Abstract:
A touchscreen is constructed directly on the glass surface of a cathode ray tube (CRT). To solve the problem of insufficient space between the CRT&#39;s bezel and frontal region to accommodate the transducers for the touchscreen, the transducers are moved away from the frontal region, to the highly curved shoulder region of the CRT. To preserve acoustic signal strength, the positioning of the transducers is chosen to take advantage of the fact that an acoustic wave on a non-Euclidean surface travels along a geodesic path. Allowance is also made for the acoustic lens and prism effect of the corner regions of the CRT, where the transducer may be located.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates to an acoustic touchscreen constructed directly on a cathode ray tube, and methods therefor. 
     2. Description of Related Art 
     An acoustic touchscreen has a touch-sensitive area on which the occurrence and location of a touch is sensed via the touch&#39;s effect on the transmission of acoustic waves thereacross. A common type of acoustic touchscreen employs Rayleigh waves (a term which, as used herein, subsumes quasi-Rayleigh waves). Illustrative disclosures relating to Rayleigh wave touchscreens include Adler, U.S. Pat. No. 4,642,423 (1987); U.S. Pat. No. 4,645,870 (1987); U.S. Pat. No. 4,700,176 (1987); U.S. Pat. No. 4,746,914 (1988) (hereinafter “Adler &#39;914”); U.S. Pat. No. 4,791,416 (1988); and Re 33,151 (1990); Adler et al., U.S. Pat. No. 4,825,212 (1989); U.S. Pat. No. 4,859,996 (1989); and U.S. Pat. No. 4,880,665 (1989); Brenner et al., U.S. Pat. No. 4,644,100 (1987); Davis-Cannon et al., U.S. Pat. No. 5,739,479 (1998); and Kent, U.S. Pat. No. 5,708,461 (1998) and U.S. Pat. No. 5,854,450 (1998). Acoustic touchscreens employing other types of acoustic waves such as Lamb or shear waves, or combinations of different types acoustic waves (including combinations involving Rayleigh waves) are also known, illustrative disclosures including Kent, U.S. Pat. No. 5,591,945 (1997) and U.S. Pat. No. 5,854,450 (1998); Knowles, U.S. Pat. No. 5,072,427 (1991); U.S. Pat. No. 5,162,618 (1992); U.S. Pat. No. 5,177,327 (1993); U.S. Pat. No. 5,243,148 (1993); U.S. Pat. No. 5,329,070 (1994); and U.S. Pat. No. 5,573,077; and Knowles et al., U.S. Pat. No. 5,260,521 (1993). The documents cited in this paragraph are incorporated herein by reference. 
     FIG. 1 illustrates the operation of a typical acoustic touchscreen  1 , having an active, or touch-sensitive area  2 . A first transmitting transducer  3   a  is positioned outside of touch-sensitive area  2 , acoustically coupled to the surface of touchscreen  1 , and sends an acoustic signal in the form of an acoustic wave  11   a  traveling parallel to the top edge of touchscreen  1  and generally in the plane of touchscreen  1  . Aligned in the transmission path of acoustic wave  11   a  is a linear array of partially acoustically reflective elements  4   a , each of which partially reflects (by approximately 90°) and partially transmits the acoustic signals, creating a plurality of acoustic waves (exemplarily  5   a ,  5   b , and  5   c ) traveling vertically (parallel to the Y-axis) across touch-sensitive area  2 . (The spacing of reflective elements  4   a  is variable to compensate for the attenuation of the acoustic signals with increasing distance from first transmitter  3   a .) Acoustic waves  5   a ,  5   b , and  5   c , upon reaching the lower edge of touchscreen  1 , are again reflected by approximately 90° (arrow  11   b ) by another linear array of similarly partially acoustically reflective elements  4   b  towards a first receiving transducer  6   a , where they are detected and converted to electrical signals for data processing. Along the left and right edges of touchscreen  1  are located a similar arrangement. A second transmitting transducer  3   b  generates an acoustic wave  12   a  along the left edge, and a linear array of partially acoustically reflective elements  4   c  creates therefrom a plurality of acoustic waves (exemplarily  7   a ,  7   b , and  7   c ) traveling horizontally (parallel to the X-axis) across touch-sensitive area  2 . Acoustic waves  7   a ,  7   b , and  7   c  are redirected (arrow  12   b ) by yet another linear array of partially acoustically reflective elements  4   d  towards receiving transducer  6   b , where they are also detected and converted to electrical signals. 
     If touch-sensitive area  2  is touched at position  8  by an object such as a finger or a stylus, some of the energy of the acoustic waves  5   b  and  7   a  is absorbed by the touching object. The resulting attenuation is detected by receiving transducers  6   a  and  6   b  as a perturbation in the acoustic signal. Analysis of the data with the aid of a microprocessor (not shown) allows determination of the coordinates of position  8 . 
     Those skilled in the art will appreciate that it is not essential to have two sets of transmitting/receiving transducers to make a touchscreen. The device of FIG. 1, without one set of transducers, will still function as a touchscreen, detecting the occurrence of a touch and providing limited location information (one of the coordinates). Or, a touchscreen can be designed with only two transducers by using a common transmit/receive transducer scheme, as disclosed in Adler &#39;914 (FIG. 8). 
     In normal usage a housing  9 , typically made of molded polymer, is associated with touchscreen  1 . Housing  9  contains a bezel  10  that overlays touchscreen  1 , concealing the transmitting and receiving transducers, the reflective elements, and other components, but exposing touch-sensitive area  2 . This arrangement protects the concealed components from contamination and/or damage, presents a more aesthetically pleasing appearance, and defines the touch-sensitive area for the user. 
     A touchscreen may comprise a separate faceplate (typically made of glass, but other hard substrates may be used) overlaid on a display panel such as a cathode ray tube (CRT), a liquid crystal display (LCD), plasma, electroluminescent, or other type of display. Alternatively it has been proposed to construct a touchscreen directly on the glass surface of a CRT, so that the CRT surface is the touch-sensitive surface, Adler &#39;914 discloses such a construction. A direct-on-CRT touchscreen construction is desirable because it eliminates a piece of glass or other material between the viewer and the CRT, increasing the perceived display brightness. Also, there are economic advantages in dispensing with the overlay glass and not having to modify CRT chassis to make room for the overlay glass. 
     FIG. 2 a  shows a conventional CRT  15  on which a touchscreen may be constructed. CRT  15  comprises two glass sections, a rear tapering section referred to as a funnel  28  and, in front thereof, a panel  27 . In turn, panel  27  includes a substantially rectangular frontal region  16  on which an image is displayed and which, if a touchscreen is installed, also serves as touch-sensitive area  2 . Ancillary features include mounting ears  18  for attaching the housing (not shown) and a protective steel implosion band  23 . 
     Frontal region  16  typically is not truly flat, but curved to an extent varying from CRT to CRT, with the more expensive CRT&#39;s tending to be less curved. But, for general purposes and also for the purposes of this invention, frontal region  16  may be considered to be substantially planar and defining a plane. Panel  27  further has, outside of the viewing area (and the touch-sensitive area, if a touchscreen has been installed) and below frontal region  16 , a shoulder region  17  where the glass curves down and away from the plane of frontal region  16 . Shoulder region  17  includes corner regions  26  having complex non-Euclidean topography, at the confluences of the corners of frontal region  16  and shoulder region  17 . The degree of curvature of CRT  15 &#39;s glass surface in shoulder region  17  (including corner regions  26 ) may be quite high, compared to that of frontal region  16 . The radius of curvature of frontal region  16  may be on the order of 50 centimeters or more, while shoulder region  17  may have much smaller radii of curvature, on the order of a few centimeters. Thus, transition  29  from frontal region  16  to shoulder region  17  may be defined as occurring where there is a sharp discontinuity (decrease) in the radius of curvature of the glass surface. If frontal region  16  is treated as being substantially planar, the plane perpendicular to the axis of the CRT and intersecting this discontinuity may be considered to be its plane. 
     In building a direct-on-CRT touchscreen, the touchscreen manufacturer normally does not manufacture the CRT itself. Rather, the manufacturer works with the CRT as supplied by a monitor manufacturer (or, in the case of a monitor integrated with a computer CPU chassis, such as the iMac computer from Apple Computer, from the computer manufacturer). Since it is often impractical for the touchscreen manufacturer to replace the supplied housing with a new housing, the manufacturer must adapt to whatever space is available between the supplied housing and the CRT for accommodating the touchscreen elements such as the transmitting and receiving transducers (collectively referred to as transducers) and the reflective elements. Even where the touchscreen manufacturer has design control over the bezel, mechanical interference with the transducers often force a reduction in the dimensions of the bezel opening that prevents one from utilizing the full available display area of the CRT. 
     Conventionally, touchscreen components are placed on the frontal region. FIG. 2 b  is a frontal view of the CRT  15  of FIG. 2 a  having transmitting and receiving transducers  3   a ,  3   b ,  6   a  and  6   b  and arrays of reflective elements  4   a ,  4   b ,  4   c , and  4   d  mounted thereon, on frontal region  16  thereof. (A like arrangement is shown in FIG. 1 of Adler &#39;914.) 
     Normally, there is sufficient clearance for the reflective elements, which have a low profile. However, installation of the transducers is a more difficult proposition, due to their higher profile. This problem is illustrated in FIG.  3 . (Dotted line  13  denotes the plane of frontal region  16 .) When housing  9  is mounted on CRT  15  (i.e., moves in the direction indicated by arrow A), there is mechanical interference between bezel  10  and transducer  4 . This interference may impede the proper functioning of transducer  4  or, worse yet,  30  damage either transducer  4  or bezel  10 . Sometimes it is possible to create sufficient clearance by carving out a small amount of bezel material, but such a solution is not generically applicable and is anyway undesirable and/or impractical for a variety of reasons. The carving-out is a slow, labor-intensive operation; the bezel may be weakened and rendered susceptible to damage in subsequent use; and the carved out region may be visible, especially if the housing is made of translucent or transparent material. 
     Reference is also made to Davis-Cannon et al., U.S. Pat. No. 5,739,479 (1998), which discloses an acoustic touchscreen containing the transducers recessed on a beveled portion of the touchscreen. However, the invention there may not be applicable for a manufacturer installing touchscreens directly on a CRT surface, as conventional CRT&#39;s do not have such beveling. Reference is additionally made to Kambara et al., WO 98/29853 (1998), which discloses grating transducers for acoustic touchscreens. However, the piezoelectric elements of grating transducers must be placed on the underside of the touchscreen, an option not available for a direct-on-CRT construction. 
     Thus, it is desirable to develop a direct-on-CRT touchscreen construction which is compatible with tight clearances available between a CRT and its bezel and is adaptable for use with CRT&#39;s and housings as received from the CRT-monitor supplier, or which allows custom bezel designs maximizing the use of the CRT&#39;s display area. 
     BRIEF SUMMARY OF THE INVENTION 
     Accordingly, there is provided an acoustic touchscreen constructed directly on a CRT, comprising: 
     (a) a CRT comprising 
     (i) a substantially rectangular frontal region having four corners and 
     (ii) a shoulder region below the frontal region, including four corner regions at the confluences of the shoulder region and the corners of the frontal region; 
     (b) a first transducer acoustically coupled to the surface of the CRT and capable of generating an acoustic signal thereon; 
     (c) a first linear array of partially acoustically reflective elements associated with the first transducer, the first linear array being disposed on the frontal region, being capable of deflecting the acoustic signal across the frontal region, and having a longitudinal array axis; 
     (d) a second transducer acoustically coupled to the surface of the CRT and capable of detecting the acoustic signal after the acoustic signal has traveled across the frontal region, together with perturbations thereto caused by a touch on the frontal region; and 
     (e) a second linear array of partially acoustically reflective elements associated with the second transducer, the second linear array being disposed on the frontal region, being capable of deflecting the acoustic signal towards the second transducer after the acoustic signal has traveled across the frontal region, and having a longitudinal array axis; 
     the first and second transducers being located on the shoulder region, each positioned on and aimed along the geodesic defined by the longitudinal array axis of the respective associated linear array. 
     In another embodiment of the invention, there is provided an acoustic touchscreen constructed directly on a CRT, comprising: 
     (a) a CRT comprising; 
     (i) a substantially rectangular frontal region having four corners and 
     (ii) a shoulder region below the frontal region, including four corner regions at the confluences of the shoulder region and the corners of the frontal region; 
     (b) first and second transducers, each acoustically coupled to the surface of the CRT and capable of generating respective first and second acoustic signals on the surface of the CRT; 
     (c) first and second linear arrays of partially acoustically reflective elements associated with the first and second transducers respectively, for deflecting the first and second acoustic signals, respectively, across the frontal region; each of the first and second linear arrays having a respective longitudinal array axis; the first linear array being disposed along a first edge of the frontal region and the second linear array being disposed along a second edge of the frontal region substantially orthogonal to the first edge; 
     (d) third and fourth transducers, each acoustically coupled to the surface of the CRT; the third transducer being capable of detecting the first acoustic signal after the first acoustic signal has traveled across the frontal region, together with perturbations thereto caused by a touch on the frontal region; the fourth transducer being capable of detecting the second acoustic signal after the second acoustic signal has traveled across the frontal region, together with perturbations thereto caused by a touch on the frontal region; and 
     (e) third and fourth linear arrays of partially acoustically reflective elements associated with the third and fourth transducers respectively, for deflecting the first and second acoustic signals towards the third and fourth transducers, respectively, after the first and second acoustic signals have traveled across the frontal region; each of the third and fourth linear arrays having a respective longitudinal array axis; the third linear array being disposed along a third edge of the frontal region opposite the first edge thereof and the fourth linear array being disposed along a fourth edge of the frontal region opposite the second edge thereof; 
     the first, second, third and fourth transducers being located on the shoulder region, positioned on and aimed along the geodesic defined by the longitudinal array axis of the respective associated linear array. 
     In a third embodiment of the invention, there is provided a method of constructing a touchscreen directly on a CRT, comprising the steps of: 
     (a) providing a CRT comprising 
     (i) a substantially rectangular frontal region having four corners and 
     (ii) a shoulder region below the frontal region, including four comer regions at the confluences of the shoulder region and the corners of the frontal region; 
     (b) providing plural transducers; 
     (c) forming, on the frontal region, plural linear arrays of partially acoustically reflective elements, each linear array associated with a respective one of the plural transducers, each linear array having a respective longitudinal array axis; 
     (d) determining, for each linear array, the geodesic defined by the respective longitudinal array axis; and 
     (e) for each geodesic so determined, acoustically coupling the respective associated transducer to the surface of the CRT on the shoulder region, positioned on and aimed along the geodesic. 
     In a fourth embodiment of the invention, there is provided a method of situating a transducer for a touchscreen constructed directly on a CRT, comprising the steps of: 
     (a) providing a CRT comprising 
     (i) a substantially rectangular frontal region having four comers and 
     (ii) a shoulder region below the frontal region, including four comer regions at the confluences of the shoulder region and the comers of the frontal region; 
     the CRT further having formed thereon a linear array of partially acoustically reflective elements, the linear array having a longitudinal array axis; 
     (b) determining the geodesic defined by the longitudinal array axis; 
     (c) providing a transducer; 
     (d) positioning the transducer on and aimed along the geodesic, on the surface of the CRT on the shoulder region; and 
     (e) acoustically coupling the transducer to the surface of the CRT, positioned and aimed according to the preceding step. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING(S) 
     FIG. 1 shows a conventional acoustic touchscreen. 
     FIG. 2 a  shows, in perspective view, a conventional CRT on which a touchscreen ay be installed. FIG. 2 b  shows, in a frontal view, the CRT of FIG. 2 a  with acoustic touchscreen components installed thereon in a conventional manner. 
     FIG. 3 is a schematic cross-sectional view of a curved CRT frontal region and a bezel, with a transducer on the frontal region. 
     FIG. 4 shows a wedge transducer typically used in acoustic touchscreens. 
     FIG. 5 shows a CRT having touchscreen components installed according to this invention. 
     FIG. 6 is a cross-section schematic view showing the positioning of a transducer according to this invention. 
     FIG. 7 a  is a partial plan view a direct-on-CRT construction showing positioning of a transducers along a geodesic. 
     FIG. 7 b  is a corresponding partial side view. 
     FIGS. 8 a ,  8   b ,  8   c , and  8   d  are a theoretical constructs of the topography of the CRT glass surface, for explaining the lensing effect we have discovered. 
     FIGS. 9 a ,  9   b ,  9   c , and  9   d  show schematically how a corner region may act as an acoustic lens and the resultant effect on acoustic waves. 
     FIG. 10 shows a wedge transducer having a curved bottom surface, adapted for mounting on a glass surface which is not flat. 
    
    
     In this specification, numerals repeated from one figure to another denote the same or equivalent elements. 
     DETAILED DESCRIPTION OF THE INVENTION 
     Transducers typically used in acoustic touchscreens are wedge transducers, such as disclosed in Davis-Cannon et al., U.S. Pat. No. 5,739,479 (1998), incorporated herein by reference. This specification accordingly is written with particular reference to wedge transducers, although the use of our invention is not limited to wedge transducers. Other transducers may be used, such as interdigital transducers, as shown in FIG. 4 of Kent, U.S. Pat. No. 5,708,461 (1998), incorporated herein by reference. FIG. 4 herein shows a cross-sectional view of a wedge transducer  20  located on the surface of a touchscreen  1  and having as constituent parts a piezoelectric element  21  and a coupling wedge  22 , made of a plastic such as poly(methyl methacrylate) (PMMA). Wedge  22  is adhesively bonded to the surface of touchscreen  1  by, for example, an UV curable adhesive, thereby acoustically coupling one to the other. Piezoelectric element  21  is mounted to a backside of coupling wedge  22  and is electrically connected to control electronics by electrodes (not shown). In response to an electrical signal, piezoelectric element  21  vibrates to produce a pressure wave  24  that propagates across wedge  22  and in turn is transduced through the wedge  22 -touchscreen  1  interface as a quasi-Raleigh acoustic wave  14  propagating generally along the plane of touchscreen  1 . Wave  14  may then be partially deflected by reflective elements  4   a.    
     Thus, the conventional wisdom is that transducer  20  should be positioned in the plane of the touchscreen, or no more than moderately inclined with respect thereto. But such positioning may not be feasible for a direct-on-CRT, for the reasons explained above. In solving this problem, we have discovered that it is possible to locate the transducers not on the frontal region, but on the shoulder region of the CRTf—i.e., more or less on the side of the CRT—provided location parameters we have discovered are followed. 
     A direct-on-CRT construction according to our invention is shown in FIG. 5. A feature of our invention is positioning of the transmitting and receiving transducers  3   a ,  3   b ,  6   a , and  6   b  on shoulder region  17 , as opposed to frontal region  16 . Because shoulder region  17  slopes away from frontal region  16 , sometimes precipitously, the transducers are positioned below the plane of frontal region  16  and do not mechanically interfere with a bezel (not shown in this figure) when it comes down on CRT  15 . FIG. 6 is a cross-section view showing schematically how such positioning avoids mechanical interference between transducer  4  and bezel  10 . 
     It is not sufficient to merely place a transducer on a shoulder region. Consider a transmitting transducer placed there. The acoustic wave it generates initially will be aimed within the local plane of the glass surface to which the transducer is attached. Unlike the instance of a transducer located on the touchscreen plane (e.g., FIG. 2 b ) or on a beveled portion of the touchscreen (e.g., Davis-Cannon et al., U.S. Pat. No. 5,739,479 (1998)), this initial plane (indicated by line  25  in FIG. 6) will be highly inclined with respect to the plane of frontal region  16  (line  13  in FIG.  6 ). Without some method of efficiently acoustically connecting the transmitting transducer and the linear array located on the frontal region, the touchscreen will not function or will function poorly, due to high acoustic energy loss. 
     An efficient acoustic connection can be established by taking advantage of the fact that an acoustic wave traveling on a non-Euclidean surface such as the CRT glass surface follows a geodesic (for example, a great circle route on a spherical surface). See, for instance, FIG. 20 in Kent, U.S. Pat. No. 5,854,450 (1998), incorporated herein by reference. By positioning the transducer at a location calculated to take advantage of this fact, we can move the transducers below the plane of the frontal region but yet maintain acoustic efficiency—i.e., have an acceptable amount of the acoustic energy generated by the transmitting transducers sensed by the receiving transducers, as opposed to having such energy dissipated. This positioning is illustrated in FIG. 7 a . Transducer  20  is placed such that it is along a geodesic  31  defined by the longitudinal array axis  33 . On frontal region  16  geodesic  31  substantially tracks axis  33 , because frontal region  16  is quasi-planar. But, when geodesic  31  crosses transition  29  and reaches the highly curved surface of shoulder region  17 , it curls away from axis  33 . Transducer  20  should be placed on shoulder region  17 , along geodesic  31 . Transducer  20  is aimed along geodesic  31 , instead of along longitudinal axis  33  as taught in the prior art (compare FIG. 7 a  against FIGS. 1 and 2 b ). That is, transducer  20  is tilted with respect to axis  33 . The aim of transducer  20  (the direction of propagation of an acoustic signal generated by it) is perpendicular to the width of transducer  20 &#39;s piezoelectric element. Because we are here talking about an infinitely thin theoretical line (geodesic  31 ) and a very small part (transducer  20 ) which is difficult to position with absolute precision, transducer  20  is said to be on geodesic  31  if any part of transducer  20  lies on geodesic  31 . Thus, constructions in which transducer  20  is not perfectly positioned, but is somewhat off-center, so that, for example, only an upper (or lower) corner thereof intercepts geodesic  31  are within the scope of this invention. Similarly, transducer  20  is said to be aimed along geodesic  31  if it is aimed generally in such direction; it is not necessary that the aim be mathematically exact. 
     FIG. 7 b  is a partial side view corresponding to FIG. 7 a . Preferably, frontal region is substantially planar, having a radius of curvature of at least 50 cm. 
     A pragmatic method for locating geodesic  31  uses a length of flexible material, such as a strip of fabric or paper or a string. The flexible material is stretched on the glass surface along axis  33  and permitted to follow the curvature of the surface as it reaches transition  29 , leaves frontal region  16  and enters shoulder region  17 . The path traced by the material represents geodesic  31 . Transducer  20  then can be attached to the glass surface on shoulder region  17  and aimed along geodesic  31 . (It may be desirable to do some trial-and-error fine tuning of the positioning by measuring the signal strength with appropriate test equipment while moving transducer  20  slightly back-and-forth.) 
     Following this technique, a transducer was positioned on the shoulder region of a CRT. Healthy signals were observed, with amplitudes well within the dynamic range of commercial touchscreen controllers such as Elo TouchSystems (Fremont, Calif.) controller model no. E281-2310. No undesirable parasitic signals were observed. 
     Once the desired location for a transducer has been identified for a particular model of CRT, a template or guide can be made for easy positioning of the transducers in other CRT&#39;s of the same model. A jig can be made to hold the transducer in place while it is being bonded to the glass. 
     We have further discovered that corner regions  17  have a strong lensing effect, i.e., act as a lens with a very short focal length. While we do not wish to be bound by theory, we believe that the lensing and prism effects we have observed may be explained as follows. FIG. 8 a  shows a corner region  26 /shoulder region  17  approximated by having a plane  35  represent the substantially planar frontal region surface. Shoulder region  17  is approximated by a radiused edge  36  of radius r which links plane  35  with planes  37 , plane  35  being orthogonal to planes  37 . At corner region  26 , plane  37  is replaced by a cylindrical cross-section  38  of radius R (or, more precisely, R+r). Let λ represent the wavelength of an acoustic wave propagating on the CRT glass, a typical value for λ being about ½mm. FIG. 8 b  is a further simplified approximation, for the limiting case in which the following inequality holds: 
     
       
         R&gt;&gt;r&gt;&gt;λ 
       
     
     Then, radiused edge  36  may be replaced by a sharp edge  39 . As illustrated by a representative acoustic path crossing the radiused edge in FIGS. 8 a  and  8   b , the acoustic path&#39;s angle with respect to the edge does not change when going from surface  35  to surfaces  37  or  38 . 
     FIG. 8 c  illustrates two parallel acoustic paths on surface  35  that intersect the radiused edge at a corner of radius R. With respect to the center of the circular arc of radius R, the parallel paths intersect the radiused edge and angles φ and (φ+δφ), respectively. The distance between the intersection points is Rδφ. Then as this pair of acoustic paths continue onto (Euclidean) surface  38  they continue with angles φ and (φ+δφ); see FIG. 8 d . Note that by traversing the corner edge, the formerly parallel acoustic paths are no longer parallel, but rather approach each other with a relative angle of δφ. It is straight-forward geometry and mathematics to determine that the formerly parallel paths intersect at a distance f given by the equation 
     
       
         
           f=R*cos(φ) 
         
       
     
     The distance f is measured from the point where the geodesics cross edge  39 . Hence the curved radiused edge forms a lens of focal length R*cos (φ). Given a typical value of R in the centimeter range, this is a very short focal length. That is, it is a strong acoustic lens. In fact, the focal length is quite comparable to the distance along geodesic  31  from the transducer to the radiused edge. 
     While the limiting condition R&gt;&gt;r is particularly amenable to mathematical analysis, this is not a requirement for a strong lensing effect. At the other extreme, namely where R≈r, the corner region approximates a section of a sphere of radius R. A sphere of radius R is also a strong lens. Its focal length measured as an arc length is ({fraction (π/2+L )})R. This can be seen by imagining a set of parallel rays intersecting a globe&#39;s equator and traveling due north. These initially parallel geodesics (great circles) come to a focus at the north pole. Whether R&gt;&gt;r or R≈r, we have a focal length of order R. Thus, the comer region is a strong focusing lens, independent of the precise details of its geometry. 
     The lensing effect of comer regions  26  is generally undesirable, as can be seen by reference to FIGS. 9 a  and  9   b . In FIG. 9 a , a transducer  20  generates a parallel beam of acoustic waves  40  in the direction of a linear array of partially acoustically reflective elements  4 . If, as shown in FIG. 9 b , a short focal length acoustic lens  41 —e.g., a corner region  26 —is interposed between transducer  20  and reflective elements  4  there is a de-focusing effect, with resultant dissipation of acoustic energy. In the context of an acoustic touchscreen according to this invention, it means that it is undesirable to have the acoustic path—the geodesic—traverse a corner region  26 . Referring back to FIG. 7 a , it is seen that if the linear array of partially acoustically reflective elements  4  is placed near the edge of frontal region, the projection of axis  33  and geodesic  31  both traverse corner region  26 . In principle, it is possible to avoid this situation by moving reflective elements  4  further towards the center of frontal region  16 , in the direction of arrow B. However, such movement will reduce the proportion of frontal region  26  usable as a touch-sensitive area and is therefore commercially unattractive. 
     Accepting that it may be, from a practical standpoint, difficult to avoid having geodesic  31  traverse a corner region, we have discovered ways to neutralize the adverse effect of such traversal. One such way is to use a diverging transducer. Consider the situation of FIG. 9 c , in which a diverging transducer  20 ′ is used to aim a beam at a linear array of reflective elements  4  and compare that against the situation of FIG. 9 a . The diverging transducer of FIG. 9 c  is acoustically less efficient than parallel-beam transducer  20  of FIG. 9 a , delivering less acoustic energy to reflective elements  4 . For this reason, diverging transducers are normally not used in acoustic touchscreens. 
     But now suppose that a short focal length acoustic lens  41  is placed between diverging transducer  20 ′ and reflective elements  4 , at a distance equal to the focal length of lens  41  (FIG. 9 d ). Lens  41  acts on the divergent acoustic waves  40  emitted by transducer  20 ′ and converts it to a parallel beam. In effect, two undesirable characteristics —the defocusing effect of lens  41  and the divergent beam of transducer  20 ′ can be made to neutralize each other. In practice, this means that if a divergent transducer is used in a touchscreen of this invention, the undesirable effect of having the geodesic traverse a corner region  26  is neutralized. 
     FIG. 9 d  illustrates the case where the negative effects of lens  41  are completely cancelled by the divergence of transducer  20 ′. The scope of this invention also includes cases in which this compensation is partial. Even if the divergence of transducer  20 ′ does not completely cancel the beam spread induced by lens  41 , the divergence of transducer  20 ′ is still contributing to improved touchscreen signal amplitudes. 
     One method of achieving a divergent transducer is actually beneficial in another regard. Because the glass surface of the shoulder region is curved, it may be desirable to have the bottom surface of a transducer be complementarily curved, to provide a mating relationship with the curved glass surface, to provide a mechanically and acoustically superior coupling. FIG. 10 shows a wedge transducer  20  in which the bottom surface  30  of coupling wedge  22  is concave along its long axis. Such concavity may be obtained by making a transducer containing the concavity, or, in the case of the production of our prototypes, by scraping material away from an initially flat bottom surface with a metal file with a cylindrical cross-section. However, the concave cylindrical surface of coupling wedge  22  has an defocusing effect. If both the wedge and the glass are flat, the advancing acoustic wave front is flat; but if wedge is concave, there is an undesirable phase advance at the center of the acoustic wave—and consequently creating a divergence in the acoustic beam. Thus, using a transducer having a curved bottom offers the dual benefits of better mating with the curved surface of the CRT and providing a diverging transducer to offset the defocusing effect of a corner region. 
     If the cylindrical surface  30  of FIG. 10 has a radius of curvature R C , then the diverging beam comes to a virtual focus at a distance of 
     
       
         R C*tan θ   
       
     
     where θ is the wedge angle, i.e., the angle between the plane of the piezoelectric element and the plane tangential to surface  30  at its center. In a prototype, R C  was 16 mm and θ was  64 °. Hence, the diverging focal length was 32 mm. 
     Another type of divergent transducer is, simply, a smaller transducer. Due to diffractive effects, an acoustic beam from a transducer of narrow width tends to diverge. As is well known in optics and other fields of wave mechanics, the first node in the diffraction pattern from an aperture of width w is at an angle θ={fraction (λ/w)} where λ is the wavelength. For example, for w=6 mm and λ=½ mm, this angle is θ={fraction (1/12)} radians. Normally, such transducer beam divergence would be considered undesirable. After an array of length 30 cm, this {fraction (1/12)} radian beam spread corresponds to a 30 cm*({fraction (1/12)})=2.5 cm beam width,—i.e. much wider than the array. However, in the context of the present invention, such divergence is beneficial for neutralizing the corner region problem. Thus, for the practice of our invention, a preferred embodiment comprises using wedge transducers wherein the width of the piezoelectric element is no greater than 6 mm, preferably no greater than 4 mm. 
     A smaller transducer offers another advantage: it is easier to bond to a highly curved glass surface because, when looked at in a sufficiently small point-like region, the surface may be treated as quasi-flat. It is much easier to design a 3 mm wide wedge transducer for a curved surface than a 12 mm wide wedge transducer for the same curved surface. 
     Yet another way to counter lost acoustic intensity due to the defocusing effect of a comer region is to select CRT&#39;s wherein the frontal region glass is acoustically a low-loss glass, such a borosilicate glass or barium-containing glass, as described in Kent, U.S. Pat. No. 5,708,461 (1998), incorporated herein by reference. The use of a low-loss glass means that less of an acoustic signal is absorbed by the glass, so that less acoustic power is required to begin with. 
     Those skilled in the art will understand the same transducer can be used as a transmitting or a receiving transducer. A transducer is capable of either converting an electrical signal into an acoustic wave (i.e., act as a transmitting transducer) or converting an acoustic wave into an electrical signal (i.e., operate in the reverse mode, as a receiving transducer). The same principles of physics apply. A “transmitting” and a “receiving” transducer basically differ in how they are connected to the control electronics: One of us once accidentally reversed the connections of the transmit and receive wires in an acoustic touchscreen and observed that the touchscreen still operated. Thus, in this specification the discussions have focused on a “transmitting” transducer as a matter of convenience, but they are equally applicable to a “receiving” transducer. 
     Those skilled in the art will understand that the angle the piezoelectric element in a wedge transducer to the surface on which it is mounted affects the efficiency of generation of an acoustic wave on the touchscreen surface. For a direct-on-CRT construction, we have used wedge transducers mounted at an angle of 64°. If there is an error and the transducer is mounted with at an angle deviating too far from the aforesaid, coherence in the acoustic wave may be lost. Preferably, the deviation should be within ±8° of 64°. 
     For acoustically coupling transducers to the CRT, we prefer to use a UV curing adhesive. The adhesive may also perform a gap-filling function, where the bottom surface of the transducer does not quite match the curve of the CRT glass surface. Generally an adhesive having good bonding characteristics to glass and PMMA (assuming the coupling wedge of the transducer is made of PMMA) is required. We have used Dymax® 628-T UV curable adhesive. 
     Preferably, the partially acoustically reflective elements are made of an organic matrix, as disclosed in Rinde et al., U.S. Pat. No. 5,883,457 (1999), incorporated herein by reference. The organic matrix may comprise a polymer including a curable composition selected from the group consisting of epoxy resin, cyanate ester resin, polyester resin, phenolic resin, bismaleimide resin, and combinations thereof. The organic matrix may include a dense filler, preferably one having a density greater than 4.0 g/cm 3 . Examples of suitable dense fillers include powdered tungsten, tungsten trioxide, tungsten carbide, calcium carbonate, lead oxide, zinc oxide, barium sulfate, zinc sulfide, silicon dioxide, and combinations thereof. The material disclosed in the Rinde patent is especially suitable for acoustic reflective elements for direct-on-CRT touchscreens because it does not require a high temperature heating step during manufacture, compared to other acoustic reflector materials such as glass frit. A high temperature step is undesirable because it would pose a threat of damage to delicate electronic components of the CRT. 
     The foregoing detailed description of the invention includes passages that are chiefly or exclusively concerned with particular parts or aspects of the invention. It is to be understood that this is for clarity and convenience, that a particular feature may be relevant in more than just the passage in which it is disclosed, and that the disclosure herein includes all the appropriate combinations of information found in the different passages. Similarly, although the various figures and descriptions herein relate to specific embodiments of the invention, it is to be understood that where a specific feature is disclosed in the context of a particular figure or embodiment, such feature can also be used, to the extent appropriate, in the context of another figure or embodiment, in combination with another feature, or in the invention in general. 
     Further, while the present invention has been particularly described in terms of certain preferred embodiments, the invention is not limited to such preferred embodiments. Rather, the scope of the invention is defined by the appended claims.