Patent Publication Number: US-2021162461-A1

Title: Methods and systems for a multi-frequency transducer array

Description:
FIELD 
     Embodiments of the subject matter disclosed herein relate to a transducer for a medical device. 
     BACKGROUND 
     Transducer probes are used in a variety of applications to convert energy from a physical form to an electrical form. For example, a transducer probe may include piezoelectric materials which generate electrical voltage from a mechanical stress or strain exerted on the materials. Piezoelectric transducer probes are configured to be highly sensitive to provide large signal amplitudes, broad bandwidth for use across a wide range of frequencies, and short-duration impulse for high axial resolution. Such properties are desirable for medical applications such as imaging, non-destructive evaluation, fluid flow sensing, etc. Furthermore, frequency apodization of the transducer probe may mitigate loss of signal resolution due to signal attenuation and dispersion as the signal travels away from its source. 
     BRIEF DESCRIPTION 
     It should be understood that the brief description above is provided to introduce in simplified form a selection of concepts that are further described in the detailed description. It is not meant to identify key or essential features of the claimed subject matter, the scope of which is defined uniquely by the claims that follow the detailed description. Furthermore, the claimed subject matter is not limited to implementations that solve any disadvantages noted above or in any part of this disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will be better understood from reading the following description of non-limiting embodiments, with reference to the attached drawings, wherein below: 
         FIG. 1  shows an example of an acoustic stack of an ultrasound transducer. 
         FIG. 2  shows an example of a homogeneous multi-element transducer array. 
         FIG. 3  shows a first graph of an apodization function along an elevation direction provided by the multi-element transducer array of  FIG. 2 . 
         FIG. 4  shows a first example of a piezoelectric element formed of two sub-elements. 
         FIG. 5  shows a second example of a piezoelectric element formed of two sub-elements. 
         FIG. 6  shows a third example of a piezoelectric element formed of two sub-elements. 
         FIG. 7  shows a first example of a multi-element transducer array with varying spatial frequency distribution. 
         FIG. 8  shows a second example of a multi-element transducer array with varying spatial frequency distribution. 
         FIG. 9  shows a third example of a multi-element transducer array with varying spatial frequency distribution. 
         FIG. 10  shows a first example of an acoustic stack block. 
         FIG. 11  shows a first comb structure formed from the acoustic stack block of  FIG. 10 . 
         FIG. 12  shows a second example of an acoustic stack block. 
         FIG. 13  shows a second comb structure formed from the acoustic stack of  FIG. 12 . 
         FIG. 14  shows a third example of an acoustic stack block, formed by coupling the first example of  FIG. 10  with the second example of  FIG. 12 , from a view along the elevation direction. 
         FIG. 15  shows the third example of the acoustic stack block from a view along the azimuth direction. 
         FIG. 16  shows a coupling of the third example of the acoustic stack block with a base package from a view along the elevation direction. 
         FIG. 17  shows the coupling of third example of the acoustic stack block with the base package from a view along the azimuth direction 
         FIG. 18  shows a first example of a base package from a perspective view. 
         FIG. 19  shows a fourth example of an acoustic stack block, formed from the coupling of the third example of the acoustic stack block with the base package, viewed along the elevation direction. 
         FIG. 20  shows the fourth example of an acoustic stack block viewed along the azimuth direction. 
         FIG. 21  shows the fourth example of the acoustic stack block of  FIG. 19  with a portion of a back side of the acoustic stack block ground away, viewed along the elevation direction. 
         FIG. 22  shows the fourth example of the acoustic stack block of  FIG. 20  with the portion of the back side of the acoustic stack block ground away, viewed along the azimuth direction. 
         FIG. 23  shows the fourth example of the acoustic stack block with a conductive layer coupled to the ground back side, viewed along the elevation direction. 
         FIG. 24  shows the fourth example of the acoustic stack block with the conductive layer coupled to the ground back side, viewed along the azimuth direction. 
         FIG. 25  shows a dicing of the fourth example of the acoustic stack block, viewed along the elevation direction. 
         FIG. 26  shows the dicing of the fourth example of the acoustic stack block, viewed along the azimuth direction. 
         FIG. 27  shows a coupling of a matching layer block to a front side and a backing layer block to a back side of the fourth example of the acoustic stack block, viewed along the elevation direction. 
         FIG. 28  shows the coupling of the matching layer block to the front side and the backing layer block to the back side of the fourth example of the acoustic stack block, viewed along the azimuth direction. 
         FIG. 29  shows singulation of the fourth example of the acoustic stack block, viewed along the elevation direction. 
         FIG. 30  shows singulation of the fourth example of the acoustic stack block, viewed along the azimuth direction. 
         FIG. 31  shows a fifth example of a multi-element acoustic stack. 
         FIG. 32  shows a sixth example of a multi-element acoustic stack. 
         FIG. 33  shows a seventh example of a multi-element acoustic stack. 
         FIG. 34  shows an eighth example of a multi-element acoustic stack. 
         FIG. 35  shows a variation in dicing of the fourth example of the acoustic stack block of  FIGS. 29 and 30 . 
         FIG. 36  shows a combining of two multi-element comb structures to form an acoustic stack with four sub-elements. 
         FIG. 37  shows an example of a routine for fabricating a multi-frequency acoustic stack. 
         FIG. 38  shows an example of a method for forming multi-frequency elements for the acoustic stack that may be executed as part of the routine of  FIG. 37 . 
         FIG. 39  shows a second graph of an apodization function along an elevation direction provided by a multi-element transducer array with non-homogeneous spatial frequency distribution. 
         FIG. 40  shows a second example of a base package from a perspective view. 
         FIG. 41  shows a third example of a base package from a perspective view. 
         FIG. 42  shows an example of an acoustic stack formed from comb structures with different kerf dimensions. 
     
    
    
     DETAILED DESCRIPTION 
     The following description relates to various embodiments of an acoustic stack for a transducer probe. The acoustic stack may be configured with a broad frequency bandwidth by adapting the acoustic stack with a piezoelectric element formed from more than one sub-element. An example of an acoustic stack for a transducer probe is shown in  FIG. 1 . Each of the more than one sub-element may be a different type of element with a different resonance frequency. Relative proportions of the more than one sub-element may be maintained constant along both an azimuth direction and an elevation direction of the transducer probe to form a homogeneous array. An example of a homogeneous multi-frequency transducer array is depicted in  FIG. 2  and a first graph showing a frequency apodization function provided by the homogeneous multi-element (e.g., more than one sub-element) array is illustrated  FIG. 3 . In contrast, a tapered apodization function is shown in  FIG. 39  which may be produced by a multi-frequency transducer array with varying percent content of sub-elements included in each element of the transducer array. As described above, relative proportions of the sub-elements forming the piezoelectric element may be varied, as shown in  FIGS. 4-6 . In some examples, a multi-frequency transducer array may not be homogeneous along at least one of the azimuth and elevation directions, instead exhibiting a varying spatial frequency distribution. Examples of different spatially distributed multi-frequency transducer arrays are shown in  FIGS. 7-9 . A multi-element transducer array may be fabricated via a wafer scale approach to enable scalable, low cost manufacturing. Various processes included in the wafer scale approach are depicted in  FIGS. 10-36 and 40-42 . An example of a first routine for fabricating a multi-frequency acoustic stack for a transducer probe by the wafer scale approach is shown in  FIG. 37 . An example of a second routine for forming multi-frequency elements for the acoustic stack is depicted in  FIG. 38  and may be included in the first routine of  FIG. 37 . 
       FIGS. 1-2, 4-36, and 40-42  show example configurations with relative positioning of the various components. If shown directly contacting each other, or directly coupled, then such elements may be referred to as directly contacting or directly coupled, respectively, at least in one example. Similarly, elements shown contiguous or adjacent to one another may be contiguous or adjacent to each other, respectively, at least in one example. As an example, components laying in face-sharing contact with each other may be referred to as in face-sharing contact. As another example, elements positioned apart from each other with only a space there-between and no other components may be referred to as such, in at least one example. As yet another example, elements shown above/below one another, at opposite sides to one another, or to the left/right of one another may be referred to as such, relative to one another. Further, as shown in the figures, a topmost element or point of element may be referred to as a “top” of the component and a bottommost element or point of the element may be referred to as a “bottom” of the component, in at least one example. As used herein, top/bottom, upper/lower, above/below, may be relative to a vertical axis of the figures and used to describe positioning of elements of the figures relative to one another. As such, elements shown above other elements are positioned vertically above the other elements, in one example. As yet another example, shapes of the elements depicted within the figures may be referred to as having those shapes (e.g., such as being circular, straight, planar, curved, rounded, chamfered, angled, or the like). Further, elements shown intersecting one another may be referred to as intersecting elements or intersecting one another, in at least one example. Further still, an element shown within another element or shown outside of another element may be referred as such, in one example. 
     Piezoelectric elements may be implemented in transducer probes for a wide range of medical applications, including imaging, non-destructive testing, diagnosis, measuring blood flow, etc. The piezoelectric elements may be formed of a class of crystalline materials that become electrically polarized when subjected to a mechanical strain. When stressed, the piezoelectric elements output a voltage that is proportional to the applied stress. 
     A piezoelectric transducer probe, e.g., a device utilizing a piezoelectric effect to convert energy from one form to another, may offer high sensitivity, high frequency response and high transient response. In some examples, such as in ultrasound transducer probes, a converse piezoelectric effect may be leveraged where electricity is applied to the piezoelectric elements, causing deformation of the material and generation of ultrasonic waves. As such, an external, mechanical force is not demanded and the piezoelectric transducer probe may be packaged as a compact, easily transportable device. 
     Although the piezoelectric transducer probe is a highly sensitive instrument, an operational frequency bandwidth of the probe may be narrow. For example, the piezoelectric material may be associated with a low frequency, e.g., between 0.5-2.25 MHz, or a high frequency, e.g., between 15.0-25.0 MHz, but not both. Similarly, the transducer probe may be adapted for transmitting or receiving but may not be equipped for high performance in both applications due to a focused frequency range of the particular type of piezoelectric material. Broadband transducer probes may provide wider operational frequency ranges but adapting the probes with electrical impedance matching may be challenging and cost prohibitive. 
     In one example, the issues described above may be addressed by a piezoelectric transducer probe adapted with a multi-frequency transducer array. The multi-frequency transducer array may include elements in each transducer that are formed from more than one sub-element, each sub-element having a different resonance frequency. In other words, each element may be a hybrid element with an overall resonance frequency modified by the resonance frequencies of the sub-elements. Thus, configuring the transducer array with hybrid elements of varying compositions may enable the transducer array operate across a range of frequencies while maintaining a sensitivity and resolution of a multi-frequency transducer probe in which the transducer array is implemented. Furthermore, the transducers may be fabricated via a wafer level approach that provides ground recovery, frequency apodization, and frequency agility in both the azimuth and elevation directions. A spatial frequency distribution may thereby be controlled and the transducers may be manufactured through a cost-effective, scalable manner. 
     Multi-frequency piezoelectric transducers, as described herein, may be used in a variety of medical devices. For example, as shown in  FIG. 1 , a piezoelectric transducer may be included in an ultrasound probe, used to create an image based on ultrasonic signals. It will be appreciated that the ultrasound probe is a non-limiting example of a medical device utilizing the piezoelectric transducer and incorporation of the piezoelectric transducer in other medical devices have been envisioned. For example, the piezoelectric transducer may be used to convert energy in non-destructive testers, Jetter systems, high voltage power sources, etc. The following description of  FIG. 1  is an exemplary overview of how the piezoelectric transducer may be implemented in the ultrasound transducer probe. 
     An ultrasound probe includes one or more active components for generating an ultrasonic signal. An example of an active component, or piezoelectric element  102  of an ultrasound probe is shown in a schematic diagram of an acoustic stack  100  in  FIG. 1 , with a central axis  104 . A set of reference axes are provided, indicating an azimuth direction  101 , an elevation direction  103 , and a transverse direction  105  perpendicular to both the azimuth and elevation directions. In other examples, the set of reference axes may represent a z-axis  101 , an x-axis  103 , and a y-axis  105 . The piezoelectric element  102  is shown in  FIG. 1  with the central axis  104  parallel with the azimuth direction  101 . 
     It will be noted that while the acoustic stack  100  is shown configured for a linear ultrasound probe and the azimuth direction is described as parallel with the z-axis in  FIG. 1 , other examples may include an azimuth direction that is angled relative to the z-axis, depending on a shape of a piezoelectric element array. For example, the ultrasound probe may be curvilinear or phased array, thus generating non-linear beams that are not parallel with the z-axis. 
     While a single piezoelectric element is shown in  FIG. 1 , the ultrasound probe may include a plurality of piezoelectric elements arranged in an array and individually coupled to an electrical energy source by wires. Each electrical circuit formed of one or more piezoelectric elements may be a transducer. In some examples, the transducer may include an array of piezoelectric elements which may arranged in a variety of patterns, or matrices, including one-dimensional (1D) linear, two-dimensional (2D) square, 2D annular, etc. In one example, the transducer may be formed from more than one type of piezoelectric element, thereby providing a multi-frequency piezoelectric transducer. A frequency distribution along each of the azimuth and elevation directions may adapted to be uniform or non-uniform. Further details of the multi-frequency piezoelectric transducer are provided below, with reference to  FIGS. 2-42 . 
     Each transducer may be electrically insulated from adjacent transducers but may all be coupled to common layers positioned above and below the piezoelectric element, with respect to the azimuth direction. The plurality of piezoelectric elements and accompanying layers may be enclosed by an outer housing of the ultrasound probe which may be, for example, a plastic case with a variety of geometries. For example, the outer housing may be a rectangular block, a cylinder, or a shape configured to fit into a user&#39;s hand comfortably. As such, components shown in  FIG. 1  may be adapted to have geometries and dimensions suitable to fit within the outer housing of the ultrasound probe. 
     The piezoelectric element  102  may be a block formed of a natural material such as quartz, or a synthetic material, such as lead zirconate titanate, that deforms and vibrates when a voltage is applied by, for example, a transmitter. In some examples, the piezoelectric element  102  may be a single crystal with crystallographic axes, such as lithium niobate and PMN-PT (Pb(Mg 1/3 Nb 2/3 )O 3 —PbTiO 3 ). The vibration of the piezoelectric element  102  generates an ultrasonic signal formed of ultrasonic waves that are transmitted out of the ultrasound probe in a direction indicated by arrows  107 , e.g., along the azimuth direction  101 . The piezoelectric element  102  may also receive ultrasonic waves, such as ultrasonic waves reflected from a target object, and convert the ultrasonic waves to a voltage. The voltage may be transmitted to a receiver of the ultrasound imaging system and processed into an image. 
     Electrodes  114  may be in direct contact with the piezoelectric element  102  to transmit the voltage via wires  115 , the voltage converted from ultrasonic waves. The wires  115  may be connected to a circuit board (not shown) to which a plurality of wires from electrodes of the plurality of piezoelectric elements may be fixed. The circuit board may be coupled to a coaxial cable providing electronic communication between the ultrasound probe and the receiver. 
     An acoustic matching layer  120  may be arranged above the piezoelectric element  102 , with respect to the azimuth direction  101 , oriented perpendicular to the central axis  104 . The acoustic matching layer  120  may be a material positioned between the piezoelectric element  102  and a target object to be imaged. By arranging the acoustic matching layer  120  in between, the ultrasonic waves may first pass through the acoustic matching layer  120 , and emerge from the acoustic matching layer  220  in phase, thereby reducing a likelihood of reflection at the target object. The acoustic matching layer  220  may shorten a pulse length of the ultrasonic signal, thereby increasing an axial resolution of the signal. 
     A backing  126  may be arranged below the piezoelectric element  102 , with respect to the z-axis. In some examples, the backing  126  may be a block of material that extends along the elevation direction  103  so that each of the plurality of piezoelectric elements in the ultrasound probe are directly above the backing  126 , with respect to the azimuth direction  101 . The backing  126  may be configured to absorb ultrasonic waves directed from the piezoelectric element  102  in a direction opposite of the direction indicated by arrows  107  and attenuate stray ultrasonic waves deflected by the outer housing of the ultrasound probe. A bandwidth of the ultrasonic signal, as well as the axial resolution, may be increased by the backing  126 . 
     A piezoelectric transducer (PZT) probe may provide high penetration into a target as well as high frequency and transient responses, enabling high resolution data to be obtained. However, a type of piezoelectric element included in the probe may operate within a frequency bandwidth that constrains use of the probe to a particular application. For example, probe with a low central frequency piezoelectric element may be used to produce ultrasound images of deep tissues or organs but may not provide sufficient flaw resolution or thickness measurement capabilities. Thus, use of piezoelectric transducer probes for a variety of applications may demand access to multiple probes with different piezoelectric elements. 
     In contrast, a capacitive micromachined ultrasonic transducer (CMUT) probe, when used in ultrasonic applications, may offer broader bandwidth as well as more efficient fabrication, due to construction of the CMUTs on silicon via micromachining techniques. The broader CMUT bandwidth enables the CMUT probes to achieve greater axial resolution than the PZT probe. However, a sensitivity and penetration of the CMUT probe may be less than the PZT probe. Furthermore, CMUTs may be more prone to acoustic crosstalk than PZTs. 
     In one example, high penetration and broad bandwidth may be provided in a PZT probe by adapting the PZT probe with transducers equipped with piezoelectric elements formed from more than one type of sub-element, each sub-element being a different type of piezoelectric material. By combining piezoelectric sub-elements with different resonance frequencies into one transducer, an array of multi-frequency piezoelectric elements may be provided. Each of the multi-frequency elements may have a distinct frequency, depending on relative proportions of the sub-elements, allowing the multi-frequency elements to transmit and receive signals over a wider range of frequencies in comparison to a single element transducer probe. 
     For example, as shown in  FIG. 2 , an example of a first matrix  200  with multi-frequency elements may be a homogeneous bi-dimensional array, such as a butterfly-type matrix array, with homogeneous multi-frequency elements  202 . The first matrix  200  may represent an arrangement of the elements  202  within a transducer of an acoustic stack, such as the acoustic stack  100  of  FIG. 1 . At least one of the acoustic stack may be incorporated within a PZT probe. The first matrix  200  is shown oriented along the azimuth direction  101  and the elevation direction  103 . 
     Each of the elements  202  includes a first sub-element  204  and a second sub-element  206 . As an example, the first sub-element  204  may be a higher frequency element and the second sub-element  206  may be a lower frequency element, where the first and second sub-elements  204 ,  206  may be coupled via a fabrication technique discussed further below, with reference to  FIGS. 10-38 . The elements  202  may be spaced apart from one another and thereby electrically insulated from adjacent elements  202 . Each of the elements  202  may be coupled to an electrical circuit  208  to enable application of a voltage to induce deformation of each of the elements  202 . Furthermore, each of the elements  202  may transmit an individual signal, as induced by deformation. It will be noted that each of the elements  202  are coupled to the electrical circuit  208  but only the bottom row of elements  202  are shown directly coupled to the electrical circuit  208  in  FIG. 2  for brevity. 
     The first matrix  200  may be coupled to other layers of the acoustic stack, e.g., an acoustic lens, a backing, etc., as shown in  FIG. 1 . As a result of forming the elements from the first sub-element  204  and the second sub-element  206 , the elements may transmit and/or receive across a wide range of frequencies. For example, the first sub-element  204  may have a central (e.g., resonance) frequency of 2.0 MHz and the second sub-element  206  may have a central frequency of 15 MHz. By combining the first sub-element  204  with the second sub-element  206  with equal relative proportions, the elements  202  may transmit and/or receive ultrasonic signals across a wider range of frequencies than either the first sub-element  204  or the second sub-element  206  alone. 
     For example, the each of the elements  202  may have a frequency range of 1.5 to 15 MHz. The array of the elements  202  in the first matrix  200  may provide symmetric and linear apodization functions along the elevation direction  103 , as shown in  FIG. 3 . Apodization provided by both a high frequency sub-element (e.g., the first sub-element  204  of  FIG. 2 ), as indicated by plot  302 , and a low frequency sub-element (e.g., the second sub-element  206  of  FIG. 2 ), as indicated by plot  304 , are illustrated in graph  300 . The apodization functions are plotted relative to percent content of the high frequency and low frequency sub-elements in each element of a transducer array along the y-axis and to the elevation direction  103  along the x-axis. The equal proportions of the high frequency sub-element and low frequency sub-element distributed along the elevation direction results in a uniform apodization function. 
     As described above, a symmetric and non-tapering apodization function may be provided by the high frequency and low frequency sub-elements  204 ,  206  of the elements  202  of  FIG. 2  with equal proportions of the sub-elements in a homogeneous matrix array, e.g., each multi-frequency element of the array is configured similarly. However, in order to bring a sampled signal down to zero, or near zero, at edges of a sample region to suppress leakage sidelobes, a tapering of the apodization function may be desired. For example, a tapered apodization function (non-discretized) provided by an element formed of a high frequency sub-element and a low frequency sub-element is shown in a second graph  3900  in  FIG. 39 . 
     Plot  3902  represents an apodization function of the high frequency sub-element in each element of a transducer array relative to percent content (y-axis) along the elevation direction  103  and plot  3904  represents an apodization function of the low frequency sub-element in each element of the transducer array. Plot  3902  and plot  3904  are inversely correlated so that a maximum of the first plot  3902 , relative to the y-axis, at a central region of the transducer array along the elevation direction  103  corresponds to a minimum of plot  3904 . To either side of the maximum, plot  3902  decreases along the y-axis and the plot  3904  increases proportionally. While the maximum percent content of each of the high frequency and low frequency sub-elements is shown at 80% and the minimum percent content is shown at 20%, other examples may include any other values of the maximum and minimum percent content, such as 100% and 0%, respectively. 
     A sum of the high frequency and low frequency apodization functions may provide side lobe reduction. For example, it may be desirable to have a higher proportion of high frequency elements at a central region of the transducer array and higher proportion of the low frequency elements along the sides of the transducer array to achieve maximum suppression of leakage side lobes. The tapered apodization function shown in graph  3900  may be generated by configuring the elements of the transducer array with unequal relative proportions of each of the high and low frequency sub-elements. For example, a central region of the transducer may include elements with higher percent content of the high frequency sub-element than the outer edges. Suppression of side lobes is thereby enhanced. 
     Examples of elements with unequal sub-element proportions are shown in  FIGS. 4-6 . A first example of a multi-frequency element  400  with unequal distribution is shown in  FIG. 4 . The multi-frequency element  400  is formed of a first, high frequency sub-element  402  and a second, low frequency sub-element  404 , similar to the first and second sub-elements  204 ,  206  of the elements  202  of  FIG. 2 . 
     A first width  406  of the first sub-element  402  may be greater than a second width  408  of the second sub-element  404 . For example, the first width  406  may be four times greater than the second width  408 , resulting in 80% of the multi-frequency element  400  formed of the first, high frequency sub-element  402  and 20% formed of the second, low frequency sub-element  404 . The relative widths of the sub-elements may be reversed in other examples. A second example of a multi-frequency element  500  is shown in  FIG. 5  and includes a first, high frequency sub-element  502  and a second, low frequency sub-element  504 . In the second example, a first width  506  of the first sub-element  502  may be half of a second width  508  of the second sub-element  504 . 
     In a third example of a multi-frequency element  600  with unequal distribution, as illustrated in  FIG. 6 , the multi-frequency element  600  is similarly formed of a first, high frequency sub-element  602  and a second, low frequency sub-element  604 . A first width  606  of the first sub-element  602  is also less than a second width  608  of the second sub-element  604 . The first width  606  may be, for example, a quarter of the second width  608 . 
     The examples of multi-frequency elements with unequal distribution of sub-elements shown in  FIGS. 4-6  are non-limiting examples of multi-frequency elements. Other examples, may include multi-frequency elements with any variation in relative proportions between the first sub-element and the second sub-element of the elements. Furthermore, other examples of the multi-frequency elements may include more than two sub-elements. For example, the multi-frequency elements may be formed of three or four sub-elements, with a variety of proportions of each of the sub-elements. 
     An array of non-homogeneous multi-frequency elements may be configured to provide the frequency apodization function shown in  FIG. 39 . The array may be non-homogeneous with respect to a percent content of different sub-elements forming each multi-frequency element included in the array. In other words, a number of sub-elements, each of the sub-elements having a different resonance frequency, as well as relative proportions of the sub-elements in each element may not be uniform across the array, enabling a spatial distribution of elements with different frequency ranges. In one example, as shown in  FIG. 7 , a second matrix  700 , configured to provide an apodization function similar to that shown in graph  3900  of  FIG. 39 , may be an example of a one-dimensional (1D) linear array formed of a plurality of elements  702 . A first row  701 , a second row  703 , and third row  705  of the plurality of elements  702  are depicted. Dotted lines between the second row  703  and the third row  705  represent a presence of optional additional rows arranged between the second row  703  and the third row  705 , omitted from  FIG. 7  for brevity. In other words, the second matrix  700  may have at least one row and may include any number of additional rows. Each of the plurality of elements  702  may be coupled to an electrical circuit and transmit an individual signal based on a composition of each element. 
     Each of the plurality of elements  702  includes a first, high-frequency sub-element  704  and/or a second, low-frequency sub-element  706 . Some of the plurality of elements  702  include both the first sub-element  704  and the second sub-element  706  with varying widths of the sub-elements relative to one another (where the width is defined along the elevation direction  103 ). As well, some of the plurality of elements  702  include only the first sub-element  704  or only the second sub-element  706 . 
     For example, a central region  720  of the second matrix  700  includes a portion of the plurality of elements  702  formed of only the first sub-element  704  while edge regions  722 , distal to a central axis  708  of the second matrix  700 , are formed of only the second sub-element  706 . Regions  724  of the second matrix  700  between the central region  720  and the edge regions  722  are formed of both the first sub-element  704  and the second sub-elements  706  in varying ratios. As a result of a spatial distribution of the first and second sub-elements  704 ,  706  along the elevation direction  103 , a resonance frequency of each of the plurality of elements  702  may vary along the elevation direction  103 . 
     For example, in the central region  720  of the second matrix  700 , the portion of the plurality of elements  702  that include only the first sub-element  704  may each transmit (and receive) signals at a resonance frequency associated with the first sub-element  704 . At the edge regions  722 , the portion of the plurality of elements  702  formed from only the second sub-element  706  may each transmit (and receive) signals at a resonance frequency associated with the second sub-element  706 . In the regions  724  between the central region  720  and the edge regions  722 , the plurality of elements  702  are hybrids, e.g., combinations of the first and second sub-elements  704 ,  706 , and may therefore have a range of resonance frequency values in between those of the first and second sub-elements  704 ,  706 . 
     As an example, a first element  707  of the plurality of elements  702  may be composed of 50% of the first sub-element  704  and 50% of the second sub-element  706 . The resonance frequency of the first element  707  may be a value mid-way between that of the first sub-element  704  and the second sub-element  706 . A second element  709  of the plurality of elements  702 , positioned between the first element  707  and the central region  720  of the second matrix  700 , may have a higher percent composition of the first sub-element  704  compared to the first element  707 . The second element  709  may therefore have a resonance frequency that is higher than the first element  707  but lower than the resonance frequency of the first sub-element  704 . A third element  711  of the plurality of elements  702 , positioned between the first element  707  and the left-hand edge region  722  may have a higher percent composition of the second sub-element  706  than the first element  707 . The third element  711  may there have a resonance frequency that is lower than the first element  707  but higher than the second sub-element  706 . 
     By incrementally changing the composition of the plurality of elements  702  along the elevation direction  103 , the plurality of elements  702  may have a continuum of resonance frequencies ranging between the resonance frequency of the first sub-element  704  and the resonance frequency of the second sub-element  706 . In other examples, the composition of the plurality of elements  702  may be similarly varied along the azimuth direction  101  instead of the elevation direction  103  or in addition to the elevation direction  103 . Thus the second matrix  700  may transmit and receive signals through a wider range of frequencies than a transducer array with a uniform element composition. In the example shown in  FIG. 7 , highest frequencies may be transmitted and received at the central region  720  of the second matrix while lowest frequencies may be transmitted and received at the edge regions  722 . 
     The second matrix  700  may be symmetric about the central axis  708  of the second matrix  700 , the central axis parallel with the azimuth direction  101 . The symmetry of the second matrix  700 , regardless of variations in distribution of the sub-elements amongst the plurality of elements  702 , allows the second matrix to provide the apodization function as shown in  FIG. 39 . 
     An example of a third matrix  800  is illustrated in  FIG. 8 , which may be an example of a 1.5-dimensional (1.5D) matrix array. The third matrix  800  includes a plurality of elements  802  arranged in a first row  804 , a second row  806 , and a third row  808 . Similarly, dotted lines between the first row  804  and the second row  806  indicate a presence of additional rows of the third matrix  800 , omitted for brevity. The third matrix  800  has a central axis  810  parallel with the azimuth direction  101 . 
     At least a portion of the plurality of elements  802  of the third matrix  800  may be multi-frequency elements  816  formed of a first, high-frequency sub-element  812  and a second, low-frequency sub-element  814 . For example, the multi-frequency elements  816  of the plurality of elements  802  may include two of the first sub-element  812  alternating with two of the second sub-element  814  along the elevation direction  103 . A central region  820  of the third matrix  800  may be formed only of the first sub-element  812  while edge regions  822  of the third matrix  800  may be formed of only the second sub-element  814 . Furthermore, a thickness of each of the plurality of elements  802 , defined along the elevation direction  103 , may vary across each row of the third matrix  800 . 
     As a result of a spatial distribution of the first and second sub-elements  812 ,  814  along the elevation direction  103 , a resonance frequency of the plurality of elements  802  may vary across the elevation direction  103 . For example, similar to the second matrix  700  of  FIG. 7 , a portion of the plurality of elements  802  in the central region  820  may transmit and receive signals at a higher resonance frequency equal to a resonance frequency of the first sub-element  812 , while a portion of the plurality of elements  802  at the edge regions may transmit and receive signals at a lower resonance frequency equal to a resonance frequency of the second sub-element  814 . A portion of the plurality of elements  802  between the central region  820  and the edge regions  822  may have intermediate resonance frequencies between those of the first sub-element  812  and the second sub-element  814 . Thus a range of frequencies encompassed by the third matrix  800  may be broadened in comparison to use of a single frequency element in the array of the third matrix  800 . 
     The third matrix  800  may be symmetric across the central axis  810 , along the elevation direction  103 . Similar to the second matrix  700  of  FIG. 7 , the symmetry of the third matrix  800  enables the third matrix  800  to provide the apodization function as shown in  FIG. 39 . The 1.5D array (as well as a 1.75D array) may provide an optimized beam pattern as an active aperture of a transducer probe changes. As such, the array is able to optimize a near field with a narrow aperture as well as a far field with a larger aperture. By manufacturing the 1.5D or 1.75D array via a process shown in  FIGS. 10-38 , the process allows mixing of elements with different central frequencies and frequency ranges within a single array. The manufacturing process provides increased flexibility in array configuration with incurring extensive additional costs. An example of a fourth matrix  900 , which may be an example of a 1.25 linear array, is shown in  FIG. 9 . The fourth matrix  900  also has a plurality of elements  902 , arranged in rows along the elevation direction  103 , and a central axis  904 , parallel with the azimuth direction  101 . The plurality of elements  902  may each be formed of a single type of element and are not hybrid elements. 
     The fourth matrix  900  includes a first, high-frequency sub-element  906  and a second, low-frequency sub-element  908 . Each of the plurality of elements  902  may be formed of either the first sub-element  906  or the second sub-element  908  and may vary in width along the elevation direction  103 . A symmetry of the fourth matrix  900  across the central axis  904  along the elevation direction  103  also allows the fourth matrix  900  to provide apodization along the elevation direction  103 . Incorporation of more than one type of element allows the fourth matrix  900  to operate across a wider range of frequencies. However, the frequency distribution may be less continuous and more discretized than the matrices of  FIGS. 7 and 8  without incorporation of hybrid elements, e.g., elements formed of more than one sub-element. 
     It will be noted that each element of the plurality of elements of  FIGS. 7-9  may be coupled to an electrical circuit, as shown in  FIGS. 1 and 2 . Additionally, other examples of a multi-frequency transducer array may also include control of frequency apodization and agility along the azimuth direction  101 . For example, a distribution of multi-frequency elements may be varied along the azimuth direction  101  in a similar manner as shown along the elevation direction  103 . Varying a spatial frequency distribution along the azimuth direction may be implemented in an array as an alternative or in addition to frequency variation along the elevation direction. By configuring the array with multi-frequency elements along both the azimuth and elevation directions, more complex apodization is enabled relative to frequency apodization in a transducer array with uniform elements. By providing a method to vary the elements along both directions, a configuration of the array is more flexible and may be implemented more easily as a matrix. Furthermore, the frequency agility, e.g., an ability of a transducer to quickly shift a transmitted frequency over a pre-selected range to mitigate jamming, mutual interference or account for atmospheric effects, may be enabled along both the azimuth and elevation directions. 
     Incorporation of multi-frequency elements into a transducer array may enable enhanced sensitivity for both transmission and reception of signals while increasing a frequency bandwidth of the transducer array. Signal transmission at a specific frequency, based on an application of a transducer probe, may be selected, resulting in energization of multi-frequency elements in the transducer array with a corresponding resonance frequency. By configuring the transducer array with elements with a broad range of frequencies, different operation of the transducer probe is enabled. The transducer probe may thereby be used for a variety of applications that would otherwise demand use of multiple single element transducer probes with different resonance frequencies. 
     In some examples, post-processing of signals received by the transducer array may be similar to conventional post-processing, utilizing already existing post-processing algorithms to convert the signals into, for example, images. Bandpass filtering of the signals may be modified based on the frequency of the signal. 
     Fabrication of an array of multi-frequency transducer elements may be achieved via a cost-effective process leveraging a wafer level approach. The wafer level approach allows multiple transducer arrays to be generated simultaneously, thereby increasing efficiency and throughput. A fabrication process for a multi-frequency transducer array is now described with reference to  FIGS. 10-38 and 40-42 . The wafer level approach may begin with a block of a first acoustic stack  1000 , as shown in  FIG. 10 . The first acoustic stack  1000  is viewed along the elevation direction in  FIG. 10  and includes a matching layer  1002 , similar to the acoustic matching layer  120  of  FIG. 1 , which may be an electrically conductive layer such as graphite or a metal. The matching layer  1002  may be formed of more than one layer stacked along a vertical axis of the first acoustic stack  1000 , e.g., along the transverse direction  105 , configured to be electrically conductive along the vertical axis. 
     The matching layer  1002  is arranged above, relative to the transverse direction  105 , a first piezoelectric layer  1004 . An acoustic impedance difference between an ultrasound transducer probe and a target medium may be buffered by the matching layer  1002 . The first piezoelectric layer  1004  is formed of a piezoelectric material configured to transmit and/or receive ultrasound signals and used to form transducer elements of an ultrasound transducer probe, as described above. 
     A dematching layer  1006  may be positioned below the first piezoelectric layer  1004 . The dematching layer may be a high impedance layer that may decrease insertion losses and enhance a frequency bandwidth of a transducer probe. In some examples, the dematching layer may be optionally omitted. A backing layer  1008 , similarly to the backing  126  of  FIG. 1 , may be arranged below the dematching layer  1006 . The backing layer  1008  may be formed of an electrically conductive material, such as a composite, for example, and may dampen a ringing effect which may occur when the piezoelectric material switches from a transmission mode to a receiving mode. The first piezoelectric layer  1004  may be bonded to the matching layer  1002  and to the dematching layer  1006  (or to the backing layer  1008  when the dematching layer  1006  is not present) with an adhesive such as epoxy. 
     The first piezoelectric layer  1004  of the first acoustic stack  1000  may have a first height  1010 , defined along the transverse direction  105 . The first height  1010  may visually differentiate a piezoelectric element with a higher resonance frequency from a resonance frequency piezoelectric element of a second piezoelectric layer  1204  with a larger second height  1210 , shown in  FIGS. 12 and 13  and described further below. A first comb structure  1100  may be produced from the first acoustic stack  1000  of  FIG. 10  by dicing kerfs  1102  evenly spaced along the transverse direction  105  on the first acoustic stack  1000 . The kerfs  1102  extend downwards, along the azimuth direction  101 , from the matching layer  1002  into the backing layer  1008  but not entirely through the backing layer  1008 . Dicing of the kerfs  1102  forms first fins  1104 , each of the first fins  1104  spaced apart from adjacent first fins  1104  by one of the kerfs  1102 . The first fins  1104  extend upwards along the azimuth direction  101  from the backing layer  1008  and may extend along the elevation direction  103  across an entire depth of the first comb structure  1100 . 
     It will be noted that dicing refers to cutting of kerfs into a wafer to form cavities or slots in the wafer that do not extend entirely through a height of the wafer. Thus dicing may electrically isolate portions of the wafer, e.g., renders a section electrically discontinuous from an adjacent section along a plane perpendicular to the height, but does not divide the wafer into individual, separate sections. In contrast, singulation facilitates singularizing of the wafer into individual transducer arrays that are physically separated, as described below. Herein, dicing and singulation are conducted only along the height of the wafer, e.g., along the transverse direction so that portions of the wafer are electrically isolated and/or physical separated only along the plane formed by the azimuth and the elevation directions. 
     The first comb structure  1100  may be diced into a geometry to complement or match a second comb structure (e.g., a second comb structure  1300  shown in  FIG. 13 . The second comb structure  1300  may be formed from a second acoustic stack  1200 , depicted in  FIG. 12 . The second acoustic stack  1200  may have similar layers to the first acoustic stack  1000 , including a matching layer  1202 , formed of a same or different material (or stack of electrically conductive layers) as the matching layer  1002  of the first acoustic stack  1000 , a second piezoelectric layer  1204 , formed of a different material as the first piezoelectric layer  1004  of  FIG. 10 , an optional dematching layer  1206 , similar to the dematching layer  1006  of the first acoustic stack  1000 , and a backing layer  1208 , formed of a same or different material as the backing layer  1008  of the first acoustic stack  1000 . 
     As described above, the second height  1210 , defined along the azimuth direction  101 , of the second piezoelectric layer  1204  may be greater than the height  1010  of the first piezoelectric layer  1004  of the first acoustic stack  1000 . Piezoelectric elements formed from the second piezoelectric layer  1204  may have a lower resonance frequency than the piezoelectric elements formed from the first piezoelectric layer  1004 . The diced piezoelectric elements corresponding to the first piezoelectric layer  1004 , e.g., in the first comb structure  1100 , are hereafter referred to as high frequency sub-elements  1004  and the diced piezoelectric elements corresponding to the second piezoelectric layer  1204 , e.g., in the second comb structure  1300 , are hereafter referred to as low frequency sub-elements  1204 . 
     A height, also defined along the azimuth direction  101 , of the matching layer  1202  of the second acoustic stack  1200  may be greater than a height of the matching layer  1002  of the first acoustic stack  1000  while a height of the backing layer  1208  of the second acoustic stack  1200  may be less than a height of the backing layer  1008  of the first acoustic stack  1000 . The difference in heights between the matching layers and the backing layers may allow the layers of each of the first and second comb structures  1100 ,  1300  to have a desired alignment when the comb structures are combined into a single structure, described further below. 
     The second acoustic stack  1200  may be diced in an opposite direction from the first acoustic stack  1000 , as shown in  FIG. 13 . As such, the second acoustic stack  1200  is diced so that kerfs  1302  extend from the backing layer  1208  upwards, along the azimuth direction  101 , into the matching layer  1202 . The kerfs  1302  do not extend entirely through the matching layer  1202 . The kerfs  1302  are evenly spaced apart along the transverse direction  105 , forming second fins  1304  between each of the kerfs  1302 . The second fins  1304  may extend across an entire depth of the second comb structure  1300  along the elevation direction  103 . 
     A width  1306  of each of the kerfs  1302  of the second comb structure  1300  may be equal to a width  1106  (as shown in  FIG. 11 ) of each of the first fins  1104  of the first comb structure  1100 . Similarly, a width  1308  of each of the second fins of the second comb structure  1300  may be equal to a width  1108  (as shown in  FIG. 11 ) of each of the kerfs  1102  of the first comb structure  1100 . A height  1310 , defined along the azimuth direction  101 , of both the kerfs  1302  of the second comb structure  1300  and the second fins  1304  may equal a height of both the first fins  1104  and the kerfs  1102  of the first comb structure  1100 . The complementary geometries of the first comb structure  1100  and the second comb structure  1300  allow the comb structures to fit together to form a third acoustic stack  1402  with interdigitated comb structures, as shown in  FIG. 14  from a first view  1400  along the elevation direction  103  and in  FIG. 15  from a second view  1500  along the azimuth direction  101 . 
     In the first view  1400  of the third acoustic stack  1402 , illustrated in  FIG. 14 , a first layer of adhesive  1404  is arranged between the first comb structure  1100  and the second comb structure  1300  to enable lamination of the comb structures. The first layer of adhesive  1404  may be a non-conductive glue, such as epoxy, that electrically insulates the first comb structure  1100  from the second comb structure  1300 . The first comb structure  1100  and the second comb structure  1300  may be nested into one another so that there are no gaps between the first comb structure  1100  and the second comb structure  1300 . 
     As shown in the second view  1500  of the third acoustic stack  1402 , the first fins  1104  and the second fins  1304 , each fin forming a digit of the interdigitated structure of the third acoustic stack  1402 , extends along a depth  1502  of the third acoustic stack  1402  along the elevation direction  103 . It will be appreciated that the first view  1400  and the second view  1500  of the third acoustic stack  1402  may represent a section of the third acoustic stack rather than the entire acoustic stack  1402 . While the third acoustic stack  1402  is shown with three of the first fins  1104  and three of the second fins  1304  in  FIG. 14 , the third acoustic stack  1402  may have any number of the fins. The third acoustic stack  1402  may have a width  1406  and depth  1502  greater or less than shown in  FIGS. 14 and 15 , respectively. 
     Additionally, in some examples, the third acoustic stack  1402  may be further combined with one or more additional comb structures to increase a number of sub-elements with different resonance frequencies incorporated into an acoustic stack. For example, as shown in  FIG. 36 , a first multi-frequency comb structure  3602  and a second multi-frequency comb structure  3604  may each be formed from an acoustic stack such as the third acoustic stack  1402 . 
     At least one first fin  3603  of the first multi-frequency comb structure  3602  may include a first sub-element  3606  and a second sub-element  3608 . The first multi-frequency comb structure  3602  may be formed by dicing an acoustic stack similarly to the dicing of the first acoustic stack  1000  as shown in  FIG. 11 , with a first kerf  3610  extending downwards from a top of the first multi-frequency comb structure  3602 , along the transverse direction  105 , through a portion of a height  3612  of the first multi-frequency comb structure  3602 . 
     The second multi-frequency comb structure  3604  may have at least one second fin  3614 , the second fin  2614  including a third sub-element  3616  and a fourth sub-element  3618 . Each of the first, second, third, and fourth sub-elements  3606 ,  3608 ,  3616 ,  3618  may have different resonance frequencies. The second multi-frequency comb structure  3604  may be diced similarly to the second acoustic stack  1200  as shown in  FIG. 13 , with a second kerf  3620  extending upwards from a bottom of the second multi-frequency comb structure  3604 , along the transverse direction  105 , through a portion of a height  3622  of the second multi-frequency comb structure  3604 . 
     A width  3624  and a height  3626  of the first kerf  3610  may be similar to a width and a height of the second fin  3614 . A width  3628  and a height  3630  of the second kerf  3620  may be similar to a width and a height of the first fin  3603 . The second fin  3614  of the second multi-frequency comb structure  3604  may be inserted into the first kerf  3610  of the first multi-frequency comb structure  3602  while the first fin  3603  may be inserted into the second kerf  3620  of the second multi-frequency comb structure  3604 , as indicated by arrows  3632  to form a combined stack with four sub-elements. The combined stack may be laminated and further processed as described below. 
       FIG. 36  shows a non-limiting example of how a multi-frequency acoustic stack with four different sub-elements may be formed. In other examples, either of the first multi-frequency comb structure  3602  or the second multi-frequency comb structure  3604  may be a single element comb structure. In such instances, a resulting combined acoustic stack may include three sub-elements. Furthermore, widths, defined along the azimuth direction  101 , of each of the sub-elements are shown to be similar, resulting in a combined stack with equal proportions of each sub-elements. In other examples, however, the widths of the sub-elements may be varied so that the percent content of each of the sub-elements is not equal. 
     Furthermore, while the third acoustic stack  1402  of  FIGS. 14-15  show the first and second comb structures  1100 ,  1300  having complementary geometries that result in a gap-free combining of the comb structure, e.g., no spaces are present between the comb structures when coupled, the comb structures may be diced to have non-matching geometries. For example, as shown in  FIG. 42 , an alternate example of an acoustic stack  4200  may include a first comb structure  4202  and a second comb structure  4204 , combined to form an interdigitated structure. 
     Kerfs of the first comb structure  4202  may not have dimensions that match dimensions of fins of the second comb structure  4204  and kerfs of the second comb structure  4204  may not have dimensions matching fins of the first comb structure  4202 . For example a first kerf  4206  of the first comb structure  4202  may have a depth  4208  that is greater than a depth  4210  of a first fin  4212  of the second comb structure  4204 . When the first fin  4212  of the second comb structure  4204  is inserted into the first kerf  4206  of the first comb structure  4204 , gaps may be present around the first fin  4212 , e.g., along the azimuth direction. 
     A second kerf  4214  of the first comb structure  4202  may also have a depth  4216  that is greater than a depth  4218  of a second fin  4220  of the second comb structure  4204 . When the second fin  4220  of the second comb structure  4204  is inserted into the second kerf  4214  of the first comb structure  4202 , gaps may be present around the second fin  4220 , e.g., along the azimuth direction  101 . The gaps around the second fin  4220  may be greater than the gaps around the first fin  4212  due to either non-uniform depths of the kerfs of the first comb structure  4204  and/or non-uniform depths of the fins of the second comb structure  4204 . The fins of the first comb structure  4202  may be similarly surrounded by gaps due to greater depths of the kerfs of the second comb structure  4204  compared to depths of the fins of the first comb structure  4204 . 
     As shown in  FIG. 42 , a variety of geometries of the acoustic stack, formed by combining at least two comb structures, may be enabled by adjusting dimensions of the kerfs and fins. The dicing and combining of the comb structures introduces a high degree of flexibility in a final configuration of a transducer array. Thus modification of the transducer may be efficiently modified. 
     Turning now to  FIGS. 16-17 , the third acoustic stack  1402  may be combined with a first example of a base package  1602 , as shown in a first view  1600  along the elevation direction  103  in  FIG. 16  and in a second view  1700  along the azimuth direction  101  in  FIG. 17 . The base package  1602  may be formed from a conductive material such as graphite, porous graphite filled with resin, stainless steel, aluminum etc. The base package  1602  may be diced to have first fins  1604 , extending along the transverse direction  105 , and kerfs  1606 . The third acoustic stack  1402  may also be diced to have first kerfs  1608 , also extending along the elevation direction  103 , that match the first fins  1604  of the base package  1602  in a width  1610  and a height  1612 . Dicing of the third acoustic stack  1402  also forms blocks  1614  with the same height  1612  as the first fins  1604  of the base package  1602  and with a width  1616  of each of the blocks  1614  equal to a width of the kerfs  1606  of the base package  1602 . 
     The dicing of the third acoustic stack  1402  and the base package  1602  are further shown in  FIG. 17 . The third acoustic stack  1402  may have second kerfs  1702 , extending along the azimuth direction  101 , in addition to the kerfs  1606 . The base package  1602  has second fins  1704  which may be continuous with the first fins  1604  but extending along a perpendicular direction from the first fins  1604 , e.g., along the azimuth direction  101 . As such, the first fins  1604  and the second fins  1704  may form a structure as shown in a perspective view  1800  in  FIG. 18 . 
     The base package  1602  is depicted in the perspective view  1800  to show an overall geometry of the first fins  1604 , the second fins  1704  and the kerfs  1606  of the base package  1602 . The first fins  1604  and the second fins  1704  frame each of the kerfs  1606  so that each of the kerfs  1606  has a uniform rectangular geometry. In other examples, however, the kerfs  1606  may have a variety of other geometries, such as circular, hexagonal, square, etc. As such, transducers produced by the manufacturing process depicted in  FIGS. 10-35  may have a shape corresponding to a geometry of the kerfs  1606 . 
     The kerfs  1606  form cavities in the base package  1602  and the blocks  1614  of the third acoustic stack  1402  (as shown in  FIGS. 16 and 17 ) are shaped to match the geometry of the kerfs  1606 . In this way, the kerfs  1606  of the base package  1602  receive the blocks  1614  of the third acoustic stack  1402 , as indicated by arrows  1618  in  FIGS. 16 and 17 , the first kerfs  1608  of the third acoustic stack  1402  receive the first fins  1604  of the base package  1602 , and the second kerfs  1702  of the third acoustic stack  1402  receive the second fins  1704  of the base package  1602 . 
     In other examples, a base package may be configured differently than the base package  1602  of  FIG. 18 . For example, as shown in  FIG. 40 , a second example of a base package  4000 , may have kerfs  4002  extending linearly and continuously along the elevation direction  103 . The kerfs  4002  are parallel and may extend across an entire depth of the base package  4000 , the depth defined along the elevation direction  103 , or across at least a portion of the depth. Fins  4004  of the base package  4000 , spaced apart by the kerfs  4002 , may also extend along the elevation direction  103 . An acoustic stack may be similarly diced along the elevation direction  103  to match the kerfs  4002  and fins  4004  of the base package  4000 . 
     Alternatively, a base package may be diced entirely along the azimuth direction  101 , as shown in  FIG. 41 .  FIG. 41  depicts a third example of a base package  4100  with kerfs  4102  and fins  4104  extending along the azimuth direction  101 . The kerfs  4102  and fins  4104  may extend entirely or partially across a width of the base package  4100 , the width defined along the azimuth direction  101 . An acoustic stack may be diced with kerfs and blocks to match a geometry of the base package  4100 , e.g., with kerfs and blocks extending along the azimuth direction  101 . 
     Turning now to a first view  1900  along the elevation direction in  FIG. 19  and a second view  2000  along the azimuth direction  101  in  FIG. 20 , the third acoustic stack  1402  and the base package  1602  may be laminated with a second layer of adhesive  1904 , disposed between the third acoustic stack  1402  and the base package  1602 , to form a fourth acoustic stack  1902 . The second layer of adhesive  1904  is illustrated as a dotted line to differentiate the second layer of adhesive  1904  from the first layer of adhesive  1404 . The second layer of adhesive  1904  may also be a non-conductive glue that electrically isolates the third acoustic stack  1402  from the base package  1602 . 
     As shown in a first view  2100  of the fourth acoustic stack  1902  along the elevation direction  103  in  FIG. 21  and in a second view  2200  of the fourth acoustic stack  1902  along the azimuth direction in  FIG. 22 , a back side  2102  of the fourth acoustic stack  1902  may be subjected to grinding. Ground recovery in both the elevation direction  103  and the azimuth direction  101  is enabled by grinding the back side  2102  so that a portion of the base package  1602 , a portion of the backing layer  1008  of the first comb structure  1100 , and a portion of the backing layer  1208  of the second comb structure  1300  (the backing layers  1008 ,  1208  shown in  FIGS. 14-15 ) is removed. The back side  2102  of the fourth acoustic stack may provide a positive terminal connectivity. A height  1906  of an overall portion of the fourth acoustic stack  1902  that is ground away is shown in  FIGS. 19 and 20 . 
     The back side  2102  of the fourth acoustic stack  1902  is ground until portions of both the first layer of adhesive  1404  and the second layer of adhesive  1904  that are parallel with the elevation direction  103  (as shown in  FIGS. 19 and 20 ) are removed. By removing the portions of the adhesive layers, e.g., bottom portions of the adhesive layers relative to the azimuth direction  101 , ground recovery in both the elevation and azimuth directions is enabled. In other words, electrical continuity between the elements (e.g., the high frequency sub-elements  1004  and the low frequency sub-elements  1204 ) and electrical contacts or electrodes (not shown in  FIGS. 21 and 22 ), arranged in contact with the back side  2102  of the fourth acoustic stack  1902 , is provided by removing the insulating adhesive layers. 
     Ground recovery may further include sputtering a layer of an electrically conductive material, such as a metal, on the back side  2102  of the fourth acoustic stack  1902 , as shown in  FIG. 23  in a first view  2300  along the elevation direction  103  and in  FIG. 24  in a second view  2400  along the azimuth direction  101 . The fourth acoustic stack  1902  is depicted in  FIGS. 23 and 24  flipped upside, relative to the azimuth direction  101 . A sputtered layer  2302  is deposited onto the back side  2102  of the fourth acoustic stack  1902 , forming a uniform, continuous film. A height, measured along the azimuth direction, of the sputtered layer  2302  is less than the heights of the any of other layers, e.g., the matching layers, the high and low frequency elements, the dematching layers, the backing layers, of the fourth acoustic stack  1902 . 
     In other examples, however, sputtering may be precluded by grinding the back side of the fourth acoustic stack  1902  to a lesser extent, so that a portion of the base package  1602  remains. For example, the back side may be ground by an amount indicated by arrow  1907  shown in  FIG. 19 . The remaining portion of the base package may be common to each of the sub-elements and may provide an electrically conductive layer along the backside of the fourth acoustic stack  1902 . 
     The fourth acoustic stack  1902  may be diced after deposition of the sputtered layer  2302 , as shown in  FIG. 25  in a first view  2500  of the fourth acoustic stack  1902  along the elevation direction  103  and in  FIG. 26  in a second view  2600  along the azimuth direction  101 . A plurality of kerfs  2503  are formed in the fourth acoustic stack  1902 , extending from the back side  2302  towards a front side  2502  of the fourth acoustic stack  1902  but not entirely through the fourth acoustic stack  1902 , along the transverse direction  105 . 
     The plurality of kerfs  2503  may separate the fourth acoustic stack  1902  into a plurality of elements  2501 . The plurality of elements  2501  may include multi-frequency elements  2504  and single frequency elements  2506 , as shown in  FIG. 25 . The multi-frequency elements  2504  each include one of the high frequency sub-elements  1004  and one of the low frequency sub-elements  1204 . The single frequency elements  2506  include either one of the high frequency sub-elements  1004  or one of the low frequency sub-elements  1204  but not both. 
     In other examples, each element of an acoustic stack, such as the fourth acoustic stack  1902 , may be formed from a single element but the acoustic stack may include various different types of single elements. For example, a first and second comb structure may be combined to form a similar acoustic stack as the third acoustic stack  1402  of  FIGS. 14-15 . The acoustic stack may be processed as described above with reference to  FIGS. 16-24 , and kerfs may be diced into the acoustic stack, as shown in  FIGS. 25 and 26 . However, the kerfs may be positioned between each fin of each comb structure, thus separating the elements into single element digits of the diced acoustic stack. In other words kerfs may also separate the high frequency sub-elements  1004  from the low frequency sub-elements  1204 . In this way, the acoustic stack may be a multi-frequency acoustic stack with single elements, rather than elements formed from more than one sub-element, where each transducer may have more than one type of element, each element coupled to an electrical circuit. 
     Returning to  FIG. 25 , a resonance frequency of the multi-frequency elements  2504  may be determined by a percent content of each of the high and low frequency sub-elements  1004 ,  1204 . A first width  2510 , defined along the azimuth direction  101 , of the high frequency sub-element  1004  is similar to a second width  2512  of the low frequency sub-element  1204 . As such the multi-frequency elements  2504  may each be formed of 50% of the high frequency sub-element  1004  and 50% of the low frequency sub-element  1204  and have a resonance frequency mid-way between that of the high frequency sub-element  1004  and the low frequency sub-element  1204 . In other examples, however, the widths of the sub-elements may be varied, e.g., not equal, and may be non-uniform throughout an acoustic stack, resulting in a range of resonance frequencies. Variations in sub-element widths are depicted in  FIGS. 31-34  and described further below. 
     The plurality of kerfs  2503  may be filled with an electrically insulating material, thereby insulating each of the plurality of elements  2501  from adjacent elements. However, in other examples the plurality of kerfs  2503  may be maintained as air-filled spaces (e.g., not filled with any additional materials), which may similarly provide electrical insulation. Furthermore, maintaining the plurality of kerfs  2503  as spaces may reduce an overall amount of material of the transducer array and reduce a weight of the array. The filled plurality of kerfs  2503  are depicted in  FIG. 27  in a first view  2700  along the elevation direction  103  and in  FIG. 28  in a second view  2800  along the azimuth direction  101 . The fourth acoustic stack  1902  is shown incorporated in a wafer  2702  in  FIGS. 27 and 28 . 
     In addition to filling the plurality of kerfs  2503 , a portion of the front side  2502  of the fourth acoustic stack  1902  may be mechanically removed, similar to the grinding of the back side  2102 , to further enable ground recovery. The front side  2502  of the fourth acoustic stack  1902  may provide electrical grounding. A height  2508  of the portion of the fourth acoustic stack  1902  that is removed from the front side  2502  is shown in  FIGS. 25 and 26 . The amount ground away from the front side  2502  of the fourth acoustic stack  1902  may remove portions of the first layer of adhesive  1404  parallel with the azimuth direction  101 , as shown in  FIG. 25 . Grinding of the front side  2502  may also contribute to ground recovery in the azimuth and elevation directions by enabling electrical continuity between the plurality of elements  2501  and an electrically conductive layer coupled to the front side  2502  of the fourth acoustic stack  1902 , described further below. 
     Returning to  FIGS. 27 and 28 , a matching layer block  2704  is laminated to the front side  2502  of the fourth acoustic stack  1902  after grinding. Although not depicted in  FIGS. 27 and 28 , in some examples, a conductive layer, such as the sputtered layer  2302 , may be sputtered onto the ground front side  2502  of the fourth acoustic stack  1902  before coupling the matching layer block  2704  to the front side  2502 . The matching layer block  2704  may be laminated using a conductive adhesive and may be a same or different material as the matching layers  1002 ,  1202  of the first comb structure  1100  and the second comb structure  1300 , respectively. For example, the material of the matching layer block  2704  may be a gold-coated material, flex conductive materials such as a spring mass structure, etc. The matching layer block  2704  may be formed of more than layer and may be formed of an electrically conductive material or a non-conductive material. 
     The matching layer block  2704  provides a common matching layer to each transducer of the fourth acoustic stack  1902 , each transducer including one of the plurality of elements  2501  and defined along the transverse direction  105  by the plurality of kerfs  2503 , filled with the non-conductive material. In other words, the matching layer block  2704  is a continuous layer that extends entirely across the front side  2502  of the fourth acoustic stack  1902 . Similarly, a backing layer block  2706  may be coupled to the back side  2102  of the fourth acoustic stack  1902 , and connected to each transducer of the fourth acoustic stack  1902  to provide a common backing layer for each transducer. The backing layer block  2706  may also be a continuous layer that extends entirely across the back side  2102  of the fourth acoustic stack  1902 . 
     A backing layer block  2706  may be laminated to the back side  2102  of the fourth acoustic stack  1902  to form the wafer  2702 , also using a conductive adhesive. The backing layer block  2706  may be formed of one or more layers, laminated in a stack along the transverse direction  105 , and may provide an electrical path to enable application of a voltage to the plurality of elements  2501 . In some examples, the backing layer block  2706  may include an application specific integrated circuit (ASIC), a flex conductive material, a printed circuit board (PCB), a metal block, etc. In other examples, a backing of some type may be coupled to the back side  2102  of the fourth acoustic stack  1902  instead of the backing layer block  2706 . For example, the backing may be an interposer connecting a flex circuit to the acoustic stack. 
     In addition, other examples may include the acoustic stack configured with non-continuous matching and backing layer blocks that do not extend continuously across each transducers. For example, a plurality of smaller matching and backing layer blocks may be coupled to a transducer array, each block attached to one transducer. Alternatively, the matching and backing layer blocks may cover a few transducers, such as two or three adjacent transducers, coupling to the acoustic stack in segments. 
     The wafer  2702  may then be singulated, e.g., singularized, to form individual transducer arrays  2902 , as shown in  FIG. 29  in a first view  2900  along the elevation direction  103  and in  FIG. 30  in a second view  3000  along the azimuth direction  101 . Each of the transducer arrays  2902  includes an array of the plurality of elements  2501 , each of the plurality of elements  2501  included in an individual integrated circuit. Singulation may include various methods of die singulation, including conventional dicing, laser dicing, scribe and break, and dice before grind. Each of the transducer arrays  2902  are therefore spaced away from neighboring transducer arrays as a result of singulation and each transducer may be installed in a transducer probe. 
     Although a width  2904 , defined along the azimuth direction  101 , of each of sub-elements (e.g., the high frequency sub-element  1004  and the low frequency sub-elements  1204 ), a width  2906  of each of the plurality of elements  2501 , as well as a width  2908  of each of the transducer arrays  2902  is depicted to be uniform in  FIG. 29 , the dicing of each of the above components of the wafer  2702  may be modified to produce non-uniform widths. Variations in widths of the sub-elements, of the plurality of elements, and of the transducers are shown in  FIGS. 31-35 . 
     In a first example  3100  of a non-uniform transducer array  3101 , a width  3102  of a plurality of elements  3104  may be uniform along the azimuth direction  101 . The plurality of elements  3104  may each include a first sub-element  3106  and a second sub-element  3108 . A first comb structure may be diced to form the first sub-element  3106  with a width  3110  that is greater than a width  3112  of the second sub-element  3108 . In other words the first comb structure may be diced to form wider sub-elements (e.g., the first sub-elements  3106 ) than dicing of a second comb structure to form the second sub-element  3108 . 
     Alternatively, as shown in a second example  3200  of the non-uniform transducer array  3103 , the first comb structure may be diced so that the first sub-element  3106  has a narrower width  3202  than a width  3404  of the second sub-element  3108 , formed by dicing of the second comb structure. The width  3104  of each of the plurality of elements  3104  may be uniform along the azimuth direction  101  and the widths of each of the first sub-element  3106  and of the second sub-element  3108  may be similar in each of the plurality of elements  3104 . Thus the widths of the sub-elements may be readily varied based on dicing of the comb structures. 
     Furthermore, the comb structures may be diced so that each of the sub-elements have non-uniform widths, as shown in a third example  3300  of the non-uniform transducer array  3101 . A first element  3302  may be formed of a first sub-element  3304  with a width  3306  that is similar to a width  3308  of a second sub-element  3310 . However, in a second element  3312 , adjacent to the first element  3302 , a width  3314  of the first sub-element  3304  is greater than a width  3316  of the second sub-element  3310 . A width  3318  of the first element  3302  may be similar to a width  3320  of the second element  3312 . In other examples, the non-uniform transducer array  3103  may include elements where the width of the second sub-element  3310  is greater than the width of the first sub-element  3304 . 
     Additionally or alternatively, dicing of an acoustic stack formed by combining the first and second comb structures, e.g., the third acoustic stack  1402  of  FIGS. 14-17 , may be modified to vary a width of the plurality of elements. For example, as shown in a fourth example  3400  of the non-uniform transducer array  3101 , a width  3402  of a first element  3404  may be greater than a width  3406  of a second element  3408 . Widths of a first sub-element  3410  and a second sub-element  3412  of each of the elements may be similar, as shown in the first element  3404 , or different, as shown in the second element  3408 . 
     Furthermore, singulation of a wafer into individual transducer arrays may be adjusted to form transducers of varying widths. As illustrated in  FIG. 35 , a first transducer array  3502  may be diced to have a first width  3504 . A second transducer array  3506  may be diced to have a second width  3508  that is wider than the first width  3504  of the first transducer array  3502 . Other transducer arrays formed from the same wafer as the first and second transducer arrays  3502 ,  3506  may have widths similar to either the first transducer array  3502  or the second transducer array  3506  or widths that are different from either of the first and second transducer arrays  3502 ,  3506 . Widths of a first sub-element  3510  and a second sub-element  3512  incorporated in each of the elements of each transducer array may be similar to one another or different and may be uniform or non-uniform through the transducer array. 
     Electrical leads may be coupled to the matching layer block and the backing layer block of the transducers array before or after singulation. For example, positive electrodes may be coupled to the matching layer block and ground electrodes may be coupled to the backing layer block. Alternatively, the positive electrodes may be coupled to the backing layer block and the ground electrodes may be coupled to the matching layer block. Formation of individual circuits with each transducer is thereby completed by coupling the transducers arrays to electrical leads. 
     In this way, a manufacturing method for multi-frequency transducers may be fabricated to produce multi-frequency elements and transducer arrays as shown in  FIGS. 2 and 4-36 . It will be appreciated that while  FIGS. 31-35  depict views of the transducers(s) along the elevation direction  103  and describe variations in widths of the transducer(s), elements, and sub-elements relative to the elevation direction  103 , similar variations may be applied along the azimuth direction  101 . For example, dicing of the comb structures may be modified along the azimuth direction  101  to provide sub-elements with varying depths (e.g., a thickness of the sub-elements along the azimuth direction  101 ). The comb structures may be combined so that the sub-elements are arranged adjacent to one another along the azimuth direction  101 , instead of or in addition to arrangement of the sub-elements next to one another along the elevation direction  103 . 
     A combined comb structure may be diced to generate elements of varying depths along the azimuth direction  101  while also varying widths of the elements along the elevation direction  103 . Alternatively, the widths of the elements may be maintained uniform along the elevation direction  103  and varied along the azimuth direction  101 . Furthermore, depths of the singulated transducers may similarly be varied along the azimuth direction  101  in addition to or instead of along the elevation direction  103 . 
     By enabling dimensions of the transducers, elements, and sub-elements to be varied along both the azimuth direction  101  and elevation direction  103 , scalable fabrication of the transducers is enabled. A variety of transducers with different and broad bandwidths and spatial frequency distribution may be produced from a single wafer. Electrical circuits are coupled to the wafer prior to singulation, increasing an efficiency of manufacturing. A quantity of interconnects and control signals in a multi-frequency transducer probe may be similar to a quantity used in a single-frequency transducer probe. Thus, implementation of multi-frequency transducer arrays does not introduce additional complexity to transducer probes. 
     Ground recovery along both the elevation and azimuth directions allows greater flexibility in packaging of a transducer array in a probe. For example, a transducer array with a reduced footprint in the elevation direction may be desirable. In conventional methods, ground recovery may be difficult when the transducer array is shortened along the elevation direction. The fabrication process described above with reference to  FIGS. 10-38 and 40-42 , however, allows for ground recovery along the azimuth direction instead. Additionally, an apodization function provided by the spatial frequency distribution of the broad bandwidth transducers may allow a transducer probe to be used for more than one application. For example, a single transducer probe may be used for both therapy and imaging. Image quality may be optimized in both near and far fields due to an enhanced beam focus profile enabled by the apodization function. A footprint of the transducer probe may be optimized for more efficient packaging. As well, a manufacturing process of an acoustic stack of the transducer probe, as illustrated in  FIGS. 10-36  may provide a universal architecture, based on a collective wafer approach, applicable to all transducer portfolios. 
     An example of a first routine  3700  for fabricating a multi-frequency acoustic stack for a transducer probe is depicted in  FIG. 37 . A second routine  3800 , as shown in  FIG. 38 , is an example of a routine for forming multi-frequency elements which may be included in the first routine  3700 . The first and second routines  3700 ,  3800  describe a process similar to the manufacturing process illustrated in  FIGS. 10-36 . Turning now to  FIG. 37 , at  3702 , the first routine  3700  includes forming a first acoustic stack, as shown in the second routine  3800  in  FIG. 38 . 
     At  3802  of  FIG. 38 , the second routine  3800  includes forming a first comb structure, such as the first comb structure  1100  of  FIG. 11 , which has a first sub-element. The first comb structure may be formed by dicing a first acoustic stack, such as the first acoustic stack  1000  of  FIG. 10 . A second comb structure is formed at  3804 , such as the second comb structure  1300  of  FIG. 13 , which has a second sub-element with a different resonance frequency than the first sub-element. The second comb structure may be formed by dicing a second acoustic stack, such as the second acoustic stack  1200  of  FIG. 12 . Both the first acoustic stack and the second acoustic stack may each include a matching layer, a sub-element layer, an optional dematching layer, and a backing layer, the layers stacked along a transverse direction perpendicular to both an azimuth direction and an elevation direction. 
     The first acoustic stack and the second acoustic stack may be diced along opposite directions from one another to impart the first and second comb structures with complementary fins. For example, as shown in  FIG. 11 , the first acoustic stack may be diced downwards from a top surface of the first acoustic stack and, as shown in  FIG. 13 , the second acoustic stack may be diced upwards from a bottom surface of the second acoustic stack. Alternatively, the first acoustic stack may be diced upwards from a bottom surface while the second acoustic stack may be diced downwards from a top surface. 
     At  3806 , the first comb structure is combined with the second comb structure to form an interdigitated combined stack, such as the third acoustic stack  1402  of  FIG. 14 . The combined stack may be laminated to adhere the comb structures to one another. 
     At  3808 , the routine includes determining if an additional sub-element is to be incorporated into the combined stack. If no additional sub-element is to be included, the routine continues to  3704  of the first routine  3700  of  FIG. 37 . If at least one additional sub-element is to be incorporated, an additional comb structure is formed at  3810 . The additional comb structure may be diced similar to the first comb structure  1100  of  FIG. 11  or the second comb structure  1300  of  FIG. 13  while the combined stack may be diced at  3812  in an opposite manner to complement a geometry of the diced additional comb structure. The additional comb structure may have a third sub-element with a different resonance frequency than the first or second sub-elements. 
     In some examples, the additional comb structure may be a combined comb structure, formed via a similar process as described in  3802 - 3806  of the second routine  3800 , so that the additional comb structure has a fourth sub-element in addition to the third sub-element. The additional comb structure with both the third and fourth sub-elements may be similarly diced to have a complementary geometry to the diced combined stack. 
     At  3814 , the second routine  3800  includes combining the diced combined stack with the additional comb structure to form a new combined stack which may be laminated to adhere the combined stack and the additional comb structure to one another. During lamination, a layer of non-conductive adhesive may be disposed between the first and second comb structures. The method returns to  3808  to again determine if an additional sub-element is to be incorporated into the (new) combined stack. 
     Returning to  FIG. 37 , at  3704  of the first routine  3700 , the first acoustic stack, e.g., the combined stack formed via the second routine  3800 , is diced. Dicing of the first acoustic stack forms a plurality of fins separated by a plurality of kerfs in the first acoustic stack. At  3706 , a base package formed of a conductive material, such as the base package  1602  of  FIG. 16 , is diced to have fins with a similar geometry to the plurality of kerfs in the first acoustic stack and kerfs with a similar geometry to the plurality of fins in the first acoustic stack. 
     The base package and the first acoustic stack are coupled to one another and laminated at  3708  to form a second acoustic stack. At  3710 , a portion of a back side of second acoustic stack may be removed by grinding to provide ground recovery. For example, a portion of a thickness of a backing layer of the first acoustic stack, as well as portions of the non-conductive adhesive used to laminate the first acoustic stack, may be removed. By removing a part of the backing layer and the portions of the non-conductive adhesive, ground recovery along the azimuth and elevation directions may be enabled. 
     At  3712 , a conductive layer is sputtered on the ground back side of the second acoustic stack. The conductive layer may allow electrical connections to be coupled to the back side of the second acoustic stack, each of the electrical connections included in an integrated circuit of a final transducer array formed via processing of the second acoustic stack. The second acoustic stack is diced at  3714  and kerfs formed by dicing may be filled with a non-conductive material, thereby electrically insulating each integrated circuit, or transducer, of the second acoustic stack from adjacent integrated circuits. 
     A front side of the second acoustic stack is ground at  3716 . The front side is opposite of the back side and a portion of a thickness of the front side may be removed by grinding. For example, a matching layer of the second acoustic stack may be partially removed. At  3718 , a matching layer block and a backing layer block may be coupled to the front and back sides, respectively, of the second acoustic to further enable ground recovery in the azimuth and elevation directions. At  3720 , the first routine  3700  includes singulating the second acoustic stack to divide the second acoustic stack into separate transducer arrays. The transducer arrays may each be implemented in a transducer probe. The first routine  3700  ends. 
     In this way, a multi-element transducer array may be provided for a transducer probe. The multi-element transducer array may include sub-elements with different resonance frequencies, distributed along the azimuth and elevation directions in a homogeneous pattern. Alternatively, the sub-elements may be positioned to provide varying spatial frequency distributions along at least one of the azimuth and elevations directions. Frequency apodization and agility is enabled along the elevation direction and on different structures, e.g., 1D, 1.5D, 2D, etc., enabling spatial frequency distribution in complex structures. Furthermore, frequency apodization and agility is achieved at low cost by fabricating the multi-element transducer through a wafer scale approach. A processing of an acoustic stack during the wafer scale approach may result in a large distribution of frequency content over a transducer aperture that allows one transducer probe to be use for multiple applications. Image quality may be optimized in both a near and far field due to a beam focus profile enabled by frequency apodization. The multi-element transducer array may be packaged more efficiently within the transducer probe due to ground recovery in both the azimuth and elevation directions and may be used in a variety of transducer portfolios. 
     The technical effect of fabricating the transducer array via the wafer scale approach is that a broad bandwidth transducer array is produced via a cost efficient method. Another technical effect is that frequency apodization and agility is enabled along the azimuth and elevation directions. 
     As used herein, an element or step recited in the singular and proceeded with the word “a” or “an” should be understood as not excluding plural of said elements or steps, unless such exclusion is explicitly stated. Furthermore, references to “one embodiment” of the present invention are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features. Moreover, unless explicitly stated to the contrary, embodiments “comprising,” “including,” or “having” an element or a plurality of elements having a particular property may include additional such elements not having that property. The terms “including” and “in which” are used as the plain-language equivalents of the respective terms “comprising” and “wherein.” Moreover, the terms “first,” “second,” and “third,” etc. are used merely as labels, and are not intended to impose numerical requirements or a particular positional order on their objects. 
     In one embodiment, a transducer array includes an element formed of one or more sub-elements, at least one sub-element having a different resonance frequency. In a first example of the transducer array, the transducer array is formed of at least one element and wherein the element is driven by an electrical circuit and electrically isolated from adjacent elements. A second example of the transducer array optionally includes the first example, and further includes, wherein relative proportions of the one or more sub-elements are equal in the element and each element of the transducer array has a similar resonance frequency. A third example of the transducer array optionally includes one or more of the first and second examples, and further includes, wherein widths of the one or more sub-elements vary through the transducer array, the widths defined along one of elevation direction and an azimuth direction. A fourth example of the transducer array optionally includes one or more of the first through third examples, and further includes, wherein relative proportions of each of the one or more sub-elements varies along the transducer array and at least one element of the transducer array has a different frequency range. A fifth example of the transducer array optionally includes one or more of the first through fourth examples, and further includes, wherein the relative proportions of each of the one or more sub-elements varies amongst each element of the transducer array along at least one of an azimuth direction and an elevation direction. A sixth example of the transducer array optionally includes one or more of the first through fifth examples, and further includes more than one type of element, each type of element having a different resonance frequency and frequency range, incorporated in the transducer array. A seventh example of the transducer array optionally includes one or more of the first through sixth examples, and further includes, wherein the more than one type of element in the transducer array has non-uniform dimensions along at least one of an azimuth and an elevation direction. An eighth example of the transducer array optionally includes one or more of the first through seventh examples, and further includes, wherein a quantity of the one or more sub-elements in the element varies across the transducer array. 
     In another embodiment, a multi-frequency acoustic stack includes a first comb structure coupled to a second comb structure, the first comb structure having a first type of element with a first resonance frequency and the second comb structure having a second type of element with a second resonance frequency, a plurality of electrical circuits, each circuit including at least one of the first type of element and the second type of element and configured to vary in frequency bandwidth to provide frequency apodization along at least one of an azimuth and an elevation direction. In a first example of the acoustic stack, the first comb structure has a geometry complementary to a geometry of the second comb structure and coupling of the first and second comb structure forms an interdigitated structure. A second example of the acoustic stack optionally includes the first example, and further includes, wherein each electrical circuit of the plurality of electrical circuits includes one or more additional types of element in addition to at least one of the first and second types of elements, the one or more additional types of elements having different resonance frequencies than the first or second types of elements. A third example of the acoustic stack optionally includes one or more of the first and second examples, and further includes, wherein each electrical circuit is coupled to a matching layer and a backing layer. A fourth example of the acoustic stack optionally includes one or more of the first through third examples, and further includes, wherein each element of the plurality of elements is separated from adjacent elements by kerfs filled with one of a non-conductive material and air. A fifth example of the acoustic stack optionally includes one or more of the first through fourth examples, and further includes, wherein each element is electrically coupled to positive and ground connections to form individual integrated circuits. 
     In yet another embodiment, a method includes dicing a first acoustic stack with a first sub-element and a second acoustic stack with a second sub-element to have complementary geometries, combining the first acoustic stack and the second acoustic stack to form a interdigitated structure, coupling a common matching layer and a common backing layer to opposite sides of the interdigitated structure, and singularizing the interdigitated structure to form one or more transducer arrays. In a first example of the method, dicing the first and second acoustic stacks includes forming kerfs in each of the acoustic stacks and wherein the first acoustic stack has a first set of kerfs extending downwards from a top surface of the first acoustic stack and the second acoustic stack has a second set of kerfs extending upwards from a bottom surface of the second acoustic stack. A second example of the method optionally includes the first example, and further includes dicing the interdigitated structure and coupling the diced interdigitated structure to a base package configured with a complementary geometry to the diced interdigitated structure to form a third acoustic stack prior to coupling the matching and backing layers. A third example of the method optionally includes one or more of the first and second examples, and further includes, dicing the third acoustic stack prior to coupling the matching and backing layers to separate the third acoustic stack into a plurality of transducers, each of the plurality of transducers including an element formed of at least one of the first sub-element and the second sub-element. A fourth example of the method optionally includes one or more of the first through third examples, and further includes, attaching electrical connections to each of the matching layer and the backing layer to form individual electronic circuits with each element. 
     This written description uses examples to disclose the invention, including the best mode, and also to enable a person of ordinary skill in the relevant art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those of ordinary skill in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims.