  FIG. 1  includes an active CLC element  18  and a passive CLC element  19 . The former includes a cholesteric liquid crystal member  60 , a transparent electrode  62 , a ground plane (not shown), and a controllable half-wave retarder  61  while the latter includes a cholesteric liquid crystal member which is identical to member  60 . Since each of the branches  3 ,  4 ,  5 - 8  and  9 - 16  is identical with branch  2  of  FIG. 1 , each cholesteric liquid crystal element and each half-wave retarder of each branch is identified with the same reference numbers  60 ,  61  respectively. 
   In  FIG. 1 , active CLC element  18  and passive CLC element  19  of branch  2  both include cholesteric liquid crystal members  60  which are disposed at an angle, preferably 45°, within each of the elements  18 ,  19 . Members  60  are made from a nematic liquid crystal material with chiral additives or polysiloxane side-chain polymers which cause the cigar-shaped molecules to be spontaneously aligned in an optically active structure of either a left-handed or right-handed helix with a helical pitch, P. The twisting direction and the pitch, P, of the helices are determined by the nature and concentration of the additives. A CLC member, like member  60 , has all its helices aligned in one direction and is capable of reflecting light, for example, having one circular polarization having a characteristic wavelength or band of wavelengths. Cholesteric Liquid Crystal (CLC) members  60  which are used in the practice of the present invention and their method of fabrication are shown in U.S. Pat. No. 5,221,982, filed Jul. 5, 1991 and issued on Jun. 22, 1993 in the name of S. M. Faris. This patent is herewith incorporated by reference. While CLC members  60  are shown in  FIG. 1  as being single elements, it should be understood that a plurality of CLC members  60  may be substituted for each of the members  60  to provide for the reflection and transmission of circularly polarized radiation having a plurality of wavelengths or band of wavelengths which are provided by a plurality of sources of electromagnetic radiation. It should be appreciated that, in the practice of the present invention, members  60  may be made of any material which can be switched to reflect and/or transmit electromagnetic energy by the application of electric or magnetic fields to that material. 
   Half-wave retarders or π-cells  61  shown schematically in  FIG. 1  are of the type shown and described in U.S. Pat. No. 4,670,744, filed Mar. 14, 1985 and issued on Jun. 2, 1987 in the name of T. S. Buzak and may be utilized in the practice of the present invention. The Buzak patent is herewith incorporated by reference. Alternatively, instead of CLC films, polarizing reflectors, polarizing prisms or McNeill prisms may be utilized in the practice of the present invention and are commercially available. When more than a single wavelength of electromagnetic radiation is used in the arrangement of  FIG. 1 , a broad band π-cell may be utilized to provide half-wave retardation of each wavelength to maintain the same intensity level for each wavelength. 
   Logic tree  1  of  FIG. 1  is activated from a source  17  of electromagnetic radiation which may be a laser or any other source of radiation the output of which may be converted from a linearly polarized orientation to a circularly polarized orientation by means of a quarter-wave plate (not shown) in a manner well known to those skilled in the optical arts. If the resulting output is not appropriately polarized, a half-wave retarder may be utilized to provide the conversion from one circular polarization to the other polarization. 
   For purposes of the present application, radiation emanating from source  17  is circularly polarized in either a clockwise or counter-clockwise direction. Lasers which are commercially available may be utilized to provide outputs which fall within the visible, infrared or ultraviolet spectra. While source  17  is shown as a single source in  FIG. 1 , it should be appreciated that it also represents a plurality of sources each having a different wavelength. Thus, source  17  may include lasers which emit at the red, green and blue wavelengths of the visible spectrum so that the projected beam of radiation is a beam of light having a single color or combinations of these wavelengths. 
   It should also be appreciated that source  17  may comprise lasers or other sources of electromagnetic radiation which are capable of being intensity modulated. In this way, the source output may be varied in intensity from zero to a maximum intensity including all gradations in between. 
   In  FIG. 1 , source of electromagnetic radiation  17  is shown directly irradiating a member  60  of active element  18  of branch  2  from which it is either transmitted or reflected depending on the polarization of the emitted radiation. The emitted radiation from source  17  may have a single intensity or it may be an intensity modulated signal provided by a television camera  25  or the like. By appropriately programming π-cells or half-wave retarders  61 , an unmodulated or intensity modulated signal is delivered in a scanned manner to the active and passive CLC elements  41 - 56  of branches  9 - 16  of STAGE  4 . In this way, an unmodulated or intensity modulated beam of radiation is scanned across elements  41 - 56  providing an output which is similar in every way to a single scan line of a conventional television set. 
   If an input is provided in digital form, a digital-to-analog converter  26  may be interposed between camera  25  and source  17  in a well-known manner. 
   In  FIG. 1 , variable half-wave retarders  61  are activated by a programmable pulsed source  27  which gets timing information from camera  25  via interconnection  28 . A plurality of driver interconnections  29  extend from pulsed source  27  and each interconnection  29  is connected to a separate electrode  62  which applies an electric field to an associated half-wave retarder  61  when activated by pulsed source  27 . In  FIG. 1 , fifteen driver interconnections  29  would be utilized each one of which, when pulsed, activates a separate variable half-wave retarder  61 . 
   In operation, logic tree  1  is activated when source  17  is activated. The object is to provide a scanned output from a single input to a plurality of outputs in STAGE  4  of logic tree  1 . It is, therefore, required that the outputs of active and passive elements  41 ,  43 ,  45 ,  47 ,  49 ,  51 ,  53 ,  55  and  42 ,  44 ,  46 ,  48 ,  50 ,  52 ,  54  and  56 , respectively, be activated so that outputs are obtained from these elements in the order shown in FIG.  1 . Since element  41  is to provide the first output, if the input signal is right-hand circularly polarized (RCP) radiation and all members  60  are designed to be reflective of left-hand circularly polarized (LCP) radiation, the RCP light passes through active elements  18 ,  21 ,  31  and  41  unhindered since these elements reflect LCP radiation and transmit RCP radiation. An RCP radiation output, therefore, appears at the output port of element  41 . 
   In the next time period, half-wave retarder  61  of element  41  is activated by a pulse from pulsed source  27  via an interconnection  29  to electrode  62  causing retarder  61  to introduce a half-wave delay into the input RCP radiation which has passed through active elements  18 ,  21  and  31  causing the RCP radiation to be converted to LCP radiation. The LCP radiation then reflects from member  60  of element  41  which is reflective of LCP radiation toward member  60  of element  42  which is also reflective of LCP radiation. The impinging LCP radiation is then reflected to the output port of element  42 . 
   In the next time period, an output is desired from the output port of active element  43 . To accomplish this, retarders  61  at the inputs of active elements  31  of STAGE  3  and active elements  43  of STAGE  4  are activated by applying pulses to their associated transparent electrodes  62 . 
   Once this is done, the RCP radiation at the input of active element  31  is converted to LCP radiation and reflects from LCP reflective member  60  over to LCP reflective member  60  of passive element  32  where it is reflected toward active element  43 . The LCP input at active element  43  encounters a half-wave retarder  61  and is converted to RCP radiation. The latter then passes unaffected to the output port of active element  43  because its CLC member  60  reflects only LCP radiation. 
   In the next interval, pulsed source  27  deactivates half-wave retarder  61  associated with active element  43  and continues activation of the half-wave retarder  61  associated with active element  31 . In this way, the LCP radiation impinging on element  43  encounters no delay and remains as LCP radiation which is then reflected from LCP reflective member  60  of element  43  toward passive element  44 . The thus reflected LCP radiation is reflected from LCP reflective member  60  of element  44  to its output port. 
   Rather than tediously describing every passage through every element, the order of the activation of half-wave retarders  61  will be described since every path from input to output port can be gleaned from the previous description and drawing shown in FIG.  1 . To obtain an output at active element  45 , only the variable half-wave retarders  61  associated with active elements  21  and  33  must be activated. To obtain an output at active element  46 , variable half-wave retarders  61  associated with active elements  21 ,  33  and  45  must be activated. To obtain an output at active element  47 , the variable half-wave retarders associated with active elements  21  and  47  must be activated. To obtain an output at passive element  48 , only the variable half-wave retarder associated with active element  21  need be activated. An output at active element  49  may be obtained by activating the half-wave retarders associated with active elements  18  and  23 . An output at passive element  50  may be obtained by activating the half-wave retarders associated with active elements  18 ,  23  and  49 . To obtain an output at active element  51 , the half-wave retarders associated with active elements  18 ,  35  and  51  must be activated. An output may be obtained from passive element  52  by activating half-wave retarders  61  associated with active elements  18 ,  23  and  35 . To obtain an output at active element  53 , half-wave retarders  61  associated with active elements  18  and  37  must be activated. An output at passive element  54  may be obtained by activating half-wave retarders  61  associated with active elements  18 ,  37  and  53 . To obtain an output at active element  55 , half-wave retarders  61  associated with active elements  18  and  55  are activated. Finally, active element  56  is activated by activating half-wave retarder  61  associated with active element  18 . 
   Once half-wave retarders  61  are activated by applying pulses to transparent electrodes  62  from programmable pulsed source  27  as described hereinabove, a scanned output varying in intensity at each of the active and passive elements  41  through  56  is obtained. The outputs do not all have the same polarization and, for the embodiment of  FIG. 1 , have a polarization pattern of alternating RCP and LCP as the elements are scanned from left to right. Recognizing that such variation is present is important where outputs having the same circular polarization are desired or required so that fixed half-wave retarders may be placed to convert all the polarization&#39;s to the same polarization. Thus, in  FIG. 1 , for example, fixed half-wave retarders  63  may be placed at the outputs of active elements  41 ,  43 ,  45 ,  47 ,  49 ,  51 ,  53  and  55  to convert their RCP outputs to LCP. The ability to do this conversion is particularly important in arrangements which provide a 3-D output because the perception of 3-D is based on having two spatially displaced images each of which has a different polarization. 
   If the input to active CLC element  18  in  FIG. 1  is changed to LCP and all the CLC members  60  in logic tree  1  are changed to be reflective of RCP, the outputs obtained are exactly the same as those shown in FIG.  1 . 
   An identical output pattern to that shown in  FIG. 1  is obtainable where the input is LCP and all the members  60  are reflective of LCP. 
   A pattern opposite to that shown in  FIG. 1  is obtainable where the input is RCP and all the members  60  are reflective of RCP. 
     FIG. 2  is a schematic diagram of a logic tree  1  similar to that shown in FIG.  1 . It shows only the logic tree without the associated laser and electronics. The purpose is to show that the polarization of members  60  reflective of different polarizations may be varied to produce outputs having different polarizations from those shown in FIG.  1 . Each of the boxes representing active and passive elements in  FIG. 2  contains either the letter L or R indicating that the CLC member  60  therein is reflective of either left-handed or right-handed circular polarization. Without going into exhaustive detail, suffice it to say that the outputs shown in  FIG. 2  are obtained from an LCP input having the following polarization pattern when retarders  61  are switched in the same order as described in connection with FIG.  1 :
 LRRL RLLR RLLR LRRL 
   A pattern different from that shown above would be obtained if the input polarization were changed to RCP and members  60  of logic tree  1  were reflective of polarization&#39;s opposite to those shown in FIG.  2 . The output pattern is as follows:
 
RLLR LRRL LRRL RLLR
 
   The foregoing illustrates how the output polarization may be controlled for applications where information is polarization encoded or scrambled; transmitted and decoded or unscrambled by using a key which controls the variable half-wave retarders  61 . 
   From the point of view of ease of manufacturing, logic trees having the same CLC members  60  are the most advantageous as will be seen when the fabrication process is described hereinbelow. 
   The arrangement of  FIG. 1  provides an advantage over the scanning arrangement shown in U.S. Pat. No. 5,459,591 in that input light has to traverse, in a 1024×1024 array, 1024 CLC members  2  (in the patent) to provide an output at its furthest imaging cell  1  (in the patent). If each CLC member has transmissibility (T), the final imaging cell will have a transmissibility of (T) 1024 . Thus, even with a transmissibility approaching 1, say 0.999, the output at the 1024 TH  imaging cell would be: (0.999) 1024  which, to all intents and purposes, is zero. 
   Opposed to this is the present approach where, to provide the last output in a 1024×1024 array, only twenty CLC members  60  or two per stage need to be traversed providing a transmissibility of (T) 20 . Under these conditions the 1024th output, assuming T=0.999, would be (0.999) 20  which is approximately ninety percent of the input intensity. The minimum transmissibility for a ten stage array would be (T) 10  or one transition per stage. 
   From the foregoing, while logic tree  1  of  FIG. 1  represents an improvement over the prior art in terms of output light intensity, it should be clear that each logic tree  1  requires its own input laser or source of electromagnetic radiation  17 . Thus, to provide an 8×8 array, for example, eight logic trees  1  would have to be stacked in the manner shown in FIG.  3 . 
     FIG. 3  is an orthographic projection of eight logic trees  1  positioned one atop the other which, in accordance with the teaching of the present application, provide 64 outputs. One source of electromagnetic radiation  17  per logic tree  1  is required. 
   Because of space limitations, the showing of  FIG. 3  has been limited to the use of only three of the STAGES of FIG.  1 . Also, since each of logic trees  1  in  FIG. 3  is identical with the other logic trees  1 , only the topmost logic tree  1  with its CLC members  60  and variable half-wave retarders  61  have been shown. Also, as will become clear hereinafter, the dimensions shown are not to scale. 
   In  FIG. 3 , 8×8 array  70  is shown which comprises eight logic trees  1  stacked one atop the other. Each logic tree  1  is comprised of three stages, STAGE  1 , STAGE  2 , and STAGE  3 . STAGE  1  comprises branch  2 ; STAGE  2  comprises branches  3 ,  4  and STAGE  3  comprises branches  5 - 8  as shown in FIG.  1 . Each branch includes active and passive CLC elements similar to those shown in STAGES  1 - 3  of FIG.  1  and each of the active and passive elements includes a cholesteric liquid crystal member  60  which is positioned at an angle of 45° within each of the active and passive elements of array  70 . Also, included are variable half-wave retarders  61  which are arranged in  FIG. 3  just like the variable retarders  61  in STAGES  1 - 3  of FIG.  1 . In  FIG. 3 , each logic tree  1  is activated by an associated source of electromagnetic radiation  17 , preferably a laser, thus requiring a total of eight sources  17 . As each laser is actuated, variable half-wave retarders  61  are actuated as described in connection with  FIG. 1  hereinabove and the output of each laser  17  appears as a scanned modulated signal going from left to right at the outputs of imaging cells  71  of each of logic trees  1 . In the arrangement shown in  FIG. 3 , sources  17  and retarders  61  may be actuated sequentially or simultaneously. If the outputs of sources  17  are converted to right-hand circular polarization (RCP) and all CLC members  60  are reflective of left-hand circular polarization (LCP), the outputs of each logic tree  1  of  FIG. 3  will be the same as those shown in  FIG. 1 , namely:
 
RLRL RLRL
 
   As suggested in connection with the description of  FIG. 1 , fixed half-wave retarders may be appropriately positioned to make all the outputs have the same polarization. 
   While the number of lossy transitions per logic tree has been reduced over that shown in the prior art, this has been accomplished by the use of a source  17  for each logic tree  1  incorporated in an array  70 . With arrangements like that shown in  FIG. 3  expanded to a 1024×1024 array, for example, 1024 sources  17  would be required. This requirement can be eliminated and the number of sources reduced to one by using a logic tree  1  like that shown in  FIG. 1 , the outputs of which, provided from a single source  17 , act as inputs to an array  70  like that shown in FIG.  3 . 
   This will become clear from a consideration of  FIG. 4  which is an orthographic projection similar to  FIG. 3  except that, instead of a plurality of sources  17 , only a single source  17 , in combination with a logic tree  1  like that shown in  FIG. 1 , disposed perpendicularly to the logic trees  1  of  FIG. 3  is required. 
   Considering  FIG. 4  in more detail, array  70  is identical with array  70  shown in FIG.  3 . Also, source of electromagnetic radiation  17  in  FIG. 4  is similar to sources  17  shown in FIB.  3 . In  FIG. 4 , an input logic tree  72  is shown disposed between array  70  and source  17  such that each imaging cell  71  of logic tree  72  acts as an input to an associated logic tree  1  of array  70 . Thus, the uppermost imaging cell  71  of input logic tree  72  provides an input to the leftmost element of the topmost of logic trees  1  of array  70 . This input which may be an intensity modulated signal from source  17 , is scanned across the imaging cells  71  of the topmost logic tree  1  of array  70  in a manner analogous to the scan of a television frame. When the scanned output of the topmost logic tree  1  reaches its last imaging cell  71 , the output of source  17  is switched to the next imaging cell  71  (immediately beneath the topmost imaging cell  71 ) of logic tree  72 . The output of that next imaging cell then acts as the input to the logic tree  1  immediately beneath the topmost logic tree  1  of array  70 . The inputs to the last mentioned logic tree  1  are then delivered to the imaging cells  71  of that logic tree  1  in sequence from left-to-right providing a scanned, intensity modulated signal similar to that of a television scan line. 
   Each of the remaining imaging cells  71  of input logic tree  72  is then actuated by programming electrodes  62  and variable half-wave retarders  61  associated with logic tree  72  in the same manner described hereinabove in connection with FIG.  1 . Similarly, each of the logic trees  1  of array  70  is actuated by outputs from an associated imaging cell  71  of input logic tree  72 . Then, under control of programmed electrodes  62  and half-wave retarders  61 , these outputs, now inputs, to an associated logic tree  1 , are delivered to the imaging cells  71  of each logic tree  1  as a scanned line having portions which may vary in intensity from imaging cell  71 -to-imaging cell  71 . In this way, by accessing logic trees  1  from top-to-bottom, for example, in  FIG. 4 , an image is built up which, depending on the imaging cell density, can provide images of extremely high resolution. 
   From the foregoing, it should be clear that the modulated output of a single source  17 , preferably a laser, may be delivered to the imaging cells  71  of a plurality of stacked logic trees  1  like array  70  in FIG.  4 . As shown in  FIG. 4 , the use of an input logic tree  72  permits the use of a single source  17  as opposed to the multiplicity of sources  17  shown in FIG.  3 . The value of the arrangement shown in  FIG. 4  becomes more apparent when it is recalled that for a 1024×1024 array embodiment like  FIG. 3 , 1024 lasers would be required. Thus, in addition to reducing the number of lossy transitions as provided by the embodiment of  FIG. 3 , the embodiment shown in  FIG. 4  also reduces the number of sources  17  required to the absolute minimum of one. While the electronic equipment required to operate displays like those shown in  FIGS. 3 ,  4 , has not been shown, it should be appreciated that the same components as shown in FIG.  1  and which are well-known in the imaging arts may be utilized in the practice of the present invention. Thus, timing information obtained from camera  25 , for example, is applied via interconnection  28  to programmable pulsed sources  27 . The latter then applies switching signals to both logic tree  72  and each of logic trees  1  to appropriately control their electrodes  62  and half-wave retarders  60  so that a scanned energy output may be delivered from the imaging cells  71  of each logic tree  1  and input logic tree  72 . 
   Referring now to  FIG. 5 , an orthographic projection of an imaging array is shown which, in combination with viewing glasses and stereo displaced images provides a 3-D display. 
   In  FIG. 5 , input logic tree  72  is accessed by a source  17  of electromagnetic radiation which is modulated by outputs of a stereoscopic television camera  73  via interconnection  74 . The two outputs from stereo camera  73  are stereo displaced so that, if they are separated one from the other by some characteristic like polarization, the two resulting images may be delivered one to each eye (using appropriate glasses) and combined in the brain to provide a three-dimensional image. 
   One of the images is provided by applying scanned lines from stereo camera  73  via interconnection  74  to laser  17 . The output of the latter is then applied to input logic tree  72  from which scanned line outputs are delivered from the topmost and alternate imaging cells  71  under control of programmable pulsed source  75  which actuates variable half-wave retarders  61  thereof via interconnections  76 . The output from the topmost of imaging cells  71  of input logic tree  72  is applied for a given interval to leftmost member  60  of the uppermost of logic trees  1 . At the same time, variable half-wave retarders  61  under control of programmable pulsed source  27  are appropriately actuated so that a portion of the scanned line from stereo camera  73  is delivered to each of the imaging cells  71  of the uppermost of logic trees  1  of array  70 . 
   In the instance of  FIG. 5 , each imaging cell  71  of array  70  is illuminated for a time equal to ⅛ the given interval of a scanned line from camera  73 . For a 1024×1024 array, the illuminating time would be {fraction (1/1024)} TH  of the scanned line interval. 
   The first image is completed by applying scanned lines from stereo camera  73  via interconnection  74  which modulate laser  17  during each alternate interval after the first to each alternate imaging cell  71  after the first imaging cell  71  of input logic tree  72 . Each scanned line is delivered to the imaging cells  71  of each alternate logic tree  1  of array  70  in the same manner described in connection with the delivery of the first scanned line to the uppermost of logic trees  1  of array  70 . 
   The stereo displaced image from stereo camera  73  is delivered as scanned lines via interconnection  74  to laser  17  where they modulate the output of laser  17 . The stereo displaced scanned line outputs are delivered to laser  17  during the second and alternate intervals after the second interval. The first stereo displaced output from laser  17 , under control of programmable pulsed source  75  which appropriately actuates the variable half-wave retarders  61  of input logic tree  72 , is delivered to the second-from-the-top of imaging cells  71  of logic tree  72  as a scanned line. This last mentioned output acting as an input to the leftmost CLC member  60  of the second-from-the-top of logic trees  1  of array  70  is delivered to the imaging cells  71  of the second-from-the-top of logic trees  1  of array  70  under control of programmable pulsed source  27  as portions of the scanned line output of laser  17 . 
   As with the first image generation, the imaging cells  71  of the stereo displaced image are illuminated for a time equal to ⅛ the given interval of a scanned line. 
   The stereo displaced image is completed by applying scanned lines from stereo camera  73  via interconnection  74  to laser  17  during each alternate interval after the second interval to each alternate imaging cell  71  after the second imaging cell  71  of input logic tree  72 . Each stereo displaced scanned line is delivered to the imaging cells  71  of the second and alternate logic trees  1  of array  70  in the same manner described in connection with the delivery of the first stereo displaced scanned line to the second-from-the-top of logic trees  1  of array  70 . 
   If the polarization applied to logic trees  1  is RCP and the members  60  thereof are designed to reflect LCP, logic trees  1  provide an image at their imaging cells  71  in the same way described in connection with FIG.  1  and the resulting outputs will have polarizations like those shown in FIG.  1 . The polarizations at STAGE  3  for each of logic trees  1  are:
 
RLRL RLRL
 
   To obtain this result, however, input logic tree  72  must provide RCP at all its imaging cells  71 . This requires an RCP input from laser  71 , a logic tree with elements which reflect LCP and fixed half-wave retarders  63  (not shown) disposed after imaging cells  71  which provide LCP outputs. 
   To obtain a single polarization for all of the outputs of first and alternate logic trees  1  of array  70 , for example, RCP, the LCP outputs of these logic trees  1  must be converted to RCP. This is accomplished by interposing fixed half-wave retarders  63  over the imaging cells  71  having LCP outputs. 
   Similarly, to obtain a single but opposite polarization for all of the outputs of the second and alternate logic trees  71 , for example, LCP, the RCP outputs of these logic trees  1  must be converted to LCP. This is accomplished by interposing fixed-half wave retarders  63  over the imaging cells  71  having RCP outputs. 
   At this point, two stereo-displaced images appear at the output imaging cells  71  of array  70 . One image has an RCP polarization while the other has an LCP polarization. Then, using glasses which have one lens which passes RCP and another lens which passes LCP, a 3-D image is perceived by a viewer. 
   In connection with the 3-D embodiment of  FIG. 5 , it should be appreciated that outputs from stereo camera  73  may be in either digital or analog form. If the former, the digital signals may be converted to analog signals using a digital-to-analog converter in a well-known way. Also, to the extent that logic trees  1  are provided with signals representing a scanned line of an image and a stereo displaced image, these signals are arranged to alternately access alternate ones of logic trees  1  in succession until two stereo displaced images are formed at the imaging cells  71  of array  70 . The scanned lines of an image and a stereo displaced image are electronically interlaced so that source  17  is modulated first by signals representing a scanned image and then by signals representing a scanned stereo displaced image and so on in succession until the two images are formed. 
   From  FIG. 5 , it can be seen that, for a 3-D array, two 4×8 interleaved arrays are required, one for an image and another for a stereo displaced image. Extrapolating this information to a practical level, if 1024 imaging cells are wanted for each image, an array of 2048×1024 imaging cells would be required. Using the same approach as demonstrated by  FIG. 5 , two 512×1024 interleaved arrays may be used with the sacrifice of some resolution. In  FIG. 5 , logic trees  1  have been interleaved horizontally for ease of fabrication but, they may be interleaved vertically without departing from the spirit of the present application. 
   Referring now to  FIG. 6 , there is shown an orthographic, cut-away projection of a plurality of layers  80  of insulating material, like SiO 2 , polycarbonate, acrylic or any other appropriate optically transparent material, and a plurality of layers  81  of cholesteric liquid crystal (CLC) material interleaved with layers  80 . 
   In  FIG. 6 , layers  80 ,  81  are subjected to a slicing operation which cuts into layers  80 ,  81  at an angle, preferably 45°. Layers  80 ,  81  may be cut by saws, lasers, jets or other appropriate tool to provide layers  82  which contain CLC members  60  disposed at an angle of 45° in insulating material as shown in FIG.  7 . 
     FIG. 7  is a cross-sectional view of a layer of insulating material in which CLC members  60  are disposed at an angle of 45°. The spacing of CLC members  60  is determined by controlling the thicknesses of insulating layers  80  prior to the slicing step of FIG.  6 . Since alignment of CLC members  60  is important in transmitting electromagnetic energy from stage-to-stage the spacing of members  60  must be carefully controlled. Thus, in  FIG. 7 , the spacing between CLC members  60  is t units and could comprise STAGE  1 , for example, of array  70  of FIG.  4 . 
     FIG. 8  is a cross-sectional view of a layer of insulating material in which members  60  are disposed at an angle of 45° and is similar to  FIG. 7  except that members  60  are spaced apart by t/2 units. Layer  82  and other like layers are fabricated by slicing an arrangement like that shown in  FIG. 6  except that the thicknesses of layers  80  of insulating material are reduced to half that shown in FIG.  6 . After slicing a stack like that shown in  FIG. 6 , the resulting layer  82  with a spacing of t/2 between members  60  could comprise stage  2 , for example, of array  70  of FIG.  4 . 
     FIG. 9  is a cross-sectional view of a layer of insulating material in which members  60  are disposed at an angle of 45° and is similar to  FIG. 7  except that members  60  are spaced apart by t/4 units. Layer  82  in  FIG. 9  is fabricated by slicing an arrangement like that shown in  FIG. 6  except that the thicknesses layers  80  would be reduced to one-quarter that shown in FIG.  6 . After slicing a stack like that shown in  FIG. 6 , the resulting layer  82  with a spacing of t/4 between members  60  could comprise STAGE  3 , for example, of array  70  of FIG.  4 . 
   The spacing of members  60  is always reduced by half as additional stages are added so that higher and higher resolutions may be obtained. Thus, for an array with ten stages, the spacing between CLC members  60  would be t/512 units. 
   By slicing arrangements like that shown in FIG.  6  and controlling the thicknesses of layers  80 , layers  82  with members  60  spaced apart by different amounts like those shown in  FIGS. 7-9  may be easily obtained. As will be seen below, layers  82  with appropriately spaced members  60  may be stacked to produce an array  70  like that shown in  FIG. 4  or an array having as many stages as desired. This can be done on a mass-production basis to produce literally thousands of layers like layers  82  of  FIGS. 7-9 . 
     FIG. 10  is a cross-sectional, orthographic projection of a layer  82  which contains CLC members  60  disposed at an angle of 45° therein. Layer  82  in  FIG. 10  is similar to layer  82  of  FIG. 8  except that in  FIG. 10 , a ground plane  83  is deposited or formed on the bottom of layer  82 . Layer  83  is transparent and metallic in character and acts as a ground plane for subsequently deposited electrodes which activate variable half-wave retarders  61 . A material like indium-tin oxide (ITO) may be deposited or formed in a well-known way on the bottom of layer  82  of FIG.  10 . The transparency of ITO, of course, permits the transmission of light energy from stage-to-stage with little or no loss in intensity. 
   Referring to  FIG. 11 , there is shown a cross-sectional, orthographic projection similar to  FIG. 10  except that electrodes  84  are shown disposed over every other CLC member  60 , like they would be if layer  83  of  FIG. 11  were to be utilized as a STAGE  2  in an array  70  like that shown in FIG.  4 . This pattern of electrode spacing will always be the same regardless of which stage is being considered. A reconsideration of  FIG. 1  shows this to be true since each stage always comprises at least one branch consisting of active and passive CLC elements. Electrode  84  ( 62  in  FIG. 1 ) is always associated with and forms a part of variable half-wave retarders  61  which, in turn, is always associated with the active CLC element of any branch. Like ground plane  83 , electrode  84  is comprised of indium-tin-oxide (ITO) material which is transparent to the electromagnetic radiation being utilized. To obtain electrodes  84  in the form shown in  FIG. 11 , indium-tin oxide is formed atop layer  82  and, using well-known lithographic, masking and etching techniques, electrodes  84  are appropriately positioned over every other CLC member  60 . Rather than carrying out two separate deposition steps for ground plane  83  and electrodes  84 , the ITO material may be formed simultaneously on each side of layer  82 . Then, the photolithographic, masking and etching steps are carried out. 
   Referring now to  FIG. 12 , there is shown a cross-sectional view of a layer  82  similar to that shown in  FIG. 11  except that a spacer is added around the periphery of layer  82  and the thus enclosed volume is filled with a phase-shifter material in liquid form. 
   In  FIG. 12 , a spacer  85  is formed around the periphery of layer  82  by, for example, gluing a spacer  85  of insulating material around the edge of layer  82 . Spacer  85  separates layers  82  from other overlying layers and defines the volume into which phase-shifter material  86  is placed. 
     FIG. 13  is a top view of a logic tree  1  made up of layers  82  like those shown in  FIGS. 7-12 . The arrangement of  FIG. 13  shows the topmost logic tree  1  of  FIG. 4  after it has been fabricated in accordance with the teaching of the present application.  FIG. 13  can also be considered a side-view of input logic tree  72  since its structure does not depart in any way from the structure of logic tree  1 . 
   One way of assembling the structure of  FIG. 13 , is to stack a finished layer  82  like that shown in  FIG. 12  on a finished layer  82  like that shown at the bottom of FIG.  13 . Another layer  82  like that shown at the top of  FIG. 13  is stacked atop the finished layer  82  of FIG.  12 . The layers are glued together with the topmost layer  82  forming STAGE  1  as shown in  FIG. 4 ; the middle layer  82  forming STAGE  2  as shown in FIG.  4  and the bottom layer  82  forming STAGE  3  as shown in FIG.  4 . Thus, inputs provided to the leftmost CLC member  60  of topmost layer  82  will, under control of inputs to electrodes  84  from pulsed source  27 , appear as outputs emanating, from left-to-right, from CLC members  60  of bottommost layer  82  as a scanned line of modulated or unmodulated light. 
   For the array, once stacked, the top and bottom thereof may be covered with insulating layers, one of which contains holes which register with the ends of electrodes  84  and ground planes  83 . Thus, even when logic trees  1  are not being utilized, their associated electrodes  61 ,  84  which extend from top-to-bottom of array  70  and are electrically connected as shown in  FIG. 5  are simultaneously energized. 
   Inputs to the stacked logic trees  1  are provided, as shown in  FIG. 4 , from imaging cells  71  of input logic tree  72 . The orientation of input logic tree  72  with respect to array  70  is best shown in  FIG. 4  which does not depart in any way from the arrangement of FIG.  13 . The latter figure merely shows the structural details to better effect. Thus, as previously explained in  FIG. 4 , outputs from imaging cells  71  of input logic tree  72  are scanned from top-to-bottom of tree  72  and each output initially accesses the leftmost member  60  of its associated logic tree  1  such that outputs appear at imaging cells  71  of array  70  as a plurality of left-to-right scans which go from the topmost logic tree  1  to the bottommost logic tree  1  of array  70 . 
   Input logic tree  72  may take the form of an array  70  rotated 90° so that imaging cells  71  there of register with the leftmost retarder  61  of each of the logic trees  1  like lasers  17  as shown in FIG.  3 . In this instance, only a single logic tree  1  of the rotated array  70  is energized. 
   Alternatively, the array shown in  FIG. 13  may be fabricated without introducing the phase shifter material  86 . The structure of  FIG. 13  is then sliced in a direction parallel to the surface there of resulting in a structure similar to input logic tree  72  as shown in FIG.  4 . The resulting slice is placed on an insulating layer and bonded to it. A cover layer of insulating material having holes therein which register with electrodes  84  and ground planes  83  is fabricated by drilling or etching using well-known photolithographic techniques. The volumes enclosed by the insulation layer are now filled with liquid phase shifter material  86 . The cover layer is affixed to the other side of the logic tree slice. A metallic layer such as aluminum is then deposited on the surface of the cover layer and in the holes previously formed therein. Then, using well-known photolithographic masking and etching techniques, conductors to electrodes  84  in a ground planes  83  are formed 
   Without going into exhaustive detail, it should be appreciated that the side of input logic tree  72  of  FIG. 4  may be butted against the back of array  70 . In this way, the overall thickness of the arrangement of  FIG. 4  is substantially reduced. Well-known optical techniques using reflectors may be used to apply a 90° turn to light emanating from imaging cells  71  of tree  72  when it is butted against the back of array  70 . 
   Since electrodes  84  extend from front-to-back on each logic tree  1  as shown, for example, in  FIG. 13 , they are best accessed from the front or back of the array with activating metallic lines  29 , as shown in  FIG. 4 , extending in insulated spaced relationship with a surface of array  70  to a plug which can be connected to pulsed source  27 , for example. This may be accomplished using well-known photolithographic and etching techniques. 
   The arrangements shown in  FIGS. 6-12  may have the following typical dimensions: 
   
     
       
             
             
             
           
         
             
                 
                 
             
           
           
             
                 
               Layers 82 
               0.5 mm thick and up 
             
             
                 
               Electrodes 84 
               500 Å to 1000 Å thick 
             
             
                 
               Ground Planes 83 
               500 Å to 1000 Å thick 
             
             
                 
               Spacer 85 
               1μ to 10μ thick 
             
             
                 
               Elements 60 
               2μ to 30μ thick 
             
             
                 
               Cells 71 
               0.5 mm wide and up. May exceed 10 cm 
             
             
                 
                 
             
           
        
       
     
   
   Typical voltages applied to electrodes  84  may range between 5V and 100V. 
   From the foregoing, it should be clear that arrays  70  may range in size from that typical of T.V. sets used in the home to displays similar to those used in stadia. The resulting arrays are flat, light weight, require but a single laser source or multiple laser sources and are inexpensive and easily fabricated.