Patent Publication Number: US-10325136-B1

Title: Acoustic imaging of user input surfaces

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a nonprovisional patent application of, and claims the benefit of, U.S. Provisional Patent Application No. 62/234,283, filed Sep. 29, 2015, and titled “Acoustic Imaging System for Spatial Demodulation of Acoustic Waves,” and U.S. Provisional Patent Application No. 62/234,492, filed Sep. 29, 2015, and titled “Methods for Biometric Imaging of Input Surfaces,” and U.S. Provisional Patent Application No. 62/289,797, filed Feb. 1, 2016, and titled “Acoustic Imaging System for Spatial Demodulation of Acoustic Waves,” and U.S. Provisional Patent Application No. 62/316,091, filed Mar. 31, 2016, and titled “Acoustic Pulse Coding for Imaging of Input Surfaces,” the disclosures of which are hereby incorporated by reference herein in their entirety. 
    
    
     FIELD 
     This disclosure relates generally to acoustic imaging systems, and more particularly, to systems and methods for operating an acoustic imaging system as a biometric sensor in conjunction with an input surface of an electronic device. 
     BACKGROUND 
     An electronic device can include a biometric sensor, such as a fingerprint sensor, to verify a user&#39;s identity. For example, the electronic device can compare fingerprint information obtained by the biometric sensor to fingerprint information stored in a database of verified users. 
     A conventional fingerprint sensor detects changes in capacitance across an array of electrodes positioned below a dielectric. However, the performance of the conventional sensor is limited by the number and density of electrodes, the thickness and scratch-resistance of the dielectric, the time required to sample each electrode, the processing power of the electronic device, and so on. As such, a user operating an electronic device that incorporates a conventional fingerprint sensor typically perceives delay when operating the sensor, which can negatively affect user experience. 
     SUMMARY 
     Embodiments described herein reference an acoustic imaging system configured to obtain an image of the features of an object contacting a surface of a user input surface (e.g., an image of the locations of acoustic impedance mismatch on the surface). In many embodiments, the acoustic imaging system may be configured to resolve an image of a fingerprint of a user contacting an input surface of an electronic device by mapping the ridges of the user&#39;s fingerprint to the input surface. 
     The acoustic imaging system includes a number of acoustic transducers that are configured to generate acoustic outputs (e.g., mechanical waves, acoustic waves, or pulses) into the user input surface in response to a signal from a controller. The controller is configured to provide coded signals such that the acoustic outputs are also coded. 
     In some embodiments, the acoustic imaging system can employ one or more tomographic reconstruction techniques (e.g., reflection, diffraction, transmission, and so on) to obtain the image of the fingerprint. A tomographic acoustic imaging system includes a controller configured to induce an acoustic pulse or wave within the user input surface. The controller generates the acoustic pulse by applying a drive signal to one or more acoustic transducers then operating in a drive mode. When in the drive mode, an acoustic transducer deforms in response to the drive signal. The drive signal is configured to induce an acoustic pulse (such as a surface wave, shear wave, plane wave, or other acoustic pulse type) that propagates through the thickness of, or across a surface of, the user input surface. In some examples, the acoustic pulse can be a Gaussian pulse, a chirp signal (e.g., multiple periods of varying frequency), a sinusoidal burst (e.g., multiple periods of a single frequency), or any other suitable pulse type or shape. 
     In many embodiments, the tomographic acoustic imaging system also includes an image resolver configured to construct an image of the object at the contact area. The image resolver receives multiple planar projections (filtered or otherwise) from the controller and assembles an image of the object at the contact area using, in one example, a filtered back projection technique. 
     In another embodiment, an acoustic imaging system includes a first set of transducers disposed on a first area of a user input surface and a second set of transducers disposed on a second area of the user input surface. The second set of transducers is spaced apart from the first set of transducers. Each transducer in the first set of transducers and the second set of transducer may operate in a drive mode and a sense mode. In the drive mode, the transducer generates a wave that propagates through the user input surface. In the sense mode, the transducer generates an electronic signal when a section of the user input surface adjacent the transducer mechanically deforms as a result of the wave propagating over or through the section. The electronic signal is demodulated based at least in part, on a distance between the first set of transducers and the second set of transducers. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Reference will now be made to representative embodiments illustrated in the accompanying figures. It should be understood that the following descriptions are not intended to limit the disclosure to one preferred embodiment. To the contrary, each is intended to cover alternatives, modifications, and equivalents as may be included within the spirit and scope of the described embodiments as defined by the appended claims. 
         FIG. 1  depicts an example electronic device that can incorporate an acoustic imaging system as such as described herein. 
         FIG. 2  depicts a simplified block diagram of an acoustic imaging system. 
         FIG. 3A  depicts a distribution of acoustic transducers associated with an acoustic imaging system. 
         FIG. 3B  depicts another distribution of acoustic transducers associated with an acoustic imaging system. 
         FIG. 3C  depicts another distribution of acoustic transducers associated with an acoustic imaging system. 
         FIG. 3D  depicts another distribution of acoustic transducers associated with an acoustic imaging system. 
         FIG. 3E  depicts another distribution of acoustic transducers associated with an acoustic imaging system. 
         FIG. 3F  depicts another distribution of acoustic transducers associated with an acoustic imaging system. 
         FIG. 3G  depicts another distribution of acoustic transducers associated with an acoustic imaging system. 
         FIG. 4A  depicts an acoustic imaging system such as described herein, particularly illustrating a planar wavefront traversing an imaging surface at an angle relative to a horizontal axis of the imaging surface. 
         FIG. 4B  is a graphical representation of the planar wavefront of  FIG. 4A , particularly illustrating local attenuation of the wavefront after the wavefront is affected by the object in contact with the imaging surface. 
         FIG. 5A  depicts a simplified block diagram of an acoustic imaging system operating according to a method of transmission-based tomographic image reconstruction. 
         FIG. 5B  depicts a simplified block diagram of an acoustic imaging system operating according to a method of diffraction-based tomographic image reconstruction. 
         FIG. 6  depicts an acoustic imaging system, particularly showing one example distribution of acoustic transducers positioned relative to a top and bottom edge of a rectangular subarea of the imaging surface. 
         FIG. 7  depicts a simplified block diagram of an acoustic imaging system incorporating a reflection-based image resolver configured to generate a two-dimensional image of a fingerprint in contact with an imaging surface such as described herein. 
         FIG. 8A  is a graphical representation of one example voltage waveform that may be applied to an acoustic transducer such as described herein. 
         FIG. 8B  is a graphical representation of one example coded voltage waveform that may be applied to an acoustic transducer such as described herein. 
         FIG. 8C  is a graphical representation of another example coded voltage waveform that may be applied to an acoustic transducer such as described herein. 
         FIG. 8D  is a graphical representation of yet another example coded voltage waveform that may be applied to an acoustic transducer such as described herein. 
         FIG. 8E  is a graphical representation of yet another example coded voltage waveform that may be applied to an acoustic transducer such as described herein. 
         FIG. 8F  is a graphical representation of two coded voltage waveforms that may be applied to two acoustic transducers such as described herein. 
         FIG. 9A  depicts a simplified cross-section of a portion of an acoustic imaging system such as described herein. 
         FIG. 9B  depicts another simplified cross-section of a portion of an acoustic imaging system such as described herein. 
         FIG. 9C  depicts an acoustic imaging system implemented with a distributed controller. 
         FIG. 9D  depicts another acoustic imaging system implemented with a distributed controller. 
         FIG. 10A  depicts another acoustic imaging system such as described herein, specifically showing an extended thin-film transistor layer, associated with a display of an electronic device, supporting an acoustic transducer. 
         FIG. 10B  depicts another acoustic imaging system such as described herein, specifically showing an extended thin-film transistor layer, associated with a display of an electronic device, supporting an acoustic transducer. 
         FIG. 10C  depicts another acoustic imaging system such as described herein, specifically showing an extended thin-film transistor layer, associated with a display of an electronic device, supporting an acoustic transducer. 
         FIG. 10D  depicts another acoustic imaging system such as described herein, specifically showing an extended thin-film transistor layer, associated with a display of an electronic device, supporting an acoustic transducer. 
         FIG. 11  depicts a shift register topology that can be used to drive more than one acoustic transducer substantially simultaneously. 
         FIG. 12  is a simplified system diagram of a sense chip that can be used with one or more acoustic imaging systems such as described herein. 
         FIG. 13  is a flow chart that corresponds to a method of operating an acoustic imaging system. 
         FIG. 14  is a flow chart that corresponds to another method of operating an acoustic imaging system. 
         FIG. 15  depicts example operations of another method of operating an acoustic imaging system. 
     
    
    
     The use of the same or similar reference numerals in different drawings indicates similar, related, or identical items where appropriate. 
     The use of cross-hatching or shading in the accompanying figures is generally provided to clarify the boundaries between adjacent elements and also to facilitate legibility of the figures. Accordingly, neither the presence nor the absence of cross-hatching or shading conveys or indicates any preference or requirement for particular materials, material properties, element proportions, element dimensions, commonalities of similarly illustrated elements, or any other characteristic, attribute, or property for any element illustrated in the accompanying figures. 
     Additionally, it should be understood that the proportions and dimensions (either relative or absolute) of the various features and elements (and collections and groupings thereof) and the boundaries, separations, and positional relationships presented therebetween, are provided in the accompanying figures merely to facilitate an understanding of the various embodiments described herein and, accordingly, may not necessarily be presented or illustrated to scale, and are not intended to indicate any preference or requirement for an illustrated embodiment to the exclusion of embodiments described with reference thereto. 
     DETAILED DESCRIPTION 
     Embodiments described herein generally reference an electronic device that incorporates an acoustic imaging system. Typically, the acoustic imaging system is configured to operate as a fingerprint sensor suitable to obtain fingerprint images from a user that touches an external surface of the electronic device, generally referred to herein as an “imaging surface.” 
     Generally and broadly, an acoustic imaging system can be configured to operate or function in a number of ways, several of which are described herein. In one example, the acoustic imaging system generates a mechanical wave or pulse that propagates across the imaging surface. A finger touching the imaging surface interferes with the propagating wave in a specific manner (e.g., via reflection, attenuation, diffraction, absorption, and so on) that corresponds to locations and sizes of the ridges and valleys of the fingerprint of that finger. The acoustic imaging system thereafter analyzes the interference to resolve an image of the fingerprint. Typically, the acoustic imaging system implements tomographic imaging reconstruction techniques, although this may not be required and other suitable image reconstruction techniques can be used. 
     In many embodiments, the acoustic imaging system includes a number of acoustic transducers (e.g., piezoelectric elements, ultrasonic transducers) arranged in a pattern and mechanically coupled to the imaging surface. In many examples, the acoustic transducers of an acoustic imaging system are arranged to circumscribe a rectangular portion of the imaging surface, although this may not be required. 
     In many embodiments, the acoustic transducers are multimodal and are configured to convert electrical signals into mechanical energy and, additionally, mechanical energy into electrical signals. In other cases, certain acoustic transducers may be purpose-configured to convert electrical signals into mechanical energy, or may be purpose-configured to convert mechanical energy into electrical signals. 
     The acoustic imaging system also includes a controller and an image resolver. The controller is adapted to apply an electrical signal to one or more of the acoustic transducers which, in response, generate one or more mechanical waves or pulses into the imaging surface. This operation is referred to herein as a “drive operation” or a “transmission operation” in which a “drive signal” is applied to one or more acoustic transducers. The acoustic transducers can be driven individually, simultaneously, or according to a particular timing pattern (e.g., beam-forming). In many cases, acoustic transducers are driven with a wide-band pulse centered at a selected fundamental frequency, but this may not be required. For example, an acoustic transducer can be driven with a signal having a specific envelope, such as a pulse-coded envelope or a chirp envelope. 
     As noted above, a finger in contact with the imaging surface interferes with the mechanical wave(s) generated during a drive operation. More specifically, ridges of the fingerprint introduce an acoustic impedance mismatch boundary that causes the mechanical wave(s) to be absorbed, to reflect, and/or to diffract. Accordingly, the controller is also adapted to receive electrical signals generated by the acoustic transducers as a result of those reflections, diffractions, and absorptions. This operation is referred to herein as a “sensing operation” or a “read operation” in which signals generated by one or more acoustic transducers are “read.” 
     Thereafter, the image resolver obtains the electrical signals read by the controller and constructs a map or image of the finger in contact with the imaging surface. Typically, the image resolver implements a tomographic image reconstruction technique, although this may not be required. 
     For example, in one embodiment, the image resolver is configured to receive acoustic reflections caused by a user&#39;s fingerprint. The image resolver reconstructs an image of the fingerprint using spatial and temporal filtering techniques to isolate reflections that result from a particular vector path from an acoustic transducer, to the finger, and back to an acoustic transducer. Once a sufficient number of reflections and/or vector paths are obtained, an image of the fingerprint can be calculated using reflection tomography and/or diffraction tomography techniques, several of which are described below. 
     In another example, the image resolver is configured to receive acoustic waves that are affected by attenuation caused by a user&#39;s fingerprint (e.g., transmitted across a user&#39;s fingerprint). As with reflection and/or diffraction tomography embodiments referenced above, the image resolver in this embodiment reconstructs an image of the fingerprint using spatial and temporal filtering techniques to isolate particular vector paths from an acoustic transducer, across the fingerprint, and to another acoustic transducer. Once a sufficient number of vector paths are obtained, an image of the fingerprint can be calculated using transmission tomography techniques, several of which are described below. 
     In many embodiments, the operational configuration of an image resolver can affect the distribution of acoustic transducers on the imaging surface. Several example distributions of acoustic transducers, each of which may be suitable in certain configurations for transmission tomography embodiments, reflection tomography embodiments, or diffraction tomography embodiments, are described herein. 
     Further, for simplicity of description, the embodiments that follow are described in reference to an acoustic imaging system associated with a display of a portable electronic device, such as a cellular phone or a tablet. In this example, the imaging surface is typically a cover glass or other external surface positioned over the display. The acoustic imaging system is typically coupled to an underside of the imaging surface, accommodated within the housing of the portable electronic device. However, it may be appreciated that this specific configuration is not required and a system such as described herein can be implemented in any suitable manner and can be incorporated into any suitable electronic device including, but not limited to, wearable electronic devices, laptop devices, desktop devices, automotive or aeronautical information or entertainment systems, gaming devices, home or commercial appliances, industrial control devices, and so on. 
     These and other embodiments are discussed below with reference to  FIGS. 1-15 . However, those skilled in the art will readily appreciate that the detailed description given herein with respect to these figures is for explanatory purposes only and should not be construed as limiting. The section headings which appear throughout the description are provided for convenience and organizational purposes only and are not intended to restrict or limit the disclosure within any particular section to the embodiments, modifications, alternatives, details, features, and/or characteristics described in that section. 
       FIG. 1  depicts an example electronic device that can include an acoustic imaging system such as described herein. The acoustic imaging system can be configured in any suitable manner to obtain an image of a fingerprint of a user that touches a display of the electronic device. The acoustic imaging system can be configured to implement reflection tomography, diffraction tomography, transmission tomography, or any other suitable image reconstruction technique. 
     In the illustrated example, the electronic device  100  is implemented as a portable electronic device such as a cellular phone, although such a form factor is not required. The electronic device  100  includes a housing  102  and a display  104 . The display  104  is disposed below a cover configured to protect the display  104 . In many cases, the cover can be formed from an optically transparent and mechanically rigid material such as glass, sapphire, polycarbonate, and the like. The cover can be flat or curved. The cover can extend around the edges or sidewalls of the housing  102 , although this may not be required. The cover can be layered or formed from a single material. 
     In many examples, the display  104  includes one or more of a variety of display elements or layers. For example, the display  104  may include a liquid crystal display, a thin film transistor display, an organic light emitting diode display, organic electroluminescence display, or other type of display. The display  104  may be used to present visual information to the user and may be operated in accordance with one or more display modes or the software applications being executed on the electronic device  100 . In many cases, the display  104  can include or operate in conjunction with one or more input devices. For example, the display  104  may be configured to receive touch, gesture, and/or force input. 
     The electronic device  100  can also include one or more input elements such as a button  106 . The button  106  may be a physical button such as a push button or switch. In other examples, the button  106  can be a touch input device that does not physically depress such as a capacitive button. In other cases, the button  106  can be a virtual button shown on the display  104 . 
     In many embodiments, an acoustic imaging system (not shown) is disposed within the housing  102  of the electronic device  100  and coupled to the cover of the display  104 . The acoustic imaging system is configured to obtain an image of an object, such as the pad of a finger (e.g., fingerprint) of a user  108 , in physical contact with the cover. 
     In one example, the acoustic imaging system is positioned around the perimeter of a portion of the cover that may regularly receive touch input of a user  108 , such as a bottom portion of the cover adjacent the button  106 . In this manner, each time (or at selected times based on operational modes of the electronic device  100 ) the user  108  presses a bottom portion of the display  104 , the acoustic imaging system can be used to resolve an image of a fingerprint of the user  108 . In other cases, more than one fingerprint image can be resolved at the same time. 
     In another example, the acoustic imaging system is positioned around the entire perimeter of the display  104 . In this manner, each time the user  108  presses any portion of the display  104 , the acoustic imaging system can be used to resolve an image of a fingerprint of the user  108 . 
     In other examples, the acoustic imaging system is positioned adjacent a non-display portion of the electronic device  100 . For example, the acoustic imaging system can be positioned around the perimeter of a cap of the button  106 . The acoustic imaging system depresses with the button  106 . In this manner, each time the user  108  presses the button  106 , the acoustic imaging system can be used to map a fingerprint of the user  108 . 
     In yet another example, the acoustic imaging system is positioned adjacent a non-input portion of the electronic device  100 . For example, the acoustic imaging system can be within or coupled to the housing  102  of the electronic device  100 . In this manner, each time the user  108  holds the electronic device  100  in the user&#39;s hand, the acoustic imaging system can be used to map a fingerprint or handprint of the user  108 . 
     Once an image of fingerprint (or other biometrically-unique surface characteristics such as handprints, ear prints, and so on) of the user  108  is mapped by the acoustic imaging system, the obtained image (and/or data derived therefrom, such as the output of a mathematical function such as a hashing function) can be compared to a database of known images or data to determine if the obtained image matches a known image. If an affirmative match is obtained, the electronic device  100  can perform a function or task related to the match. In one example, the electronic device  100  performs an authenticated function, such as displaying financial information or trade secret information on the display  104 . 
     In another example, an acoustic imaging system can be configured to map the biometrically-unique features of a user&#39;s ear (e.g., size, shape, skin patterns, and so on) each time the user raises the electronic device  100  to the user&#39;s ear. In another example, an acoustic imaging system can be configured to map the biometrically-unique features of a user&#39;s hand print (e.g., skin patterns, scar patterns, and so on) each time the user grasps the electronic device  100  in the user&#39;s hand. In some cases, the electronic device can respond differently if the electronic device determines that it is being held by the user  108  in the user&#39;s left or right hand. 
     In still further examples, the acoustic imaging system can be used for more than one purpose. For example, the acoustic imaging system may be used as a touch sensor in addition to a fingerprint sensor. In other cases, the acoustic imaging system can be used exclusively for touch sensing. 
     The foregoing embodiments depicted in  FIG. 1  and the various alternatives thereof and variations thereto are presented, generally, for purposes of explanation, and to facilitate an understanding of various possible methods for dividing and/or distributing the processing and/or signal conditioning load of an acoustic imaging system such as described herein. Instead, the depicted examples are understood to be merely a subset of the representative embodiments of an electronic device that can incorporate an acoustic imaging system such as described herein that may be implemented within the spirit and scope of this disclosure. 
       FIG. 2  depicts a simplified block diagram of an acoustic imaging system. The acoustic imaging system  200  includes a distribution of acoustic transducers, identified as the acoustic transducers  202 , arranged in a rectangular configuration (although this is not required of all embodiments and other patterns and arrangements are possible). Each of the acoustic transducers  202  contract or expand in response to an electrical signal supplied by a controller  204 . In many examples, the acoustic transducers are formed with a piezoelectric material as lead zircanate titinate, zinc oxide, aluminum nitride, potassium niobate, bismuth titinate, or any other piezoelectric material. 
     The acoustic transducers can be coupled to an imaging surface (not shown), such as the cover of the display  104  of the electronic device  100  as shown in  FIG. 1 . In another example, the acoustic transducers can be coupled to a support or a frame within the electronic device  100 . 
     In many examples, the acoustic transducers are arranged to circumscribe an interior portion of the imaging surface. For example, the acoustic transducers  202  can circumscribe a rectangular area. In this manner, the acoustic transducers  202  follow the periphery or perimeter of the circumscribed portion. In other cases, the distribution of acoustic transducers  202  can circumscribe a different area, such as a square, circular, polygonal, or arbitrarily-shaped area. In many cases, the acoustic transducers are formed onto a top or bottom imaging surface nearby the imaging surface&#39;s edge, although this is not required. 
     In many embodiments, the acoustic transducers are configured for both inducing and detecting mechanical waves (e.g., shear waves, surface waves, longitudinal waves, transverse waves, cylindrical waves, and so on) in or on the imaging surface. In other words, an acoustic transducer can be operated in more than one mode. An acoustic transducer operated in a drive mode generates a mechanical wave in the imaging surface in response to an electrical signal from the controller  204 . The same acoustic transducer operated in a sense mode generates an electrical signal in response to a mechanical wave within the imaging surface. 
     In other embodiments, certain acoustic transducers of the distribution of acoustic transducers  202  can be configured to operate in only a drive mode or a sense mode. A drive acoustic transducer can be paired with, or positioned adjacent to, a sense acoustic transducer. In one example, a row of drive acoustic transducers is positioned adjacent a row of sense acoustic transducers. Other implementation-specific configurations, groups, and arrangements of drive acoustic transducers and sense acoustic transducers can be used in particular embodiments. 
     The controller  204  is configured to provide electrical energy in the form of an electrical signal (e.g., impulse, square wave, triangular wave, sine wave, or other waveform) to each acoustic transducer of the distribution of acoustic transducers  202 . In some cases, an acoustic transducer may be configured to resonate at a particular frequency, but this may not be required. 
     In one example, the controller  204  can provide a first voltage to a first acoustic transducer and a second voltage to a second acoustic transducer. In addition, the controller  204  can control the duration, envelope, and magnitude of the voltage applied to each independent acoustic transducer of the one or more acoustic transducers. In some cases, the controller  204  applies the same electrical signal to each acoustic transducer simultaneously, whereas in others, different signals and/or different timing patterns are provided to different acoustic transducers. 
     In one embodiment, the controller  204  applies an electrical signal to groups or sets of acoustic transducers. For example, if the distribution of acoustic transducers  202  are arranged to circumscribe a rectangular area, the controller  204  can apply an electrical signal the group of acoustic transducers forming a top edge of the rectangular area. Thereafter, the controller  204  can apply an electrical signal to the group of acoustic transducers forming a right edge, left edge, or bottom edge of the rectangular area. In other cases, alternating acoustic transducers can be driven at the same time. 
     The controller  204  can also operate in one or more modes. In certain embodiments, the controller  204  is operated in a transmission mode. Herein, the term “transmission mode” refers to a controller mode in which the controller provides electrical energy (e.g., drives) to one or more acoustic transducers. 
     When in the transmission mode, the controller  204  is configured to provide electrical energy in the form of an electrical signal to one or more of the acoustic transducers of the distribution of acoustic transducers  202 . In response, the acoustic transducers produce an acoustic output in the form of a mechanical wave within the imaging surface, directed inwardly toward the circumscribed portion. In many embodiments, the electrical energy provided by the controller  204  is an abbreviated electrical pulse that induces a mechanical wave in the imaging surface. In many cases, the controller  204 , in a transmission mode, induces the acoustic transducers to generate a substantially longitudinal and/or planar mechanical wave with minimal transverse components (e.g., pressure pulse, surface wave, or pulse wave). 
     As noted above, the controller  204  can apply an electrical signal to groups of acoustic transducers. In this case, the controller  204 , in a transmission mode, induces a selected group of acoustic transducers to generate a substantially longitudinal and/or planar mechanical wave, with minimal transverse components, that traverses the imaging surface substantially parallel to the group. For example, if the distribution of acoustic transducers  202  are arranged to circumscribe a rectangular area, the controller  204  can apply an electrical signal the group of acoustic transducers forming a top edge of the rectangular area, which, in turn, induces a substantially longitudinal and/or planar mechanical wave that traverses the rectangular area toward a bottom edge thereof. Similarly, the controller  204  can induce a mechanical wave that traverses the rectangular area from a right edge to a left edge, from a left edge to a right edge, and from a bottom edge to a top edge. 
     In still other examples, the controller  204  can induce a mechanical wave from a portion of one edge, or a mechanical wave that traverses the circumscribed portion at an angle. For example, a controller  204  can induce a mechanical wave to traverse the circumscribed portion from a right edge of the circumscribed portion to the top edge of the circumscribed portion. 
     In other embodiments, in a transmission mode, the controller  204  can apply an electrical signal to an individual acoustic transducer. More generally, the controller  204  can apply an electrical signal to a single acoustic transducer, a group of acoustic transducers, a line of acoustic transducers, all acoustic transducers, a pattern of acoustic transducers, and so on. The controller  204  may (in the transmission mode), in some embodiments, apply the electrical signal(s) at different times to induce different mechanical waves within the imaging surface. For example, the controller  204  can be configured to induce a plane wave, a series of plane waves, an angular wave, a patterned wave, or any other suitable wave or waves. 
     After producing the mechanical wave or waves within the imaging surface with one or more acoustic transducers, the controller  204  can transition into a receiving mode. In a receiving mode, the controller  204  couples to one or more acoustic transducers, sampling electrical signals generated thereby over a period of time. In many cases, the controller  204  transitions to the receiving mode immediately after generating the mechanical wave in the transmission mode. For example, the controller  204  (in the transmission mode) can apply an electrical signal to a single acoustic transducer, after which the same acoustic transducer and/or other acoustic transducer(s) adjacent to or separated from that acoustic transducer can be monitored by the controller  204  (in the receiving mode) for electrical signals generated in response to received acoustic reflections, diffractions, or absorptions. 
     An image resolver  206  communicates with the controller  204  and a touch sensor  208 . The image resolver obtains the electrical signals received by the controller  204  in the receiving mode. If a finger is not in physical contact with the imaging surface (as determined by the touch sensor  208 ), the mechanical wave is not disturbed and only minimal, if any, reflection, diffraction, or attenuation the energy of the mechanical wave occurs as the wave traverses of the circumscribed portion of the imaging surface. 
     Alternatively, if a finger is in contact with the imaging surface, one or more acoustic impedance mismatch boundaries are introduced that cause the mechanical wave generated during a drive operation (e.g., transmission mode of the controller  204 ) to reflect, diffract, or attenuate the energy of that mechanical wave. The image resolver  206  constructs an approximated map (e.g., image) of the object by analyzing the signals received by the controller  204 . In many cases, the image resolver  206  employs a spatial filtering technique to generate an image of the object in contact with the imaging surface. 
     As used herein, the term “image” or the phrase “resolved image” refers to a two-dimensional collection of pixels, generated by an image resolver or similar component, system or system (e.g., the image resolver  206 ). The coordinates of a resolved image can correspond to local surface characteristics of an imaging surface that may change when an object, such as a user&#39;s finger, is placed in contact with the imaging surface at that location. The area over which an object contacts the input surface is referred to herein as the “contact area.” In many cases, the contact area is determined by the touch sensor  208 . 
     Reflection/Diffraction-Based Image Resolver 
     In some embodiments, each pixel of a resolved image corresponds to a partial reflection of an acoustic pulse propagating through the input surface at that respective pixel location. Such embodiments are referred to here as “reflection-based” image resolver embodiments. In certain embodiments, an image resolver can operate in more than one mode, which may include a reflection mode. 
     For a reflection-based image resolver (or an image resolver in a reflection mode), the amount of reflection or diffraction (e.g., collectively, a “reflection coefficient”) associated with a particular location of an imaging surface corresponds to a value (e.g., darkness, lightness, color, brightness, saturation, hue, and so on) of the associated pixel of the resolved image. 
     The resolution of the resolved image generated by a reflection-based image resolver (and thus the number and/or distribution of pixels) can be based, at least in part, on the expected or average size of various features of the user&#39;s fingerprint. In one example, the resolution of the resolved image generated by a reflection-based image resolver is greater than 100 pixels per centimeter. In some cases, the resolution of the resolved image may be non-uniform; certain areas of the resolved image may have a higher resolution than other areas. 
     As may be appreciated, the reflection coefficient(s) associated with a particular location of the imaging surface (e.g., a “local reflection coefficient”) changes when a fingertip (or more particularly, a “feature” of a fingertip, such as a ridge) is in physical contact with the imaging surface at that specific location. As noted with respect to other embodiments described herein, this is due to an acoustic impedance mismatch introduced at that location by features of the fingerprint. 
     In this manner, the value of each pixel of the resolved image corresponds to whether or not a feature of a fingertip is in contact with the imaging surface—and causes a reflection—at that pixel location. As such, the pixels of the resolved image generated by a reflection-based image resolver correspond to whether a ridge or a valley of a user&#39;s fingerprint is present at that pixel location. 
     Accordingly, an acoustic imaging system incorporating a reflection-based image resolver such as described herein (e.g., the acoustic imaging system  200 ) can be configured to resolve an image of a user&#39;s fingerprint by resolving an image of the acoustic reflection effects provided by various features of the fingertip that make physical contact with the imaging surface at different locations. Embodiments employing such techniques are generally referred to herein as “reflection/diffraction tomography acoustic imaging system.” The acoustic imaging system  200  can be implemented as a reflection/diffraction tomography acoustic imaging system. 
     Generally and broadly, a reflection/diffraction tomography acoustic imaging system such as described herein may be multimodal or may be configured to operate only in a single mode. For example, a reflection/diffraction tomography acoustic imaging system may be configured to obtain an estimation of an acoustic reflection map by reflection/diffraction-based tomographic reconstruction techniques or by diffraction-based tomographic reconstruction techniques. 
     In other examples, a reflection/diffraction tomography acoustic imaging system may be configured to use both reflection/diffraction and diffraction based tomographic reconstruction techniques. In still further examples, a reflection/diffraction tomography acoustic imaging system may be configured to use additional tomographic reconstruction techniques associated with, but not limited to: acoustic diffraction, acoustic impedance, acoustic reflection, acoustic transmittance, acoustic pulse phase shifting, and so on. 
     Generally, the phrase “reflection information” as used herein references the raw spatial and temporal information received by an acoustic transducer that corresponds to the reflection(s) that result from the introduction of one or more acoustic pulses into an imaging surface, whether such information is contained in one or more electrical signals, digital values, voltage or current values, mechanical waves, or any other suitable format or translation. In many cases, reflection information will include noise, parasitic acoustic modes, multipath propagation effects, attenuation, and so on, that may be filtered, reduced, or otherwise eliminated in a processing operation performed by the image resolver  206 . 
     The quantity of reflection information accumulated by the acoustic imaging system incorporating a reflection-based image resolver generally increases with the number of transmitting operations performed. As such, it may be typical for an acoustic imaging system incorporating a reflection-based image resolver to perform a large number of transmitting operations prior to generating a fingerprint image. 
     For example, an transmitting operation can be performed with a single acoustic transducer. In this example, the single acoustic transducer generates an acoustic pulse and collects reflection information while all other acoustic transducers are idle. Such embodiments are referred to herein as “single-pulse transmitting operations.” The acoustic imaging system incorporating a reflection-based image resolver may be idle during the travel time of the acoustic pulse from the acoustic transducer to the contact area and during the return travel time of the acoustic pulse from the contact area back to the acoustic transducer. A subsequent single-pulse transmitting operation performed with the same or a different acoustic transducer may be initiated after a short dissipation period has elapsed. As used herein the term “dissipation period” refers to a period of time required for acoustic energy introduced to the imaging surface to dissipate. In this manner, the full “time of flight” for a single-pulse transmitting operation is defined by the propagation time required for the acoustic pulse to reach the contact area, the reflection propagation time required for the reflection of the contact area to reach the acoustic transducer, and the dissipation period required before a subsequent transmitting operation can be performed. 
     In other cases, multiple single-pulse transmitting operations may be performed in sequence with the same acoustic transducer. The reflection information accumulated as a result of these multiple single-pulse transmitting operations may be averaged. 
     Once a sufficient number of transmitting operations are performed, the acoustic imaging system  200  incorporating a reflection-based image resolver, such as the image resolver  204 , can manipulate, filter, or process the accumulated reflection information associated with certain vector paths through the imaging surface to generate to an image of the user&#39;s fingerprint. The image resolver  204  can implement any suitable image reconstruction technique. In one example, the image resolver  204  uses a tomographic image reconstruction technique, but this is not required. 
     The acoustic pulse of a particular transmitting operation may be generated in any suitable manner. For example, an acoustic pulse can be generated by applying a varying voltage signal to an acoustic transducer. 
     In other embodiments, each acoustic transducer of the acoustic imaging system incorporating a reflection-based image resolver is tuned and/or configured to resonate at a particular frequency. Any suitable resonant frequency can be selected, although in many embodiments, the resonant frequency is based, at least in part, on the Nyquist sampling rate required to reliably distinguish the ridges and valleys of the average user&#39;s fingerprint from one another. More specifically, the Nyquist sampling rate relates to the spatial frequency bandwidth (e.g., maximum wavelength defined by the speed of sound through the input surface) required to reliably distinguish the ridges and valleys of a fingerprint. In other embodiments, the resonant frequency of the acoustic transducers may also be based, at least in part, on the speed of sound through the imaging surface. 
     Although many embodiments provide acoustic transducers that are tuned to the same resonant frequency, this may not be required. For example, an acoustic transducer disposed near an edge of the imaging surface may be tuned to resonate at a different frequency than an acoustic transducer disposed near a centerline of the same imaging surface. In other embodiments, adjacent acoustic transducers may be tuned to different resonant frequencies so that adjacent acoustic transducers can be operated simultaneously. Without regard to a particular resonant frequency, the phrase “resonant mode” is used herein to refer to an acoustic transducer operated at or near resonance, whether such an acoustic transducer is associated with a reflection-based image resolver or any other suitably-configured image resolver or acoustic imaging system. 
     For embodiments in which an acoustic transducer has a specifically-tuned resonant mode, an acoustic pulse can be generated by applying an impulse voltage signal (e.g., a voltage signal of finite duration) to the acoustic transducer. The impulse voltage signal, having a bandwidth that includes the resonant frequency, triggers the resonant mode. During the resonant mode, the acoustic transducers outputs acoustic energy for one or more periods of the resonant frequency resulting in an acoustic pulse that propagates across the imaging surface. In this manner, the acoustic pulse has a carrier frequency approximately equal to the resonant frequency. In one example, the resonant frequency is approximately 5 MHz. In these embodiments, a single-pulse transmitting operation can be performed by applying an impulse voltage signal to a single acoustic transducer. 
     In other embodiments, a coded series of impulse voltage signals can be applied to one or more acoustic transducers. The series of impulse voltage signals generates a coded series of acoustic pulses that traverse the imaging surface as a series. 
     As a result of the coding, the acoustic imaging system incorporating a reflection-based image resolver may be able to perform several transmitting operations in rapid sequence. These embodiments are referred to herein as “multi-pulse transmitting operations.” The reflection information associated with each pulse in a multi-pulse transmitting operation may be averaged together. In this manner, the full time of flight for a multi-pulse transmitting operation is defined by the propagation time required for the last acoustic pulse of the series to reach the contact area, the reflection propagation time required for the last reflection of the contact area to reach the acoustic transducer, and the dissipation period required before a subsequent transmitting operation can be performed. It is appreciated that the full time of flight for a multi-pulse transmitting operation is similar to, albeit slightly longer than, the full time of flight for a single-pulse transmitting operation. 
     The series of impulse voltage signals of a multi-pulse transmitting operation may be coded in any suitable manner including, but not limited to, phase coding, multi-level coding, chirp coding, and so on. The phrases “impulse coding,” “impulse-coded,” or “impulse-coded acoustic pulse” generally refer to the acoustic pulses generated as a result of a series of discrete voltage impulses provided to at least one acoustic transducer in a particular pattern of phase, amplitude, and/or timing. 
     In some embodiments, the acoustic imaging system incorporating a reflection-based image resolver may exclusively perform single-pulse transmitting operations. In other embodiments, the acoustic imagining system may exclusively perform multi-pulse transmitting operations. In many embodiments, however, the acoustic imaging system incorporating a reflection-based image resolver may shift between single-pulse transmitting operations and multi-pulse transmitting operations. For example, a single-pulse transmitting operation may be performed when a contact area is nearby an edge of the imaging surface or when the contact area is nearby the acoustic transducers. In other cases, a multi-pulse transmitting operation may be performed when the contact area is within a central portion of the imaging surface. It may be appreciated that the listing given above is not exhaustive; other embodiments may perform a variety of transmitting operations in any other suitable implementation-specific or appropriate manner or pattern. 
     In still further embodiments, two or more transmitting operations, whether single-pulse or multi-pulse, may be propagated simultaneously. These acoustic pulses may be propagated orthogonal to one another such that reflections corresponding to one of the acoustic pulses do not destructively interfere with reflections corresponding to the other acoustic pulse. The phrases “spatial coding,” “spatially-coded,” or “spatially-coded acoustic pulse” generally refer to the acoustic pulses generated as a result of one or more voltage impulses provided to at least two acoustic transducers that are generally oriented orthogonal to one another. 
     In these embodiments, the acoustic imaging system incorporating a reflection-based image resolver maybe configured to generate multiple impulse-coded and spatially-coded acoustic pulses that can be propagated across an imaging surface simultaneously, thereby operating in a more time-efficient manner. 
     Example embodiments of acoustic imaging systems incorporating reflection-based image resolver, and various techniques for implementing reflection or diffraction tomography are described in greater detail in reference to  FIGS. 6-8F . 
     Attenuation-Based Image Resolver 
     In other embodiments, each pixel of a resolved image corresponds to an attenuation to an acoustic pulse propagating through that respective pixel location. Such embodiments are referred to here as “attenuation-based” image resolver embodiments. In certain embodiments, an image resolver can operate in more than one mode, which may include an attenuation mode. 
     The amount of attenuation (e.g., an “attenuation coefficient”) at a particular location corresponds to a value (e.g., darkness, lightness, color, brightness, saturation, hue, and so on) of the associated pixel of the resolved image. For example, the attenuation coefficient may be a number from 0 to 1.0, and the corresponding pixel may include a brightness value from 0 to 255 units. In other cases, other resolutions or representations are possible. In this example, the attenuation coefficient and the brightness of the corresponding pixel value may be linearly related, although such a relationship is not necessarily required of all embodiments. 
     As with other embodiments described herein, the resolution of the resolved image generated by an attenuation-based image resolver (and thus the number and/or distribution of pixels forming the same) can be based, at least in part, on the expected or average size of various features of the user&#39;s fingerprint. In one example, the resolution of the resolved image is greater than 120 pixels per centimeter (approximately 300 pixels per inch). In further examples, the resolution of the resolved image is greater than or equal to 200 pixels per centimeter (approximately 500 pixels per inch). In still further examples, other resolutions may be suitable. In some cases, the resolution of the resolved image may be non-uniform; certain areas of the resolved image may have a higher resolution than other areas. 
     As may be appreciated, the attenuation coefficient associated with a particular location of the input surface (e.g., a “local attenuation coefficient”) changes when a fingertip is in physical contact with the input surface at that specific location. This is due to an acoustic impedance mismatch introduced by the fingertip to the input surface at that location. 
     For example, a feature of a fingertip in direct physical contact with the input surface at a particular location (e.g., a ridge of a fingerprint) attenuates an acoustic pulse propagated therethrough, thereby affecting the value of the associated pixel of the resulting image. Conversely, a feature that does not contact the input surface (e.g., a valley of a fingerprint) may not substantially attenuate acoustic pulses propagated therethrough, similarly not affecting the value of the associated pixel of the resulting image. 
     In this manner, the value of each pixel of the resolved image corresponds to whether or not a feature of a fingertip is in contact with the input surface at that pixel location. More specifically, the pixels of the resolved image generated by an attenuation-based image resolver correspond to whether a ridge or a valley of a user&#39;s fingerprint is present at that pixel location. In this manner, the resolved image may serve as a direct proxy for an image of the user&#39;s fingerprint. 
     Furthermore, different features of a fingertip may introduce different acoustic impedance mismatches, thus resulting in different local attenuation coefficients and different pixel values in the resolved image. For example, denser features of the fingertip (e.g., scar tissue) contacting the input surface may change local attenuation coefficient(s) differently than less dense features contacting the input surface. In other cases, the force with which the user touches the input surface may affect local attenuation coefficients by compressing the fingertip against the input surface. In this manner, the resolved image may exhibit contrast corresponding to the relative density of features of the fingertip. 
     Accordingly, generally and broadly, an acoustic imaging system that incorporates an attenuation-based image resolver such as described herein is configured to resolve an image of a user&#39;s fingerprint by resolving an image of the acoustic attenuation effects provided by various features of the fingertip that make physical contact with the input surface at various location. Such an image is referred to herein as an “acoustic attenuation map” of an input surface or contact area. 
     In some embodiments, an acoustic attenuation map can be modeled as a matrix, a vector, or as a function, the inputs of which are coordinates that correspond to locations on the input surface. In one example, the estimated attenuation coefficient α x     1     ,y     1    associated with a point (x 1 , y 1 ) on the input surface can be modeled by the following equation:
 
α x     1     ,y     1     =f   m ( x   1   ,y   1 )  Equation 1
 
     It may be appreciated that an acoustic imaging system such as described herein can obtain, resolve, or estimate an acoustic attenuation map (such as the function f m (x, y) of Equation 1) of an input surface (or contact area of the input surface) using any suitable or implementation-specific method or combination of methods, several of which are described in detail below. 
     For example, in one embodiment, an acoustic imaging system incorporating an attenuation-based image resolver employs tomographic reconstruction techniques to estimate an acoustic attenuation map of a contact area. Embodiments employing such techniques are generally referred to herein as “transmission tomography acoustic imaging system.” The acoustic imaging system  200  can be implemented as a transmission tomography acoustic imaging system. 
     Generally and broadly, a transmission tomography acoustic imaging system such as described herein may be multimodal or may be configured to operate only in a single mode. For example, a transmission tomography acoustic imaging system may be configured to obtain an estimation of an acoustic attenuation map by transmission-based tomographic reconstruction techniques or by diffraction-based tomographic reconstruction techniques. 
     In other examples, a transmission tomography acoustic imaging system may be configured to use both transmission and diffraction based tomographic reconstruction techniques. In still further examples, a transmission tomography acoustic imaging system may be configured to use additional tomographic reconstruction techniques associated with, but not limited to: acoustic diffraction, acoustic impedance, acoustic reflection, acoustic transmittance, acoustic pulse phase shifting, and so on. 
     For embodiments configured to operate with transmission-based tomographic techniques, the transmission tomography acoustic imaging system can be configured to estimate an acoustic attenuation map of a contact area at which a user&#39;s fingertip touches the input surface through analysis of multiple planar projections of that contact area. A planar projection of the contact area may be obtained by propagating an acoustic pulse across the input surface and thereafter measuring, at multiple locations, the amplitude of the acoustic pulse that transmitted through the contact area. The acoustic pulse typically has a high-frequency carrier. 
     Collectively, the multiple measured amplitudes represent a discretized projection of the contact area onto a plane orthogonal to the input surface. This projection is referred to herein as a “planar projection” of the contact area and the angle between the projection plane and the plane of the input surface is referred to, generally, as the “angle” of the planar projection, or more particularly, the angle at which the planar projection is taken. 
     In some examples, the acoustic pulse can be a plane wave generated to exhibit a planar wavefront that is oriented in any suitable manner relative to an axis (e.g., horizontal axis or vertical axis) of the plane of the input surface. As used herein the term “wavefront” generally refers to portions of an input surface affected by the same phase of the acoustic pulse, at the same amplitude, at a particular time. For example, the acoustic pulse can exhibit a planar wavefront that traverses the input surface parallel to a horizontal axis thereof (e.g., traversing the contact area from right to left or left to right). In other cases, the acoustic pulse can be a plane wave with a planar wavefront that traverses the input surface perpendicular to the horizontal axis thereof (e.g., traversing the contact area from top to bottom or bottom to top). In still further cases, the acoustic pulse can be a plane wave with a planar wavefront that traverses the input surface at any arbitrary angle relative to the horizontal axis thereof. 
     Herein, the term “direction” of an acoustic pulse refers to the angle at which a wavefront of an acoustic pulse traverses the input surface, relative to a horizontal axis of the input surface. In some cases, the controller can implement beam-forming techniques in order to direct the acoustic pulse along a particular path. Typically, as may be appreciated, the direction of a planar wavefront is equal to the angle of the planar projection obtained after propagating that wavefront. 
     In some examples, the acoustic pulse can be generated from a point source, inducing a wave that exhibits a spherical wavefront. In these embodiments, the direction of the acoustic pulse may be based on the angle of a vector originating at the point source and intersecting the geometric center of the contact area. In these examples, the transmission tomography acoustic imaging system may apply spatial filtering techniques to the planar projection in order to spatially normalize (e.g., linearize) the various values of the same, each of which may be at a different angle relative to the point source. In other cases, different values of different planar projections which are approximately parallel to one another may be combined into a single planar projection. 
     In many embodiments, a transmission tomography acoustic imaging system configured for transmission-based reconstruction obtains a number of differently-angled planar projections as a set. In some cases, the various planar projections of the set of planar projections may be taken at regular angular intervals around the contact area, although this is not required. The set of planar projections of the contact area, each taken at different angles, is referred to herein as the Radon transform (e.g., sinogram) of the contact area. 
     The transmission tomography acoustic imaging system can calculate or estimate the inverse Radon transform of the contact area in any number of suitable ways. In one embodiment, the transmission tomography acoustic imaging system constructs a system of equations based on, at least, the location of each pixel and the values of each planar projection. 
     In other embodiments, the transmission tomography acoustic imaging system can utilize a filtered back projection technique (or any other suitable inverse Radon transform calculation technique, either discrete or continuous) to combine and/or interlace the set of planar projections together in order to generate an acoustic attenuation map of the contact area which, in turn, can be used as a direct proxy for an image of the user&#39;s fingerprint. 
     To perform the operations described above, a transmission tomography acoustic imaging system includes several acoustic transducers that are coupled to the input surface. Additionally, the transmission tomography acoustic imaging system includes a controller and an image resolver. Generally and broadly, the controller provides electrical signals to, and obtains electrical signals from, the acoustic transducers. As noted above, the received electrical signals correspond to (either before or after filtering), a planar projection of the contact area. The controller then provides the received electrical signals (e.g., the planar projection(s)) to the image resolver which processes the signals to obtain the acoustic attenuation map by determining or approximating the inverse Radon transform of the same. 
     Alternatively or additionally, a transmission tomography acoustic imaging system can be configured to utilize diffraction-based reconstruction techniques. In these embodiments, the transmission tomography acoustic imaging system can be configured to estimate an acoustic attenuation map of a contact area at which a user&#39;s fingertip touches the input surface through analysis of various frequency-domain spectra received as a result of diffraction of an acoustic pulse traversing the contact area. As with other embodiments described herein, the transmission tomography acoustic imaging system may propagate an acoustic pulse across the input surface and thereafter measure, at multiple locations, the amplitude of the acoustic pulse that transmitted through the contact area. As with other embodiments, the acoustic pulse typically has a high-frequency carrier. 
     In this example, when an acoustic pulse reaches the contact area, a portion of the energy of the acoustic pulse may be absorbed (e.g., attenuated), such as described above. Additionally, the acoustic pulse may be diffracted (e.g., de-focused or spread). The amount of diffraction at a particular point is based on the properties, both physical and acoustic, of the feature of the object in contact with the surface of the contact area at that point. 
     Furthermore, the envelope of the diffraction pattern may be predictable based on the location of the feature. For example, a feature that is physically close to the point (or points) from which the acoustic pulse was generated may diffract the pulse in a fan pattern (e.g., a conic section of the input surface oriented parallel to the direction of the wavefront of the acoustic pulse). The width of the diffraction pattern envelope may depend upon the relative distance between the feature causing the diffraction and the source of the acoustic pulse and/or the distance between the feature causing the diffraction and the location(s) at which the system measures the diffraction. Utilizing the predicted diffraction envelope, the transmission tomography acoustic imaging system can spatially filter signals received (e.g. the received electrical signals) in order to obtain electrical signals that fall within a fan pattern (e.g., diffraction envelope) that may be generated as a result of the acoustic pulse passing through a particular point of the contact area. 
     After spatial filtering, the transmission tomography acoustic imaging system can calculate the Fourier transform (or any other suitable frequency-domain transform, in either discrete or continuous time) of the electrical associated with a particular spatially-filtered fan pattern. In many embodiments, the transmission tomography acoustic imaging system may utilize frequency and/or phase information of the Fourier transform in order to back-project an estimated attenuation value onto the specific location of the contact area. After a sufficient number of back projections for a particular location of the contact area are obtained, the attenuation coefficient of the location may be estimated. 
     Example embodiments of acoustic imaging systems incorporating attenuation-based image resolver are described in greater detail in reference to  FIGS. 4A-5B . 
     The foregoing description of the embodiments depicted in  FIGS. 1-2 , and various alternatives and variations, are presented, generally, for purposes of explanation, and to facilitate a thorough understanding of the detailed embodiments presented below. However, it will be apparent to one skilled in the art that some of the specific details presented herein may not be required in order to practice a particular described embodiment, or an equivalent thereof. 
     Thus, the foregoing and following descriptions of specific embodiments are presented for the limited purposes of illustration and description. These descriptions are not targeted to be exhaustive or to limit the disclosure to the precise forms recited herein. To the contrary, it will be apparent to one of ordinary skill in the art that many modifications and variations are possible in view of the above teachings. For example, transducers can be arranged on the right and left of an input surface, on the top and bottom of an input surface, around a portion of an input surface, below an input surface, on an edge of an input surface (which may be curved or flat), coupled to the input surface by a waveguide, and so on. In some embodiments, the transducer arrangement can accommodate other components, ports, or parts of an associated electronic device by including gaps. 
     Example Acoustic Transducer Distributions 
     As noted above, an acoustic imaging system, whether such a system incorporates a reflection-based image resolver or an attenuation-based image resolver, is associated with multiple acoustic transducers distributed at various locations along the imaging surface.  FIGS. 3A-3G  depict various example distributions of acoustic transducers that may be used with an acoustic imaging system such as described herein. 
     For example  FIG. 3A  depicts one example distribution of acoustic transducers associated with an acoustic imaging system disposed on a bottom surface of an imaging surface  300   a  so as to circumscribe a substantially rectangular area. The imaging surface  300   a  forms a portion of an external surface of an electronic device, such as the electronic device  100  depicted in  FIG. 1 . 
     The imaging surface  300   a  can take substantially any shape appropriate for a particular implementation. As illustrated, the imaging surface  300   a  is a rounded rectangle. The imaging surface  300   a  is formed from a rigid material such as strengthened glass or sapphire. The rigidity of the imaging surface  300   a  serves to protect the internal components of an electronic device onto which the imaging surface  300   a  is disposed. More particularly, the imaging surface  300   a  may be disposed over a display of the electronic device, such as the electronic device  100  depicted in  FIG. 1 . 
     A number of acoustic transducers can be distributed on the bottom surface of the imaging surface  300   a . The acoustic transducers circumscribe a circumscribed portion  302 . The circumscribed portion  302  is approximately equal to the area of a display that the imaging surface  300   a  is configured to protect. In many cases, the circumscribed portion  302  of the imaging surface  300   a  is transparent, whereas the remainder of the imaging surface  300   a  (e.g., bezel) is opaque. The opaque portions of the imaging surface  300   a  hide the acoustic transducers from view. 
     The acoustic transducers are disposed around the circumscribed portion  302  in four separate linear groups (e.g., rows and/or columns). A top edge group  304   a , a bottom edge group  304   b , a right edge group  304   c , and a left edge group  304   d.    
     As noted with respect to other embodiments described herein, the acoustic transducers can be formed directly onto the bottom surface of the imaging surface  300   a . In other examples, the acoustic transducers can be adhered to the bottom surface of the imaging surface  300   a . In yet other examples, the acoustic transducers are disposed at least partially within the imaging surface  300   a.    
     Also as noted with respect to other embodiments described herein, the acoustic transducers can be operated in one or more modes. For example, the top edge group  304   a  can operate in a drive mode when the bottom edge group  304   b  operates in a sense mode. In another example, every acoustic transducer within, for example, the top edge group  304   a  alternate between drive acoustic transducers and sense acoustic transducers. In other cases, each acoustic transducer can be operated in either a drive mode or a sense mode. 
     Each of the top edge group  304   a , the bottom edge group  304   b , the right edge group  304   c , and the left edge group  304   d  are illustrated as a single linear distribution of acoustic transducers, such a configuration is not required. For example, as shown in  FIG. 3B , each of the top edge group  304   a , the bottom edge group  304   b , the right edge group  304   c , and the left edge group  304   d  may be comprised of multiple subgroups of acoustic transducers  302 . Although a specific number of subgroups are illustrated, any number of subgroups may be used. In addition, each subgroup may have any number of acoustic transducers  302 . 
     The arrangement of the acoustic transducers  302  into various subgroups enables each subgroup to operate independently. As such, routing of timing signals of each acoustic transducer (e.g., driving a first acoustic transducer, followed by a second acoustic transducer, and so on) may be limited to a particular subgroup rather than every acoustic transducer  302  that is positioned around the imaging surface  300   a . In addition, a first subgroup and a third subgroup may be fired without firing a second subgroup 
     For example, as shown in  FIG. 3B , each of the top edge group  306   a , the bottom edge group  306   b , the right edge group  306   c , and the left edge group  306   d  can be defined as include more than one adjacent linear distribution of acoustic transducers. In one embodiment, the outermost linear distribution of acoustic transducers may be configured to operate in a receive mode whereas the innermost linear distribution of acoustic transducers may be configured to operate in a drive mode. 
     In some cases, more than one row of acoustic transducers can be used.  FIG. 3C  depicts each group of acoustic transducers (top edge group  308   a , the bottom edge group  308   b , the right edge group  308   c , and the left edge group  308   d ) as having two adjacent linear distributions of acoustic transducers. In other embodiments, such a configuration is not required and other embodiments can include a larger number of adjacent linear distributions of acoustic transducers or a smaller number of adjacent linear distributions of acoustic transducers. In still further embodiments, linear distributions of acoustic transducers need not be aligned with one another. For example, a second linear distribution may be offset with respect to a first linear distribution. 
     In still other examples, groups of acoustic transducers need not include the same number of acoustic transducers, the same distributions of acoustic transducers, or the same relative alignment of acoustic transducers. 
     In yet another example, multiple adjacent linear distributions of acoustic transducers may be provided on an imaging surface  300   d . For example, as shown in  FIG. 3D , each of the top edge group  304   a , the bottom edge group  304   b , the right edge group  304   c , and the left edge group  304   d  can include multiple rows and/or columns of acoustic transducers. In one embodiment, the outermost linear distribution of acoustic transducers  312  may be configured to operate in a receive mode whereas the innermost linear distribution of acoustic transducers  314  may be configured to operate in a drive mode or vice versa. In other implementations, the outermost linear distribution of acoustic transducers  312  and the innermost linear distribution of acoustic transducers  314  may both be configured to operate in a drive mode or may both be configured to operate in a sense mode. 
     In this particular implementation, each of the linear distributions of acoustic transducers may be separated by a space or a gap  316 . The size of the gap  316 , or the spacing caused by the gap  316 , may be based, at least in part, on a wavelength of a wave that is transmitted from the acoustic transducers. More specifically, the gap  316  may be based on an order of a drive frequency of a wave that is transmitted from one or both of the outermost linear distribution of acoustic transducers  312  or the innermost linear distribution of the acoustic transducers  314 . 
     For example, each linear distribution of acoustic transducers may be separated by a quarter of a given wavelength (or some other fractional amount) or may be spaced such that the wavelengths are phase shifted by approximately 90 degrees. Although specific values have been discussed, other values may be used. 
     In some embodiments, the gap  316  may also be based on the type of material used for the imaging surface  300   d  and one or more material properties (e.g., a hardness) of the imaging surface  300   d . For example, a wave may travel over or through a first user input surface (e.g., sapphire) at a first speed and may travel over or through a second user input surface (e.g., glass) at a second, different speed. Thus, the gap  316  between the outermost linear distribution of acoustic transducers  312  and the innermost linear distribution of acoustic transducers  314  may be adjusted accordingly. 
     The gap  316  between the outermost linear distribution of acoustic transducers  312  and the innermost linear distribution of acoustic transducers  314  may also be used to demodulate the signals received by the acoustic transducers. More specifically, the spacing or the gap  316  between the outermost linear distribution of acoustic transducers  312  and the innermost linear distribution of acoustic transducers  314  is used to demodulate a received signal to find phase information and amplitude information from the signal. Because the gap  316  is known, demodulating circuitry from the analog front end, may be omitted. In other implementations, demodulating circuitry may be included but simplified as the gap  316  accounts for the phase shift of the waveforms. 
     More specifically, because waves generated and/or received by the innermost linear distribution of acoustic transducers  312  and the outermost linear distribution of acoustic transducers  314  are 90 degrees out of phase with respect to one another (or are effectively separated by an order of magnitude of a given wavelength, such as, for example, a quarter of a wavelength), the waveforms received are analog signals having quadrature-encoded carriers. Accordingly, summing the waveforms received by the innermost linear distribution of acoustic transducers  312  with the outermost linear distribution of acoustic transducers  314  yields a waveform that includes information corresponding to the amplitude of the received waveform. When this information is combined with other demodulated signals, an image of a user&#39;s finger may be reproduced such as described above. 
     In the embodiments described above, the demodulation may be I/Q demodulation. In embodiments where I/Q demodulation is used, the receive signal&#39;s information may be moved to baseband frequencies (e.g., low frequencies) and the rest of the analog front end may be implemented using low frequency requirements. 
     Although  FIG. 3B  depicts each group as having two adjacent linear distributions of acoustic transducers, such a configuration is not required. In other embodiments, larger number of adjacent linear distributions of acoustic transducers or a smaller number of adjacent linear distributions of acoustic transducers may be used. 
     In still further embodiments, each of the outermost linear distribution of acoustic transducers  312  and the innermost linear distribution of acoustic transducers  314  may be grouped into various subgroups such as described above. In yet other implementations, each of the linear distributions of acoustic transducers need not be aligned with one another. For example, the outermost linear distribution of acoustic transducers  312  may be offset from the innermost linear distribution of acoustic transducers  314 . In still other examples, groups of acoustic transducers need not include the same number of acoustic transducers, the same distributions of acoustic transducers, or the same relative alignment of acoustic transducers. 
     In still further examples, the acoustic transducers can be disposed over only a portion of user input surface. For example,  FIG. 3E  depicts another configuration of acoustic transducers, showing four arrangements or groupings of acoustic transducers  318  that generally frame, at two corners, a circumscribed portion of the user input surface. In this example, as with others described herein, the circumscribed portion may be associated with an outer protective layer of a display, such as the display  104  depicted in  FIG. 1 . 
     In still further examples, the acoustic transducers can be disposed over only a portion of the user input surface, such as shown in  FIG. 3F . In this embodiment, the acoustic transducers form a bucket shape  320  along a bottom portion of a circumscribed portion of the user input surface. In this example, as with others described herein, the circumscribed portion that may be associated with an outer protective layer of a display, such as the display  104  depicted in  FIG. 1 . 
     In still further examples, the acoustic transducers can be disposed over a portion of the user input surface that is not associated with a display, such as shown in  FIG. 3F . In this embodiment, the acoustic transducers form a bucket shape  322  below a bottom portion of a circumscribed portion of the user input surface. In this example, as with others described herein, the circumscribed portion that may be associated with an outer protective layer of a display, such as the display  104  depicted in  FIG. 1 . 
     The foregoing description of the embodiments depicted in  FIGS. 3A-3H , and various alternatives thereof and variations thereto are presented, generally, for purposes of explanation, and to facilitate a thorough understanding of the detailed embodiments presented herein. However, it will be apparent to one skilled in the art that some of the specific details presented herein may not be required in order to practice a particular described embodiment, or an equivalent thereof. Thus, the foregoing and following descriptions of specific embodiments are presented for the limited purposes of illustration and description. These descriptions are not target to be exhaustive or to limit the disclosure to the precise forms recited herein. To the contrary, it will be apparent to one of ordinary skill in the art that many modifications and variations are possible in view of the above teachings. 
     For example, the manner in which an acoustic transducer or a group of acoustic transducers is coupled to the imaging surface may vary from embodiment to embodiment. In some cases, an acoustic transducer is directly coupled to an underside of the imaging surface via an adhesive. The adhesive is typically a rigid adhesive, but this may not be required of all embodiments. In some cases, an electrode associated with an acoustic transducer interposes the transducer and the underside of the imaging surface. 
     In some cases, acoustic transducers can share one or more electrodes. The shared electrode can be a ground electrode, although this configuration is not required and can be a signal and/or power supply electrode instead. In some cases, each acoustic transducer associated with a shared electrode can be made from the same material, although this is not required; in some embodiments, different acoustic transducers can be made from different materials. 
     In some embodiments, the independent acoustic transducers can be coupled to the shared electrode by soldering. In some embodiments, the shared electrode can be formed, layered, or otherwise disposed atop the independent acoustic transducers in a manufacturing process. In some cases, the shared electronic can be an optically transparent electrode, formed from a material such as indium tin oxide or metal nanowire. In further embodiments, the independent acoustic transducers can be coupled to the shared electrode by an electrically conductive adhesive. 
     In many examples, a series of individual electrodes electrically couple independent acoustic transducers to a combined sense and drive chip. The individual electrodes, the independent acoustic transducers, and the send/drive chip are positioned adjacent to a bottom surface of the imaging surface and are coupled to a lower surface of the shared electrode. 
     The combined sense and drive chip may be understood as the controller of other embodiments described and depicted herein, such as the controller depicted in  FIG. 2 . The combined sense and drive chip can be implemented as a circuit, as an integrated circuit, analog circuit, or as any combination thereof. 
     In some examples, the combined sense and drive chip can be configured for both high voltage operation and low voltage operation, although such a configuration is not required of all embodiments. For example, in one embodiment, the combined sense and drive chip is configured for high voltage driving of the independent acoustic transducers and low voltage sensing of the independent acoustic transducers. In another embodiment, the combined sense and drive chip is configured for low voltage driving and low voltage sensing. In still further embodiments, the combined sense and drive chip is configured for both high voltage drive and high voltage sense. 
     In this manner, in some embodiments, the combined sense and drive chip can be manufactured with both high-voltage-tolerant components and low-voltage-tolerant components. In many cases, low-voltage-tolerant components may be more sensitive to low voltage signals but may be damaged by high voltage signals. High-voltage-tolerant components may be less sensitive to low voltage signals (e.g., small changes in voltage), and therefore more sensitive to noise. As such, low-voltage-tolerant components may exhibit better performance for receiving signals whereas high-voltage-tolerant components may exhibit better performance for driving transducers. 
     In such embodiments, the low-voltage-tolerant components can be protected from damage caused by high voltage using one or more isolation and/or voltage biasing methods. For example, in one embodiment, low-voltage-tolerant components can be physically isolated from high voltage via one or more switches enabled while high-voltage-tolerant components are operating. In another embodiment, a ground node of the low-voltage-tolerant components can be biased upwardly while high-voltage-tolerant components are operating such that the potential difference between the low-voltage-tolerant components&#39; ground and the high voltage required by the high-voltage-tolerant components is within the tolerance range of the low-voltage-tolerant components. Such a process is generally referred to herein as “ground shifting” of low-voltage-tolerant components. 
     When operating in a drive mode, the combined sense and drive chip can provide a high voltage signal to one or more of the independent electrodes which can, in turn, excite the respective one or more independent acoustic transducers. In this mode, the largest potential difference between the combined sense and drive chip and the shared electrode can be a high voltage. During this operation, low-voltage-tolerant components within the combined sense and drive chip can be ground shifted. In this manner, the largest potential difference across low-voltage-tolerant components within the combined sense and drive chip can be 3.3 volts (as one example). In many cases, the combined sense and drive chip can include one or more sense and drive circuits dedicated to each independent acoustic transducer. 
     In other cases, a combination combined sense and drive chip may not be required. In such embodiments, individual acoustic transducers couple through the independent electrodes directly to a sense chip. The individual acoustic transducers couple through the shared electrode directly to a drive chip. In these examples, individual acoustic transducers can be driven as a group and read individually. Such an embodiment can employ—should it be required by a particular implementation—ground shifting, isolation, or any other suitable means to protect low-voltage-tolerant components within the sense chip from the high voltage generated during operation of the drive chip. 
     Still other embodiments are implemented in another manner. For example, a series of drive-mode acoustic transducers can be separated from a corresponding series of sense-mode acoustic transducers. In this embodiment, the drive-mode acoustic transducers and the sense-mode acoustic transducers are coupled to the imaging surface via the shared electrode. The drive-mode acoustic transducers are coupled to a drive chip and the sense-mode acoustic transducers are coupled to a sense chip. The drive chip and the sense chip may be positioned adjacent to one another, although this may not be required. In another embodiment, the drive chip and the sense chip can be different subcomponents or submodules of a single integrated circuit. 
     Still other embodiments are implemented in another manner. For example a drive acoustic transducer can be disposed over (e.g., vertically stacked) several sense-mode acoustic transducers, identified as the sense-mode acoustic transducers. In some embodiments, the drive acoustic transducer is formed from the same material as the sense-mode acoustic transducers, although this is not required. The drive acoustic transducer is coupled to the sense-mode acoustic transducers by a common electrode. The sense-mode acoustic transducers can be coupled to a sense chip via individual electrodes. The drive acoustic transducer can be coupled to a drive chip. The sense chip and the drive chip can each be implemented as a circuit, as an integrated circuit, an analog circuit, an analog/mixed signal circuit, or as any combination thereof. In other cases, sense-mode acoustic transducers can be stacked above the drive-mode acoustic transducer. 
     As a result of this topology (including separate drive acoustic transducers and sense acoustic transducers), the sense-mode acoustic transducers can operate separately from the drive-mode acoustic transducer. As a result, the sense-mode acoustic transducers can begin receiving the moment the drive-mode acoustic transducer is driven by the drive chip. 
     Still other embodiments are implemented in another manner. For example a several drive-mode acoustic transducers can be disposed over (e.g., vertically stacked) several sense-mode acoustic transducers. As with other embodiments described herein, the drive-mode acoustic transducers may be the same material or may be a different material from the sense-mode acoustic transducers. In this embodiment, the drive-mode acoustic transducers are coupled to the sense-mode acoustic transducers by a common electrode. In other embodiments, a common electrode is not required; individual electrodes can couple the drive-mode acoustic transducers to the sense mode acoustic transducers. The sense-mode acoustic transducers can be coupled to a sense chip via individual electrodes. The drive acoustic transducer can be coupled to a drive chip via individual electrodes. The sense chip and the drive chip can each be implemented as a circuit, as an integrated circuit, an analog circuit, an analog/mixed signal circuit, or as any combination thereof. In other cases, the sense-mode acoustic transducers can be stacked above the drive-mode acoustic transducers. 
     As a result of this topology, and as with other embodiments described herein, the sense-mode acoustic transducers can operate separately from the drive-mode acoustic transducer. As a result, the sense-mode acoustic transducers can begin receiving the moment the drive-mode acoustic transducer is driven by the drive chip. 
     Still other embodiments are implemented in another manner. For example, a single drive-mode acoustic transducer sheet can be disposed over (e.g., vertically stacked) several sense-mode acoustic transducers, identified as the sense-mode acoustic transducers. As with other embodiments described herein, the drive-mode acoustic transducer may be the same material or may be a different material from the sense-mode acoustic transducers. The drive-mode acoustic transducer can be a single acoustic transducer or may be made up of a series of individual acoustic transducers. 
     In many cases, the drive-mode acoustic transducer is formed from a material selected for drive-mode power efficiency whereas the sense-mode acoustic transducers can be formed from a material selected for sense-mode power efficiency (e.g., PVDF). 
     In one embodiment, the drive-mode acoustic transducer is formed from one of a bulk PZT or a piezocomposite material. In some cases, a piezocomposite material (layers of piezoelectric materials separated by adhesive or epoxy) may be selected to increase the bandwidth of the drive-mode acoustic transducer relative to a particular fundamental drive frequency. An increased drive bandwidth can increase the signal to noise ratio (e.g., reduced ringing). 
     In another embodiment, the drive-mode acoustic transducer includes a backing. The backing may be a low-durometer adhesive or other resilient material. The backing can couple the drive-mode acoustic transducer to another component, such as a supporting plate or frame. The backing serves to reduce and absorb reflections of the drive waveform that may reflect within the drive-mode acoustic transducer as a result of an acoustic impedance mismatch between the drive-mode acoustic transducer and the imaging surface, or the shared electrode. 
     In certain embodiments, the drive-mode acoustic transducers are coupled to the sense-mode acoustic transducers by a common electrode. In other embodiments, a common electrode is not required; individual electrodes can couple the drive-mode acoustic transducers to the sense mode acoustic transducers. The sense-mode acoustic transducers can be coupled to a sense chip via individual electrodes. The drive acoustic transducer can be coupled to a drive chip via individual electrodes. The sense chip and the drive chip can each be implemented as a circuit, as an integrated circuit, an analog circuit, or as any combination thereof. 
     In other cases, the sense-mode acoustic transducers can be stacked above the drive-mode acoustic transducers. In this embodiment, the drive chip, which may operate at high voltage, is separated and isolated from the sense chip, which may operate at low voltage. The common electrode can be a ground reference for both the sense chip and the drive chip. As a result of this topology, and as with other embodiments described herein, the sense-mode acoustic transducers can operate separately from the drive-mode acoustic transducer. As a result, the sense-mode acoustic transducers can begin receiving the moment the drive-mode acoustic transducer is driven by the drive chip. 
     The foregoing embodiments described above related to acoustic transducers and drive chips and sense chips, and the various alternatives thereof and variations thereto are presented, generally, for purposes of explanation, and to facilitate an understanding of various possible acoustic imaging system topologies. More specifically, these embodiments are presented to illustrate that acoustic transducers of an acoustic imaging system such as described herein can be configured to operate in both a drive mode and a sense mode, can be configured to operate in one of a drive mode or a sense mode, can be configured to operate in one of a drive mode or a sense mode. Further, the depicted embodiments are provided to facilitate an understanding that drive acoustic transducers may share one or more electrodes with sense electrodes, drive electrodes and sense electrodes may be formed from the same or different material, drive and sense electrodes may be segmented (e.g., pixelated) or unitary, drive or sense electrodes can be operated from the same silicon or from different silicon, drive chips can be integrated with or can be separate from sense chips, and so on. As such, it may be appreciated that these embodiments are not intended to be exhaustive of all possible combinations, layouts, or topologies of drive electrodes, sense electrodes, drive acoustic transducers, sense acoustic transducers, multi-modal acoustic transducers, drive chips, sense chips, multimodal chips, and so on. Instead, the depicted examples are understood to be merely a subset of the representative embodiments of an acoustic imaging system such as described herein that may be implemented within the spirit and scope of this disclosure. 
     In still further embodiments, one or more acoustic transducers can be capacitively driven. In these examples, individual electrodes are separated from independent acoustic transducers by a dielectric material. In these examples, the dielectric material is disposed to encapsulate the independent electrodes. In some cases, the dielectric material may be an adhesive, a layer deposited via vapor deposition, an epoxy, or any other suitable layer. In many embodiments, the dielectric material has a high dielectric constant and is disposed as a thin layer. 
     As a result of this configuration, the individual electrodes each form a capacitor with one respective acoustic transducer. As a result, the operation of driving the acoustic transducers can be modeled as a circuit including a capacitor having a very large capacitance inserted between a voltage source (e.g., drive chip) and an acoustic transducer (e.g., individual acoustic transducer). Similarly, the operation of reading the acoustic transducers can be modeled as a circuit including a capacitor having a very large capacitance inserted between a voltage source (e.g., individual acoustic transducer) and a sense circuit (e.g., sense chip). As may be appreciated, such a configuration can be more easily and efficiently manufactured at scale; precise alignment and precise electrical connection between electrodes and acoustic transducers may not be required. 
     In still further embodiments, either or both the drive chip and/or the sense chip may be implemented as a series of interconnected analog or digital circuits that are each associated with an individual acoustic transducer or a group of individual transducers. Such embodiments are referred to herein as acoustic imaging systems incorporating “distributed controllers.” 
     More specifically, a distributed controller is implemented as a series of subgroup controllers, one of which is labeled as the subgroup controller and the master controller. The series of subgroup controllers can be communicably coupled to the master controller in a hub-and-spoke configuration, although this is not required. 
     In this example, the subgroup controller is associated with a subgroup of transistors nearby or adjacent to the subgroup controller. Similarly, other subgroup controllers of the series of subgroup controllers are each associated with a respective one subgroup of acoustic transducers. More specifically, the subgroup controller may be purpose-configured to drive and/or read only certain acoustic transducers of the acoustic imaging system. 
     In this example, the master controller couples to, and coordinates the actions of, each subgroup controller of the series of subgroup controllers, including the subgroup controller. 
     A subgroup controller can be implemented in any number of suitable ways. In certain embodiments, a subgroup controller can be implemented as a combination of individual purpose-configured circuits that are, directly or indirectly, communicably coupled to one another. In one embodiment, a series of acoustic transducers are coupled, via a common electrode, to the underside of the imaging surface. An opposite side of the series of acoustic transducers is coupled, via a series of electrical contacts (or via capacitive signaling through a dielectric material, to a first section of the subgroup controller. 
     In many examples, the first section can include one or more analog or digital circuits configured to facilitate driving or sensing of the series of the acoustic transducers. For example, in one embodiment, the first section is a thin-film transistor imaging surface strip that includes at least one amplification stage. The amplification stage can serve as a pre-amp for signals obtained when reading one or more of the series of acoustic transducers. In this example, the first section can be manufactured in a time and cost-efficient manner. 
     In another example, the first section can be made from a flexible circuit. The flexible circuit can include at least one amplification stage such as described above. In other cases, other circuits and/or purpose configured circuit topologies can be included such as, but not limited to: addressing circuits (e.g., shift registers), power control or regulation circuits, drive circuits, switch circuits, filtering circuits, multi-stage amplification circuits, analog-to-digital conversion stages and/or circuits, encryption and/or decryption circuits, compression circuits, data streaming or protocol conformity circuits, and so on. In still further embodiments, the first section may be implemented without circuitry; the first section may be a passive interposer. 
     In certain embodiments, the first section can couple, via an interposer (or other suitable connection) to a second section. The second section can be an integrated circuit that is purpose-configured for driving and/or reading the series of acoustic transducers via the first section. In this manner, by separating certain functions of the subgroup controller into a first section and a second section manufacturing and signal processing efficiency can be improved. As with the first section, the second section can include other circuits and/or purpose configured circuit topologies can be included such as, but not limited to: addressing circuits (e.g., shift registers), power consumption regulation circuits, drive circuits, switch circuits, filtering circuits, multi-stage amplification circuits, analog-to-digital conversion stages and/or circuits, encryption and/or decryption circuits, compression circuits, data streaming or protocol conformity circuits, and so on. 
     The foregoing embodiments and the various alternatives thereof and variations thereto are presented, generally, for purposes of explanation, and to facilitate an understanding of various possible methods for dividing and/or distributing the processing and/or signal conditioning load of an acoustic imaging system such as described herein. Instead, the depicted examples are understood to be merely a subset of the representative embodiments of an acoustic imaging system such as described herein that may be implemented within the spirit and scope of this disclosure. 
     Example Operation of an Attenuation-Based Image Resolver 
     Generally and broadly,  FIGS. 4A-5B  reference a transmission tomography acoustic imaging system  400  incorporating an attenuation-based image resolver (not shown). 
     The transmission tomography acoustic imaging system  400  is configured to drive one or more acoustic transducers  402  and, thereafter to obtain multiple planar projections, each taken at a different angle, of a contact area  404  determined by a touch sensor (such as the touch sensor depicted in  FIG. 2 ). 
     Once the transmission tomography acoustic imaging system  400  obtains a sufficient number of planar projections (the number and angles of which may vary from embodiment to embodiment), the system may estimate or approximate the acoustic attenuation map  406  (e.g., the inverse Radon transform) of the contact area  404  using any suitable method. Once estimated, the acoustic attenuation map  406  can serve as a direct proxy for the fingerprint of a user. 
     Initially, reference is made to the operation of the controller of the transmission tomography acoustic imaging system  400  when in the transmission mode. When in the transmission mode, the controller propagates the acoustic pulse  408  (typically of uniform magnitude) through the user input surface in the direction of the contact area  404  determined by a touch sensor (e.g., the touch sensor depicted in  FIG. 2 ). The acoustic pulse  408  can have any suitable wavefront shape although in many embodiments, the wavefront takes a linear shape perpendicular to the direction D along which the controller propagates the acoustic pulse  408 . 
     Once the acoustic pulse  408  reaches the contact area  404 , portions of the acoustic pulse  408  are progressively attenuated by the various features of the object in contact with the surface thereof, such as the ridges of a user&#39;s fingerprint. In other words, portions of the acoustic pulse  408  are progressively attenuated by an amount defined by unknown function that is based on the local attenuation coefficient(s) of each point through which that particular portion of the acoustic pulse  408  passes. After passing through the contact area  404 , the acoustic pulse  408  no longer exhibits uniform magnitude; in the illustrated embodiment the portion of the acoustic pulse  408  that has passed through the contact area  404  is identified as the acoustic pulse  408 ′. 
     The amount of total attenuation in the acoustic pulse  408 ′ is a function of the acoustic attenuation map  406  that the topographic acoustic imaging system seeks to estimate. In this manner, the amplitude of a particular portion of the acoustic pulse  408 ′, is equal to the solution of a line integral of the acoustic attenuation map  406  that is defined along the linear path taken by that portion of the acoustic pulse  408 . 
     In another non-limiting phrasing, the aggregate effect of the cumulative attenuation provided by a particular path through the contact area  404  can be mathematically modeled as the solution of a line integral (see, e.g., the line integral  412  shown in  FIG. 4B ) of the acoustic attenuation map  406  f m (x, y) of the contract area, the line integral defined over a line that follows the selected path. In many embodiments, the line may be defined using the Hessian normal form (e.g., x cos(θ)+y sin(θ)−r=0) to ensure that the line equation is defined for all possible values of the slope of that line, particularly to ensure that the line equation is defined when the slope of the line is infinite (e.g., 
     
       
         
           
             
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     For example, the line integral may be defined over a straight line angled at angle θ and offset by a perpendicular distance r from the geometric center  410  of the contact area  404 . In this manner, the aggregate effect of the of the cumulative attenuation provided by the contact area  404  to the acoustic pulse  408  traversing the same can be modeled mathematically by a function such as: 
     
       
         
           
             
               
                 
                   
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     As may be appreciated, the model presented above by Equation 2 is typically referred to as the Radon transform of the acoustic attenuation map  406  f m (x, y) of the contact area  404 . In some examples, Equation 2 may be solved analytically with a sufficient number of values for r and θ. 
     For embodiments in which the controller induces the acoustic pulse  408  exhibiting a planar wavefront, the set of line integrals represents a planar projection of the contact area  404  taken along an angle equal to the propagation direction D of the acoustic pulse  408 . This is due to the fact that a planar wavefront can be mathematically modeled as a series of parallel rays. 
     Alternatively, for other embodiments in which the controller induces the acoustic pulse  408  having a non-planar wavefront (e.g., point source, phase-encoded point sources, and so on), the set of line integrals may be spatially filtered, linearized, combined with other sets of line integrals, or otherwise processed using appropriate techniques in order to obtain a planar projection of the contact area  404  taken along an angle equal to the propagation direction D of the acoustic pulse  408 . For example, in one embodiment, the controller may propagate phase-encoded acoustic pulses from multiple single point sources. Thereafter, the controller can demodulate and de-code the set of line integrals associated with each point source and combine line integrals with one another (e.g., parallel ray matching) as necessary. 
     As noted above, the transmission tomography acoustic imaging system  400  may be configured to obtain a number of individual planar projections of the contact area  404 , each at a different angle. Typically, these planar projections may be taken at regular angular intervals but this is not required for all embodiments. 
     As noted above, once the transmission tomography acoustic imaging system  400  obtains a sufficient number of planar projections (the number and angles of which may vary from embodiment to embodiment), the system may estimate the inverse Radon transform thereof which, as noted above, corresponds to the acoustic attenuation map  406 . 
     In one example, the inverse Radon transform may be determined analytically by solving Equation 2. In other examples the inverse Radon transform may be estimated using any suitable discrete or continuous time method. For example, in one embodiment, the transmission tomography acoustic imaging system  400  employs a back projection technique that re-projects (e.g., back-projects) each planar projection back over the contact area  404 , additively overlapping each of back projections over one another. The points of the resulting overlapped image correspond to the attenuation effects provided by the features of the user&#39;s fingerprint at those locations; the greater the number of planar projections, the greater the resolution, contrast, and/or clarity of the acoustic attenuation map  406 . 
     In further embodiments, and as noted above, the transmission tomography acoustic imaging system  400  applies a high pass filter to one or more of the planar projections in order to further increase the resolution, contrast, and/or clarity of the acoustic attenuation map  406 . In many cases, the high pass filter may be a ramp filter (e.g., a high-pass, compensatory filter that mitigates or eliminates DC output bias, and that is configured to attenuation low frequencies and to amplify high frequencies up to a cutoff frequency). 
     The foregoing description of the embodiments depicted in  FIGS. 4A-4B , and various alternatives thereof and variations thereto are presented, generally, for purposes of explanation, and to facilitate a thorough understanding of the detailed embodiments presented herein. However, it will be apparent to one skilled in the art that some of the specific details presented herein may not be required in order to practice a particular described embodiment, or an equivalent thereof. Thus, the foregoing and following descriptions of specific embodiments are presented for the limited purposes of illustration and description. These descriptions are not target to be exhaustive or to limit the disclosure to the precise forms recited herein. To the contrary, it will be apparent to one of ordinary skill in the art that many modifications and variations are possible in view of the above teachings. 
     Particularly, it may be understood that the transmission tomography acoustic imaging system depicted in  FIGS. 4A-4B  can be implemented in a number of suitable and implementation-specific ways. However, broadly and generally, the transmission tomography acoustic imaging system determines and/or estimates an acoustic attenuation map  406  of the contact area  404  and/or changes therein over time, to obtain an image of a user&#39;s fingerprint. The transmission tomography acoustic imaging system performs these operations by sending an acoustic pulse  408  at an angle toward the contact area  404  and measuring the portions of that acoustic pulse  408  that are attenuated by the contact area  404  (e.g., features of the user&#39;s fingertip that are in contact with the surface of the contact area  404 ). The measured portions of the acoustic pulse  408  that are attenuated by the contact area  404  can be treated as a planar projection of the contact area  404  onto a plane orthogonal to the contact area  404 , taken at the angle at which the acoustic pulse  408  was propagated toward the contact area  404 . These operations are repeated until a sufficient number of parallel projections of the contact area  404  are obtained. Thereafter, the parallel projections are combined using, in one example, a filtered back projection technique. 
     Any of these operations, or portions of these operations, may be performed by the controller of  FIG. 2 , by the image resolver  206  of  FIG. 2 , by the touch sensor of  FIG. 2 , and/or performed, at least in part, as a result of cooperation and communication therebetween. In other words, the example components of the transmission tomography acoustic imaging system depicted in  FIG. 2  may be independently or cooperatively configured, adapted, or otherwise implemented to perform, coordinate, or monitor any number of suitable operations of the transmission tomography acoustic imaging system described above. 
     For example, an appropriately configured controller (in the transmission mode) can induce an acoustic pulse (e.g., the acoustic pulse  408 ) in any suitable manner. In one example, the controller drives the acoustic transducers  402  with a single pulse, a chirp signal, or several periods of a sinusoidal signal in order to produce the acoustic pulse  408 , an acoustic chirp, or a monochromatic acoustic signal within the imaging surface, respectively. 
     Additionally, the controller can shape the acoustic pulse  408  in any suitable manner. For example, the controller can be configured to generate the acoustic pulse  408  such that the acoustic pulse  408  exhibits a wavefront that takes a particular shape. For example, a longitudinal acoustic pulse  408  may exhibit a planar wavefront, whereas an omnidirectional acoustic pulse  408  may exhibit a circular or curved wavefront. Other acoustic pulses can exhibit other wavefront shapes. The controller can employ beam-forming techniques in order to shape the wavefront of a particular acoustic pulse  408  into any suitable or implementation-specific shape. 
     Additionally, an appropriately-configured controller can cause the acoustic pulse  408  to propagate in any suitable direction. The controller can employ beam-forming techniques in order to direct the wavefront of a particular acoustic pulse  408  to propagate along a particular direction. 
     Thus, generally and broadly, the controller can induce any suitable acoustic pulse  408 , exhibiting any suitable wavefront shape, that propagates along any suitable direction. In one example, the controller is configured to induce a monochromatic acoustic pulse  408  that exhibits a substantially planar wavefront directed toward the geometric center  408  of the contact area  404 . 
     Once the controller (in the transmission mode) has induced a suitable acoustic pulse  408  into the imaging surface that is directed toward the contact area  404 , the controller can transition into the receiving mode. In a receiving mode, the controller couples to one or more acoustic transducers, sampling electrical signals generated thereby over a period of time. In many cases, the controller transitions to the receiving mode immediately after generating the acoustic pulse  408  in the transmission mode. As noted above, the electrical signals collected by the controller can correspond to planar projections of the contact area  404 . 
     Similarly, an appropriately configured contact sensor can be configured to determine the area over which an object, such as a fingertip, physically contacts the imaging surface. 
       FIGS. 5A-5B  generally and broadly depict simplified block diagrams of two example transmission tomography acoustic imaging systems that may be configured and/or configurable to obtain an estimation of an acoustic attenuation map of a contact area of an imaging surface. 
       FIG. 5A  depicts a simplified block diagram of a transmission tomography acoustic imaging system configured for employing transmission-based tomographic reconstruction techniques. As with other embodiments described herein, the transmission tomography acoustic imaging system  500   a  includes several acoustic transducers  502  that are coupled to a controller  504  which, in turn, is coupled to an image resolver  506 . 
     Each acoustic transducer  502  can include an acoustic transducer  506  and a pre-amplifier  510 . The acoustic transducer  506  can be formed from a piezoelectric material. The pre-amplifier  510 , in many examples is formed to be physically adjacent to the acoustic transducer  506  in order to mitigate the introduction of noise from parasitics that may affect the signal output from the acoustic transducer  506  before that signal is amplified by the pre-amplifier  510 . In some examples, the pre-amplifier  510  can be formed within, layered onto, or positioned immediately adjacent the acoustic transducer  506 . 
     The controller  504  may thereafter provide a drive signal  512  to each of the acoustic transducers  502 . The drive signal  512  may be specifically timed by a high-resolution timing controller  514  based on the physical location of a particular acoustic transducer  502 . More specifically, for embodiments in which the controller  504  is configured to shape the wavefront and/or the direction of the acoustic pulse generated by the acoustic transducer(s) of the acoustic transducers  502  (e.g., beamforming, beam focusing, and so on), the timing at which each of the acoustic transducers  502  receive the drive signal  512  may be of elevated importance. 
     For example, as may be appreciated, a first acoustic pulse may propagate in a generally spherical manner at a velocity v within the imaging surface from a first acoustic transducer of a particular acoustic transducer  502 . In an alternative phrasing, the acoustic pulse may traverse a distance d 0  in a particular time period t based on the acoustic velocity of that pulse within the material (or materials) forming the imaging surface. 
     A second acoustic transducer may be a linear distance d 1  from the first acoustic transducer. A second acoustic pulse may be propagated from the second acoustic transducer. The second acoustic pulse may constructively or destructively interfere with the first acoustic pulse at a particular location based, specifically, on the time at which the second acoustic pulse was generated relative to the first acoustic pulse. For example, if the first acoustic pulse and the second acoustic pulse are generated at precisely the same moment, the two pulses may constructively interfere to propagate a generally-planar wavefront in a directly parallel to a vector defined between the first acoustic transducer and the second acoustic transducer. In other words, the generally-planar wavefront may propagate straight outward from the first and second acoustic transducer. 
     In another example, the second acoustic pulse may be generated after the first acoustic pulse is already propagated in the imaging surface. The time at which the second acoustic pulse is generated affects the point or points at which the first acoustic pulse and the second acoustic pulse interfere with one another (either constructively or destructively). The time at which the second acoustic pulse is generated may also depend upon the velocity v, and the distances d 0  and d 1 . 
     In this manner, it is appreciated that the timing provided by the timing controller  514  may facilitate any number of suitable wavefront shapes and/or directions. It may be further appreciated that the accuracy with which a particular shape and/or direction of a particular wavefront may be generated may depend upon the accuracy with which the timing controller  514  can control the timing of the various acoustic transducers  502 . 
     As noted above with respect to other embodiments described herein, the transmission tomography acoustic imaging system may be configured to transition from a drive mode (e.g., transmission mode) to a sense mode after an acoustic pulse has been propagated into the imaging surface. 
     Once in the sense mode, an acoustic transducer  506  of a particular acoustic transducer  502  may be configured to output an electrical signal. The electrical signal output by an acoustic transducer  506  corresponds to the amplitude of a portion of a previously-propagated acoustic pulse. As may be appreciated, the electrical signal output by an acoustic transducer  506  has been attenuated by each point of the contact area. The electrical signal may also contain a noise component. 
     As noted above, the electrical signal output by an acoustic transducer  506  may be first be amplified by a pre-amplifier  510  that is physically proximate to the acoustic transducer  506 . Also as noted above, the physical proximity of this initial amplification stage increases the signal to noise ratio of the signal output from a particular acoustic transducer  502  to the controller  504 . 
     Each acoustic transducer  502 , and more specifically the output of the respective pre-amplifier  510 , is connected to a multiplexer  516  within the controller  504 . The multiplexer  516  may be configured to connect to one or more acoustic transducers  502  at a time. In many cases, the multiplexer  516  is a time multiplexer that couples iteratively couples to different acoustic transducers in order to obtain amplified electrical signals therefrom. 
     The multiplexer  516  is connected to a carrier rejection module  518 . The carrier rejection module  518  is typically implemented as a demodulator configured to demodulate the signal received from the multiplexer  516  to baseband. In many cases, the carrier rejection module  518  includes one or more filters. For example, a band pass filter may be applied to the output of the multiplexer  518 , the band pass filter centered (generally) on the carrier frequency. In other examples, a low pass filter may be applied to the output of the carrier rejection module  518  so that high frequency noise may be filtered therefrom. In other cases, other suitable filters may be used. In some cases, a cascade of filters may be used. In other cases, filtering of the signal may be optional. 
     The carrier rejection module  518  may be (optionally) connected to a gain and/or offset correction module  520 . In some examples, the gain and/or offset correction module  520  may be implemented as a low pass filter (e.g., rolling average filter) such as described above. In other cases, the gain and/or offset correction module  520  may be implemented in another manner to normalize the gain and/or the direct current offset present in the signal output from the carrier rejection module  518 . 
     The carrier rejection module  518  or the (optional) gain and/or offset correction module  520  may be coupled to an envelope detection module  522 . The envelope detection module  522  may be configured to detect the amplitude of the signal output from the previous stages of the controller  504 , within specifically-selected statistical bounds. For example, the envelope detection module  522  may determine that the amplitude of a signal has changed only when that signal exceeds a particular threshold. In other cases, the envelope detection module  522  may determine that the amplitude of a signal has changed only when that signal exceeds a particular average value or is beyond one standard deviation from mean. In other cases, the envelope detection module  522  may employ other suitable techniques. 
     The envelope detection module  522  may be (optionally) connected to a gain and/or offset correction module  524 . In some examples, the gain and/or offset correction module  524  may be implemented as a low pass filter (e.g., rolling average filter) such as described above. In other cases, the gain and/or offset correction module  524  may be implemented in another manner to normalize the gain and/or the direct current offset present in the signal output from the carrier rejection module  518 . In many cases, the gain and/or offset correction module  524  includes an analog to digital converter. 
     Finally, the output of the envelope detection module  522  or the (optional) gain and/or offset correction module  524  may be connected to the image resolver  506 . The image resolver  506  may use the values obtained from the gain and/or offset correction module  524  in order to estimate the acoustic attenuation map of the contact area. 
       FIG. 5B  depicts a simplified block diagram of a transmission tomography acoustic imaging system configured for employing diffraction-based tomographic reconstruction techniques. As with other embodiments described herein, the transmission tomography acoustic imaging system  500   b  includes several acoustic transducers  502  that are coupled to a controller  504  which, in turn, is coupled to an image resolver  506 . 
     As with the tomographic imaging system depicted in  FIG. 5A , each acoustic transducer  502  can include an acoustic transducer  506  and a pre-amplifier  510 . The acoustic transducer  506  can be formed from a piezoelectric material. The pre-amplifier  510 , in many examples is formed to be physically adjacent to the acoustic transducer  506  in order to mitigate the introduction of noise from parasitics that may affect the signal output from the acoustic transducer  506  before that signal is amplified by the pre-amplifier  510 . In some examples, the pre-amplifier  510  can be formed within, layered onto, or positioned immediately adjacent the acoustic transducer  506 . 
     The controller  504  may thereafter provide a drive signal  512  to each of the acoustic transducers  502 . In some examples, the controller  504  may employ beam forming and/or beam focusing techniques such as described with respect to  FIG. 5A . However, in other cases, the controller  504  may be configured to drive each individual acoustic transducer  502  individually, thereby effectively propagating an acoustic pulse with a spherical wavefront. 
     In many cases, the power output (e.g., the maximum amplitude) from a single acoustic transducer may be low. Accordingly, the controller  504  may be configured to apply the drive signal  502  to several acoustic transducers  502  at the same time. Each of these drive signals may be I/Q-encoded (e.g., phase coded) so that the acoustic pulses generated from each of the individual acoustic transducer can be decoded and separated from one another in a subsequent I/Q-demodulation step. 
     As noted above with respect to other embodiments described herein, the transmission tomography acoustic imaging system may be configured to transition from a drive mode (e.g., transmission mode) to a sense mode after an acoustic pulse has been propagated into the imaging surface. 
     As with the tomographic imaging system depicted in  FIG. 5A , once in the sense mode, an acoustic transducer  506  of a particular acoustic transducer  502  may be configured to output an electrical signal. The electrical signal output by an acoustic transducer  506  corresponds to the amplitude of a portion of a previously-propagated acoustic pulse. As may be appreciated, the electrical signal output by an acoustic transducer  506  has been attenuated by each point of the contact area. The electrical signal may also contain a noise component. Additionally, the output of a particular acoustic transducer may also include multiple components associated with each of the diffraction pattern envelopes that overlap that point. 
     As noted above, the electrical signal output by an acoustic transducer  506  may be first be amplified by a pre-amplifier  510  that is physically proximate to the acoustic transducer  506 . Also as noted above, the physical proximity of this initial amplification stage increases the signal to noise ratio of the signal output from a particular acoustic transducer  502  to the controller  504 . 
     Each acoustic transducer  502 , and more specifically the output of the respective pre-amplifier  510 , is connected to a multiplexer  516  within the controller  504 . The multiplexer  516  may be configured to connect to one or more acoustic transducers  502  at a time. In many cases, the multiplexer  516  is a time multiplexer that couples iteratively couples to different acoustic transducers in order to obtain amplified electrical signals therefrom. 
     The multiplexer  516  is connected to a carrier rejection module  518 . The carrier rejection module  518  is typically implemented as a demodulator configured to demodulate the signal received from the multiplexer  516  to baseband. In many cases, the carrier rejection module  518  includes one or more filters. For example, a band pass filter may be applied to the output of the multiplexer  518 , the band pass filter centered (generally) on the carrier frequency. In other examples, a low pass filter may be applied to the output of the carrier rejection module  518  so that high frequency noise may be filtered therefrom. In other cases, other suitable filters may be used. In some cases, a cascade of filters may be used. In other cases, filtering of the signal may be optional. 
     The carrier rejection module  518  may be (optionally) connected to a gain and/or offset correction module  520 . In some examples, the gain and/or offset correction module  520  may be implemented as a low pass filter (e.g., rolling average filter) such as described above. In other cases, the gain and/or offset correction module  520  may be implemented in another manner to normalize the gain and/or the direct current offset present in the signal output from the carrier rejection module  518 . 
     The carrier rejection module  518  (or the output of the gain and/or offset correction module  520 ) may be connected to an I/Q demodulation module  526 . The I/Q demodulation module  526  may be configured to separate the in-phase components from the quadrature-encoded components, which, in turn may be correlated to individual acoustic transducers (and the locations thereof). In this manner, the I/Q demodulation module  526  may effectively separate different diffraction patterns from one another. 
     The I/Q demodulation module  526  may be (optionally) connected to a gain and/or offset correction module  526 . In some examples, the gain and/or offset correction module  526  may be implemented as a low pass filter (e.g., rolling average filter) such as described above. In other cases, the gain and/or offset correction module  526  may be implemented in another manner to normalize the gain and/or the direct current offset present in the signal output from the carrier rejection module  518 . In many cases, the gain and/or offset correction module  526  includes an analog to digital converter. 
     Finally, the output of the I/Q demodulation module  526  or the (optional) gain and/or offset correction module  526  may be connected to the image resolver  506 . The image resolver  506  may use the values obtained from the gain and/or offset correction module  524  in order to estimate the acoustic attenuation map of the contact area. 
     Example Operation of a Reflection-Based Image Resolver 
     Generally and broadly,  FIGS. 6-8F  reference an acoustic imaging system  800  incorporating a reflection-based image resolver (not shown). As with other embodiment described herein, the acoustic imaging system  600  includes a number of acoustic transducers, a controller, an image resolver, and a touch sensor. 
     As with other embodiments described herein, when a user touches the imaging surface, the touch sensor determines the contact area. Once the contact area is determined, the controller initiates one or more transmitting operations, often specifically targeted to the contact area, with one or more of the acoustic transducers. The transmitting operations may be single-pulse transmitting operations and/or multi-pulse transmitting operations that are coded using any suitable coding pattern or technique. 
     Once the acoustic imaging system  600  obtains a sufficient quantity of reflection information, the image resolver may estimate or approximate an acoustic properties map of the contact area—corresponding to local acoustic reflection coefficients—using any suitable method. 
     The acoustic transducers of the acoustic imaging system  600  can be distributed on the imaging surface in any suitable pattern or manner (see, e.g.,  FIGS. 3A-3G ). Typically, the acoustic transducers are disposed relative to a periphery of the imaging surface, but this may not be required of all embodiments. For example, as shown in  FIG. 6 , the acoustic transducers  602  can be disposed relative to a top edge and a bottom edge of a rectangular section of an imaging surface  604 . In this example, the imaging surface  604  may be an outer protective layer positioned over a display, such as the display  104  depicted in  FIG. 1 . 
     In other examples, the acoustic transducers are disposed relative to the imaging surface in another manner. For example, the acoustic transducers can be disposed to circumscribe an entire perimeter of a subarea of the imaging surface. In this example, the acoustic transducers define a substantially enclosed rectangular subarea that may be associated with an outer protective layer of a display, such as the display  104  depicted in  FIG. 1 . 
     When in the transmission mode, the controller causes the acoustic pulse  606  to propagate through the imaging surface in the direction of the contact area  608 . The acoustic pulse  606  can have any suitable wavefront shape. 
     Once the acoustic pulse  606  reaches the contact area  608 , portions of the acoustic pulse  606  are progressively attenuated and/or reflected by the various features of the object (not shown) in contact with the imaging surface, such as the ridges of a user&#39;s fingerprint. In other words, portions of the acoustic pulse  606  are progressively attenuated and/or reflected by an amount defined by unknown function that is based on the local reflection coefficient(s) of each point through which that particular portion of the acoustic pulse  606  passes. 
     In other words, the acoustic pulse  606  may be progressively reflected, at different locations and times, as the acoustic pulse  606  propagates through the contact area  608 . Each of these reflections (collectively, the reflection information) may be received at the acoustic transducers at different times and at different attenuations. 
     Once the reflection information corresponding to the acoustic pulse  606  is received, the controller of the acoustic imaging system  600  can perform another transmitting operation. The transmitting operation can be associated with the acoustic transducers, or another acoustic transducer of the acoustic transducers. 
     In some embodiments, the acoustic imaging system  600  may exclusively perform single-pulse transmitting operations. In these examples, the controller may sequentially (or otherwise) cycle through acoustic transducers individually, collecting and accumulating reflection information associated with each. 
     In other embodiments, the acoustic imaging system  600  may exclusively perform multi-pulse transmitting operations. The controller may sequentially (or otherwise) cycle through acoustic transducers individually, collecting and accumulating reflection information associated with each. 
     In many embodiments, however, the acoustic imaging system  600  may shift between single-pulse transmitting operations and multi-pulse transmitting operations. For example, a single-pulse transmitting operation may be performed when the contact area  608  is nearby an edge of the imaging surface (below a threshold distance d from an edge of the imaging surface or a subarea of the imaging surface) or when the contact area  608  is nearby the acoustic transducers. In other cases, a multi-pulse transmitting operation may be performed when the contact area is within a central portion of the imaging surface. It may be appreciated that the listing given above is not exhaustive; other embodiments may perform a variety of transmitting operations in any other suitable implementation-specific or appropriate manner or pattern. 
     As noted above, once the acoustic imaging system  600  obtains a sufficient amount of reflection information, an acoustic properties map  610  can be generated by the image resolver using a suitable technique such as, but not limited to, reflection tomography techniques. 
     It is appreciated that the acoustic imaging system  600  depicted in  FIG. 6  can be implemented in a number of suitable and implementation-specific ways. However, broadly and generally, the acoustic imaging system  600  determines and/or estimates an acoustic properties map of the contact area and/or changes therein over time, to obtain an image of a user&#39;s fingerprint. The acoustic imaging system  600  performs single- and/or multi-pulse transmitting operation that may be generally targeted toward a contact area determined by a touch sensor. Thereafter, reflection information can be obtained from one or more acoustic transducers. 
     Any of these operations, or portions of these operations, may be performed by the controller, by the touch sensor, by the image resolver, and/or performed, at least in part, as a result of cooperation and communication therebetween. In other words, the example components of the acoustic imaging system  600  may be independently or cooperatively configured, adapted, or otherwise implemented to perform, coordinate, or monitor any number of suitable operations of the acoustic imaging system  600  described above. 
     For example, the controller (in the transmission mode) can induce the acoustic pulse  606  in any suitable manner. For example, the controller can drive the acoustic transducers with a single pulse, an impulse, a chirp signal, or several periods of a sinusoidal signal in order to produce the acoustic pulse  606 , an acoustic chirp, or a monochromatic acoustic signal within the imaging surface, respectively. 
     Additionally, the controller can shape the acoustic pulse  606  in any suitable manner, using one or more acoustic transducers. For example, the controller can be configured to generate the acoustic pulse  606  such that the acoustic pulse  606  exhibits a planar wavefront that takes a particular shape. For example, a longitudinal acoustic pulse may exhibit a wavefront, whereas an omnidirectional acoustic pulse may exhibit a circular or curved wavefront. Other acoustic pulses can exhibit other wavefront shapes. The controller can employ beam-forming techniques in order to shape the wavefront of a particular acoustic pulse  606  into any suitable or implementation-specific shape. 
     Additionally, the controller can cause the acoustic pulse  606  to propagate in any suitable direction. The controller can employ beam-forming techniques in order to direct the wavefront of a particular acoustic pulse  606  to propagate along a particular direction. 
     Thus, generally and broadly, the controller can induce any suitable acoustic pulse, exhibiting any suitable wavefront shape, that propagates along any suitable direction. In one example, the controller is configured to induce a monochromatic acoustic pulse by causing a resonant mode of one or more acoustic transistors. 
     Once the controller (in the transmission mode) has induced a suitable acoustic pulse into the imaging surface that is directed toward the contact area  608 , the controller can transition into the receiving mode to obtain reflection information. In a receiving mode, the controller couples to one or more acoustic transducers, sampling electrical signals generated thereby over a period of time. In many cases, the controller transitions to the receiving mode immediately after generating the acoustic pulse  606  in the transmission mode. 
     The touch sensor may be configured to determine a single contact area (e.g., single touch by a user) or may be configured to determine multiple independent or overlapping contact areas (e.g., multiple simultaneous touches by a user, or multiple simultaneous touches by multiple users). For simplicity of description of the embodiments that follow, a single contact area, the contact area  608 , is referenced. However, it may be appreciated that for any embodiment described herein, and variants and modifications of the same, multiple contact areas may be detected by the touch sensor, and, correspondingly, imaged by the acoustic imaging system  600 . 
     In many embodiments, the image resolver, the touch sensor, and the controller are implemented as separate components of the acoustic imaging system  600 , although such a configuration is not required. For example, in one embodiment the image resolver and the controller can be subcomponents of a single component, such as instructions or subroutines executed by a single processor. 
     As noted above, the foregoing description of the various acoustic imaging system  600  embodiments depicted and described with respect to  FIG. 6 , and the various alternatives thereof and variations thereto are presented, generally, for purposes of explanation, and to facilitate a thorough understanding of the detailed embodiments presented herein. Accordingly, it may be understood that any suitable system may be configured to perform the operations recited with respect thereto. 
       FIG. 7  depicts a simplified block diagram of an acoustic imaging system such as described herein. The acoustic imaging system  700  includes several acoustic transducers  702  that are coupled to a controller  704  which, in turn, is coupled to an image resolver  706 . 
     Each acoustic transducer of the several acoustic transducers  702  can include an acoustic transducer  708  and a pre-amplifier  710 . The acoustic transducer  708  can be formed from a piezoelectric material. The pre-amplifier  710 , in many examples is formed to be physically adjacent to the acoustic transducer  708  in order to mitigate the introduction of noise from parasitics that may affect the signal output from the acoustic transducer  708  before that signal is amplified by the pre-amplifier  710 . In some examples, the pre-amplifier  710  can be formed within, layered onto, or positioned immediately adjacent the acoustic transducer  708 . 
     The controller  704  may thereafter provide a drive signal  712  to each of the acoustic transducers  702 . The drive signal  712  may be specifically timed by a high-resolution timing controller  714  based on the physical location of a particular acoustic transducer. In many case, the drive signal  712  may be an impulse voltage signal. In further embodiments, the drive signal may be a coded voltage signal, including multiple independent impulses. Example impulses are shown and described with reference to  FIGS. 8A-8F . 
     As noted above with respect to other embodiments described herein, the acoustic imaging system  700  may be configured to transition from a transmission mode to a sense mode after an acoustic pulse, or a series of acoustic pulses, has been propagated into the imaging surface. 
     Once in the sense mode, an acoustic transducer  708  of a particular acoustic transducer may be configured to output an electrical signal. The electrical signal output by an acoustic transducer  708  corresponds to the amplitude of a portion of a previously-propagated acoustic pulse (e.g., reflection information). As may be appreciated, the electrical signal output by an acoustic transducer  708  has been attenuated and reflected by each point of the contact area. The electrical signal may also contain one or more noise components, multi-path artifacts, and so on. 
     The electrical signal output by an acoustic transducer  708  may be first be amplified by a pre-amplifier  710  that is physically proximate to the acoustic transducer  708 . Also as noted above, the physical proximity of this initial amplification stage increases the signal to noise ratio of the signal output from a particular acoustic transducer to the controller  704 . 
     Each acoustic transducer, and more specifically the output of the respective pre-amplifier  710 , is connected to a multiplexer  716  within the controller  704 . The multiplexer  716  may be configured to connect to one or more acoustic transducers  702  at a time. In many cases, the multiplexer  716  is a time multiplexer that couples iteratively couples to different acoustic transducers in order to obtain amplified electrical signals therefrom. 
     The output of the multiplexer  716  may be connected to the image resolver  706 . The image resolver  706  may use the values obtained from the multiplexer  716  in order to estimate the acoustic properties map of the contact area. 
     In further embodiments, additional or fewer components or stages may be included. These can include, but are not limited to: gain correction stages, spatial filtering stages, high-pass filtering stages, low-pass filtering stages; band-stop filtering stages; band-pass filtering stages; and so on. 
     Generally and broadly,  FIGS. 8A-8F  depict different coded drive signals that may be used by a controller, such as the controller depicted in  FIG. 2 . It may be appreciated that these are merely examples of different drive signals and that other embodiments may be implemented differently. 
     In particular,  FIG. 8A  depicts one example of an impulse voltage signal  800  that causes a resonant mode of an acoustic transducer. As noted above, the resonant mode may cause the acoustic transducer to resonate for a brief period of time, thereby causing an acoustic output  802  at the resonant frequency. The acoustic output  802  is depicted as a decaying sinusoidal wave having five periods, but it may be appreciated that this is merely one example and other possible resonant waveforms are possible. For example, in some embodiments, the acoustic transducer may resonate for a longer or shorter period of time. 
     The impulse voltage signal  800  can have any suitable impulse shape; the figure shows the impulse voltage signal  800  as having a square wave shape, although this is merely one example. Other example, impulse voltage shapes include a half-sine impulse, a triangular impulse, a ramp impulse, and so on. 
     The impulse voltage signal  800  may be associated with a single-pulse transmitting operation. 
       FIG. 8B  depicts one example of a coded impulse voltage signal that causes multiple resonant modes of an acoustic transducer. In particular, three impulse voltages having different polarities are shown and labeled, respectively, as the impulse voltage signal  804 , the impulse voltage signal  806 , and the impulse voltage signal  808 . These impulse voltage signals may cause three corresponding acoustic outputs  810 ,  812 , and  814 . The phase of the acoustic outputs may depend upon the polarity of the associated impulse voltage signal. 
     As with the embodiment depicted in  FIG. 8A , the impulse voltage signals  804 ,  806 ,  808  can have any suitable impulse shape; the figure shows the impulse voltage signals as having a square wave shape. Other example, impulse voltage shapes include a half-sine impulse, a triangular impulse, a ramp impulse, and so on. 
     The impulse voltage signals  804 ,  806 , and  808  may be associated with a multi-pulse transmitting operation. Although impulse voltage signals are shown, it may be appreciated that other numbers of impulses can be provided. The impulse voltage signals  804 ,  806 , and  808  are depicted as separated by a repeating gap, although this may not be required. 
     In other examples, a coded multi-pulse transmitting operation can be provided with impulse voltage signals that impart different amounts of acoustic energy into an acoustic transducer. For example, as shown in  FIG. 8C , three impulse voltage signals  816 ,  818 , and  820  are provided with different magnitudes and polarities. Correspondingly, the associated acoustic outputs  822 ,  824 , and  826  may have different have different magnitudes and different polarities. In other example, as shown in  FIG. 8D , three impulse voltage signals  816 ,  818 , and  820  are provided with different polarities and durations. 
     In other examples, an transmitting operation can be provided with a voltage signal that takes a chirp waveform  828 , such as shown in  FIG. 8E . The chirp waveform can be any suitable chirp waveform. 
     In yet other examples, two transmitting operations can be performed at the same time by providing two differently-coded signals  830 ,  832  to two different acoustic transducers. For example, as shown in  FIG. 8F , a first and a second encoding may be used. 
     It is appreciated that the voltage signals depicted in  FIGS. 8A-8F  can be implemented in a number of suitable and implementation-specific ways. However, broadly and generally, it may be understood that an electrical signal is applied to an acoustic transducer in a manner that causes the acoustic transducer to generate an acoustic output that typically takes the form of an acoustic pulse. In some examples, a single acoustic pulse may be generated. In other examples, multiple acoustic pulses may be generated in rapid succession. In many cases, multiple acoustic pulses are coded. In some cases, the codes may be shift-insensitive, but this may not be required of all embodiments. In some examples, an transmitting operation can be spatially coded. These acoustic pulses may be propagated orthogonal to one another such that reflections corresponding to one of the acoustic pulses do not destructively interfere with reflections corresponding to the other acoustic pulse. 
     In some cases, an transmitting operation completes before a subsequent transmitting operation begins. In other examples, a subsequent transmitting operation that is coded differently from the current transmitting operation may be initiated once the acoustic pulse(s) of the current transmitting operation reach the contact area. 
     The foregoing description of the embodiments depicted in  FIGS. 4A-8F , and various alternatives and variations, are presented, generally, for purposes of explanation, and to facilitate a thorough understanding of various techniques that may be employed to operate an image resolver of an acoustic imaging system such as described herein. However, it will be apparent to one skilled in the art that some of the specific details presented herein may not be required in order to practice a particular described embodiment, or an equivalent thereof. 
     Thus, the foregoing and following descriptions of specific embodiments are presented for the limited purposes of illustration and description. These descriptions are not targeted to be exhaustive or to limit the disclosure to the precise forms recited herein. To the contrary, it will be apparent to one of ordinary skill in the art that many modifications and variations are possible in view of the above teachings. 
     For example, in some cases, the function and/or operation of an image resolver (regardless of configuration) can be assisted by a specific distribution of acoustic transducers. More specifically, an acoustic imaging system can include a controller configured to propagate a mechanical wave or pulse that has a fundamental frequency. The image resolver of this acoustic imaging system may be configured to demodulate any received signals (e.g., reflections, attenuations, diffractions, and so on) before processing said signals. In another phrasing, the image resolver may include one or more demodulation or carrier rejection operations. 
     In such examples, acoustic transducers can be arranged in rows that are separated from one another at an interval related to the fundamental frequency at which those transistors are driven during a drive operation (e.g., one period, one half period, ninety degrees out of phase, and so on). For example,  FIG. 9A  depicts a simplified cross-section of a portion of an acoustic imaging system  900  in a first configuration. The acoustic transducers  902  are coupled to an imaging surface  904  and may be grounded using a ground layer  906 . The acoustic transducers  902  may also be bonded or otherwise coupled to a first circuit layer  908  using an epoxy  910 , a pressure sensitive adhesive or other techniques. 
     The first circuit layer  908  may include various components for processing, receiving and/or transmitting the electrical signal received from the acoustic transducers  902 . For example, in one implementation, the first circuit layer  908  includes one or more electrodes and a shift register. The shift register may include row and column drivers for the acoustic transducers  902  and one or more multiplexers. Although specific components are mentioned, the first circuit layer  908  may have additional (or fewer) components. In some embodiments, the first circuit layer  908 , and more specifically the electrodes within the first circuit layer  908 , are placed as close to the acoustic transducers  902  as possible so as to avoid signal degradation. 
     The first circuit layer  908  may be arranged in a stacked configuration with or otherwise coupled to a second circuit layer  912 . The second circuit layer  912  may include additional components for processing and/or transmitting the signals received by the acoustic transducers  902 . For example, in one embodiment, the second circuit layer  912  may include an analog front end, a processor, a controller and other such components that are used to process or otherwise transmit the information received from the first circuit layer  908 . In one implementation, the first circuit layer  908  is coupled to the second circuit layer using one or more vias  914 . 
     The first circuit layer  908  and/or the second circuit layer  912  may also be coupled to a user input surface  916 . The user input surface  916  may be a flexible user input surface. The user input surface  916  may include various components, transmission lines and the like for transmitting and/or processing the signals received from the acoustic transducers  902  via the first circuit layer  908  and the second circuit layer  912 . 
       FIG. 9B  depicts a simplified cross-section of a portion of an acoustic imaging system  900  in a second configuration. The acoustic imaging system  900  includes one or more acoustic transducers  902 . The acoustic transducers  902  may be similar to the acoustic transducers  302  shown and described above with respect to  FIGS. 3A-3G . 
     The acoustic transducers  902  may be coupled to an imaging surface  904  of an electronic device and be adjacent a display  918 . The acoustic transducers  902  may also be grounded using a ground layer  906  positioned underneath the imaging surface  904 . As with the embodiment described above with respect to  FIG. 9A , the acoustic transducers  902  may be bonded or otherwise coupled to a first circuit layer  908  using an epoxy  910 , a pressure sensitive adhesive or other techniques. The first circuit layer  908  may include one or more electrodes, a shift register, one or more multiplexers, drive circuitry and the like. In some implementations, the first circuit layer  908  may be a thin-film transistor layer. 
     The first circuit layer  908  may be coupled to a first portion of a user input surface  916 . The user input surface  916  may be a flexible user input surface. The user input surface may be manipulated, bent or folded such as shown. The acoustic imaging system  900  may also include a second circuit layer  912  such as described above. However, in this implementation, the second circuit layer  912  is separated from the first circuit layer  908  and positioned on a second portion of the user input surface  916 . In some implementations each of the first circuit layer  908  and the second circuit layer  912  may be bonded to their respective portions of the user input surface  916  using a wirebond  921 . 
       FIG. 9C  illustrates a third example arrangement of acoustic transducers  902  in an acoustic imaging system  900  implemented with a distributed controller topology. As shown in  FIG. 9C , the acoustic transducers  902  are arranged or otherwise grouped in a subgroup  920 . 
     In this implementation, the acoustic transducers  902  may be coupled to a user input surface  916 . The user input surface  916  may be a flexible user input surface such as describe above. The user input surface  916  includes one or more routings that connect the acoustic transducers  902  to a circuitry layer  922 . 
     For example, each of the acoustic transducers  902  in a subgroup  920  may be coupled to a single circuitry layer  922 . In this particular implementation, the circuitry layer  922  includes some or all of the components in the first circuit layer  908  and the second circuit layer  912  described above. For example, the circuitry layer  922  may include one or more electrodes, a multiplexer, an analog front end and so on. In other implementations, a single acoustic transducer  920  may be connected to a single circuitry layer  922 . 
       FIG. 9D  illustrates a fourth arrangement of acoustic transducers  902  in an acoustic imaging system  900  implemented with a distributed controller topology. In this implementation, the acoustic transducers  902  may be made up of an array of acoustic transducers  902 . Each acoustic transducer  902  or the array of acoustic transducers, may be connected to a first circuit layer  908 . The first circuit layer  908  may include the various circuitry and components described above. 
     The first circuit layer  908  may also be coupled or otherwise connected to a second circuit layer  912 . The second circuit layer  912  may include the various circuitry and components described above. For example, the second circuit layer  912  may include an analog front end. In some implementations, the second circuit layer  912  may include an analog front end for each acoustic transducer  902  in the array. In another implementation, a single analog front end may be shared by multiple acoustic transducers  902 . 
     The array of acoustic transducers  902 , the first circuit layer  908  and the second circuit layer  912  may make up a subgroup  920  such as described above. Each subgroup may be operated independently. For example, a clock tree  924 , or other timing component, may be used to determine when to fire the each of the acoustic transducers  902  in each subgroup  920  and/or the order and timing of firing each subgroup  920 . For example, a first acoustic transducer array in a first subgroup may transmit and/or receive a first signal at a first time period and a second acoustic transducer array in a second subgroup may transmit and/or receive a second signal at a second time period. 
     The foregoing description of the embodiments depicted in  FIGS. 9A-9D , and various alternatives and variations, are presented, generally, for purposes of explanation, and to facilitate a thorough understanding of various techniques that may be employed to couple a group of acoustic transducers to a drive circuit and/or a read circuit and, separately or additionally, various techniques that may be employed to couple an acoustic transducer to an imaging surface. However, it will be apparent to one skilled in the art that some of the specific details presented herein may not be required in order to practice a particular described embodiment, or an equivalent thereof. 
     Thus, the foregoing and following descriptions of specific embodiments are presented for the limited purposes of illustration and description. These descriptions are not targeted to be exhaustive or to limit the disclosure to the precise forms recited herein. To the contrary, it will be apparent to one of ordinary skill in the art that many modifications and variations are possible in view of the above teachings. 
     Generally and broadly,  FIGS. 10A-10D  depict various cross-sections of an acoustic imaging system such as described herein. In particular, these embodiments show various means of coupling an acoustic transducer to an imaging surface. More specifically, in these embodiments, one or more portions of a display (e.g., thin-film transistor layer, polarizer layer, and so on) may be used to support one or more acoustic transducers. 
       FIG. 10A  depicts another acoustic imaging system  1000   a  such as described herein, specifically showing an extended thin-film transistor layer, associated with a display of an electronic device, supporting an acoustic transducer. In this example, an outer cover positioned over the display is the imaging surface  1002 . A thin-film transistor layer  1004  (or another layer within a display stack), associated with the display, includes a shelf portion  1004   a  that is configured to support an acoustic transducer  1006 . More specifically, the acoustic transducer  1006  is positioned over a spacer  1008  that directly contacts the shelf portion  1004  of the thin-film transistor layer  1004 . In some cases, the spacer  1008  also connects the acoustic transducer  1006  to a circuit formed on or otherwise associated with the thin-film transistor layer  1004 . In some cases, the circuit may include an amplifier configured to pre-amplify signals received from the acoustic transducer  1006  but this is not required. The acoustic transducer  1006  couples to an electrode  1010  disposed and/or formed on an underside of the imaging surface  1002 . In this example, the acoustic transducer  1006  is oriented generally perpendicular to the underside the imaging surface  1002 , although this is not required. 
     For example,  FIG. 10B  depicts another acoustic imaging system  1000   b  such as described herein, specifically showing an extended thin-film transistor layer (associated with a display of an electronic device) supporting an acoustic transducer. In this example, the shelf portion  1004   a  accommodates the acoustic transducer  1006  at an angle relative to the underside of the imaging surface  1002 , supported by an angled electrode extension  1012 . 
     In yet another example, the thin-film transistor layer can accommodate an electrical connection and/or circuit that can be used to drive or reads the acoustic transducer  1006  in another manner. For example, as shown in  FIG. 10C , a flex  1004   b  that extends from the thin-film transistor layer can connect to the acoustic transducer  1006  via a second flex or interposer  1014 . In still further cases, such as shown in  FIG. 10D , a drive/sense chip  1016  can be coupled via an interposer or a flex  1020  to any suitable element within the display stack, identified as the display stack layer  1018 . In these examples, the acoustic imaging system can integrate within the display of the electronic device. 
     The foregoing description of the embodiments depicted in  FIGS. 10A-10D , and various alternatives and variations, are presented, generally, for purposes of explanation, and to facilitate a thorough understanding of various techniques that may be employed to couple a group of acoustic transducers to a drive circuit and/or a read circuit that may be integrated with or otherwise associated with a display (or a display stack layer) of an electronic device and, separately or additionally, various techniques that may be employed to couple an acoustic transducer to an imaging surface. However, it will be apparent to one skilled in the art that some of the specific details presented herein may not be required in order to practice a particular described embodiment, or an equivalent thereof. 
     Thus, the foregoing and following descriptions of specific embodiments are presented for the limited purposes of illustration and description. These descriptions are not targeted to be exhaustive or to limit the disclosure to the precise forms recited herein. To the contrary, it will be apparent to one of ordinary skill in the art that many modifications and variations are possible in view of the above teachings. 
       FIG. 11  depicts a shift register topology that can be used to drive more than one acoustic transducer substantially simultaneously. More specifically, an acoustic imaging system  1100  can include a drive register  1102  and a read register  1106  that are each associated with a line of adjacent transducers, identified as the transducer array  1106 . In this example, the drive register  1102  and the read register  1106  can be implemented in any suitable manner; in one embodiment, both registers are implemented as a series of flip-flops sharing a single clock signal. In other cases, the drive register  1102  and the read register  1106  can be implemented in another manner. In many cases, the drive register  1102  and the read register  1106  can be implemented in the same silicon packaging (e.g., integrated circuit) as a display driver or touch controller of a touch-sensitive display of an electronic device that accommodates the acoustic imaging system  1100 . 
     The drive register  1102  receives a serial transmit-enable signal (identified as the TX pattern) and the read register  1004  receives a serial read-enable signal (identified as the RX pattern). Once the registers are filled, a drive operation or a read operation can be performed by a controller associated with the acoustic imaging system. 
     A controller for such a system, described above with reference to  FIG. 2 , can be implemented in a number of ways. For example,  FIG. 12  is a simplified system diagram of a sense-mode portion of a controller (e.g., sense chip) that can be used with one or more acoustic imaging systems such as described herein. In some cases, the sense-mode portion of a controller is referred to as an “analog front end.” 
       FIG. 12  depicts one example analog front end, identified as the analog front end  1200 . As with the registers depicted in  FIG. 11 , the analog front end  1200  can be partially or entirely implemented in the same silicon packaging as a display driver or input driver/controller of a touch and/or force-sensitive display of an electronic device. 
     The analog front end  1200  can include multiple stages, modules, and/or interconnected operational circuit components, some of which are shown in the illustrated example. 
     The analog front end  1200  receives an input  1202  from one or more acoustic transducers. The input  1202  is typically pre-amplified by a thin-film transistor circuit disposed and/or implemented in close physical proximity to an acoustic transducer. In other cases, the pre-amplifier can be implemented in another way. 
     The analog front end  1200  can optically receive the input  1202  at one or more multiplexers  1204  configured to direct signals received from particular acoustic transducers to particular processing modules or circuit components. In other cases, the one or more multiplexers  1204  may not be required. 
     The analog front end  1200  can include a gain and offset correction block that can be implemented with one or more amplification stages, each associated with one or more analog-to-digital converters. In the illustrated embodiment, two amplifiers are identified, each associated with one or more digital-to-analog converters configured to correct gain and/or offset in the signals output from the amplifiers. More specifically, the amplifier  1206  is associated with a digital-to-analog converter  1208  (to adjust gain and/or offset) and the amplifier  1210  is associated with a digital-to-analog converter  1212  (to adjust gain and/or offset). The output from the amplifiers and converters can be optionally received by a filtering module, identified as the filter  1214 . After filtering, the amplified and filtered analog signal can be converted to digital by an analog-to-digital converter  1216 . Thereafter, the digital signal is received at an input port  1218  of a processing module that may be associated with an image resolver such as described herein. 
     The foregoing description of the embodiments depicted in  FIGS. 11 and 12 , and various alternatives and variations, are presented, generally, for purposes of explanation, and to facilitate a thorough understanding of various techniques for driving and reading one or more acoustic transducers of an acoustic imaging system. However, it will be apparent to one skilled in the art that some of the specific details presented herein may not be required in order to practice a particular described embodiment, or an equivalent thereof. 
     Thus, the foregoing and following descriptions of specific embodiments are presented for the limited purposes of illustration and description. These descriptions are not targeted to be exhaustive or to limit the disclosure to the precise forms recited herein. To the contrary, it will be apparent to one of ordinary skill in the art that many modifications and variations are possible in view of the above teachings. 
       FIG. 13  depicts example operations of a simplified method of operating an acoustic imaging system of an electronic device. The method begins at operation  1300  in which an acoustic imaging system receives a signal (e.g., from an electronic device processor) to assemble an image of an imaging surface to which the acoustic imaging system is coupled. At operation  1302 , a mechanical wave is generated within the imaging surface. Next, at operation  1304 , a mechanical wave is received. Finally, at operation  1304 , data associated with the mechanical wave received at operation  1304  is used to generate an image of an object in physical contact with the imaging surface. 
     In some cases, the image may be used as touch input to an electronic device. In other cases, the image may be used to authenticate a function, operation or task of the electronic device. In still further cases, the image may be used to determine an amount of force applied to the electronic device. 
       FIG. 14  depicts example operations of a method of operating an acoustic imaging system that is coupled to a user input surface. The method depicted can be performed by the acoustic imaging system  200  of  FIG. 2 . The method  1400  begins at operation  1402  in which a contact area is determined. The contact area is the area over which an object, such as the finger of a user, physically contacts an outer surface of the user input surface. In many embodiments, the contact area is determined by a contact sensor (e.g., touch sensor). Next, at operation  1404 , multiple transmitting operations are performed. The transmitting operations can be associated with a single acoustic transducer or multiple acoustic transducers. The transmitting operations can be single-pulse or multi-pulse transmitting operations. The transmitting operations can be coded or non-coded. The transmitting operations may be spatially coded. Next, at operation  1406 , reflection information associated with each transmitting operation may be accumulated. 
       FIG. 15  depicts example operations of a method of operating a tomographic acoustic imaging system that is coupled to a user input surface. The method depicted can be performed by the tomographic acoustic imaging system  200  of  FIG. 2 . The method  1500  begins at operation  1502  in which a contact area is determined. The contact area is the area over which an object, such as the finger of a user, physically contacts an outer surface of the user input surface. In many embodiments, the contact area is determined by a contact sensor (e.g., touch sensor). Next, at operation  1504 , the Radon transform of the contact area is determined. Typically, as noted above, the Radon transform is determined by performing a number of parallel projections of the contact area at a variety of angles around the contact area. Finally at operation  1506 , an estimate of the inverse Radon transform may be estimated. In one embodiment, the inverse of the Radon transform may be estimated by performing a filtered back projection of the various planar projections obtained at operation  1504 . 
     Many embodiments of the foregoing disclosure may include or may be described in relation to various methods of operation, use, manufacture, and so on. Notably, the operations of methods presented herein are meant only to be exemplary and, accordingly, are not necessarily exhaustive. For example an alternate operation order or fewer or additional steps may be required or desired for particular embodiments. 
     For example, although many embodiments are described herein with reference to systems and methods for generating an image of a user&#39;s fingerprint, these systems and methods can alternatively or additionally be used to perform other operations, or to obtain non-fingerprint information, such as, but not limited to: generating an image of a palm; generating an image of an ear, face, or cheek; determining the location of a stylus on an input surface of an electronic device; determining a physiological characteristic of a user such as heart rate, respiration rate, blood oxygenation, and so on; determining characteristics of a non-input surface; determining the force with which a user touches an input surface; determining the location at which a user touches an input surface; and so on. Accordingly, it may be appreciated that the various systems and methods presented below are merely examples and that other embodiments, systems, methods, techniques, apparatuses, and combinations thereof are contemplated in view of the disclosure provided above. 
     The foregoing description, for purposes of explanation, used specific nomenclature to provide a thorough understanding of the described embodiments. However, it will be apparent to one skilled in the art that the specific details are not required in order to practice the described embodiments. Thus, the foregoing descriptions of the specific embodiments described herein are presented for purposes of illustration and description. They are not meant to be exhaustive or to limit the embodiments to the precise forms disclosed. It will be apparent to one of ordinary skill in the art that many modifications and variations are possible in view of the above teachings. In particular, any features described with respect to one embodiment may also be used in some embodiments, where compatible. Likewise, the features of the different embodiments may be exchanged, substituted, or omitted where compatible and appropriate. 
     The present disclosure recognizes that personal information data, including biometric data, in the present technology, can be used to the benefit of users. For example, the use of biometric authentication data can be used for convenient access to device features without the use of passwords. In other examples, user biometric data is collected for providing users with feedback about their health or fitness levels. Further, other uses for personal information data, including biometric data, which benefit the user, are also contemplated by the present disclosure. 
     The present disclosure further contemplates that the entities responsible for the collection, analysis, disclosure, transfer, storage, or other use of such personal information data will comply with well-established privacy policies and/or privacy practices. In particular, such entities should implement and consistently use privacy policies and practices that are generally recognized as meeting or exceeding industry or governmental requirements for maintaining personal information data private and secure, including the use of data encryption and security methods that meets or exceeds industry or government standards. For example, personal information from users should be collected for legitimate and reasonable uses of the entity and not shared or sold outside of those legitimate uses. Further, such collection should occur only after receiving the informed consent of the users. Additionally, such entities would take any needed steps for safeguarding and securing access to such personal information data and ensuring that others with access to the personal information data adhere to their privacy policies and procedures. Further, such entities can subject themselves to evaluation by third parties to certify their adherence to widely accepted privacy policies and practices. 
     Despite the foregoing, the present disclosure also contemplates embodiments in which users selectively block the use of, or access to, personal information data, including biometric data. That is, the present disclosure contemplates that hardware and/or software elements can be provided to prevent or block access to such personal information data. For example, in the case of biometric authentication methods, the present technology can be configured to allow users to optionally bypass biometric authentication steps by providing secure information such as passwords, personal identification numbers (PINS), touch gestures, or other authentication methods, alone or in combination, known to those of skill in the art. In another example, users can select to remove, disable, or restrict access to certain health-related applications collecting users&#39; personal health or fitness data.