NON-PLANAR HOLOGRAPHIC BEAM SHAPING LENSES FOR ACOUSTICS

Abstract

Non-planar holographic beam shaping lenses for acoustics are disclosed herein. In one embodiment, an ultrasonic therapy system that is configured to apply ultrasound to a target in a body includes: an ultrasonic transducer configured to generate the ultrasound; and a customizable holographic lens configured to focus the ultrasound onto a focal area of a target that is an object or a portion of the object in the body. The customizable holographic lens is designed and produced based on the target. Furthermore, the customizable holographic lens is curved to mate with a front surface of the ultrasonic transducer.

Claims

1. An ultrasonic therapy system configured to apply ultrasound to a target in a body, comprising: an ultrasonic transducer configured to generate the ultrasound; and a curved holographic lens configured to focus the ultrasound onto a focal area of a target that is an object or a portion of the object in the body, wherein the curved holographic lens is designed and produced based on the target, and wherein the curved holographic lens is curved to mate with a front surface of the ultrasonic transducer.

2. The system of claim 1, wherein the curved holographic lens is designed based on an iterative angular spectrum approach (IASA) and Rayleigh integral.

3. The system of claim 1, wherein the target is defined by at least one acquired image of the object in the body.

4. The system of claim 1, wherein a curvature of the front surface of the ultrasonic transducer is a spherical, parabolic or elliptical curvature.

5. The system of claim 1, wherein the front surface of the ultrasonic transducer comprises more than one curvature.

6. The system of claim 1, wherein a curvature of the front surface of the ultrasonic transducer is a non-constant curvature disposed along multiple directions.

7. The system of claim 1, wherein the curved holographic lens is a three-dimensional (3D) printed lens.

8. The system of claim 1, wherein the curved holographic lens is produced by machining or injection molding.

9. The system of claim 1, wherein the ultrasound is configured to produce at least one of a thermal therapy, a histotripsy, a lithotripsy, a drug delivery, a diagnostic imaging, an image guidance, a microbubble manipulation, and a manipulation and removal of urinary stone fragments at the target.

10. A method for applying an ultrasound to a target in a body, comprising: defining, based on the target, an intermediate plane that is a customizable holographic velocity or pressure plane, wherein the target is an object or a portion of the object in the body, and wherein the intermediate plane is a flat, two-dimensional surface; defining a customizable holographic lens as a curved holographic lens by back-propagating the intermediate plane to a curved surface that matches a front surface of an ultrasonic transducer; defining a thickness of the curved holographic lens in a direction normal to the front surface of the ultrasonic transducer using a phase from the ultrasonic transducer to define the thickness; generating the ultrasound by the ultrasonic transducer; and focusing the ultrasound onto a focal area of the object by the curved holographic lens.

11. The method of claim 10, further comprising: acquiring an image of the object, wherein the curved holographic lens is defined at least in part based on the image of the object.

12. The method of claim 10, further comprising manufacturing the curved holographic lens by three-dimensional (3D) additive-printing.

13. The method of claim 10, further comprising manufacturing the curved holographic lens by machining or injection molding.

14. The method of claim 10, further comprising: applying an interface material to a surface of the curved holographic lens; mating the customizable lens with the ultrasonic transducer via the interface material; and after focusing the ultrasound onto the focal area, removing the curved holographic lens from the ultrasonic transducer.

15. The method of claim 10, wherein focusing the ultrasound onto the focal area of the object includes focusing ultrasound pressure amplitude distribution or ultrasound pressure phase distribution over the focal area.

16. The method of claim 10, wherein a curvature of the front surface of the ultrasonic transducer is a spherical, parabolic or elliptical curvature.

17. The method of claim 10, wherein the front surface of the ultrasonic transducer comprises more than one curvature.

18. The method of claim 10, wherein a curvature of the front surface of the ultrasonic transducer is a non-constant curvature disposed along multiple directions.

Description

DESCRIPTION OF THE DRAWINGS

[0032] The foregoing aspects and many of the attendant advantages of the inventive technology will become more readily appreciated as the same are understood with reference to the following detailed description, when taken in conjunction with the accompanying drawings, where:

[0033] FIG. 1 is a side plan view of an ultrasound system in accordance with conventional technology;

[0034] FIG. 2 is a side plan view of an ultrasound system in accordance with conventional technology;

[0035] FIG. 3 is a view of a sample target object;

[0036] FIG. 4 is a schematic diagram of a method for designing a customizable lens in accordance with an embodiment of the present technology;

[0037] FIG. 5 is a graph of thickness of a holographic lens in accordance with an embodiment of the present technology;

[0038] FIG. 6A is an isometric view of the lens in accordance with conventional technology;

[0039] FIG. 6B is a cross-sectional view of the lens of FIG. 6A;

[0040] FIG. 7 is a schematic view of pressure waves produced by a lens in accordance with conventional technology;

[0041] FIG. 8 is a graph of pressure amplitude for a sample target shown in FIG. 3 in accordance with conventional technology;

[0042] FIG. 9 is a schematic diagram of a method for designing a customizable lens in accordance with an embodiment of the present technology;

[0043] FIG. 10 is a schematic diagram of determining holographic features of the lens in accordance with an embodiment of the present technology;

[0044] FIG. 11A is a phase solution at aperture plane a graph of a target phase boundary condition in accordance with an embodiment of the present technology;

[0045] FIG. 11B illustrates a phase solution on a transducer surface in accordance with an embodiment of the present technology;

[0046] FIG. 12 is an isometric view of a curved holographic lens in accordance with an embodiment of the present technology;

[0047] FIG. 12A is a cross sectional view of a curved holographic lens in accordance with an embodiment of the present technology;

[0048] FIG. 13 is a cross-sectional view of a curved holographic lens in accordance with an embodiment of the present technology; and

[0049] FIGS. 14A and 14B are graphs of simulated and measured pressure amplitude, respectively, at a target image plane of ultrasound in accordance with an embodiment of the present technology.

DETAILED DESCRIPTION

[0050] In order to better understand the technical solutions of the present disclosure, the embodiments of the present disclosure are described in detail below with reference to the accompanying drawings. It should be clear that the described embodiments are only a part of the embodiments of the present disclosure, but not all of the embodiments. Based on the embodiments in the present disclosure, all other embodiments obtained by those of ordinary skill in the art fall within the protection scope of the present disclosure.

[0051] The terms used in the embodiments of the present disclosure are only for the purpose of describing specific embodiments, and are not intended to limit the present disclosure. As used in the embodiments of this application and the appended claims, the singular forms “a,” “the,” and “the” are intended to include the plural forms as well, unless the context clearly dictates otherwise.

[0052] It should be understood that the term “and/or” used in this document is only an association relationship to describe the associated objects, indicating that there can be three relationships, for example, A and/or B, which can indicate that A alone, A and B, and B alone. The character “I” in the present description generally indicates that the related objects are an “or” relationship.

[0053] It should be understood that although the terms ‘first’, ‘second’, and ‘third’ can be used in the present disclosure to describe thin film transistors, these thin film transistors should not be limited to these terms. These terms are used only to distinguish the thin film transistors from each other.

[0054] In the context of this disclosure, the terms “about,” “approximately,” “generally” and similar mean+/−5% of the stated value.

[0055] FIG. 1 is a side plan view of an ultrasound system 10 in accordance with conventional technology. The ultrasound system 10 is a test system that includes a housing 30 that is filled with a medium 32 (typically water) that facilitates transmission of the ultrasound within the system 10. The ultrasound system 10 includes a test target 22 representing, for example, a hypothetical calcification or tumor in a body. The target 22 is held by a target holder 24.

[0056] A transducer 12 generates vibrations at ultrasound frequencies (e.g., from about 20 kHz to about 10 MHz). The transducer 12 can be a piezoelectric element that expands and shrinks with changing electrical polarity applied to the transducer. Such a change in electrical polarity can be applied by an alternating current (AC) at a target ultrasound frequency. An interface 14 attaches a lens to the transducer 14. The interface 14 is typically a permanent epoxy or other suitable strong adhesive. In operation, the lens 16 focuses the ultrasound generated by the transducer 12 through an acoustic window 18 onto a target 22. Much like optical systems, acoustic waves obey Snell's law. For that reason, ultrasound can be shaped by the lens 16 in the path of a propagating acoustic wave. Acoustic lenses (refractive lenses) bend the propagating wave in proportion to the ratio of indices of refraction of the lens and of a target medium, such as biological tissue. The index of refraction is a material property, depending on the speed of sound in the material.

[0057] A coupling 17 (e.g., gel, oil, etc.) provides acoustic coupling for the ultrasound propagating toward the target 22. The ultrasound system 10 includes an absorber 26 that prevents ultrasound from escaping into the environment. The operation of the transducer 12 can be controlled by a controller 40.

[0058] FIG. 2 is a side plan view of an ultrasound system 10 in accordance with conventional technology. The illustrated conventional system 10 includes a holographic lens 16. However, the illustrated holographic lens 16 is relatively thick in the middle of the transducer 12, therefore increasing the acoustic losses and degrading targeting precision of the ultrasound system 10.

[0059] A person of ordinary skill would know that one of the challenges in developing ultrasound instruments for moving and breaking urinary tract stones is generating the appropriate acoustic pressure and beam shape to effectively apply force to or fragment the stone. For example, if a beam is too narrow, it may not fragment a stone because it does not impart enough energy on the entire stone. On the other hand, if a beam is too wide, ultrasound energy is wasted on collateral tissue. Therefore, ultrasound focusing is often necessary to achieve sufficient pressure on the stone.

[0060] FIG. 3 is a view of a sample target object. The horizontal and vertical axes represent the target size in millimeters. Illustrated sample target image is 32 mm away from the source of the ultrasound. The illustrated target image is binary, the bright areas representing the maximum target pressure and dark areas representing zero target pressure. However, in different embodiments non-binary distributions of target pressure amplitude or phase may be used. The circle that is around the image shows the outline of the transducer aperture (which is in the 0 mm plane). The combination of transducer and lens attempts to re-create the illustrated pressure field at 32 mm distance from the source of the ultrasound. A method of designing such customizable lens is described with reference to FIG. 5 below.

[0061] FIG. 4 is a schematic diagram of a method for designing a customizable lens in accordance with an embodiment of the present technology. In operations, the lens stimulates additive and destructive interference in a propagating wave front to generate a desired pressure and/or phase pattern at a target focal surface. The iterative angular spectrum approach (IASA) develops precise phase mappings for the lenses, which in turn provide a physical design for the lens geometry. As explained with reference to the conventional technology, typical approaches to lens design, such as the Fresnel approximation, fail to produce the desired pressure pattern with sufficient precision when the feature size in desired pressure pattern approaches the wavelength of the propagating wave front.

[0062] In some embodiments, the customizable lens may be designed using the iterative angular spectrum approach (IASA). In some embodiments, an algorithm implements IASA numerically by iteratively comparing simulated conditions at the target focal surface against the target conditions at the focal surface. In some embodiments, an algorithm implements IASA numerically by iteratively comparing simulated conditions at the focal surface against the target conditions at the focal surface; and the complex pressure distribution at the source to the results from the previous iterative step.

[0063] In a first step, the algorithm introduces lens geometry, propagating wave front, and target focal surface in a given medium. The target focal surface may be defined by its pressure pattern (p), made up of an amplitude map (A) and a phase map (Φ). The target focal surface is located some known distance from the lens.

[0064] The pressure wave equation includes amplitude and phase functions describing pressure at a given position in Euclidean space:

p(x,y,z)={circumflex over (p)}(x,y,z)e.sup.jΔΦ(x,y,z)  (1)

where {circumflex over (p)}(x, y, z) and ΔΦ(x, y, z) are the amplitude and phase functions, respectively.

[0065] The IASA method uses fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT) methods to converge to an optimum error criterion, calculated as an error between the target focal surface and conditions at the focal surface. The general form of the FFT equation in Euclidean space is shown in Equation 2:

[00001]$\begin{array}{cc}P\left(k_x,k_y\right)=\int {\int }_{-\infty }^{+\infty }p\left(x,y,0\right)e^{-j\left(k_{x}x+k_{y}y\right)}\mathrm{dxdy}& \left(2\right)\end{array}$

[0066] The output of the FFT equation, P(kx,ky), gives an angular spectrum, where ki is the wavenumber in i space. The IFFT equation, excluding the evanescent wave components, is shown in Equation 3:

[00002]$\begin{array}{cc}p\left(x,y,z\right)=\frac{1}{4{\pi }^2}\int {\int }_{k_x^2+k_y^2\le k^2}P\left(k_x{k}_y\right)e^{j\left(k_{x}x+k_{y}y+\sqrt{k^2-k_x^2-k_y^{2}z}\right)}{\mathrm{dk}}_x{\mathrm{dk}}_y& \left(3\right)\end{array}$

[0067] which provides the conditions at the focal surface in Euclidean space from the angular spectrum (P).

[0068] In the initial iteration of the loop shown in FIG. 5, the propagating wave front is transformed by FFT into an angular spectrum. A propagation function, shown in Equation 4, then calculates the effect of movement through a given medium on the angular spectrum:

[00003]$\begin{array}{cc}P\left(k_x,k_y,z\right)=P\left(k_x,k_y,0\right)e^{\mathrm{jz}\sqrt{k^2-k_x^2-k_y^2}}& \left(4\right)\end{array}$

[0069] which is used to calculate both propagation and backpropagation through the given medium between the focal surface and the lens. The propagating wave front then propagates through the lens and the given medium to produce an angular spectrum for a propagated wave front at the focal surface (the conditions at the focal surface).

[0070] As shown in FIG. 4, IFFT provides a wave equation in spatial coordinates for comparison to the desired conditions at the target focal surface. The error criterion indicates whether the lens design at the current iteration produces the target focal surface. In initial iterations, the error between the conditions at the focal surface and the target focal surface may be significant, due to near field effects that impact the propagating wave front.

[0071] To account for the near field effects, the IASA incorporates a back-propagation of the propagated wave front from the focal surface to the lens, shown as a clockwise lower arrow in FIG. 5, and modulates the propagating wave front, and its angular spectrum, for iterative propagation forward to the focal surface. The algorithm retains the latest iteration of the phase information at the focal surface to calculate convergence.

[0072] In addition to conventional IASA method, the method uses the multiple checks in the convergence criterion to meet our desired goals. The algorithm iteratively compares the convergence of the simulated conditions to the target image specified at each target location. Second, after the first iteration step and in parallel to the previous check, the algorithm compares the complex pressure distribution at the source to that of the previous step as well to speed up and improve the convergence calculation criterion. The comparisons in the previous two checks are specified to be within a specific error tolerance below which convergence to the optimal hologram solution is achieved. Finally, a maximum number of iterations is determined for each run, such that when it is exceeded the method terminates and saves the optimal hologram solution. The error tolerance and maximum number of iterations is determined based on the complexity of the hologram, such as, the number of target locations for phase and or amplitude at different frequencies. These checks of convergence are checked at each iteration step to yield the optimal solution.

[0073] Incorporating back propagation into an iterated forward propagating wave equation permits a more precise calculation of the conditions at the focal surface for subsequent adjustment of the lens geometry. With each cycle of forward propagation and back propagation the conditions at the focal surface and the conditions at the lens converge to an optimal solution.

[0074] An output of the IASA algorithm is the lens geometry. As described in Equation 5, a spatial thickness parameter describes the lens geometry by taking into account the transmission coefficient (a) of the system, including acoustic impedances (Z) of the lens material (h), the given medium (m), and a transducer (t), a source of acoustic waves:

[00004]$\begin{array}{cc}{a}_T\left(x,y\right)=\frac{4Z_t{Z}_h^2{Z}_m}{{z_h^2\left(Z_t+Z_m\right)}^2{\cos \left(k_{h}T\left(x,y\right)\right)}^2+{\left(Z_h^2+Z_t{Z}_m\right)}^2{\sin \left(k_{h}T\left(x,y\right)\right)}^2}& \left(5\right)\end{array}$

[0075] The thickness of the lens (T) can be calculated from the angular spectrum of the converged solution by creating a phase map for the surface of the lens. The lens creates constructive and destructive interference in the near-field by introducing phase offsets (ΔΦ) in the propagating wave front as it passes through the holographic lens. The thickness of the lens is described as follows in Equations 6-7:

ΔΦ(x,y)=(k.sub.m−k.sub.h)ΔT(x,y)  (6)

where

T(x,y)=T.sub.0−ΔT(x,y).  (7)

[0076] The IASA algorithm is capable of designing a lens that produces multiple target focal surfaces at as many distances from the lens in a given medium. To accomplish this, the IASA algorithm separately incorporates the backpropagation from the wave equations of each of the target focal surfaces when modulating the propagating wave equation.

[0077] The IASA method can be used with different transducer geometries. For instance, for a focused transducer, the exact pressure field can be simulated and verified through holographic scanning in a plane. Next, the pressure field at the transducer aperture (obtained by back-projection) is used as the initial boundary condition over which we can impose the required phase to obtain the desired beam shape.

[0078] When compared to the conventional lens design methods, the IASA-based design method maximizes the power of the beam while producing an arbitrary pressure distribution in the plane of interest. Furthermore, the method can be extended to constrain the amplitude distribution in several different planes of propagation. Analogously, the method can be extended to produce different beam patterns using ultrasonic transducers at different frequencies. The method can also be used to constrain the phase distribution in one or more planes, or both amplitude and phase distributions simultaneously. The desired target field may be binary or continuously varying in amplitude and/or phase over the focal plane of interest.

[0079] FIG. 5 is a graph of thickness of a holographic lens in accordance with an embodiment of the present technology. In some embodiments, the holographic features of the illustrated lens may be obtained by the method described in conjunction with FIG. 4 above. For the illustrated flat holographic lens, the overall thickness of the lens changes with the height T of the particular holographic features.

[0080] FIG. 6A is an isometric view of a holographic lens in accordance with conventional technology. FIG. 6B is a cross-sectional view of the lens of FIG. 6A.

[0081] In operation, a flat holographic lens may mate with a transducer having a flat outer surface. However, when mated to a transducer having a concave surface, the back surface of the holographic lens 160 must be shaped against the curved surface of transducer by adding material to the back side of the holographic lens. An example of such additional material that makes the holographic lens thicker is shown in the cross-sectional view of FIG. 6B.

[0082] FIG. 7 is a schematic view of pressure waves produced by the lens in accordance with conventional technology. When mated with a transducer that operates at the design frequency of the ultrasound, the holographic lens 160 generates illustrated ultrasound waves that are focused on an image plane (focal plane) 20. As explained above, the additional lens thickness increases energy dissipation and reduces the targeting precision of the lens.

[0083] FIG. 8 is a graph of pressure amplitude for a sample target shown in FIG. 3. When the customizable lens is attached to the ultrasonic transducer to follow oscillations by the transducer, the local phases of the ultrasound at the surface of the customizable lens are offset due to the uneven thickness of the holographic lens. These phase offsets constructively/destructively combine to generate a pressure field at the target focal distance. In the illustrated embodiment, the pressure amplitude field attempts to emulate the target image shown in FIG. 3 at a prescribed distance from the source (i.e., at a prescribed distance from the transducer). In some applications, because of a relatively complex shape of the target, obtained pressure field may lack spatial resolution and the pressure amplitudes may be off the target values. In many cases, these shortcomings of the ultrasound pressure field at the target plane may be attributed to the additional thickness of the holographic lens, as explained above.

[0084] FIG. 9 is a schematic diagram of a method for designing a customizable lens 230 in accordance with an embodiment of the present technology. The method of designing may be understood as a two-step process. In the first step, an IASA algorithm as discussed with, for example, equations (1)-(7) may be used to design a flat holographic lens 230 based on the target pressure, phase, amplitude or velocity distribution of the ultrasound at the image plane 20. In the context of this disclosure, such flat holographic lens may be referred to as an intermediate customizable holographic lens characterized by the intermediate pressure/velocity plane that is a flat, two-dimensional surface.

[0085] In the second step, a Rayleigh integral method is used to determine the required holographic features of the curved holographic lens 230. The resulting curved holographic lens (non-planar holographic lens) 230 is characterized by the curvature of its principal plane in addition to the size and distribution of the holographic features, which in general differ from the holographic features of the corresponding flat holographic lens. In the context of this specification, the term principal plane of the holographic lens refers to the plane that approximately follows a middle of the thickness of the lens. In many practical applications of the inventive technology, the principal plane of the holographic lens 230 conforms to the curvature of the front surface (also referred to as the outer surface) of the transducer 12.

[0086] For a non-planar source like the illustrated front surface of the transducer 12, the Raileigh integral may be determined based on the boundary conditions of a focused source and complex pressure at aperture plane plus half wavelength (½λ) of the ultrasound being used. The Rayleigh integral to aperture plane may be expressed as:

[00005]$\begin{array}{cc}P=\frac{-\mathrm{ik}\rho c}{2\pi }\int \int V\frac{e^{\mathrm{ikR}}}{R}\mathrm{dS}& \left(8\right)\end{array}$

assuming that the radius of curvature (R) of the front surface of the transducer is much higher than the ultrasound wavelength (R>>λ), which is a reasonable assumption for most practical ultrasonic transducers. The ultrasonic transducer 12 is illustrated as a single element transducer. In some embodiments, a frequency of the ultrasonic transducer is within a range from 100 kHz to 20 MHz. In some embodiments, a focal number of the customizable holographic lens is greater than 0.6. In some embodiments, a ratio of an aperture of the customizable holographic lens and a wavelength of the ultrasound greater than 20.

[0087] In the process of solving the Rayleigh integral, the holographic features are determined for the curved holographic lens. In general, the holographic features of the curved holographic lens are different from those of the flat holographic lens. Stated differently, it should not be assumed that the holographic features of the curved lens can be determined by simply bending a flat holographic lens into a mating position with a surface of the transducer. A person of ordinary skill would understand that such approach would result in erroneous summation/subtraction of the phases and amplitudes at the target focal plane. Determination of the holographic features of the curved holographic lens 230 is described in conjunction with FIGS. 10-11B below.

[0088] FIG. 10 is a schematic diagram of determining holographic features of the lens in accordance with an embodiment of the present technology. In some embodiments, a focused phase solution at the aperture plane (FIG. 11A) is backpropagated to the phase solution on curved surface of the transducer 12 (FIG. 11B) as:

[00006]$\begin{array}{cc}\frac{\partial }{\partial n_{s1}}{P}_{S1}=\frac{1}{2\pi }\int \int P_{S2}\frac{\partial }{\partial n_{s1}}\frac{\partial }{\partial n_{s2}}\left(\frac{e^{\mathrm{ikR}}}{R}\right){\mathrm{dS}}_2& \left(9\right)\end{array}$

where n.sub.si is S.sub.i surface normal. The resulting thickness (T) of the holographic lens 230 may be expressed as:

[00007]$\begin{array}{cc}T=\frac{\varphi }{k_0-k_{\mathrm{lens}}}& \left(10\right)\end{array}$

where k=2π/λ.sub.i, and λ.sub.i is wavelength in material i.

[0089] The lens surface S.sub.L of the curved holographic lens now becomes:

S.sub.L−S.sub.1=(T+To).Math.n.sub.S1  (11)

where T is the height of the holographic feature, and To is a constant thickness that adds no phase change.

[0090] In operation, the small-scale features (holographic features) 232 on the surface of the lens determine the phase offsets of the emitted ultrasound. When the ultrasound is generated at the required ultrasound frequency, these phase offsets constructively/destructively combine into a target pressure, velocity, amplitude and/or phase field.

[0091] A monolithic lens is described with reference to FIG. 10. However, in different embodiments, the lens 230 may also be a multi-element lens that comprises multiple segments.

[0092] The holographic lens 230 may be designed based on the target pressure amplitude/phase distributions, for example, as shown in FIG. 3. It is possible to obtain different distributions of different parameters (e.g., pressure, velocity, amplitude and phase) at different target distances from the source of ultrasound. As explained above, the size and distribution of the holographic features 232 of the curved holographic lens 230 is determined using the method outlined by the equations (1)-(11).

[0093] In some embodiments, a time-varying signal alters the beam pattern of a single-lensed transducer. For example, a curved holographic lens 230 may generate multiple patterns at different frequencies simultaneously, or may generate a single pressure pattern for a finite temporal period. In an embodiment, the frequency of a sinusoidal ultrasound signal may be varied over time to change the pattern, either continuously as a frequency chirp, or discretely in intervals. In another embodiment, a short signal pulse may be generated by the transducer to produce a temporary holographic image for a therapy such as shock wave lithotripsy, burst wave lithotripsy, or histotripsy. In other embodiments, the customizable lens may be designed to produce a target distribution of ultrasound phases that, for example, pushes the target in a desired direction. In some embodiments, the inventive technology is used for diagnostic imaging, image guidance, or microbubble manipulation.

[0094] FIG. 12 is an isometric view of a curved holographic lens 230 in accordance with an embodiment of the present technology. The holographic lens 230 is illustrated as facing the object to be treated, i.e., the holographic features 232 face the object to be treated.

[0095] In some embodiments, the customizable lens 230 is made by machining or by additive manufacturing processes, for example, by 3D printing. In other embodiments, the customizable lens may be made by machining or injection molding. The customizable lens 230 may be manufactured from glass, graphite, metal, epoxy, composite with suitable acoustic properties or plastic that has suitable transmission coefficients for the ultrasound frequency. In some embodiments, the customizable lens 230 may have a curvature to achieve focusing or defocusing simultaneously with image formation (e.g., formation of the target pressure field or phase distribution). The lens resolution is generally determined by the method of manufacture, but in some applications the lens resolution can be smaller than a wavelength. Plane D-D indicates a cross-sectional plane of the holographic lens 230.

[0096] FIG. 12A is a cross sectional view D-D of the curved holographic lens of FIG. 12. The holographic lens 230 is designed such that the back side of the lens follows the curvature R of the transducer 12. In some embodiments, an interface 14 (not shown) is disposed between the transducer and holographic lens. The holographic lens 230 has a generally uniform thickness To, save for the differing heights T of the individual holographic features 232. As a result, the targeting accuracy and pressure amplitude/phase distribution are improved in comparison to the holographic lenses having non-uniform thickness, for example, the holographic lens illustrated in FIG. 6B.

[0097] FIG. 13 is a cross-sectional view of a curved holographic lens in accordance with an embodiment of the present technology. In some embodiments, the transducer 12 may be characterized by a wavy surface to which the curved holographic lens 230 mates. In the illustrated example, the transducer's surface is characterized by different radii R1 and R2, but in other embodiments, radii R1 and R2 may be same. In other embodiments, the transducer's surface may be characterized by more than two radii, that is, by more than two different curvatures. In some embodiments, a curvature of the front surface of the ultrasonic transducer is a spherical, parabolic or elliptical curvature. In some embodiments, a curvature of the front surface of the ultrasonic transducer is a non-constant curvature disposed along multiple directions.

[0098] FIGS. 14A and 14B are graphs of simulated and measured pressure amplitude, respectively, achieved by a curved holographic lens at a target image plane of ultrasound in accordance with an embodiment of the present technology. The horizontal and vertical axes indicate the size of the image plane in mm Pressures are normalized for comparisons. The measured field of FIG. 14B is obtained by holography field propagation, i.e., a holography scan is used to propagate the pressure field in 3D. An excellent agreement is achieved between the simulated pressure amplitude (FIG. 14A) and measured pressure amplitude (FIG. 14B). Deviation was quantified using relative change in Frobenius norm. A difference between the simulated and measured fields can be expressed (in percentage) as:

[00008]$\begin{array}{cc}\delta =\frac{<{P\left(x,y\right)}_{\mathrm{sim}.},{P\left(x,y\right)}_{\mathrm{sim}.}\text{>-<}{P\left(x,y\right)}_{\mathrm{meas}.},{P\left(x,y\right)}_{\mathrm{meas}.}>}{<{P\left(x,y\right)}_{\mathrm{sim}.},{P\left(x,y\right)}_{\mathrm{sim}.}>}\times 100& \left(12\right)\end{array}$

[0099] For the illustrated pressure amplitude fields in FIGS. 14A and 14B, the value of δ corresponds to 4.8%. This is considered a very good result, which far exceeds the performance of a flat holographic lens under the same conditions. Analogously, a difference δ between the pressure amplitude for a curved holographic lens in the xz-plane corresponds to about δ=16%, which, again, far exceeds the performance of a flat holographic lens under the same conditions.

[0100] Many embodiments of the technology described above may take the form of computer- or controller-executable instructions, including routines executed by a programmable computer or controller. Those skilled in the relevant art will appreciate that the technology can be practiced on computer/controller systems other than those shown and described above. The technology can be embodied in a special-purpose computer, controller or data processor that is specifically programmed, configured or constructed to perform one or more of the computer-executable instructions described above. Accordingly, the terms “computer” and “controller” as generally used herein refer to any data processor and can include Internet appliances and hand-held devices (including palm-top computers, wearable computers, cellular or mobile phones, multi-processor systems, processor-based or programmable consumer electronics, network computers, mini computers and the like).

[0101] From the foregoing, it will be appreciated that specific embodiments of the technology have been described herein for purposes of illustration, but that various modifications may be made without deviating from the disclosure. Moreover, while various advantages and features associated with certain embodiments have been described above in the context of those embodiments, other embodiments may also exhibit such advantages and/or features, and not all embodiments need necessarily exhibit such advantages and/or features to fall within the scope of the technology. Accordingly, the disclosure can encompass other embodiments not expressly shown or described herein.