Abstract:
An air-coupled transducer includes a ultrasonic transducer body having a radiation end with a backing fixture at the radiation end. There is a flexible backplate conformingly fit to the backing fixture and a thin membrane (preferably a metallized polymer) conformingly fit to the flexible backplate. In one embodiment, the backing fixture is spherically curved and the flexible backplate is spherically curved. The flexible backplate is preferably patterned with pits or depressions.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a conversion of and claims priority to U.S. Provisional Patent Application No. 60/683,840 filed May 24, 2005, which is herein incorporated by reference in its entirety. 
     
    
     GRANT REFERENCE 
       [0002]    The work presented in this application was supported in part by a federal grant from the NASA Grant No. NAG102098. The government may have certain rights in this invention. 
     
    
     BACKGROUND OF THE INVENTION 
       [0003]    More recently, non-contact inspection methods in nondestructive evaluation (NDE) have been receiving substantial attention compared with contact or liquid-coupled inspection methods. In particular, it is more practical and efficient to employ a non-contact inspection method if the article under inspection is wood, paper product, porous material, or hot metallic material. Unlike the contact inspection methods, the non-contact inspection methods use only gas or air as a coupling medium, so that there are no risks of contamination of the test article. In addition, the unique characteristics of air or gas as a coupling medium, such as the low sound wavespeed and minimal fluid loading, have encouraged the development of more non-contact inspection applications. Air-coupled ultrasound inspection applications have and continue to develop in various areas, including materials inspection [1-2] , characterization [3-5] , and ultrasonic imaging [6-7] . 
         [0004]    Most non-contact inspection methods employ either conventional piezoelectric (PZT) transducers or capacitive micromachined transducers. When a PZT transducer is used as a primary probe in air, it encounters very large acoustic impedance mismatch at the boundary between the piezoelectric element and the surrounding air or gas boundary. Because of this, impedance matching must be employed to improve the acoustic energy transmission in gaseous environments. Attempts to remedy this problem have been limited to success in narrow bandwidth operations. In addition, the application of a matching layer limits the overall bandwidth of the device. 
         [0005]    Capacitive ultrasonic transducers consist of a thin metallized polymer membrane and conducting backplate. Compared to the piezoelectric transducers, the capacitive ultrasonic transducers have much smaller acoustic impedance mismatch between the membrane and air, owing to the very small mechanical impedance of a thin membrane. This arrangement makes a capacitive ultrasonic transducer ideal for coupling into air. The vibration of the membrane generates ultrasound in air. Receiving the vibrating sound signals is achieved using the same transducer as a reciprocal device. 
         [0006]    Recently, microfabrication techniques have been used to fabricate capacitive air-coupled ultrasonic transducers [8-10] . Indeed, these techniques provide a means to fabricate the capacitive air-coupled transducers with low fabrication cost, high reliability, relatively high sensitivity, and reasonably wide bandwidth. Details of their operation and performance are reported elsewhere [8, 11-12] . 
         [0007]    With this high popularity and interest, additional effort is being invested in the development of transducer focusing for capacitive air-coupled transducers. A focused transducer can provide much higher transducer sensitivity than a non-focusing planar device. So far, this goal has largely eluded investigators, except for the use of mirrors [5] , cylindrical focusing [13] , and a Fresnel zone plate [14] . One group has attempted slightly to deform Si-wafers [15] . Mirrors provide only limited bandwidth and leave one dimension unfocused. Still, the Fresnel zone plate approach has inherent narrowband frequency response, image degradation by the generation of side lobes, and no specific design guidelines to decide radii of zone plates for ultrasound. Moreover, the cylindrical focusing technique relies heavily on surface conditions. Si-wafers have proven difficult to handle owing to the fragility and brittleness of the silicon. They also leave one dimension unfocused and suffer from bandwidth limitations. Because brittle silicon wafers have customarily been used to fabricate a focused ultrasonic transducer capacitor, little progress has been made in the development of a new backplate material. Therefore, the challenge still remains to fabricate a focused capacitive ultrasonic transducer. 
       BRIEF SUMMARY OF THE INVENTION 
       [0008]    Therefore it is a primary object, feature, or advantage of the present invention to improve over the state of the art. 
         [0009]    It is a further object, feature, or advantage of the present invention to provide an air-coupled transducer using a spherical radiating surface that does not require mirrors, zone plates or any similar external devise to effect focusing. 
         [0010]    It is a still further object, feature, or advantage of the present invention is to provide an air-coupled transducer that provides for native focusing. 
         [0011]    A still further object, feature, or advantage of the present invention is to provide an air-coupled transducer that provides no contact inspection, no impedance matching layer requirement, rapid inspection speed and wideband frequency response. 
         [0012]    A further object, feature, or advantage of the present invention is to provide an air-coupled transducer having native focusing that provides higher signal amplitude, improved imaging capability and wide spatial bandwidth. 
         [0013]    Another object, feature, or advantage of the present invention is to provide an air-coupled transducer that provides for focusing without aberrations. 
         [0014]    Yet another object, feature, or advantage of the present invention to provide an air-coupled transducer that provides for focusing in two-dimensions. 
         [0015]    A further object, feature, or advantage of the present invention to provide an air-coupled transducer that provides for spherical focusing. 
         [0016]    It is a further object, feature, or advantage of the present invention to provide a diffraction-limited spherical focusing transducer. 
         [0017]    Another object, feature, or advantage of the present invention is to provide a transducer that is relatively easy to fabricate. 
         [0018]    Yet another object, feature, or advantage of the present invention is to provide a transducer that is relatively inexpensive. 
         [0019]    A still further object, feature, or advantage of the present invention is to provide an air-coupled sensor for providing non-contact inspection. 
         [0020]    Another object, feature, or advantage of the present invention is to provide a transducer with high signal amplitude and high spatial resolution. 
         [0021]    Yet another object, feature, or advantage of the present invention is to provide a focusing transducer that does not use mirrors or interference plats. 
         [0022]    A further object, feature, or advantage of the present invention is to provide a focusing transducer that does not sacrifice the efficiency of a micromachine backplate. 
         [0023]    Another object, feature or advantage of the present invention is to provide a focusing transducer using a spherically deformed backplate and conformal polymer film shaped as a spherical radiator. 
         [0024]    Yet another object, feature, or advantage of the present invention is to provide a focusing transducer using a flexible copper/polyamide backplate and a conformal metallized Mylar film. 
         [0025]    A still further object, feature, or advantage of the present invention is to provide a focusing transducer that does not use a hard brittle material, such as silicon, for the transducer backplate. 
         [0026]    Another object, feature, or advantage of the present invention is to provide a focusing transducer that does not have the limited sensitivity, limited bandwidth, and limited fabrication capability of prior art devices. 
         [0027]    Yet another object, feature, or advantage of the present invention is to provide a method of manufacturing a spherical focusing transducer. 
         [0028]    A still further object, feature, or advantage of the present invention is to provide a method for designing a spherical focusing transducer. 
         [0029]    Another object, feature, or advantage of the present invention is to provide for determining relationships between performance characteristics and physical characteristics of a capacitive air-coupled transducer. 
         [0030]    Yet another object, feature, or advantage of the present invention is to provide an ultrasound transducer having an integral membrane layer. 
         [0031]    A further object, feature, or advantage of the present invention is to provide an ultrasound transducer with a membrane layer which is polarized through application of a high voltage. 
         [0032]    One or more of these and/or other objects, features, or advantages of the present invention will become apparent from the specification and claims that follow. 
         [0033]    According to one aspect of the present invention a non-contact ultrasound transducer is provided. The transducer includes a ultrasonic transducer body having a radiation end with a backing fixture at the radiation end. There is a flexible backplate conformingly fit to the backing fixture and a thin metalized polymer membrane conformingly fit to the flexible backplate. In one embodiment, the backing fixture is spherically curved and the flexible backplate is spherically curved. The flexible backplate is preferably patterned with pits or depressions. 
         [0034]    According to another aspect of the present invention, a method of manufacturing a capacitive air-coupled transducer having a backing fixture is provided. The method includes conformingly fitting a flexible backplate to the backing fixture and conformingly fitting a thin metalized polymer membrane to the flexible backplate. The backing fixture and flexible backplate may be spherically shaped. The flexible backplate is fit over a warm spherical ball bearing to set the shape to a spherical shape. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0035]      FIG. 1  is an isometric view of the transducer. 
           [0036]      FIG. 2A-D  are a schematic diagram of the backplate fabrication process. 
           [0037]      FIG. 3A-B  are SEM images of a flexible copper/polyimide backplate and cross sectional SEM image of a flexible copper/polyimide backplate. 
           [0038]      FIG. 4  is a photograph of the transducer. 
           [0039]      FIG. 5A-B  are a graph illustration of amplitude response and corresponding frequency spectrum for the transducer. 
           [0040]      FIG. 6A-E  are illustrations of measured sound pressure fields for the transducer. 
           [0041]      FIG. 7A-B  are a graph illustration of the cross sections of the focal region of the measured and theoretical sound pressure fields for the transducer. 
           [0042]      FIG. 8A-B  are illustrations of measured signal intensity and theoretical predications for the transducer. 
           [0043]      FIG. 9A-E  are the isometric views of the bottom case, backplate fixture, outer case, insulator, and top cover for the transducer according to one embodiment of the present invention. 
           [0044]      FIG. 10A-E  are the isometric views of the bottom case, backplate fixture, outer case, insulator, and top cover for the transducer according to another embodiment of the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0045]    The present invention includes a number of aspects all of which have broad and far-reaching application. Although specific embodiments are described herein, the present invention is not to be limited to these specific embodiments. One aspect of the invention relates to the use of a flexible backplate in an air-coupled ultrasonic transducer. The flexible backplate allows it to conform to a number of different geometries, including, but not limited to a spherical shape. 
         [0046]    Turning now to the drawings in which similar reference characters denote similar elements through the several views. Illustrated in  FIGS. 1-10  is the combination of various views and in-use configurations of the transducer. The transducer being described with particularity herein. 
       Principles of Operation 
       [0047]      FIG. 1  is an isometric view of the transducer. The process of generating and receiving ultrasound is very similar to the working principles of a condenser microphone. As shown in  FIG. 1 , an air coupled transducer  10  has a metallized polymer film  16  is suspended above a micromachined copper/polyimide backplate  12 . For ultrasound generation, a dc bias V dc (t)  42  is superimposed upon a transient voltage signal V ac (t)  44  from a signal source. The superimposed voltage is applied between the backplate  12  and the grounded metalized surface  12  of the metalized polymer film  16 . As a result, electrostatic force is generated and attracts the film toward the bottom of the pits. Based on the frequency content of the drive signal, the metalized polymer film  16  vibrates with certain amplitude. If the metalized film  16  vibrates near its mechanical resonance frequency, the maximum displacement will be generated, leading to a large ultrasonic signal. Conversely, receiving the vibrating sound signals is achieved using the same transducer as a reciprocal device. In the receiver mode, the received signals are modulated into minute capacitance changes, owing to the displacements of the film. The capacitance is converted into electrical signals by the transducer. For both a transmitter and receiver, a dc bias voltage  42  is always applied to charge the polymer film  16  so that the transducer is sensitive to very small changes in charge. The dc voltage  42  is highly determinative in the performance of a capacitive air-coupled transducer. 
       Transducer Construction and Backplate Fabrication Example 
       [0048]    The transducer of the present invention is referred to generally as  10 .  FIG. 1  is an isometric view of the transducer. In  FIG. 1 , the component parts of the transducer  10  are shown. The transducer has a backplate  12 , a backplate fixture  14 , a metalized polymer film  16 , a bottom case  18 , an outer case  20 , an insulator  22 , and a top cover  24 . The backplate  12  is conformably deformed and attached to the backplate fixture  14 . The backplate fixture  14  is preferably spherical in shape so that the transducer functions like an ideal spherically focused piston radiator. The backplate fixture  14  is electrically connected to the center pin of a SubMiniature version A (SMA) connector, (not shown). The shield contact of the SMA connector is connected to the bottom case  18 . An insulator  22  is added between the backplate fixture  14  and the outer case  20  to isolate the electrical connection between the backplate  12  and the ground. It is preferred that all the bottom case  18 , outer case  20 , backplate fixture  14 , backplate  12  and top cover  24  be constructed of aluminum. A one-sided metallized polymer film  16  is positioned between the backplate  12  and top cover  24 , with the metallized side facing the top cover  24 . One type of film suitable for use is a commercially available polyethylene terephthalate (PET) polymer (Mylar) film with a 200 nm deposited aluminum coating. In the preferred embodiment, the metalized polymer film  16  is placed over the entire backplate  12 , extending about 20% beyond the circumference of the pit-etched area. 
         [0049]      FIG. 2  is a schematic diagram of the backplate fabrication process. Flexible copper(Cu)/polyimide(PI) is one type of material having optimum attributes for fabricating a backplate  12 . The Cu/PI backplate  12  is a non-planar backplate  12  with curvature in two dimensions forming a spherically focused capacitive air-coupled transducer  10 . In  FIG. 2 , the fabrication of a Cu/PI backplate  12  begins with cleaning the surface  27 , as shown in  FIG. 2A . In  FIG. 2B , the circular patterns  29  are defined on the surface  27  of the copper layer  26  in a square grid by photoresist  30  using lithography and wet etching processes. After etching, the pits  32  form a well-defined bowl shape on the surface  27  of the backplate  12 . One type of etchant used is a copper etchant (Ferric Chloride etchant) and the resulting pits  32 , as best shown in  FIG. 3B , are approximately 42 μm in diameter  33  with a 9-μm pit depth  34 .  FIGS. 3A and 3B  show scanning electron microscope (SEM) images of a Cu/PI backplate  12  after the wet etching process, as shown in  FIG. 2B . The patterns shown in  FIG. 3A  exhibit an 80-μm center-to-center spacing  35  between adjacent pits  32 . The center-to-center spacing  35  corresponds to the distance between two adjacent pits  32  on a square grid, shown in  FIG. 3A . The pit depth  34  represents the maximum distance from an unetched surface  31  to the bottom of a pit  34 . 
         [0050]      FIG. 4  is a photograph of the spherically focused transducer. The Cu/polyimide backplate  12  is attached to conform to the spherically curved backplate fixture  14 , whose preferred radius  36  is 5-mm having a focal length of 25.4 mm (1 inch). The metallized polymer film  16  is positioned on the spherically deformed backplate  12  to prevent wrinkles on the film  16 . The film  16  is conformed to the spherical backplate  12 , to prevent wrinkles. One method of preventing wrinkles in the film  16  is to stretch the film  16  over a stainless steel ball bearing where the radius of the ball bearing is approximately the same as the geometric focal length of a spherically deformed backplate  12 . The stretching of the film  16  is done using a panel member having an aperture with the same radius of the bearing. The edge of the aperture is used as a boundary to; apply uniform hoop stress while stretching the film. To assist the film  16  in conforming to the spherical backplate  12 , the ball bearing is heated to 35˜40° C. Holding the film  16  in the stretched position for 20˜30 seconds creates a half sphere, for fitting the spherical backplate  12 . The film  16  is attached to the backplate  12  by applying 20˜30 V dc biased to the transducer. This same process can be used to stretch and attach such films as 12.5 μm thick Kapton polyimide film. 
         [0051]      FIG. 5  is a graph illustration of amplitude response and corresponding frequency spectrum for the transducer. In  FIG. 56 , tests of the focused capacitive spherical transducer  10  show an ideal spherically focused piston transducer&#39;s beam diameter. The sound pressure fields are measured by scanning a 200-em quasi-point receiver and recording its output voltage versus position. The focused capacitive spherical transducer  10  is driven at 250 V p-p  using a broadband sweep signal. In particular,  FIG. 5A  shows a typical response of the focused transducer at the focal zone (z) of ˜50.8 mm when the quasi point receiver is applied at 250 dc V.  FIG. 5B  shows a corresponding frequency spectrum. The frequency spectrum is centered at 805 kHz with 6-dB points and a bandwidth of approximately 800 kHz, measured at a lower and upper frequency of 400 and 1200 kHz, respectively. 
         [0052]      FIG. 6A-E  are illustrations of measured sound pressure fields for the transducer. Shown in  FIGS. 6A and 6B  are pressure fields for broadband excitation in the x-z plane at y=0 over an 8-mm×35-mm area with a spatial resolution of 100 μm, starting at z=15 mm. The origin of the coordinate system is located at the center  38  of the concave face of the spherical backplate  12  in the transducer  10 , as best illustrated in  FIG. 4 . Darker regions near the center represent stronger sound pressure fields with the adjacent lying lighter regions representing a weakened sound pressure field. The pressure field  40  shows a starting and ending of the focal zone with ˜6 dB points located at 19.1 mm and 32.2 mm.  FIG. 6C-E  shows the sound pressure fields  40  in the cross-sectional regions (x-y plane) at the focal zone over 6 mm×6 mm area, respectively. The beam diameter is approximately 2.1 mm at z=18 mm, z=25 mm and z=35 mm respectively for  FIG. 6C-E  when the transducer is driven by a broadband signal.  FIG. 6C  shows the maximum amplitude for the measured sound field occurring at ˜z=25 mm. The maximum amplitude fades in signal strength as the focal length approaches z=18 mm and z=35 mm, as best illustrated by  FIGS. 6C and 6E , respectively. 
         [0053]      FIG. 7A-7B  are a graph illustration of the cross sections of the focal region of the measured and theoretical sound pressure fields for the transducer. In these graphs, the liner scan measurements and theoretical predictions are shown along the x-axis with a spatial resolution of 0.1 mm for 800 kHz tone burst using broadband excitation. The performance of the transducer  10  is compared to the theoretical prediction using a modified Rayleigh-Sommelfield model 16 . The modified Rayleigh-Sommerfield model shows that the pressure, p, in a fluid for a circular piston transducer of radius, a, having uniform piston velocity ν 0  is: 
         [0000]        p ( R   0   ,y ,ω))=− iωρν   0   a   2 [exp( ikR   0 )/ R   0   ][J   1 ( ka  sin θ)/ ka  sin θ]  (1) 
         [0000]    where ρ is the medium density, R 0  is the focal length and k is the wavenumber. The measurements are obtained at the focal zone for each excitation signal found in the x-z plane scan. The full width at half maximum (FWHM) value is measured approximately 1.38 mm and its theoretical predication is 1.37 mm. The transducer  10  is driven by a broadband excitation signal, the measured FWHM value is approximately 2.7 mm at the focal point, z=24.9 mm. Thus, beam diameters of the focused transducer are 1.38 mm and 2.7 mm using an 800 kHz tone burst and broadband excitation. And, the transducer  10  exhibits sound pressures nearly identical to the ideal spherically focused piston transducer&#39;s beam diameter. 
         [0054]      FIG. 8A-B  are illustrations of measured signal intensity and theoretical predications for the transducer.  FIGS. 8A and 8B  show a comparison between the Airy disks of measured signal intensity and theoretical predications for an 800 kHz tone burst.  FIG. 8A  illustrates the measured signal intensity, where the adjacent rings extending out from the center or origin represent a decease in signal intensity.  FIG. 8B  illustrates the theoretical predications calculated using a modified Rayleigh-Sommerfield model. Comparison of  FIG. 8A  with  FIG. 8B  reveals little to no aberrations between the two plots. 
         [0055]    Thus, inducer  10  of the present invention is proof of a simple, yet reliable, fabrication method to produce the natively focused micromachined capacitive air-coupled spherical ultrasonic transducer. By selecting, producing and integrating a flexible substrate with a curved backplate  12  fabrication into the transducer  10  solves the most difficult and unsolved problem plaquing transducers, especially air sound generation and detection. Moreover, because the transducer  10  is natively focused, the transducer  10  eliminates the need for auxiliary devices, such as acoustic mirrors, to focus air-coupled acoustic beams, and still behaves identical to an ideal spherically focused piston radiator. The transducer  10  exhibits higher signal amplitude, wider bandwidth and better spatial resolution and significantly improves air-coupled ultrasonic nondestructive evaluation and imaging applications. 
         [0056]      FIG. 9A-E  are the isometric views of the bottom case, backplate fixture, outer case, insulator, and top cover for the transducer according to one embodiment of the present invention.  FIG. 9A-E  illustrate the design for a 10 mm spherically focused capacitive air-coupled transducer having a 25.4 mm geometric focal length and active angular sensitivity of ±15° with respect to the normal axis and according to one embodiment. The 10 mm diameter transducer is applicable to almost all phase-match angles for common engineering materials, including metals, plastics, carbon and glass fiber composites. In  FIG. 9A  the bottom case  18  is illustrated, as best shown in  FIG. 1 . The bottom case  18  is preferably manufactured by machining out of aluminum stock. Dimensions, clearances, feature parts and tolerances for manufacturing are noted in each engineering drawing.  FIG. 9B  is the backplate fixture  14 , as best shown in  FIG. 1 . The backplate fixture  14  is also preferably manufactured from aluminum stock, having a high degree of machinability. The outer case  20  is shown in  FIG. 9C . The outer case  20  is machined from aluminum stock. The outer case  20  is also shown in  FIG. 1 .  FIG. 9D  is an engineering drawing for the insulator. The insulator is preferably constructed of Delrin and is also shown in  FIG. 12 .  FIG. 9E  shows the top cover  24  of the insulator  10  device. The top cover  24  is shown in  FIG. 1 , as well. The top cover  24  is preferably manufactured from aluminum stock and has an aperture with a radius  36  of 1 inch. 
         [0057]      FIG. 10A-E  are the isometric views of the bottom case, backplate fixture, outer case, insulator, and top cover for the transducer according to one embodiment of the present invention.  FIG. 10A-E  illustrate the design for a 50 mm spherically focused capacitive air-coupled transducer having a 50.8 mm geometric focal length and active angular sensitivity of ±33° with respect to the normal axis and, according to another embodiment. The 50 mm diameter transducer is applicable to almost all phase-match angles for common engineering materials, including metals, plastics, carbon and glass fiber composites. In  FIG. 101A  the bottom case  18  is illustrated, as best shown in  FIG. 1 . The bottom case  18  is preferably manufactured by machining out of aluminum stock. Dimensions, clearances, feature parts and tolerances for manufacturing are noted in each engineering drawing.  FIG. 10B  is the backplate fixture  14 , as best shown in  FIG. 1 . The backplate fixture  14  is also preferably manufactured from aluminum stock, having a high degree of machinability. The outer case  20  is shown in  FIG. 10C . The outer case  20  is machined from aluminum stock. The outer case  20  is also shown in  FIG. 1 .  FIG. 10D  is an engineering drawing for the insulator  22 . The insulator is preferably constructed of Delrin and is also shown in  FIG. 1 .  FIG. 10E  shows the top cover  24  of the transducer  10  device. The top cover  24  is shown in  FIG. 1 , as well. The top cover  24  is preferably manufactured from aluminum stock and has an aperture with a radius  36  of 2 inches. 
       Altering Performance Characteristics 
       [0058]    Various factors determine the performance characteristics of a capacitive air-coupled transducer. Overall, both surface geometries of a backplate  12  and transducer&#39;s operating conditions strongly affect performance characteristics. These include pit diameter  33 , center-to-center spacing  35 , pit depth  34 , bias voltage, and nature of a metalized polymer film  16 . 
         [0059]    Based on the calibration results, the sensitivity of the capacitive transducer  10  is improved by utilizing a smaller pit diameter  33 , wider center-to-center spacing  35 , and increased pit depths  34  on the backplate geometry  12 , as best illustrated in  FIG. 3A-B . In particular, the strongest sound pressure amplitude in air is measured when center-to-center spacing  35  is equal to “4*(pit diameter)”. This same result holds true for both 40 μm and 80 μm pit diameters  33 . Cross couplings between the pits  32  is a strong consideration if the center to center spacing  35  of the pits  32  is too close together. For example, the sensitivity of a backplate  12  with 40 μm pit diameter  33  and 60 μm center-to-center spacing  35  has a 30% lower sensitivity than a backplate  12  with 40 μm pit diameter  33  and 160 μm center-to-center spacing  35 . This finding is evidence of the cross coupling effect when 80 μm pit diameter  33  is employed in the backplate design  12 . Comparison between 120 μm and 320 μm center-to-center spacings  35  shows that the sensitivity decreases approximately 90% when the center-to-center spacing  35  changes from 320 g/m to 120 μm. Accordingly, given a pit diameter  33 , the sensitivity of a capacitive transducer  10  is maximized in part by employing an optimal center-to-center spacing  35  which is 4*(pit diameter). Cross coupling effects increase as pit diameter  33  is increased. 
         [0060]    When a backplate  12  has deeper pits  32  rather than shallower pits  32 , the sensitivity is much higher than employing shallower pits  32  on a backplate  12  design. When pit depth  34  varies from 5.5 μm to 11.7 μm, the sensitivity increases approximately two fold. Thus, there exists an optimal point where the sensitivity is maximized. 
         [0061]    Sensitivity is also increased by either applying high dc bias to the transducer  10  or utilizing a thinner metalized polymer film  16 . In particular, the sensitivity of a capacitive air-coupled transducer  10  increases as the applied bias voltage increases, where the applied bias is higher than the critical voltage and lower than the breakdown voltage of the metallized polymer film  16 . For example, the 6 μm thick Mylar film  16  with a 20 nm thick aluminum layer on one side has a critical voltage around 100 V. The critical voltage is highly dependent on the nature of a metalized polymer film  16 , such as thickness and chemical structure of the polymer layer. 
         [0062]    A thinner metallized polymer film  16  improves the sensitivity of a capacitive transducer  10 . The resulting effect of thinning the metallized polymer film  16  correlates with the resulting effect of applying high dc bias to the transducers  10 . The correlation exists because the polymer film  16  over the pits  32  is vibrated by a high electric field, which is approximately inversely proportional to the thickness of the polymer layer  16 . At the same dc bias, a polymer film  16  with higher dielectric constant generates better sensitivity than a polymer film  16  with lower dielectric constant. For example, 0.5 mil Kapton film  16  exhibits sensitivities 10% higher than the 0.5 mil PET film  16 . Similarly, the 0.3 mil Kapton film  16  shows 20% higher sensitivity than a 0.25 mil PET&#39;s film  16 . The resulting sensitivities related to film thickness incrementally reduces the electrostatic force by 3.3% while the difference in dielectric constant exhibits a 25% increase in electrostatic force. Thus, a thinner polymer layer with high dielectric constant generates higher sensitivity. In addition to these previously noted advantages, the present invention using the Mylar film  16  can be polarized with a high voltage, and when this external voltage is removed a permanent bias voltage remains on the film  16 . This residual bias eliminates the need for an external biasing source during operation of the transducer  10  and allows the transducer  10  to be applied in just the same manner, from an electronic standpoint, as a conventional piezoelectric transducer  12 . This development makes the capacitive transducer easier and more convenient to use. 
         [0063]    The frequency characteristics of the capacitive air-coupled transducer  10  are controlled in part by the surface geometries of a backplate  12  and transducer&#39;s operating conditions, as previously stated. Moreover, the resonant frequency of a capacitive air-coupled transducer  10  significantly increases when a small pit diameter  33 , shallow pit  34 , high bias voltage or thin metalized polymer film  16  are used in the backplate  12  design. Other considerations, such as center-to-center spacing  35  of the pits  32 , are not as influential to the resonant frequency as much as other factors. Variation of center-to-center spacing  35  from 80 μm to 200 μm for a backplate  12  with 40 μm pit diameter  33 , the variation in the resonant frequency is approximately ±23.7 kHz. Variations of approximately ±12.7 kHz result from use of the backplate  12  employing 80 μm pit diameters  33  and varied center-to-center spacing  35  from 120 μm to 400 μm. 
         [0064]    A backplate  12  with shallow pit depths  34 , exhibited higher resonant frequencies, such that the resonant frequency increases linearly as pit depth  34  decreases. More notably, for pit depths  34  less than 15 μm, the resonant frequency of a capacitive air-coupled transducer  10  is inversely increasing with respect to pit depth  34 . 
         [0065]    Similar to center-to-center spacing  35 , bias voltage does not significantly change the resonant frequency. The lowest resonant frequency results when the applied bias voltage is at the critical voltage, 100 V. Except for bias voltages around 100 V, other voltages in the range between 0 and 300 V produce a constant resonant frequency. At 0 V, the resonant frequency is approximately the same as at 300 V. 
         [0066]    Utilizing a thin metalized polymer film  16 , the resonant frequency of a capacitive air-coupled transducer  10  is increased. Particularly, using a 0.25 mil PET film  16  instead of a 0.5 mil PET film  16  results in 40 kHz increase in the resonant frequency. Further, increases in resonant frequency are increased for a Kapton film  16 . The resonant frequency of a 0.3 mil Kapton film is 180 kHz higher than the 0.5 mil Kapton film  16 . 
         [0067]    Similar to the resulting resonant frequency, the bandwidth of a capacitive air-coupled transducer  10  increases with larger pit diameters  33 , shallower pits  34 , high bias voltage, and thinner polymer films  16 . However, center-to-center spacing  35  does not significantly change the bandwidth. As pit depth  34  increases, the bandwidth significantly decreases. When pit depth  34  is 5.5 μm on a copper/polyimide backplate  12 , the bandwidth increases approximately 300 kHz as compared to the 11.7 μm deep pits  34  used in the backplate  12  design. In addition to shallow pits  32 , the pits with large diameter  33  also increases the bandwidth. The order of the variations is not so significant to be considered as minor variations in design. In fact, employing the thin metalized polymer film  16  attains a wider bandwidth. Moreover, a polymer film  16  with a high dielectric constant exhibits a narrower bandwidth than a polymer film  16  with low dielectric constant. 
       Other Options and Variations 
       [0068]    The present invention contemplates numerous other options in the design and use of air-coupled non-contact sensors. It is to be understood, for example, that the air-coupled non-contact sensor need not be spherical but can be of other shapes, including conical, cylindrical, or otherwise shaped depending upon the particular application. It is also to be understood that the flexible backplate can made of other materials, including, but not limited to, the types of materials used in making flexible circuit boards. Also, the present invention contemplates variations in the type of polymer membrane used. Although it is preferred that the membrane be metallized or otherwise have a conductive layer, the membrane need not. Also, the present invention contemplates that an integral thin membrane can be used over the flexible backplate. Where an integral thin membrane is used, there is no need to apply a polymer film such as Mylar and the integral thin membrane would not be susceptible to dust particles or damage. 
         [0069]    These and other options, variations, are all within the spirit and scope of the invention. 
       References 
       [0070]    All the references as listed below are herein incorporated by reference in their entirety. 
       REFERENCES 
       [0000]    
       
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