Patent Publication Number: US-2023158337-A1

Title: Devices and methods for multi-focus ultrasound therapy

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional of U.S. application Ser. No. 16/541,476 filed Aug. 15, 2019, which is a continuation of U.S. application Ser. No. 14/193,234 filed Feb. 28, 2014, which claims the benefit of priority from U.S. Provisional Application No. 61/774,785 filed Mar. 8, 2013, which are incorporated in their entireties by reference, herein. Any and all priority claims identified in the Application Data Sheet, or any correction thereto, are hereby incorporated by reference under 37 CFR 1.57. 
    
    
     FIELD 
     Several embodiments of the present invention generally relate to noninvasive energy-based treatments to achieve cosmetic effects. For example, some embodiments generally relate to devices, systems and methods for providing multiple ultrasound treatment points or focus zones for performing various treatment and/or imaging procedures safely and effectively. Some embodiments relate to splitting an ultrasound therapy beam to two, three, four, or more focal zones for performing various treatment and/or imaging procedures with modulated and/or multiphasing. Some embodiments relate to splitting an ultrasound therapy beam to two, three, four, or more focal zones for performing various treatment and/or imaging procedures with poling techniques. Devices and methods of directing ultrasound therapy to multiple focus points in cosmetic and/or medical procedures are provided in several embodiments. 
     DESCRIPTION OF THE RELATED ART 
     Many cosmetic procedures involve invasive procedures that may require invasive surgery. Patients not only have to endure weeks of recovery time, but also are frequently required to undergo risky anesthetic procedures for aesthetic treatments. 
     SUMMARY 
     Although energy-based treatments have been disclosed for cosmetic and medical purposes, no procedures are known to Applicant, other that Applicant&#39;s own work, that successfully achieve an aesthetic effect using targeted and precise ultrasound to cause a visible and effective cosmetic result via a thermal pathway by splitting an ultrasound therapy beam to two, three, four, or more focal zones for performing various treatment and/or imaging procedures. 
     In several embodiments disclosed herein, non-invasive ultrasound is used to achieve one or more of the following effects: a face lift, a brow lift, a chin lift, an eye treatment, a wrinkle reduction, a scar reduction, a burn treatment, a tattoo removal, a vein removal, a vein reduction, a treatment on a sweat gland, a treatment of hyperhidrosis, a sun spot removal, an acne treatment, a pimple reduction. Treatment of the décolletage is provided in several embodiments. In another embodiment, the device may be used on adipose tissue (e.g., fat). In another embodiment the system, device and/or method may be applied in the genital area (e.g., vaginal rejuvenation and/or vaginal tightening, such as for tightening the supportive tissue of the vagina). 
     In accordance with various embodiments, a cosmetic ultrasound treatment system and/or method can non-invasively produce single or multiple cosmetic treatment zones and/or thermal coagulation points where ultrasound is focused in one or more locations in a region of treatment in tissue under a skin surface. Some systems and methods provide cosmetic treatment at different locations in tissue, such as at different depths, heights, widths, and/or positions. In one embodiment, a method and system comprise a multiple depth transducer system configured for providing ultrasound treatment to more than one region of interest, such as between at least two of a deep treatment region of interest, a superficial region of interest, and/or a subcutaneous region of interest. In one embodiment, a method and system comprise a transducer system configured for providing ultrasound treatment to more than one region of interest, such as between at least two points in various locations (e.g., at a fixed or variable depth, height, width, orientation, etc.) in a region of interest in tissue. Some embodiments can split a beam to focus at two, three, four, or more focal points (e.g., multiple focal points, multi-focal points) for cosmetic treatment zones and/or for imaging in a region of interest in tissue. Position of the focal points can be positioned axially, laterally, or otherwise within the tissue. Some embodiments can be configured for spatial control, such as by the location of a focus point, changing the distance from a transducer to a reflecting surface, and/or changing the angles of energy focused or unfocused to the region of interest, and/or configured for temporal control, such as by controlling changes in the frequency, drive amplitude and timing of the transducer. In some embodiments the position of multiple treatment zones or focal points with poling, phasic poling, biphasic poling, and/or multi-phasic poling. In some embodiments the position of multiple treatment zones or focal points with phasing, such as in one embodiment, electrical phasing. As a result, changes in the location of the treatment region, the number, shape, size and/or volume of treatment zones or lesions in a region of interest, as well as the thermal conditions, can be dynamically controlled over time. 
     In accordance with various embodiments, a cosmetic ultrasound treatment system and/or method can create multiple cosmetic treatment zones using one or more of phase modulation, poling, nonlinear acoustics, and/or Fourier transforms to create any spatial periodic pattern with one or multiple ultrasound portions. In one embodiment, a system simultaneously or sequentially delivers single or multiple treatment zones using poling at a ceramic level. In one embodiment, a poling pattern is function of focal depth and frequency, and the use of odd or even functions. In one embodiment, a process can be used in two or more dimensions to create any spatial periodic pattern. In one embodiment, an ultrasound beam is split axially and laterally to significantly reduce treatment time through the use of nonlinear acoustics and Fourier transforms. In one embodiment, modulation from a system and amplitude modulation from a ceramic or a transducer can be used to place multiple treatments zones in tissue, either sequentially or simultaneously. 
     In one embodiment, an aesthetic imaging and treatment system includes an ultrasonic probe that includes an ultrasound transducer configured to apply ultrasonic therapy to tissue at a plurality of locations at a focal depth with at least one of the group consisting of amplitude modulation poling and phase shifting. In one embodiment, the system includes a control module coupled to the ultrasonic probe for controlling the ultrasound transducer. 
     In various embodiments, the plurality of locations are positioned in a substantially linear sequence within a cosmetic treatment zone. In one embodiment, a first set of locations is positioned within a first cosmetic treatment zone and a second set of locations is positioned within a second cosmetic treatment zone, the first zone being different from the second zone. In one embodiment, the first cosmetic treatment zone includes a substantially linear sequence of the first set of locations and the second cosmetic treatment zone includes a substantially linear sequence of the second set of locations. In one embodiment, the ultrasound transducer is configured to apply ultrasonic therapy using amplitude modulation whereby a plurality of portions of the ultrasound transducer are configured to emit ultrasonic therapy at a plurality of amplitudes of acoustic intensity, wherein a first amplitude is different than a second amplitude. In one embodiment, the ultrasound transducer is configured to apply ultrasonic therapy phase shifting whereby a plurality of portions of the ultrasound transducer are configured to emit ultrasonic therapy at a plurality of phases of acoustic intensity, wherein a first phase is different than a second phase. In one embodiment, the ultrasound transducer is configured to apply ultrasonic therapy using amplitude modulation whereby a plurality of portions of the ultrasound transducer are configured to emit ultrasonic therapy at a plurality of amplitudes of acoustic intensity, wherein a first amplitude is different than a second amplitude, and apply ultrasonic therapy phase shifting whereby a plurality of portions of the ultrasound transducer are configured to emit ultrasonic therapy at a plurality of phases of acoustic intensity, wherein a first phase is different than a second phase. In one embodiment, the plurality of phases includes discrete phase values. In one embodiment, the ultrasound transducer includes piezoelectric material and the plurality of portions of the ultrasound transducer are configured to create a plurality of corresponding piezoelectric material variations in response to an electric field applied to the ultrasound transducer. In one embodiment, the plurality of piezoelectric material variations include at least one of expansion of the piezoelectric material and contraction of the piezoelectric material. In one embodiment, at least one portion of the ultrasonic transducer is configured to emit ultrasonic therapy at two or more amplitudes of acoustic intensity, and wherein the amplitude of ultrasonic therapy emitted by the at least one portion of the piezoelectric varies over time. In one embodiment, the system also includes a movement mechanism configured to be programmed to provide variable spacing between the plurality of individual cosmetic treatment zones. In one embodiment, a sequence of individual cosmetic treatment zones has a treatment spacing in a range from about 0.01 mm to about 25 mm. In various embodiments, the ultrasonic treatment is at least one of a face lift, a brow lift, a chin lift, an eye treatment, a wrinkle reduction, a scar reduction, a burn treatment, a tattoo removal, a skin tightening, a vein removal, a vein reduction, a treatment on a sweat gland, a treatment of hyperhidrosis, a sun spot removal, a fat treatment, a vaginal rejuvenation, and an acne treatment. In one embodiment, the ultrasonic transducer is configured to provide an acoustic power of the ultrasonic therapy in a range of between about 1 W to about 100 W and a frequency of about 1 MHz to about 10 MHz to thermally heat the tissue to cause coagulation. 
     In one embodiment, an aesthetic imaging and treatment system for use in cosmetic treatment includes: an ultrasonic probe and a control module. The ultrasonic probe includes a first switch operably controlling an ultrasonic imaging function for providing an ultrasonic imaging, a second switch operably controlling an ultrasonic treatment function for providing an ultrasonic treatment, and a movement mechanism configured to direct ultrasonic treatment in at least one sequence of individual thermal cosmetic treatment zones. In one embodiment, the system also includes a transducer module. In one embodiment, the transducer module is configured for both ultrasonic imaging and ultrasonic treatment. In one embodiment, the transducer module is configured for coupling to the ultrasonic probe. In one embodiment, the transducer module includes an ultrasound transducer configured to apply ultrasonic therapy to tissue at a plurality of locations at a focal depth. In one embodiment, the transducer module is configured to be operably coupled to at least one of the first switch, the second switch and the movement mechanism. In one embodiment, the control module includes a processor and a display for controlling the transducer module. 
     In various embodiments, the plurality of locations are positioned in a substantially linear sequence within a cosmetic treatment zone. In one embodiment, a first set of locations is positioned within a first cosmetic treatment zone and a second set of locations is positioned within a second cosmetic treatment zone, the first zone being different from the second zone. In one embodiment, the first cosmetic treatment zone includes a substantially linear sequence of the first set of locations and the second cosmetic treatment zone includes a substantially linear sequence of the second set of locations. In one embodiment, the transducer module is configured to apply ultrasonic therapy using amplitude modulation whereby a plurality of portions of the transducer module are configured to emit ultrasonic therapy at a plurality of amplitudes of acoustic intensity, wherein a first amplitude is different than a second amplitude. In one embodiment, the transducer module is configured to apply ultrasonic therapy phase shifting whereby a plurality of portions of the transducer module are configured to emit ultrasonic therapy at a plurality of phases of acoustic intensity, wherein a first phase is different than a second phase. In one embodiment, the transducer module is configured to apply ultrasonic therapy using amplitude modulation whereby a plurality of portions of the transducer module are configured to emit ultrasonic therapy at a plurality of amplitudes of acoustic intensity, wherein a first amplitude is different than a second amplitude. In one embodiment, the transducer module is configured to apply ultrasonic therapy phase shifting whereby a plurality of portions of the transducer module are configured to emit ultrasonic therapy at a plurality of phases of acoustic intensity, wherein a first phase is different than a second phase. In one embodiment, the plurality of phases includes discrete phase values. In one embodiment, the transducer module is configured to the transducer module includes piezoelectric material and the plurality of portions of the transducer module are configured to create a plurality of corresponding piezoelectric material variations in response to an electric field applied to the transducer module. In one embodiment, the plurality of piezoelectric material variations include at least one of expansion of the material and contraction of the material. In one embodiment, at least one portion of the transducer module is configured to emit ultrasonic therapy at two or more amplitudes of acoustic intensity, and wherein the amplitude of ultrasonic therapy emitted by the at least one portion of the transducer module varies over time. In one embodiment, the movement mechanism is configured to be programmed to provide variable spacing between a plurality of individual thermal cosmetic treatment zones. In one embodiment, a sequence of individual thermal cosmetic treatment zones has a treatment spacing in a range from about 0.01 mm to about 25 mm. In one embodiment, the first and second switches include user operated buttons or keys. In one embodiment, at least one of the first switch and the second switch is activated by the control module. In one embodiment, the treatment function is at least one of a face lift, a brow lift, a chin lift, an eye treatment, a wrinkle reduction, a scar reduction, a burn treatment, a tattoo removal, a skin tightening, a vein removal, a vein reduction, a treatment on a sweat gland, a treatment of hyperhidrosis, a sun spot removal, a fat treatment, a vaginal rejuvenation, and an acne treatment. In one embodiment, the transducer module is configured to provide an acoustic power of the ultrasonic therapy in a range of between about 1 W to about 100 W and a frequency of about 1 MHz to about 10 MHz to thermally heat the tissue to cause coagulation. 
     In one embodiment, a treatment system includes a controlling device operably controlling an ultrasonic treatment function for providing an ultrasonic treatment and a hand wand configured to direct ultrasonic treatment in a sequence of individual thermal cosmetic treatment zones. In one embodiment, the hand wand includes a transducer configured to apply ultrasonic therapy to tissue at a location at a focal depth, the location positioned within a thermal cosmetic treatment zone, wherein the transducer is further configured to apply ultrasonic therapy to tissue at a plurality of locations at the focal depth. 
     In one embodiment, a method of performing a cosmetic procedure includes coupling a transducer module with an ultrasonic probe, wherein the ultrasonic probe includes a first switch to control acoustic imaging, wherein the ultrasonic probe includes a second switch to control acoustic therapy for causing a plurality of individual cosmetic treatment zones, wherein the ultrasonic probe includes a movement mechanism to provide desired spacing between the individual cosmetic treatment zones. In one embodiment, the method includes contacting the transducer module with a subject&#39;s skin surface. In one embodiment, the method includes activating the first switch on the ultrasonic probe to acoustically image, with the transducer module, a region below the skin surface. In one embodiment, the method includes activating the second switch on the ultrasonic probe to acoustically treat, with the transducer module, the region below the skin surface in a desired sequence of individual cosmetic treatment zones that is controlled by the movement mechanism, wherein the transducer module includes an ultrasound transducer configured to apply ultrasonic therapy to tissue at a plurality of locations at a focal depth. 
     In one embodiment, a treatment system includes a controlling device operably controlling an ultrasonic treatment function for providing an ultrasonic treatment, and a hand wand configured to direct ultrasonic treatment in a sequence of individual thermal cosmetic treatment zones. In one embodiment, the hand wand includes a transducer configured to apply ultrasonic therapy to tissue at a plurality of locations at a focal depth. 
     In one embodiment, the use of an aesthetic imaging and treatment system is for the non-invasive cosmetic treatment of skin. 
     In accordance with various embodiments, an aesthetic ultrasound treatment system for creating multiple focus points with an ultrasound transducer includes an ultrasonic probe comprising an ultrasound transducer configured to apply ultrasonic therapy to tissue at a plurality of locations at a focal depth with at least one of the group consisting of amplitude modulation poling and phase shifting, and a control module coupled to the ultrasonic probe for controlling the ultrasound transducer. 
     In one embodiment, the ultrasound transducer comprises a single ultrasound transduction element. In one embodiment, the plurality of locations are positioned in a substantially linear sequence within a cosmetic treatment zone. In one embodiment, a first set of locations is positioned within a first cosmetic treatment zone and a second set of locations is positioned within a second cosmetic treatment zone, the first zone being different from the second zone. In one embodiment, the first cosmetic treatment zone comprises a substantially linear sequence of the first set of locations and the second cosmetic treatment zone comprises a substantially linear sequence of the second set of locations. 
     In one embodiment, the ultrasound transducer is configured to apply ultrasonic therapy using amplitude modulation whereby a plurality of portions of the ultrasound transducer are configured to emit ultrasonic therapy at a plurality of amplitudes of acoustic intensity, wherein a first amplitude is different than a second amplitude. In one embodiment, the ultrasound transducer is configured to apply ultrasonic therapy phase shifting whereby a plurality of portions of the ultrasound transducer are configured to emit ultrasonic therapy at a plurality of phases of acoustic intensity, wherein a first phase is different than a second phase. In one embodiment, the ultrasound transducer is configured to apply ultrasonic therapy using amplitude modulation whereby a plurality of portions of the ultrasound transducer are configured to emit ultrasonic therapy at a plurality of amplitudes of acoustic intensity, wherein a first amplitude is different than a second amplitude, and apply ultrasonic therapy phase shifting whereby a plurality of portions of the ultrasound transducer are configured to emit ultrasonic therapy at a plurality of phases of acoustic intensity, wherein a first phase is different than a second phase. In one embodiment, the plurality of phases comprises discrete phase values. In one embodiment, the ultrasound transducer comprises piezoelectric material and the plurality of portions of the ultrasound transducer are configured to create a plurality of corresponding piezoelectric material variations in response to an electric field applied to the ultrasound transducer. In one embodiment, the plurality of piezoelectric material variations comprise at least one of expansion of the piezoelectric material and contraction of the piezoelectric material. In one embodiment, at least one portion of the ultrasonic transducer is configured to emit ultrasonic therapy at two or more amplitudes of acoustic intensity, and wherein the amplitude of ultrasonic therapy emitted by the at least one portion of the piezoelectric varies over time. 
     In one embodiment, the system further includes a movement mechanism configured to be programmed to provide variable spacing between the plurality of individual cosmetic treatment zones. In one embodiment, a sequence of individual cosmetic treatment zones has a treatment spacing in a range from about 0.01 mm to about 25 mm. 
     In various embodiments, the ultrasonic treatment is at least one of a face lift, a brow lift, a chin lift, an eye treatment, a wrinkle reduction, a scar reduction, a burn treatment, a tattoo removal, a skin tightening, a vein removal, a vein reduction, a treatment on a sweat gland, a treatment of hyperhidrosis, a sun spot removal, a fat treatment, a vaginal rejuvenation, and an acne treatment. 
     In one embodiment, the ultrasonic transducer is configured to provide an acoustic power of the ultrasonic therapy in a range of between about 1 W to about 100 W and a frequency of about 1 MHz to about 10 MHz to thermally heat the tissue to cause coagulation. 
     In accordance with various embodiments, an aesthetic treatment system for use in cosmetic treatment for creating multiple focal points with an ultrasound transducer includes an ultrasonic probe that includes a first switch operably controlling an ultrasonic imaging function for providing an ultrasonic imaging, a second switch operably controlling an ultrasonic treatment function for providing an ultrasonic treatment, and a movement mechanism configured to direct ultrasonic treatment in at least one sequence of individual thermal cosmetic treatment zones. The system includes a transducer module configured to apply ultrasonic therapy with at least one of the group consisting of amplitude modulation poling and phase shifting, wherein the transducer module is configured for both ultrasonic imaging and ultrasonic treatment, wherein the transducer module is configured for coupling to the ultrasonic probe, wherein the transducer module comprises an ultrasound transducer configured to apply ultrasonic therapy to tissue at a plurality of locations at a focal depth, wherein the transducer module is configured to be operably coupled to at least one of the first switch, the second switch and the movement mechanism, and a control module, wherein the control module comprises a processor and a display for controlling the transducer module. 
     In one embodiment, the plurality of locations are positioned in a substantially linear sequence within a cosmetic treatment zone. In one embodiment, a first set of locations is positioned within a first cosmetic treatment zone and a second set of locations is positioned within a second cosmetic treatment zone, the first zone being different from the second zone. In one embodiment, the first cosmetic treatment zone comprises a substantially linear sequence of the first set of locations and the second cosmetic treatment zone comprises a substantially linear sequence of the second set of locations. 
     In one embodiment, the transducer module is configured to apply ultrasonic therapy using amplitude modulation whereby a plurality of portions of the transducer module are configured to emit ultrasonic therapy at a plurality of amplitudes of acoustic intensity, wherein a first amplitude is different than a second amplitude. In one embodiment, the transducer module is configured to apply ultrasonic therapy phase shifting whereby a plurality of portions of the transducer module are configured to emit ultrasonic therapy at a plurality of phases of acoustic intensity, wherein a first phase is different than a second phase. In one embodiment, the transducer module is configured to apply ultrasonic therapy using amplitude modulation whereby a plurality of portions of the transducer module are configured to emit ultrasonic therapy at a plurality of amplitudes of acoustic intensity, wherein a first amplitude is different than a second amplitude, and apply ultrasonic therapy phase shifting whereby a plurality of portions of the transducer module are configured to emit ultrasonic therapy at a plurality of phases of acoustic intensity, wherein a first phase is different than a second phase. In one embodiment, the plurality of phases comprises discrete phase values. In one embodiment, the transducer module comprises piezoelectric material and the plurality of portions of the transducer module are configured to create a plurality of corresponding piezoelectric material variations in response to an electric field applied to the transducer module. In one embodiment, the plurality of piezoelectric material variations comprise at least one of expansion of the material and contraction of the material. In one embodiment, at least one portion of the transducer module is configured to emit ultrasonic therapy at two or more amplitudes of acoustic intensity, and wherein the amplitude of ultrasonic therapy emitted by the at least one portion of the transducer module varies over time. 
     In one embodiment, the movement mechanism is configured to be programmed to provide variable spacing between a plurality of individual thermal cosmetic treatment zones. In one embodiment, a sequence of individual thermal cosmetic treatment zones has a treatment spacing in a range from about 0.01 mm to about 25 mm. In one embodiment, the first and second switches comprises user operated buttons or keys. In one embodiment, at least one of the first switch and the second switch is activated by the control module. 
     In one embodiment, the treatment function is at least one of a face lift, a brow lift, a chin lift, an eye treatment, a wrinkle reduction, a scar reduction, a burn treatment, a tattoo removal, a skin tightening, a vein removal, a vein reduction, a treatment on a sweat gland, a treatment of hyperhidrosis, a sun spot removal, a fat treatment, a vaginal rejuvenation, and an acne treatment. 
     In one embodiment, the transducer module is configured to provide an acoustic power of the ultrasonic therapy in a range of between about 1 W to about 100 W and a frequency of about 1 MHz to about 10 MHz to thermally heat the tissue to cause coagulation. 
     In accordance with various embodiments, a treatment system includes a controlling device operably controlling an ultrasonic treatment function for providing an ultrasonic treatment, and a hand wand configured to direct ultrasonic treatment in a sequence of individual thermal cosmetic treatment zones. The hand wand includes a transducer configured to apply ultrasonic therapy to tissue at a location at a focal depth, the location positioned within a thermal cosmetic treatment zone, wherein the transducer is further configured to apply ultrasonic therapy to tissue at a plurality of locations at the focal depth. 
     In accordance with various embodiments, a method of performing a noninvasive cosmetic procedure on the skin by creating multiple focal points with a single transducer includes coupling a transducer module with an ultrasonic probe, wherein the ultrasonic probe comprises a first switch to control acoustic imaging, wherein the ultrasonic probe comprises a second switch to control acoustic therapy for causing a plurality of individual cosmetic treatment zones, wherein the ultrasonic probe comprises a movement mechanism to provide desired spacing between the individual cosmetic treatment zones, contacting the transducer module with a subject&#39;s skin surface, activating the first switch on the ultrasonic probe to acoustically image, with the transducer module, a region below the skin surface, and activating the second switch on the ultrasonic probe to acoustically treat, with the transducer module, the region below the skin surface in a desired sequence of individual cosmetic treatment zones that is controlled by the movement mechanism, wherein the transducer module comprises a single ultrasound transducer configured to apply ultrasonic therapy to tissue at a plurality of locations at a focal depth. 
     In accordance with various embodiments, an aesthetic treatment system for creating multiple focal points in tissue with an ultrasound transducer includes a controlling device operably controlling an ultrasonic treatment function for providing an ultrasonic treatment, and a hand wand configured to direct ultrasonic treatment in a sequence of individual thermal cosmetic treatment zones. The hand wand includes a transducer configured to apply ultrasonic therapy to tissue at a plurality of locations at a focal depth. In accordance with various embodiments, the use of an aesthetic treatment system is for the non-invasive cosmetic treatment of skin. 
     In accordance with various embodiments, an aesthetic ultrasound treatment system for creating multiple focus points with an ultrasound transducer includes an ultrasonic probe comprising an ultrasound transducer configured to apply ultrasonic therapy to tissue at a plurality of locations at a focal depth with at least one of the group consisting of amplitude modulation poling and phase shifting, and a control module coupled to the ultrasonic probe for controlling the ultrasound transducer. In one embodiment, the ultrasound transducer is configured to apply ultrasonic therapy using amplitude modulation whereby a plurality of portions of the ultrasound transducer are configured to emit ultrasonic therapy at a plurality of amplitudes of acoustic intensity, wherein a first amplitude is different than a second amplitude. In one embodiment, the ultrasound transducer is configured to apply ultrasonic therapy phase shifting whereby a plurality of portions of the ultrasound transducer are configured to emit ultrasonic therapy at a plurality of phases of acoustic intensity, wherein a first phase is different than a second phase. In one embodiment, the ultrasound transducer is configured to apply ultrasonic therapy using amplitude modulation whereby a plurality of portions of the ultrasound transducer are configured to emit ultrasonic therapy at a plurality of amplitudes of acoustic intensity, wherein a first amplitude is different than a second amplitude, and apply ultrasonic therapy phase shifting whereby a plurality of portions of the ultrasound transducer are configured to emit ultrasonic therapy at a plurality of phases of acoustic intensity, wherein a first phase is different than a second phase. In one embodiment, the plurality of phases comprises discrete phase values. In one embodiment, the ultrasound transducer comprises piezoelectric material and the plurality of portions of the ultrasound transducer are configured to create a plurality of corresponding piezoelectric material variations in response to an electric field applied to the ultrasound transducer. In one embodiment, the plurality of piezoelectric material variations comprise at least one of expansion of the piezoelectric material and contraction of the piezoelectric material. In one embodiment, at least one portion of the ultrasonic transducer is configured to emit ultrasonic therapy at two or more amplitudes of acoustic intensity, and wherein the amplitude of ultrasonic therapy emitted by the at least one portion of the piezoelectric varies over time. In various embodiments, the ultrasonic treatment is at least one of a face lift, a brow lift, a chin lift, an eye treatment, a wrinkle reduction, a scar reduction, a burn treatment, a tattoo removal, a skin tightening, a vein removal, a vein reduction, a treatment on a sweat gland, a treatment of hyperhidrosis, a sun spot removal, a fat treatment, a vaginal rejuvenation, and an acne treatment. 
     In accordance with various embodiments, an aesthetic treatment system for use in cosmetic treatment for creating multiple focal points with an ultrasound transducer includes an ultrasonic probe that includes a first switch operably controlling an ultrasonic imaging function for providing an ultrasonic imaging, a second switch operably controlling an ultrasonic treatment function for providing an ultrasonic treatment, and a movement mechanism configured to direct ultrasonic treatment in at least one sequence of individual thermal cosmetic treatment zones. The system includes a transducer module configured to apply ultrasonic therapy with at least one of the group consisting of amplitude modulation poling and phase shifting, wherein the transducer module is configured for both ultrasonic imaging and ultrasonic treatment, wherein the transducer module is configured for coupling to the ultrasonic probe, wherein the transducer module comprises an ultrasound transducer configured to apply ultrasonic therapy to tissue at a plurality of locations at a focal depth, wherein the transducer module is configured to be operably coupled to at least one of the first switch, the second switch and the movement mechanism, and a control module, wherein the control module comprises a processor and a display for controlling the transducer module. In one embodiment, the ultrasound module comprises a single ultrasound transducer. In one embodiment, the ultrasound module comprises a single ultrasound transduction element. In one embodiment, the ultrasound module comprises a single ultrasound transducer comprising a single transduction element. In one embodiment, the plurality of locations are positioned in a substantially linear sequence within a cosmetic treatment zone. In one embodiment, a first set of locations is positioned within a first cosmetic treatment zone and a second set of locations is positioned within a second cosmetic treatment zone, the first zone being different from the second zone. In one embodiment, the first cosmetic treatment zone comprises a substantially linear sequence of the first set of locations and the second cosmetic treatment zone comprises a substantially linear sequence of the second set of locations. In one embodiment, the transducer module is configured to apply ultrasonic therapy using amplitude modulation whereby a plurality of portions of the transducer module are configured to emit ultrasonic therapy at a plurality of amplitudes of acoustic intensity, wherein a first amplitude is different than a second amplitude. In one embodiment, the transducer module is configured to apply ultrasonic therapy phase shifting whereby a plurality of portions of the transducer module are configured to emit ultrasonic therapy at a plurality of phases of acoustic intensity, wherein a first phase is different than a second phase. In one embodiment, the transducer module is configured to apply ultrasonic therapy using amplitude modulation whereby a plurality of portions of the transducer module are configured to emit ultrasonic therapy at a plurality of amplitudes of acoustic intensity, wherein a first amplitude is different than a second amplitude, and apply ultrasonic therapy phase shifting whereby a plurality of portions of the transducer module are configured to emit ultrasonic therapy at a plurality of phases of acoustic intensity, wherein a first phase is different than a second phase. In one embodiment, the plurality of phases comprises discrete phase values. In one embodiment, the transducer module comprises piezoelectric material and the plurality of portions of the transducer module are configured to create a plurality of corresponding piezoelectric material variations in response to an electric field applied to the transducer module. In one embodiment, the plurality of piezoelectric material variations comprise at least one of expansion of the material and contraction of the material. In one embodiment, at least one portion of the transducer module is configured to emit ultrasonic therapy at two or more amplitudes of acoustic intensity, and wherein the amplitude of ultrasonic therapy emitted by the at least one portion of the transducer module varies over time. In one embodiment, the movement mechanism is configured to be programmed to provide variable spacing between a plurality of individual thermal cosmetic treatment zones. In one embodiment, a sequence of individual thermal cosmetic treatment zones has a treatment spacing in a range from about 0.01 mm to about 25 mm. In one embodiment, the first and second switches comprises user operated buttons or keys. In one embodiment, at least one of the first switch and the second switch is activated by the control module. In one embodiment, the treatment function is at least one of a face lift, a brow lift, a chin lift, an eye treatment, a wrinkle reduction, a scar reduction, a burn treatment, a tattoo removal, a skin tightening, a vein removal, a vein reduction, a treatment on a sweat gland, a treatment of hyperhidrosis, a sun spot removal, a fat treatment, a vaginal rejuvenation, and an acne treatment. 
     In one embodiment, an aesthetic imaging and treatment system for use in cosmetic treatment includes an ultrasonic probe configured for ultrasonic imaging and ultrasonic treatment of tissue at a plurality of locations at a focal depth. In one embodiment, the probe includes a transducer module configured for coupling to the ultrasonic probe, wherein the transducer module comprises an ultrasound transducer configured to apply an ultrasonic therapy to tissue at the plurality of locations at the focal depth. In one embodiment, a first switch operably controlling an ultrasonic imaging function for providing an ultrasonic imaging. In one embodiment, a second switch operably controlling an ultrasonic treatment function for providing the ultrasonic therapy. In one embodiment, a movement mechanism is configured to direct ultrasonic treatment in at least one sequence of individual thermal cosmetic treatment zones, wherein the transducer module is configured to be operably coupled to at least one of the first switch, the second switch and the movement mechanism. In one embodiment, the control module comprises a processor and a display for controlling the transducer module. In one embodiment, the module is removable. For example, some non-limiting embodiments transducers can be configured for a tissue depth of 1.5 mm, 3 mm, 4.5 mm, 6 mm, less than 3 mm, between 1.5 mm and 3 mm, between 1.5 mm and 4.5 mm, more than more than 4.5 mm, more than 6 mm, and anywhere in the ranges of 0.1 mm-3 mm, 0.1 mm-4.5 mm, 0.1 mm-25 mm, 0.1 mm-100 mm, and any depths therein. 
     In various embodiments, the plurality of locations are positioned in a substantially linear sequence within a cosmetic treatment zone. In one embodiment, a first set of locations is positioned within a first cosmetic treatment zone and a second set of locations is positioned within a second cosmetic treatment zone, the first zone being different from the second zone. In one embodiment, the first cosmetic treatment zone comprises a substantially linear sequence of the first set of locations and the second cosmetic treatment zone comprises a substantially linear sequence of the second set of locations. In one embodiment, the transducer module is configured to apply ultrasonic therapy using amplitude modulation whereby the transducer module comprises a plurality of portions that are configured to emit ultrasonic therapy at a plurality of amplitudes of acoustic intensity, wherein a first amplitude is different than a second amplitude. In one embodiment, the transducer module is configured to apply ultrasonic therapy phase shifting whereby the transducer module comprises a plurality of portions that are configured to emit ultrasonic therapy at a plurality of phases of acoustic intensity, wherein a first phase is different than a second phase. 
     In one embodiment, a movement mechanism is a motion mechanism. In various embodiments, a movement mechanism is configured to move a transducer within a module or a probe. In one embodiment, a transducer is held by a transducer holder. In one embodiment, the transducer holder includes a sleeve which is moved along motion constraining bearings, such as linear bearings, namely, a bar (or shaft) to ensure a repeatable linear movement of the transducer. In one embodiment, sleeve is a spline bushing which prevents rotation about a spline shaft, but any guide to maintain the path of motion is appropriate. 
     In one embodiment, the transducer holder is driven by a motion mechanism, which may be located in a hand wand or in a module, or in a probe. In one embodiment, a motion mechanism  400  includes any one or more of a scotch yoke, a movement member, and a magnetic coupling. In one embodiment, the magnetic coupling helps move the transducer. One benefit of a motion mechanism is that it provides for a more efficient, accurate and precise use of an ultrasound transducer, for imaging and/or therapy purposes. One advantage this type of motion mechanism has over conventional fixed arrays of multiple transducers fixed in space in a housing is that the fixed arrays are a fixed distance apart. 
     By placing transducer on a track (e.g., such as a linear track) under controller control, embodiments of the system and device provide for adaptability and flexibility in addition to efficiency, accuracy and precision. Real time and near real time adjustments can be made to imaging and treatment positioning along the controlled motion by the motion mechanism. In addition to the ability to select nearly any resolution based on the incremental adjustments made possible by the motion mechanism, adjustments can be made if imaging detects abnormalities or conditions meriting a change in treatment spacing and targeting. In one embodiment, one or more sensors may be included in the module. In one embodiment, one or more sensors may be included in the module to ensure that a mechanical coupling between the movement member and the transducer holder is indeed coupled. In one embodiment, an encoder may be positioned on top of the transducer holder and a sensor may be located in a portion of the module, or vice versa (swapped). 
     In various embodiments the sensor is a magnetic sensor, such as a giant magnetoresistive effect (GMR) or Hall Effect sensor, and the encoder a magnet, collection of magnets, or multi-pole magnetic strip. The sensor may be positioned as a transducer module home position. In one embodiment, the sensor is a contact pressure sensor. In one embodiment, the sensor is a contact pressure sensor on a surface of the device to sense the position of the device or the transducer on the patient. In various embodiments, the sensor can be used to map the position of the device or a component in the device in one, two, or threes dimensions. In one embodiment the sensor is configured to sense the position, angle, tilt, orientation, placement, elevation, or other relationship between the device (or a component therein) and the patient. In one embodiment, the sensor comprises an optical sensor. In one embodiment, the sensor comprises a roller ball sensor. In one embodiment, the sensor is configured to map a position in one, two and/or three dimensions to compute a distance between areas or lines of treatment on the skin or tissue on a patient. 
     Motion mechanism can be any motion mechanism that may be found to be useful for movement of the transducer. Other embodiments of motion mechanisms useful herein can include worm gears and the like. In various embodiments, the motion mechanism is located in a module  200 . In various embodiments, the motion mechanism can provide for linear, rotational, multi-dimensional motion or actuation, and the motion can include any collection of points and/or orientations in space. Various embodiments for motion can be used in accordance with several embodiments, including but not limited to rectilinear, circular, elliptical, arc-like, spiral, a collection of one or more points in space, or any other 1-D, 2-D, or 3-D positional and attitudinal motional embodiments. The speed of the motion mechanism may be fixed or may be adjustably controlled by a user. One embodiment, a speed of the motion mechanism for an image sequence may be different than that for a treatment sequence. In one embodiment, the speed of the motion mechanism is controllable by a controller. 
     In various embodiments, the transducer module is configured to apply ultrasonic therapy using amplitude modulation whereby the transducer module comprises a plurality of portions that are configured to emit ultrasonic therapy at a plurality of amplitudes of acoustic intensity, wherein a first amplitude is different than a second amplitude, and apply ultrasonic therapy phase shifting whereby the transducer module comprises a plurality of portions that are configured to emit ultrasonic therapy at a plurality of phases of acoustic intensity, wherein a first phase is different than a second phase. 
     In one embodiment, the plurality of phases comprises discrete phase values. In one embodiment, the transducer module comprises piezoelectric material and the plurality of portions of the transducer module are configured to create a plurality of corresponding piezoelectric material variations in response to an electric field applied to the transducer module. In one embodiment, the plurality of piezoelectric material variations comprise at least one of expansion of the material and contraction of the material. In one embodiment, the transducer module comprises at least one portion that is configured to emit ultrasonic therapy at two or more amplitudes of acoustic intensity, and wherein the amplitude of ultrasonic therapy emitted by the at least one portion of the transducer module varies over time. 
     In one embodiment, the movement mechanism is configured to be programmed to provide variable spacing between a plurality of individual thermal cosmetic treatment zones. In one embodiment, a sequence of individual thermal cosmetic treatment zones has a treatment spacing in a range from about 0.01 mm to about 25 mm (e.g., 1 mm, 1.5 mm, 2 mm, 1-5 mm). In one embodiment, the first and second switches comprise user operated buttons or keys. In one embodiment, at least one of the first switch and the second switch is activated by the control module. 
     In various embodiments, the treatment function is at least one of a face lift, a brow lift, a chin lift, an eye treatment, a wrinkle reduction, a scar reduction, a burn treatment, a tattoo removal, a skin tightening, a vein removal, a vein reduction, a treatment on a sweat gland, a treatment of hyperhidrosis, a sun spot removal, a fat treatment, a vaginal rejuvenation, and an acne treatment. In one embodiment, the transducer module is configured to provide an acoustic power of the ultrasonic therapy in a range of between about 1 W to about 100 W (e.g., 5-40 W, 10-50 W, 25-35 W) and a frequency of about 1 MHz to about 10 MHz to thermally heat the tissue to cause coagulation. In one embodiment, the acoustic power can be from a range of 1 W to about 100 W in a frequency range from about 1 MHz to about 12 MHz (e.g., 4 MHz, 7 MHz, 10 MHz, 4-10 MHz), or from about 10 W to about 50 W at a frequency range from about 3 MHz to about 8 MHz. In one embodiment, the acoustic power and frequencies are about 40 W at about 4.3 MHz and about 30 W at about 7.5 MHz. An acoustic energy produced by this acoustic power can be between about 0.01 joule (“J”) to about 10 J or about 2 J to about 5 J. In one embodiment, the acoustic energy is in a range less than about 3 J. 
     In various embodiments, a multi-focus ultrasound treatment system includes a controlling device operably controlling an ultrasonic treatment function for providing an ultrasonic treatment and a hand wand configured to direct ultrasonic treatment in a sequence of individual thermal cosmetic treatment zones. The hand wand includes a transducer configured to apply ultrasonic therapy to tissue at a location at a focal depth, the location positioned within a thermal cosmetic treatment zone, wherein the transducer is further configured to apply ultrasonic therapy to tissue simultaneously at a plurality of locations at the focal depth. 
     In various embodiments, an aesthetic imaging and multi-focus treatment system includes an ultrasonic probe comprising an ultrasound transducer configured to apply ultrasonic therapy to tissue at a plurality of locations at a focal depth with at least one of the group consisting of amplitude modulation poling and phase shifting, and a control module coupled to the ultrasonic probe for controlling the ultrasound transducer. In one embodiment, the plurality of locations are positioned in a substantially linear sequence within a cosmetic treatment zone. In one embodiment, a first set of locations is positioned within a first cosmetic treatment zone and a second set of locations is positioned within a second cosmetic treatment zone, the first zone being different from the second zone. In one embodiment, the first cosmetic treatment zone comprises a substantially linear sequence of the first set of locations and the second cosmetic treatment zone comprises a substantially linear sequence of the second set of locations. In one embodiment, the ultrasound transducer is configured to apply ultrasonic therapy using amplitude modulation whereby the ultrasound transducer comprises a plurality of portions that are configured to emit ultrasonic therapy at a plurality of amplitudes of acoustic intensity, wherein a first amplitude is different than a second amplitude. In one embodiment, the ultrasound transducer is configured to apply ultrasonic therapy phase shifting whereby the ultrasound transducer comprises a plurality of portions that are configured to emit ultrasonic therapy at a plurality of phases of acoustic intensity, wherein a first phase is different than a second phase. In one embodiment, the ultrasound transducer is configured to apply ultrasonic therapy using amplitude modulation whereby the ultrasound transducer comprises a plurality of portions that are configured to emit ultrasonic therapy at a plurality of amplitudes of acoustic intensity, wherein a first amplitude is different than a second amplitude, and apply ultrasonic therapy phase shifting whereby the ultrasound transducer comprises a plurality of portions that are configured to emit ultrasonic therapy at a plurality of phases of acoustic intensity, wherein a first phase is different than a second phase. In one embodiment, the plurality of phases comprises discrete phase values. 
     In one embodiment, the ultrasound transducer comprises piezoelectric material and the plurality of portions of the ultrasound transducer are configured to create a plurality of corresponding piezoelectric material variations in response to an electric field applied to the ultrasound transducer. In one embodiment, the plurality of piezoelectric material variations comprise at least one of expansion of the piezoelectric material and contraction of the piezoelectric material. In one embodiment, the ultrasonic transducer comprises at least one portion that is configured to emit ultrasonic therapy at two or more amplitudes of acoustic intensity, and wherein the amplitude of ultrasonic therapy emitted by the at least one portion of the piezoelectric varies over time. In one embodiment, the system also includes a movement mechanism configured to be programmed to provide variable spacing between the plurality of individual cosmetic treatment zones. In one embodiment, a sequence of individual cosmetic treatment zones has a treatment spacing in a range from about 0.01 mm to about 25 mm. In one embodiment, the ultrasonic treatment is at least one of a face lift, a brow lift, a chin lift, an eye treatment, a wrinkle reduction, a scar reduction, a burn treatment, a tattoo removal, a skin tightening, a vein removal, a vein reduction, a treatment on a sweat gland, a treatment of hyperhidrosis, a sun spot removal, a fat treatment, a vaginal rejuvenation, and an acne treatment. In one embodiment, the ultrasonic transducer is configured to provide an acoustic power of the ultrasonic therapy in a range of between about 1 W to about 100 W and a frequency of about 1 MHz to about 10 MHz to thermally heat the tissue to cause coagulation. 
     In various embodiments, a treatment system includes a controlling device operably controlling an ultrasonic treatment function for providing an ultrasonic treatment, and a hand wand configured to direct ultrasonic treatment in a sequence of individual thermal cosmetic treatment zones. In one embodiment, the hand wand includes a transducer configured to simultaneously apply ultrasonic therapy to tissue at a plurality of locations at a focal depth. 
     In various embodiments, a system of performing a cosmetic procedure that is not performed by a doctor, includes an ultrasonic probe comprising a transducer module. In one embodiment, the transducer module comprises an ultrasound transducer configured to apply ultrasonic therapy to tissue at a plurality of locations at a focal depth with at least one of the group consisting of amplitude modulation poling and phase shifting. In one embodiment, the ultrasonic probe comprises a first switch to control acoustic imaging, the ultrasonic probe comprises a second switch to control acoustic therapy for causing a plurality of individual cosmetic treatment zones, and the ultrasonic probe comprises a movement mechanism to provide desired spacing between the individual cosmetic treatment zones. 
     In various embodiments, aesthetic imaging and treatment system for use in cosmetic treatment, includes an ultrasonic probe. In one embodiment, a transducer module includes an ultrasound transducer configured to apply ultrasonic therapy through an aperture in an acoustically transparent member to form a thermal coagulation point (TCP) at a focal depth in tissue. In one embodiment, a first switch operably controls an ultrasonic imaging function for providing an ultrasonic imaging, a second switch operably controls an ultrasonic treatment function for providing an ultrasonic treatment, and a movement mechanism is configured to direct ultrasonic treatment in at least one sequence of individual thermal cosmetic treatment zones. In various embodiments, the transducer module is configured for both ultrasonic imaging and ultrasonic treatment, the transducer module is configured for coupling to the ultrasonic probe, the transducer module is configured to be operably coupled to at least one of the first switch, the second switch and the movement mechanism. In one embodiment, a control module comprises a processor and a display for controlling the transducer module. 
     In one embodiment, the plurality of locations are positioned in a substantially linear sequence within a cosmetic treatment zone. In one embodiment, a first set of locations is positioned within a first cosmetic treatment zone and a second set of locations is positioned within a second cosmetic treatment zone, the first zone being different from the second zone. In one embodiment, the first cosmetic treatment zone comprises a substantially linear sequence of the first set of locations and the second cosmetic treatment zone comprises a substantially linear sequence of the second set of locations. In one embodiment, the movement mechanism is configured to provide fixed spacing between a plurality of individual thermal cosmetic treatment zones. In one embodiment, a sequence of individual thermal cosmetic treatment zones has a treatment spacing in a range from about 0.01 mm to about 25 mm. In one embodiment, the first and second switches comprises user operated buttons or keys. In one embodiment, the treatment function is at least one of a face lift, a brow lift, a chin lift, an eye treatment, a wrinkle reduction, a scar reduction, a burn treatment, a tattoo removal, a skin tightening, a vein removal, a vein reduction, a treatment on a sweat gland, a treatment of hyperhidrosis, a sun spot removal, a fat treatment, a vaginal rejuvenation, and an acne treatment. In one embodiment, the transducer module is configured to provide an acoustic power of the ultrasonic therapy in a range of between about 1 W to about 100 W and a frequency of about 1 MHz to about 10 MHz to thermally heat the tissue to cause coagulation. 
     In various embodiments, a cosmetic treatment system includes a controlling device operably controlling an ultrasonic treatment function for providing an ultrasonic treatment to different depths below a skin surface, and a hand wand configured to direct ultrasonic treatment at two or more focal depths below the skin surface, the hand wand configured to connect at least two interchangeable transducer modules configured to apply the ultrasonic treatment to said two or more focal depths below the skin surface, wherein each of the transducer modules is configured to create one or more sequences of thermal coagulation points (TCPs). 
     In one embodiment, the system also includes an imaging transducer configured to provide images of at least one depth below the skin surface. In one embodiment, the system also includes a movement mechanism to place the sequence of individual discrete lesions in a linear sequence. In one embodiment, the transducer modules comprise at least one transducer module that is configured to provide ultrasound therapy in a range of between about 1 W to about 100 W and a frequency of about 1 MHz to about 10 MHz. In one embodiment, the transducer modules comprises one transducer module that is configured to provide therapy at a depth of 3 mm. In one embodiment, the transducer modules comprise one transducer module that is configured to provide therapy at a depth of 4.5 mm. 
     In one embodiment, the at least two interchangeable transducer modules comprise a first interchangeable transducer module that is configured to treat at a first focal depth below the skin surface with a first therapeutic transduction element, wherein the at least two interchangeable transducer modules comprise a second interchangeable transducer module that is configured to treat at a second focal depth below the skin surface with a second therapeutic transduction element, wherein the hand wand is configured to connect to one of the first interchangeable transducer module and the second interchangeable transducer module at a time, wherein the system further comprises a display to show a first image of the first focal depth below the skin surface and a second image of the second focal depth below the skin surface. 
     In one embodiment, the hand wand is configured to connect to one of the at least two interchangeable transducer modules at a time, the at least two interchangeable transducer modules comprise a first module that is configured to treat at a first focal depth below the skin surface with a single first ultrasound therapy element, and a second module that is configured to treat at a second focal depth below the skin surface with a single second ultrasound therapy element. In one embodiment, the creation of the one or more sequences of thermal coagulation points (TCPs) comprises the creation of multiple linear sequences of thermal coagulation points (TCPs). 
     In one embodiment, an imaging transducer is configured to provide images of at least one depth below the skin surface, wherein the individual thermal cosmetic treatment zones are individual discrete lesions, and further comprising a movement mechanism to place the sequence of individual discrete lesions in a linear sequence, wherein the transducer modules comprise at least one transducer module that is configured to provide ultrasound therapy in a range of between about 1 W to about 100 W and a frequency of about 1 MHz to about 10 MHz, wherein the transducer modules comprise one transducer module that is configured to provide therapy at a depth of 3 mm or 4.5 mm, and wherein the treatment function is at least one of a face lift, a brow lift, a chin lift, an eye treatment, a wrinkle reduction, a scar reduction, a burn treatment, a tattoo removal, a skin tightening, a vein removal, a vein reduction, a treatment on a sweat gland, a treatment of hyperhidrosis, a sun spot removal, a fat treatment, a vaginal rejuvenation, and an acne treatment. 
     In several of the embodiments described herein, the procedure is entirely cosmetic and not a medical act. For example, in one embodiment, the methods described herein need not be performed by a doctor, but at a spa or other aesthetic institute. In some embodiments, a system can be used for the non-invasive cosmetic treatment of skin. 
     The methods summarized above and set forth in further detail below describe certain actions taken by a practitioner; however, it should be understood that they can also include the instruction of those actions by another party. Thus, actions such as “coupling a transducer module with an ultrasonic probe” include “instructing the coupling of a transducer module with an ultrasonic probe.” 
     Further, areas of applicability will become apparent from the description provided herein. It should be understood that the description and specific examples are intended for purposes of illustration only and are not intended to limit the scope of the embodiments disclosed herein. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The drawings described herein are for illustration purposes only and are not intended to limit the scope of the present disclosure in any way. Embodiments of the present invention will become more fully understood from the detailed description and the accompanying drawings wherein: 
         FIG.  1    is a schematic illustration of an ultrasound system according to various embodiments of the present invention. 
         FIG.  2    is a schematic illustration of an ultrasound system coupled to a region of interest according to various embodiments of the present invention. 
         FIG.  3    is a schematic partial cut away illustration of a portion of a transducer according to various embodiments of the present invention. 
         FIG.  4    is a partial cut away side view of an ultrasound system according to various embodiments of the present invention. 
         FIGS.  5 A- 5 D  are plots illustrating time delays for reaching a focal point for various transducers according to several embodiments of the present invention. 
         FIGS.  6 A- 6 C  are plots illustrating phase delays for reaching a focal point for various transducers according to several embodiments of the present invention. 
         FIGS.  7 A- 7 C  are plots illustrating quantized phase delays for reaching a focal point for various transducers according to several embodiments of the present invention. 
         FIGS.  8 A- 8 B  are plots illustrating quantized phase delay profiles for reaching a focal point for various transducers according to several embodiments of the present invention. 
         FIG.  9    is a schematic illustration of characteristics of poled piezoelectric material according to an embodiment of the present invention. 
         FIGS.  10 A- 10 B  are plots illustrating approximations of amplitude modulation according to several embodiments of the present invention. 
         FIGS.  11 A- 11 H  are schematic illustrations and plots illustrating modulation functions and corresponding intensity distributions according to several embodiments of the present invention. 
         FIGS.  12 A- 12 D  are plots illustrating modulation functions and corresponding intensity distributions according to several embodiments of the present invention. 
         FIG.  13    is a schematic illustration of a two-phase system according to an embodiment of the present invention. 
         FIG.  14    is a schematic illustration of a selectable, four-phase system according to an embodiment of the present invention. 
         FIG.  15    is a plot illustrating performance of a discrete-phase system according to an embodiment of the present invention. 
         FIGS.  16 A- 16 B  are plots illustrating performance of discrete-phase systems at various foci according to several embodiments of the present invention. 
         FIGS.  17 A- 17 D  are schematic illustrations of hybrid systems and plots illustrating their performance according to several embodiments of the present invention. 
         FIG.  18    is a schematic illustration of a two-phase switchable system according to an embodiment of the present invention. 
         FIGS.  19 A- 19 C  are plots of an intensity distribution before focus according to an embodiment of the present invention. 
         FIGS.  20 A- 20 C  are plots an intensity distribution at focus according to an embodiment of the present invention. 
         FIG.  21    is a schematic illustration of an amplitude modulation aperture pattern according to an embodiment of the present invention. 
         FIGS.  22 A- 22 C  are plots of an intensity distribution from an amplitude modulated aperture before focus according to an embodiment of the present invention. 
         FIGS.  23 A- 23 C  are plots of an intensity distribution from an amplitude modulated aperture at focus according to an embodiment of the present invention. 
         FIG.  24    is a schematic illustration of an amplitude modulated aperture pattern with changing states according to an embodiment of the present invention. 
         FIGS.  25 A- 25 D  are plots of an intensity distribution from an amplitude modulated aperture with changing states before focus according to an embodiment of the present invention. 
         FIGS.  26 A- 26 C  are plots of an intensity distribution from an amplitude modulated aperture with changing states at focus according to an embodiment of the present invention. 
         FIG.  27 A  is a schematic illustration of an amplitude modulated aperture with two changing levels according to an embodiment of the present invention. 
         FIG.  27 B  is a state transition table of the schematic of  FIG.  27 A  according to an embodiment of the present invention. 
         FIG.  28 A  is a schematic illustration of an amplitude modulated aperture with three changing levels according to an embodiment of the present invention. 
         FIG.  28 B  is a state transition table of the schematic of  FIG.  28 A  according to an embodiment of the present invention. 
         FIG.  29 A  is a schematic illustration of an amplitude modulated aperture with four changing levels according to an embodiment of the present invention. 
         FIG.  29 B  is a state transition table of the schematic of  FIG.  29 A  according to an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     The following description sets forth examples of embodiments, and is not intended to limit the present invention or its teachings, applications, or uses thereof. It should be understood that throughout the drawings, corresponding reference numerals indicate like or corresponding parts and features. The description of specific examples indicated in various embodiments of the present invention are intended for purposes of illustration only and are not intended to limit the scope of the invention disclosed herein. Moreover, recitation of multiple embodiments having stated features is not intended to exclude other embodiments having additional features or other embodiments incorporating different combinations of the stated features. Further, features in one embodiment (such as in one figure) may be combined with descriptions (and figures) of other embodiments. 
     In various embodiments, systems and methods for ultrasound treatment of tissue are configured to provide cosmetic treatment. In various embodiments, tissue below or even at a skin surface such as epidermis, dermis, fascia, muscle, fat, and superficial muscular aponeurotic system (“SMAS”), are treated non-invasively with ultrasound energy. The ultrasound energy can be focused at one or more treatment points, can be unfocused and/or defocused, and can be applied to a region of interest containing at least one of epidermis, dermis, hypodermis, fascia, muscle, fat and SMAS to achieve a cosmetic and/or therapeutic effect. In various embodiments, systems and/or methods provide non-invasive dermatological treatment to tissue through thermal treatment, coagulation, ablation, and/or tightening. In several embodiments disclosed herein, non-invasive ultrasound is used to achieve one or more of the following effects: a face lift, a brow lift, a chin lift, an eye treatment, a wrinkle reduction, a scar reduction, a burn treatment, a tattoo removal, a vein removal, a vein reduction, a treatment on a sweat gland, a treatment of hyperhidrosis, sun spot removal, an acne treatment, and a pimple removal. In one embodiment, fat reduction is achieved. In one embodiment, décolletage is treated. In some embodiments, two, three or more beneficial effects are achieved during the same treatment session, and may be achieved simultaneously. In another embodiment, the device may be used on adipose tissue (e.g., fat). In another embodiment the system, device and/or method may be applied in the genital area (e.g., a vagina for vaginal rejuvenation and/or vaginal tightening, such as for tightening the supportive tissue of the vagina). 
     Various embodiments of the present invention relate to devices or methods of controlling the delivery of energy to tissue. In various embodiments, various forms of energy can include acoustic, ultrasound, light, laser, radio-frequency (RF), microwave, electromagnetic, radiation, thermal, cryogenic, electron beam, photon-based, magnetic, magnetic resonance, and/or other energy forms. Various embodiments of the present invention relate to devices or methods of splitting an ultrasonic energy beam into multiple beams. In various embodiments, devices or methods can be used to alter the delivery of ultrasound acoustic energy in any procedures such as, but not limited to, therapeutic ultrasound, diagnostic ultrasound, non-destructive testing (NDT) using ultrasound, ultrasonic welding, any application that involves coupling mechanical waves to an object, and other procedures. Generally, with therapeutic ultrasound, a tissue effect is achieved by concentrating the acoustic energy using focusing techniques from the aperture. In some instances, high intensity focused ultrasound (HIFU) is used for therapeutic purposes in this manner. In one embodiment, a tissue effect created by application of therapeutic ultrasound at a particular depth to can be referred to as creation of a thermal coagulation point (TCP). It is through creation of TCPs at particular positions that thermal and/or mechanical ablation of tissue can occur non-invasively or remotely. 
     In one embodiment, TCPs can be created in a linear or substantially linear zone or sequence, with each individual TCP separated from neighboring TCPs by a treatment spacing. In one embodiment, multiple sequences of TCPs can be created in a treatment region. For example, TCPs can be formed along a first linear sequence and a second linear sequence separated by a treatment distance from the first linear sequence. Although treatment with therapeutic ultrasound can be administered through creation of individual TCPs in a sequence and sequences of individual TCPs, it may be desirable to reduce treatment time and corresponding risk of pain and/or discomfort experienced by a patient. Therapy time can be reduced by forming multiple TCPs simultaneously, nearly simultaneously, or sequentially. In some embodiments, a treatment time can be reduced 10%, 20%, 25%, 30%, 35%, 40%, 4%, 50%, 55%, 60%, 65%, 70%, 75%, 80% or more by creating multiple TCPs. 
     Various embodiments of the present invention address potential challenges posed by administration of ultrasound therapy. In various embodiments, time for effecting the formation of TCPs for a desired cosmetic and/or therapeutic treatment for a desired clinical approach at a target tissue is reduced. In various embodiments, target tissue is, but is not limited to, any of skin, eyelids, eye lash, eye brow, caruncula lacrimalis, crow&#39;s feet, wrinkles, eye, nose, mouth, tongue, teeth, gums, ears, brain, heart, lungs, ribs, abdomen, stomach, liver, kidneys, uterus, breast, vagina, prostrate, testicles, glands, thyroid glands, internal organs, hair, muscle, bone, ligaments, cartilage, fat, fat labuli, adipose tissue, subcutaneous tissue, implanted tissue, an implanted organ, lymphoid, a tumor, a cyst, an abscess, or a portion of a nerve, or any combination thereof. 
     In some embodiments, amplitude modulation and/or discrete phasing techniques can be applied to an aperture configured to emit ultrasonic energy. This can cause splitting of an ultrasonic beam emitted by the aperture into multiple beams, which may simultaneously, substantially simultaneously, or sequentially deliver ultrasonic energy to multiple locations or focal points. In some embodiments, amplitude modulation can be combined with techniques configured to change modulation states of an aperture in order to reduce intensity of ultrasonic energy delivered to tissues located before and/or after focal points. In various embodiments, therapy time can be reduced by 1-24%, 1-26%, 1-39%, 1-50%, or more than 50%. 
     Various embodiments of ultrasound treatment and imaging devices are described in U.S. application Ser. No. 12/996,616, which published as U.S. Publication No. 2011-0112405 A1 on May 12, 2011, which is a U.S. National Phase under 35 U.S.C. § 371 of International Application No. PCT/US2009/046475, filed on Jun. 5, 2009 and published in English on Dec. 10, 2009, which claims the benefit of priority from U.S. Provisional No. 61/059,477 filed Jun. 6, 2008, each of which is incorporated in its entirety by reference, herein. 
     System Overview 
     With reference to the illustration in  FIG.  1   , an embodiment of an ultrasound system  20  includes a hand wand  100 , module  200 , and a controller  300 . The hand wand  100  can be coupled to the controller  300  by an interface  130 , which may be a wired or wireless interface. The interface  130  can be coupled to the hand wand  100  by a connector  145 . The distal end of the interface  130  can be connected to a controller connector on a circuit  345 . In one embodiment, the interface  130  can transmit controllable power from the controller  300  to the hand wand  100 . 
     In various embodiments, the controller  300  can be configured for operation with the hand wand  100  and the module  200 , as well as the overall ultrasound system  20  functionality. In various embodiments, multiple controllers  300 ,  300 ′,  300 ″, etc. can be configured for operation with multiple hand wands  100 ,  100 ′,  100 ″, etc. and or multiple modules  200 ,  200 ′,  200 ″, etc. The controller  300  can include an interactive graphical display  310 , which can include a touchscreen monitor and Graphic User Interface (GUI) that allows the user to interact with the ultrasound system  20 . As is illustrated, the graphical display  315  includes a touchscreen interface  315 . In various embodiments, the display  310  sets and displays the operating conditions, including equipment activation status, treatment parameters, system messages and prompts, and ultrasound images. In various embodiments, the controller  300  can be configured to include, for example, a microprocessor with software and input/output devices, systems and devices for controlling electronic and/or mechanical scanning and/or multiplexing of transducers and/or multiplexing of transducer modules, a system for power delivery, systems for monitoring, systems for sensing the spatial position of the probe and/or transducers and/or multiplexing of transducer modules, and/or systems for handling user input and recording treatment results, among others. In various embodiments, the controller  300  can include a system processor and various analog and/or digital control logic, such as one or more of microcontrollers, microprocessors, field-programmable gate arrays, computer boards, and associated components, including firmware and control software, which may be capable of interfacing with user controls and interfacing circuits as well as input/output circuits and systems for communications, displays, interfacing, storage, documentation, and other useful functions. System software running on the system process may be configured to control all initialization, timing, level setting, monitoring, safety monitoring, and all other ultrasound system functions for accomplishing user-defined treatment objectives. Further, the controller  300  can include various input/output modules, such as switches, buttons, etc., that may also be suitably configured to control operation of the ultrasound system  20 . 
     As is illustrated in  FIG.  1   , in one embodiment, the controller  300  can include one or more data ports  390 . In various embodiments, the data ports  390  can be a USB port, Bluetooth port, IrDA port, parallel port, serial port, and the like. The data ports  390  can be located on the front, side, and/or back of the controller  300 , and can be used for accessing storage devices, printing devices, computing devices, etc. The ultrasound system  20  can include a lock  395 . In one embodiment, in order to operate the ultrasound system  20 , the lock  395  should be unlocked so that a power switch  393  may be activated. In one embodiment, the lock  395  can be connectable to the controller  300  via a data port  390  (e.g., a USB port). The lock  395  could be unlocked by inserting into the data port  390  an access key (e.g., USB access key), a hardware dongle, or the like. The controller  300  can include an emergency stop button  392 , which can be readily accessible for emergency deactivation. 
     In one embodiment, the hand wand  100  includes one or more finger activated controllers or switches, such as  150  and  160 . In one embodiment, the hand wand  100  can include a removable module  200 . In other embodiments, the module  200  may be non-removable. The module  200  can be mechanically coupled to the hand wand  100  using a latch or coupler  140 . An interface guide  235  can be used for assisting the coupling of the module  200  to the hand wand  100 . The module  200  can include one or more ultrasound transducers. In some embodiments, an ultrasound transducer includes one or more ultrasound elements. The module  200  can include one or more ultrasound elements. The hand wand  100  can include imaging-only modules, treatment-only modules, imaging-and-treatment modules, and the like. In one embodiment, the control module  300  can be coupled to the hand wand  100  via the interface  130 , and the graphic user interface  310  can be configured for controlling the module  200 . In one embodiment, the control module  300  can provide power to the hand wand  100 . In one embodiment, the hand wand  100  can include a power source. In one embodiment, the switch  150  can be configured for controlling a tissue imaging function and the switch  160  can be configured for controlling a tissue treatment function 
     In one embodiment, the module  200  can be coupled to the hand wand  100 . The module  200  can emit and receive energy, such as ultrasonic energy. The module  200  can be electronically coupled to the hand wand  100  and such coupling may include an interface which is in communication with the controller  300 . In one embodiment, the interface guide  235  can be configured to provide electronic communication between the module  200  and the hand wand  100 . The module  200  can comprise various probe and/or transducer configurations. For example, the module  200  can be configured for a combined dual-mode imaging/therapy transducer, coupled or co-housed imaging/therapy transducers, separate therapy and imaging probes, and the like. In one embodiment, when the module  200  is inserted into or connected to the hand wand  100 , the controller  300  automatically detects it and updates the interactive graphical display  310 . 
     In various embodiments, tissue below or even at a skin surface such as epidermis, dermis, hypodermis, fascia, and superficial muscular aponeurotic system (“SMAS”), and/or muscle are treated non-invasively with ultrasound energy. Tissue may also include blood vessels and/or nerves. The ultrasound energy can be focused, unfocused or defocused and applied to a region of interest containing at least one of epidermis, dermis, hypodermis, fascia, and SMAS to achieve a therapeutic effect.  FIG.  2    is a schematic illustration of the ultrasound system  20  coupled to a region of interest  10 . In various embodiments, tissue layers of the region of interest  10  can be at any part of the body of a subject. In one embodiment, the tissue layers are in the head and face region of the subject. The cross-sectional portion of the tissue of the region of interest  10  includes a skin surface  501 , an epidermal layer  502 , a dermal layer  503 , a fat layer  505 , a superficial muscular aponeurotic system  507  (hereinafter “SMAS  507 ”), and a muscle layer  509 . The tissue can also include the hypodermis  504 , which can include any tissue below the dermal layer  503 . The combination of these layers in total may be known as subcutaneous tissue  510 . Also illustrated in  FIG.  2    is a treatment zone  525  which is below the surface  501 . In one embodiment, the surface  501  can be a surface of the skin of a subject  500 . Although an embodiment directed to therapy at a tissue layer may be used herein as an example, the system can be applied to any tissue in the body. In various embodiments, the system and/or methods may be used on muscles (or other tissue) of the face, neck, head, arms, legs, or any other location in the body. 
     With reference to the illustration in  FIG.  2   , an embodiment of the ultrasound system  20  includes the hand wand  100 , the module  200 , and the controller  300 . In one embodiment, the module  200  includes a transducer  280 .  FIG.  3    illustrates an embodiment of an ultrasound system  20  with a transducer  280  configured to treat tissue at a focal depth  278 . In one embodiment, the focal depth  278  is a distance between the transducer  280  and the target tissue for treatment. In one embodiment, a focal depth  278  is fixed for a given transducer  280 . In one embodiment, a focal depth  278  is variable for a given transducer  280 . 
     With reference to the illustration in  FIG.  4   , the module  200  can include a transducer  280  which can emit energy through an acoustically transparent member  230 . In various embodiments, a depth may refer to the focal depth  278 . In one embodiment, the transducer  280  can have an offset distance  270 , which is the distance between the transducer  280  and a surface of the acoustically transparent member  230 . In one embodiment, the focal depth  278  of a transducer  280  is a fixed distance from the transducer. In one embodiment, a transducer  280  may have a fixed offset distance  270  from the transducer to the acoustically transparent member  230 . In one embodiment, an acoustically transparent member  230  is configured at a position on the module  200  or the ultrasound system  20  for contacting the skin surface  501 . In various embodiments, the focal depth  278  exceeds the offset distance  270  by an amount to correspond to treatment at a target area located at a tissue depth  279  below a skin surface  501 . In various embodiments, when the ultrasound system  20  placed in physical contact with the skin surface  501 , the tissue depth  279  is a distance between the acoustically transparent member  230  and the target area, measured as the distance from the portion of the hand wand  100  or module  200  surface that contacts skin (with or without an acoustic coupling gel, medium, etc.) and the depth in tissue from that skin surface contact point to the target area. In one embodiment, the focal depth  278  can correspond to the sum of an offset distance  270  (as measured to the surface of the acoustically transparent member  230  in contact with a coupling medium and/or skin  501 ) in addition to a tissue depth  279  under the skin surface  501  to the target region. In various embodiments, the acoustically transparent member  230  is not used. 
     Coupling components can comprise various substances, materials, and/or devices to facilitate coupling of the transducer  280  or module  200  to a region of interest. For example, coupling components can comprise an acoustic coupling system configured for acoustic coupling of ultrasound energy and signals. Acoustic coupling system with possible connections such as manifolds may be utilized to couple sound into the region of interest, provide liquid- or fluid-filled lens focusing. The coupling system may facilitate such coupling through use of one or more coupling media, including air, gases, water, liquids, fluids, gels, solids, non-gels, and/or any combination thereof, or any other medium that allows for signals to be transmitted between the transducer  280  and a region of interest. In one embodiment one or more coupling media is provided inside a transducer. In one embodiment a fluid-filled module  200  contains one or more coupling media inside a housing. In one embodiment a fluid-filled module  200  contains one or more coupling media inside a sealed housing, which is separable from a dry portion of an ultrasonic device. In various embodiments, a coupling medium is used to transmit ultrasound energy between one or more devices and tissue with a transmission efficiency of 100%, 99% or more, 98% or more, 95% or more, 90% or more, 80% or more, 75% or more, 60% or more, 50% or more, 40% or more, 30% or more, 25% or more, 20% or more, 10% or more, and/or 5% or more. 
     In various embodiments, the transducer  280  can image and treat a region of interest at any suitable tissue depths  279 . In one embodiment, the transducer module  280  can provide an acoustic power in a range of about 1 W or less, between about 1 W to about 100 W, and more than about 100 W. In one embodiment, the transducer module  280  can provide an acoustic power at a frequency of about 1 MHz or less, between about 1 MHz to about 10 MHz, and more than about 10 MHz. In one embodiment, the module  200  has a focal depth  278  for a treatment at a tissue depth  279  of about 4.5 mm below the skin surface  501 . Some non-limiting embodiments of transducers  280  or modules  200  can be configured for delivering ultrasonic energy at a tissue depth of 3 mm, 4.5 mm, 6 mm, less than 3 mm, between 3 mm and 4.5 mm, between 4.5 mm and 6 mm, more than more than 4.5 mm, more than 6 mm, etc., and anywhere in the ranges of 0-3 mm, 0-4.5 mm, 0-6 mm, 0-25 mm, 0-100 mm, etc. and any depths therein. In one embodiment, the ultrasound system  20  is provided with two or more transducer modules  280 . For example, a first transducer module can apply treatment at a first tissue depth (e.g., about 4.5 mm) and a second transducer module can apply treatment at a second tissue depth (e.g., of about 3 mm), and a third transducer module can apply treatment at a third tissue depth (e.g., of about 1.5-2 mm). In one embodiment, at least some or all transducer modules can be configured to apply treatment at substantially same depths. 
     In various embodiments, changing the number of focus point locations (e.g., such as with a tissue depth  279 ) for an ultrasonic procedure can be advantageous because it permits treatment of a patient at varied tissue depths even if the focal depth  278  of a transducer  270  is fixed. This can provide synergistic results and maximizing the clinical results of a single treatment session. For example, treatment at multiple depths under a single surface region permits a larger overall volume of tissue treatment, which results in enhanced collagen formation and tightening. Additionally, treatment at different depths affects different types of tissue, thereby producing different clinical effects that together provide an enhanced overall cosmetic result. For example, superficial treatment may reduce the visibility of wrinkles and deeper treatment may induce formation of more collagen growth. Likewise, treatment at various locations at the same or different depths can improve a treatment. 
     Although treatment of a subject at different locations in one session may be advantageous in some embodiments, sequential treatment over time may be beneficial in other embodiments. For example, a subject may be treated under the same surface region at one depth in time one, a second depth in time two, etc. In various embodiments, the time can be on the order of nanoseconds, microseconds, milliseconds, seconds, minutes, hours, days, weeks, months, or other time periods. The new collagen produced by the first treatment may be more sensitive to subsequent treatments, which may be desired for some indications. Alternatively, multiple depth treatment under the same surface region in a single session may be advantageous because treatment at one depth may synergistically enhance or supplement treatment at another depth (due to, for example, enhanced blood flow, stimulation of growth factors, hormonal stimulation, etc.). In several embodiments, different transducer modules provide treatment at different depths. In one embodiment, a single transducer module can be adjusted or controlled for varied depths. Safety features to minimize the risk that an incorrect depth will be selected can be used in conjunction with the single module system. 
     In several embodiments, a method of treating the lower face and neck area (e.g., the submental area) is provided. In several embodiments, a method of treating (e.g., softening) mentolabial folds is provided. In other embodiments, a method of treating the eye region is provided. Upper lid laxity improvement and periorbital lines and texture improvement will be achieved by several embodiments by treating at variable depths. By treating at varied locations in a single treatment session, optimal clinical effects (e.g., softening, tightening) can be achieved. In several embodiments, the treatment methods described herein are non-invasive cosmetic procedures. In some embodiments, the methods can be used in conjunction with invasive procedures, such as surgical facelifts or liposuction, where skin tightening is desired. In various embodiments, the methods can be applied to any part of the body. 
     In one embodiment, a transducer module permits a treatment sequence at a fixed depth at or below the skin surface. In one embodiment, a transducer module permits a treatment sequence at a fixed depth below the dermal layer. In several embodiments, the transducer module comprises a movement mechanism configured to direct ultrasonic treatment in a sequence of individual thermal lesions (hereinafter “thermal coagulation points” or “TCPs”) at a fixed focal depth. In one embodiment, the linear sequence of individual TCPs has a treatment spacing in a range from about 0.01 mm to about 25 mm. For example, the spacing can be 1.1 mm or less, 1.5 mm or more, between about 1.1 mm and about 1.5 mm, etc. In one embodiment, the individual TCPs are discrete. In one embodiment, the individual TCPs are overlapping. In one embodiment, the movement mechanism is configured to be programmed to provide variable spacing between the individual TCPs. In several embodiments, a transducer module comprises a movement mechanism configured to direct ultrasonic treatment in a sequence so that TCPs are formed in linear or substantially linear sequences separated by a treatment distance. For example, a transducer module can be configured to form TCPs along a first linear sequence and a second linear sequence separated by a treatment distance from the first linear sequence. In one embodiment, treatment distance between adjacent linear sequences of individual TCPs is in a range from about 0.01 mm to about 25 mm. For example, the treatment distance can be 2 mm or less, 3 mm or more, between about 2 mm and about 3 mm, etc. In several embodiments, a transducer module can comprise one or more movement mechanisms configured to direct ultrasonic treatment in a sequence so that TCPs are formed in linear or substantially linear sequences of individual thermal lesions separated by a treatment distance from other linear sequences. In one embodiment, the treatment distance separating linear or substantially linear TCPs sequences is the same or substantially the same. In one embodiment, the treatment distance separating linear or substantially linear TCPs sequences is different or substantially different for various adjacent pairs of linear TCPs sequences. 
     In one embodiment, first and second removable transducer modules are provided. In one embodiment, each of the first and second transducer modules are configured for both ultrasonic imaging and ultrasonic treatment. In one embodiment, a transducer module is configured for treatment only. In one embodiment, an imaging transducer may be attached to a handle of a probe or a hand wand. The first and second transducer modules are configured for interchangeable coupling to a hand wand. The first transducer module is configured to apply ultrasonic therapy to a first layer of tissue, while the second transducer module is configured to apply ultrasonic therapy to a second layer of tissue. The second layer of tissue is at a different depth than the first layer of tissue. 
     As illustrated in  FIG.  3   , in various embodiments, delivery of emitted energy  50  at a suitable focal depth  278 , distribution, timing, and energy level is provided by the module  200  through controlled operation by the control system  300  to achieve the desired therapeutic effect of controlled thermal injury to treat at least one of the epidermis layer  502 , dermis layer  503 , fat layer  505 , the SMAS layer  507 , the muscle layer  509 , and/or the hypodermis  504 .  FIG.  3    illustrates one embodiment of a depth that corresponds to a depth for treating muscle. In various embodiments, the depth can correspond to any tissue, tissue layer, skin, epidermis, dermis, hypodermis, fat, SMAS, muscle, blood vessel, nerve, or other tissue. During operation, the module  200  and/or the transducer  280  can also be mechanically and/or electronically scanned along the surface  501  to treat an extended area. Before, during, and after the delivery of ultrasound energy  50  to at least one of the epidermis layer  502 , dermis layer  503 , hypodermis  504 , fat layer  505 , the SMAS layer  507  and/or the muscle layer  509 , monitoring of the treatment area and surrounding structures can be provided to plan and assess the results and/or provide feedback to the controller  300  and the user via a graphical interface  310 . 
     In one embodiment, an ultrasound system  20  generates ultrasound energy which is directed to and focused below the surface  501 . This controlled and focused ultrasound energy  50  creates the thermal coagulation point or zone (TCP)  550 . In one embodiment, the ultrasound energy  50  creates a void in subcutaneous tissue  510 . In various embodiments, the emitted energy  50  targets the tissue below the surface  501  which cuts, ablates, coagulates, micro-ablates, manipulates, and/or causes a lesion  550  in the tissue portion  10  below the surface  501  at a specified focal depth  278 . In one embodiment, during the treatment sequence, the transducer  280  moves in a direction denoted by the arrow marked  290  at specified intervals  295  to create a series of treatment zones  254  each of which receives an emitted energy  50  to create one or more TCPs  550 . 
     In various embodiments, transducer modules can comprise one or more transduction elements. The transduction elements can comprise a piezoelectrically active material, such as lead zirconante titanate (PZT), or any other piezoelectrically active material, such as a piezoelectric ceramic, crystal, plastic, and/or composite materials, as well as lithium niobate, lead titanate, barium titanate, and/or lead metaniobate. In various embodiments, in addition to, or instead of, a piezoelectrically active material, transducer modules can comprise any other materials configured for generating radiation and/or acoustical energy. In various embodiments, transducer modules can be configured to operate at different frequencies and treatment depths. Transducer properties can be defined by an outer diameter (“OD”) and focal length (F L ). In one embodiment, a transducer can be configured to have OD=19 mm and F L =15 mm. In other embodiments, other suitable values of OD and F L  can be used, such as OD of less than about 19 mm, greater than about 19 mm, etc. and F L  of less than about 15 mm, greater than about 15 mm, etc. Transducer modules can be configured to apply ultrasonic energy at different target tissue depths. As described above, in several embodiments, transducer modules comprise movement mechanisms configured to direct ultrasonic treatment in a linear or substantial liner sequence of individual TCPs with a treatment spacing between individual TCPs. For example, treatment spacing can be about 1.1 mm, 1.5 mm, etc. In several embodiments, transducer modules can further comprise movement mechanisms configured to direct ultrasonic treatment in a sequence so that TCPs are formed in linear or substantially linear sequences separated by a treatment spacing. For example, a transducer module can be configured to form TCPs along a first linear sequence and a second linear sequence separated by treatment spacing between about 2 mm and 3 mm from the first linear sequence. In one embodiment, a user can manually move the transducer modules across the surface of a treatment area so that adjacent linear sequences of TCPs are created. In one embodiment, a movement mechanism can automatically move the transducer modules across the surface of a treatment area so that adjacent linear sequences of TCPs are created. 
     In various embodiments, treatment advantageously can be delivered at a faster rate and with improved accuracy. This in turn can reduce treatment time and decrease pain experienced by a subject. Further, efficiency can be increased if variance is reduced in a treatment spacing between linear or substantially linear sequences of TCPs. In one embodiment, a system uses a transducer configured to produce a single focus treatment point. In one embodiment, the transducer can be mechanically moved along a line to create a linear sequence of TCPs. For example, Table 1 provides an estimate of time for creating a linear sequence of TCPs and an estimate of time for moving between linear sequences of TCPs according to one embodiment. It can be seen that time for creating a linear sequence of TCPs and time for moving between linear sequences of TCPs are nearly equivalent. 
     
       
         
           
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 Time Metric 
                 Time (in msec) 
                 Percentage of Total Time 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 Time for creating a 
                 2.9 
                 48 
               
               
                 linear sequence 
               
               
                 Time for moving between 
                 3.2 
                 52 
               
               
                 linear sequences 
                   
                   
               
               
                 Total Time 
                 6.1 
                 100 
               
               
                   
               
            
           
         
       
     
     In various embodiments, therapeutic treatment advantageously can be delivered at a faster rate and with improved accuracy by using a transducer configured to deliver multiple focus points, or TCPs. This in turn can reduce treatment time and decrease pain experienced by a subject. In several embodiments, treatment time is reduced if time for creating a linear sequence of TCPs and time for moving between linear sequences of TCPs are reduced by emitting TCPs at multiple locations from a single transducer. 
     Therapy Delivery Using Amplitude Modulation 
     Aperture Spatial Frequency Analysis and Fourier Transform 
     In various embodiments, spatial frequency analysis techniques based on Fourier analysis and Fourier optics can be used to increase efficiency of therapeutic treatment. When a system that has an impulse response h(t) is excited by a stimulus x(t), the relationship between the input x(t) and output y(t) is related by the convolution function as follows: 
         y ( t )= x ( t )* h ( t )=∫ −∞   ∞   x (τ) h ( t −τ) dτ   (1)
 
     In various embodiments, Fourier transform can be applied to compute the convolution of equation (1). Continuous one-dimensional Fourier transform can be defined as: 
         y ( t )= x ( t )* h ( t ) Y ( f )= F ( y ( t )=∫ −∞   ∞   y ( t ) e   −j2πft   dt   (2)
 
     Here f is frequency, t is time. It can be shown that convolution in the time domain is equivalent to multiplication in the frequency domain: 
         y ( t )= x ( t )* h ( t ) F ( x ( t )* h ( t ))= X ( f ) H ( f )= Y ( f )  (3)
 
     In various embodiments, the Fraunhofer approximation can be used for deriving a relationship between a transducer opening or aperture and a resulting ultrasonic beam response. Derivation of the Fraunhofer approximation is described in Joseph Goodman,  Introduction to Fourier Optics  (3d ed. 2004), which is incorporated in its entirety by reference, herein. According to the Fraunhofer approximation, a far-field complex amplitude pattern produced by a complex aperture is equal to a two-dimensional Fourier transform of the aperture amplitude and phase. In several embodiments, this relationship in optics can be extended to ultrasound since linear wave equations can be used to represent both light propagation and sound propagation. In the case of optics and/or ultrasound, the two-dimensional Fourier transform can determine a sound wave pressure amplitude distribution at the focus of a transducer. 
     In various embodiments, a Huygens-Fresnel integral determines an amplitude in the pressure field U(P 0 ) from an aperture by integrating the effect (both amplitude and phase) from each resonator or transducer on a surface E. It is expressed as: 
     
       
         
           
             
               
                 
                   
                     U 
                     ⁡ 
                     ( 
                     
                       P 
                       o 
                     
                     ) 
                   
                   = 
                   
                     ∫ 
                     
                       
                         ∫ 
                         ∑ 
                       
                       
                         
                           h 
                           ⁡ 
                           ( 
                           
                             
                               P 
                               o 
                             
                             , 
                             
                               P 
                               1 
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           U 
                           ⁡ 
                           ( 
                           
                             P 
                             1 
                           
                           ) 
                         
                         ⁢ 
                         ds 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     4 
                     ⁢ 
                         
                     a 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     h 
                     ⁡ 
                     ( 
                     
                       
                         P 
                         o 
                       
                       , 
                       
                         P 
                         1 
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         j 
                         ⁢ 
                         λ 
                       
                     
                     ⁢ 
                     
                       
                         e 
                         
                           ( 
                           
                             jkr 
                             01 
                           
                           ) 
                         
                       
                       
                         r 
                         01 
                       
                     
                     ⁢ 
                     
                       cos 
                       ⁡ 
                       ( 
                       
                         
                           n 
                           → 
                         
                         , 
                         
                           
                             r 
                             
                               01 
                                 
                             
                           
                           → 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     4 
                     ⁢ 
                         
                     b 
                   
                   ) 
                 
               
             
           
         
       
     
     where k is a wave number expressed as 2π/λ, r 01  is a distance from an aperture to the screen in a field, n is a directional vector from the aperture, U(P 1 ) is the pressure field in the aperture, and U(P 0 ) is the pressure field in the screen. 
     In various embodiments, following assumption are used to lead to an approximation that the amplitude in the pressure field U(P 0 ) is a two-dimensional Fourier transform of U(P 1 ). First, at small angles, the cosine function of the angle between n and r 01  is 1. This leads to the following simplifications: 
     
       
         
           
             
               
                 cos 
                 ⁡ 
                 ( 
                 
                   
                     n 
                     → 
                   
                   , 
                   
                     
                       r 
                       
                         01 
                           
                       
                     
                     → 
                   
                 
                 ) 
               
               ≈ 
               1 
             
             ⁢ 
             
 
             
               
                 r 
                 01 
               
               ≈ 
               z 
             
             ⁢ 
             
 
             
               
                 h 
                 ⁡ 
                 ( 
                 
                   
                     x 
                     0 
                   
                   , 
                   
                     
                       y 
                       0 
                     
                     ; 
                     
                       x 
                       1 
                     
                   
                   , 
                   
                     y 
                     1 
                   
                 
                 ) 
               
               ≈ 
               
                 
                   1 
                   
                     j 
                     ⁢ 
                     λ 
                   
                 
                 ⁢ 
                 
                   e 
                   
                     jkr 
                     01 
                   
                 
               
             
           
         
       
     
     where z represents depth. Second, Fresnel approximation of the distance r 01  can be expressed, using a binomial expansion, as: 
     
       
         
           
             
               r 
               01 
             
             = 
             
               
                 
                   e 
                   jkz 
                 
                 z 
               
               ⁢ 
               
                 e 
                 
                   [ 
                   
                     
                       jk 
                       
                         2 
                         ⁢ 
                         z 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             ( 
                             
                               
                                 x 
                                 1 
                               
                               - 
                               
                                 x 
                                 0 
                               
                             
                             ) 
                           
                           2 
                         
                         + 
                         
                           
                             ( 
                             
                               
                                 y 
                                 1 
                               
                               - 
                               
                                 y 
                                 0 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       ) 
                     
                   
                   ] 
                 
               
             
           
         
       
     
     Third, it can be assumed that the observation plane is much greater than the dimensions of the aperture as follows: 
     
       
         
           
             z 
             ≫ 
             
               
                 
                   k 
                   ⁡ 
                   ( 
                   
                     
                       x 
                       1 
                       2 
                     
                     + 
                     
                       y 
                       1 
                       2 
                     
                   
                   ) 
                 
                 max 
               
               2 
             
           
         
       
     
     If these assumptions are applied to equations (4a) and (4b), then the amplitude in the field can be expressed as: 
     
       
         
           
             
               
                 
                   
                     U 
                     ⁡ 
                     ( 
                     
                       
                         x 
                         0 
                       
                       , 
                       
                         y 
                         0 
                       
                     
                     ) 
                   
                   ≈ 
                   
                     
                       
                         
                           e 
                           jkz 
                         
                         ⁢ 
                         
                           e 
                           
                             [ 
                             
                               
                                 jk 
                                 
                                   2 
                                   ⁢ 
                                   z 
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     x 
                                     0 
                                     2 
                                   
                                   + 
                                   
                                     y 
                                     0 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                             ] 
                           
                         
                       
                       
                         j 
                         ⁢ 
                         λ 
                         ⁢ 
                         z 
                       
                     
                     ⁢ 
                     
                       ∫ 
                       
                         
                           
                             ∫ 
                             
                               - 
                               ∞ 
                             
                           
                           ∞ 
                         
                         
                           
                             U 
                             ⁡ 
                             ( 
                             
                               
                                 x 
                                 1 
                               
                               , 
                               
                                 y 
                                 1 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             e 
                             
                               
                                 - 
                                 
                                   
                                     j 
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     π 
                                   
                                   
                                     λ 
                                     ⁢ 
                                     z 
                                   
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     
                                       x 
                                       0 
                                     
                                     ⁢ 
                                     
                                       x 
                                       1 
                                     
                                   
                                   + 
                                   
                                     
                                       y 
                                       0 
                                     
                                     ⁢ 
                                     
                                       y 
                                       1 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           ⁢ 
                           
                             dx 
                             1 
                           
                           ⁢ 
                           
                             dy 
                             1 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Equation (5) includes a quadratic phase term on the outside of the integral which does not affect the overall magnitude. Comparing equation (5) to equation (2) reveals a similarity in the arguments inside the integral. In particular, instead of a one dimensional function y(t) evaluated at frequencies f, a two dimensional function U(x 1 ,y 1 ) is evaluated at spatial frequencies given as: 
     
       
         
           
             
               
                 
                   
                     f 
                     x 
                   
                   = 
                   
                     
                       x 
                       0 
                     
                     
                       λ 
                       ⁢ 
                       z 
                     
                   
                 
               
               
                 
                   ( 
                   
                     5 
                     ⁢ 
                         
                     a 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     f 
                     y 
                   
                   = 
                   
                     
                       y 
                       0 
                     
                     
                       λ 
                       ⁢ 
                       z 
                     
                   
                 
               
               
                 
                   ( 
                   
                     5 
                     ⁢ 
                         
                     b 
                   
                   ) 
                 
               
             
           
         
       
     
     Because the integral of equation (5) is the two-dimensional Fourier transform, equation (5) can be rewritten as: 
     
       
         
           
             
               
                 
                   
                     h 
                     ⁡ 
                     ( 
                     
                       
                         P 
                         
                           o 
                             
                         
                       
                       , 
                       
                         P 
                         1 
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         1 
                         
                           j 
                           ⁢ 
                           λ 
                         
                       
                       ⁢ 
                       
                         
                           e 
                           
                             ( 
                             
                               jkr 
                               
                                 01 
                                   
                               
                             
                             ) 
                           
                         
                         
                           r 
                           01 
                         
                       
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         ( 
                         
                           
                             n 
                             → 
                           
                           , 
                           
                             
                               r 
                               01 
                             
                             → 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         U 
                         ⁡ 
                         ( 
                         
                           
                             x 
                             0 
                           
                           , 
                           
                             y 
                             0 
                           
                         
                         ) 
                       
                     
                     ≈ 
                     
                       
                         
                           
                             e 
                             jkz 
                           
                           ⁢ 
                           
                             e 
                             
                               [ 
                               
                                 
                                   jk 
                                   
                                     2 
                                     ⁢ 
                                     z 
                                   
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       x 
                                       0 
                                       2 
                                     
                                     + 
                                     
                                       y 
                                       0 
                                       2 
                                     
                                   
                                   ) 
                                 
                               
                               ] 
                             
                           
                         
                         
                           j 
                           ⁢ 
                           λ 
                           ⁢ 
                           z 
                         
                       
                       ⁢ 
                       
                         F 
                         
                           x 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           F 
                           
                             y 
                             1 
                           
                         
                         ( 
                         
                           U 
                           ⁡ 
                           ( 
                           
                             
                               x 
                               1 
                             
                             , 
                             
                               y 
                               1 
                             
                           
                           ) 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     In various embodiments, the amplitude and phase functions in the aperture U(x 1 ,y 1 ) are separable into two functions, namely a function of x 1  and a function of y 1  respectively. 
         U ( x   1   ,y   1 )= g ( x   1 ) h ( y   1 )  (7)
 
     Applying equation (7) to equation (6) leads to further simplification: 
     
       
         
           
             
               
                 
                   
                     h 
                     ⁡ 
                     ( 
                     
                       
                         P 
                         o 
                       
                       , 
                       
                         P 
                         1 
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         1 
                         
                           j 
                           ⁢ 
                           λ 
                         
                       
                       ⁢ 
                       
                         
                           e 
                           
                             ( 
                             
                               jkr 
                               01 
                             
                             ) 
                           
                         
                         
                           r 
                           01 
                         
                       
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         ( 
                         
                           
                             n 
                             → 
                           
                           , 
                           
                             
                               r 
                               01 
                             
                             → 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         y 
                         ⁡ 
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           x 
                           ⁡ 
                           ( 
                           t 
                           ) 
                         
                         * 
                       
                       ⁢ 
                       
                         h 
                         ⁡ 
                         ( 
                         t 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               U 
               ⁡ 
               ( 
               
                 
                   x 
                   0 
                 
                 , 
                 
                   y 
                   0 
                 
               
               ) 
             
             ≈ 
             
               
                 
                   
                     e 
                     jkz 
                   
                   ⁢ 
                   
                     e 
                     
                       [ 
                       
                         
                           jk 
                           
                             2 
                             ⁢ 
                             z 
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               x 
                               0 
                               2 
                             
                             + 
                             
                               y 
                               0 
                               2 
                             
                           
                           ) 
                         
                       
                       ] 
                     
                   
                 
                 
                   j 
                   ⁢ 
                   λ 
                   ⁢ 
                   z 
                 
               
               ⁢ 
               
                 
                   F 
                   
                     x 
                     1 
                   
                 
                 ( 
                 
                   g 
                   ⁡ 
                   ( 
                   
                     x 
                     1 
                   
                   ) 
                 
                 ) 
               
               ⁢ 
               
                 
                   F 
                   
                     y 
                     1 
                   
                 
                 ( 
                 
                   h 
                   ⁡ 
                   ( 
                   
                     y 
                     1 
                   
                   ) 
                 
                 ) 
               
             
           
         
       
     
     Equation (8) demonstrates that a response of the aperture in the field for a separable two-dimensional function is the multiplication of two one-dimensional Fourier transforms in x 1  and y 1  directions. It can be further shown that equations (6) and (8) hold for a focused system with the exception that spatial frequency arguments change as is expressed in equations (9a) and (9b). For a focused system, the variable z which represents depth can be replaced with z f  which represents a focal distance. 
     
       
         
           
             
               
                 
                   
                     f 
                     x 
                   
                   = 
                   
                     
                       
                         
                           x 
                           0 
                         
                         
                           λ 
                           ⁢ 
                           
                             z 
                             f 
                           
                         
                       
                       ⁢ 
                       
                         y 
                         ⁡ 
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           x 
                           ⁡ 
                           ( 
                           t 
                           ) 
                         
                         * 
                       
                       ⁢ 
                       
                         h 
                         ⁡ 
                         ( 
                         t 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     9 
                     ⁢ 
                         
                     a 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     f 
                     y 
                   
                   = 
                   
                     
                       
                         
                           y 
                           0 
                         
                         
                           λ 
                           ⁢ 
                           
                             z 
                             f 
                           
                         
                       
                       ⁢ 
                       
                         y 
                         ⁡ 
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           x 
                           ⁡ 
                           ( 
                           t 
                           ) 
                         
                         * 
                       
                       ⁢ 
                       
                         h 
                         ⁡ 
                         ( 
                         t 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     9 
                     ⁢ 
                         
                     b 
                   
                   ) 
                 
               
             
           
         
       
     
     In various embodiments, Fourier optics and Fourier transform identities (some of which are listed in Table 2, below) can be used for ultrasound transducers in order to determine the intensity distribution corresponding to a transducer design. For example, Fourier transform of a rectangle rect(ax) is a sine function. As another example, Fourier transform of a two dimensional circle of uniform amplitude is a first order Bessel function which can be represented as J 1 . 
     
       
         
           
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                   
                 Aperture Function 
                 Fourier Transform 
               
               
                   
               
             
            
               
                 1 
                 rect(ax) 
                 
                   
                     
                       
                         
                           1 
                           
                             | 
                             a 
                             | 
                           
                         
                         ⁢ 
                             
                         sinc 
                         ⁢ 
                             
                         
                           ( 
                           
                             ξ 
                             a 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 2 
                 δ(x) 
                 1 
               
               
                   
               
               
                 3 
                 cos (ax) 
                 
                   
                     
                       
                         
                           
                             δ 
                             ⁢ 
                                 
                             
                               ( 
                               
                                 ξ 
                                 - 
                                 
                                   a 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                   
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             δ 
                             ⁢ 
                                 
                             
                               ( 
                               
                                 ξ 
                                 + 
                                 
                                   a 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                   
                                 
                               
                               ) 
                             
                           
                         
                         2 
                       
                     
                   
                 
               
               
                   
               
               
                 4 
                 sin (ax) 
                 
                   
                     
                       
                         
                           
                             δ 
                             ⁢ 
                                 
                             
                               ( 
                               
                                 ξ 
                                 - 
                                 
                                   a 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                   
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             δ 
                             ⁢ 
                                 
                             
                               ( 
                               
                                 ξ 
                                 + 
                                 
                                   a 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                   
                                 
                               
                               ) 
                             
                           
                         
                         
                           2 
                           ⁢ 
                           j 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 5 (two-dimensional transform pair) 
                 circ({square root over (x 2  + y 2 )}) 
                 
                   
                     
                       
                         
                           
                             J 
                             1 
                           
                           ( 
                           
                             2 
                             ⁢ 
                             π 
                             ⁢ 
                             
                               
                                 
                                   ξ 
                                   x 
                                   2 
                                 
                                 + 
                                 
                                   ξ 
                                   y 
                                   2 
                                 
                               
                             
                           
                           ) 
                         
                         
                           
                             
                               ξ 
                               x 
                               2 
                             
                             + 
                             
                               ξ 
                               y 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                   
               
               
                 6 
                 ƒ(x) * g(x) 
                 F(ξ)G(ξ) 
               
               
                 7 
                 ƒ(x)g(x) 
                 F(ξ) * G(ξ) 
               
               
                   
               
            
           
         
       
     
     In several embodiments, an ultrasound transducer can have a rectangular aperture of suitable dimensions and focal length. In several embodiments, an ultrasound transducer can have a circular aperture with suitable dimensions and focal length. In one embodiment, a transducer can have a circular aperture with an outer radius of approximately 9.5 mm, an inner diameter of approximately 2 mm, and focal length of approximately 15 mm. The aperture of a circular transducer may be described as: 
     
       
         
           
             
               
                 
                   
                     f 
                     ⁡ 
                     ( 
                     
                       x 
                       , 
                       y 
                     
                     ) 
                   
                   = 
                   
                     
                       circ 
                       ⁢ 
                       
                         ( 
                         
                           r 
                           a 
                         
                         ) 
                       
                     
                     - 
                     
                       circ 
                       ⁡ 
                       ( 
                       
                         r 
                         b 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     10 
                     ⁢ 
                         
                     a 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   r 
                   = 
                   
                     
                       
                         x 
                         2 
                       
                       + 
                       
                         y 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     10 
                     ⁢ 
                         
                     b 
                   
                   ) 
                 
               
             
           
         
       
     
     For example, a can be approximately 9.5 mm and b can be approximately 2 mm. Applying Fourier transform to equation (10a) can provide an estimate of the sound wave pressure distribution at the focus. 
     
       
         
           
             
               
                 
                   
                     
                       F 
                       
                         x 
                         , 
                         y 
                       
                     
                     ( 
                     
                       f 
                       ⁡ 
                       ( 
                       
                         x 
                         , 
                         y 
                       
                       ) 
                     
                     ) 
                   
                   = 
                   
                     
                       F 
                       ⁡ 
                       ( 
                       
                         
                           ξ 
                           x 
                         
                         , 
                         
                           ξ 
                           y 
                         
                       
                       ) 
                     
                     = 
                     
                       
                         
                           
                             aJ 
                             1 
                           
                           ( 
                           
                             2 
                             ⁢ 
                             π 
                             ⁢ 
                             a 
                             ⁢ 
                             
                               
                                 
                                   ξ 
                                   x 
                                   2 
                                 
                                 + 
                                 
                                   ξ 
                                   y 
                                   2 
                                 
                               
                             
                           
                           ) 
                         
                         
                           
                             
                               ξ 
                               x 
                               2 
                             
                             + 
                             
                               ξ 
                               y 
                               2 
                             
                           
                         
                       
                       - 
                       
                         
                           
                             bJ 
                             1 
                           
                           ( 
                           
                             2 
                             ⁢ 
                             π 
                             ⁢ 
                             b 
                             ⁢ 
                             
                               
                                 
                                   ξ 
                                   x 
                                   2 
                                 
                                 + 
                                 
                                   ξ 
                                   y 
                                   2 
                                 
                               
                             
                           
                           ) 
                         
                         
                           
                             
                               ξ 
                               x 
                               2 
                             
                             + 
                             
                               ξ 
                               y 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     where ξ x  and ξ y  are same as f x  and f y  of equations (9a) and (9b). Equation (11) demonstrates that the sound wave pressure distribution of a transducer with a circular aperture is a first order Bessel function. In one embodiment, a substantial majority of the energy is concentrated at the focus (e.g., 15 mm away from the aperture). The width of a main ultrasonic beam and the distribution of energy away from the main beam can be expressed as a function of the operating frequency as is expressed in equations (9a) and (9b). 
     In various embodiments, two identical or nearly identical beams could be created at the focus if the aperture was modulated (e.g., multiplied) by a correct function. In one embodiment, a cosine function can be applied to a circular aperture as follows: 
     
       
         
           
             
               
                 
                   
                     g 
                     ⁡ 
                     ( 
                     
                       x 
                       , 
                       y 
                     
                     ) 
                   
                   = 
                   
                     
                       cos 
                       ⁡ 
                       ( 
                       cx 
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           circ 
                           ⁡ 
                           ( 
                           
                             r 
                             a 
                           
                           ) 
                         
                         - 
                         
                           c 
                           ⁢ 
                           i 
                           ⁢ 
                           r 
                           ⁢ 
                           
                             c 
                             ⁡ 
                             ( 
                             
                               r 
                               b 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     An energy distribution or beam response at the focus of the modulated aperture of equation (12) is the convolution of the Fourier transform of the two functions of the aperture: 
     
       
         
           
             
               
                 
                   
                     G 
                     ⁡ 
                     ( 
                     
                       
                         ξ 
                         x 
                       
                       , 
                       
                         ξ 
                         y 
                       
                     
                     ) 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             δ 
                             ⁡ 
                             ( 
                             
                               
                                 ξ 
                                 x 
                               
                               - 
                               
                                 c 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                             ) 
                           
                           + 
                           
                             δ 
                             ⁡ 
                             ( 
                             
                               
                                 ξ 
                                 x 
                               
                               + 
                               
                                 c 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                             ) 
                           
                         
                         2 
                       
                       ) 
                     
                     * 
                     
                       F 
                       ⁡ 
                       ( 
                       
                         
                           ξ 
                           x 
                         
                         , 
                         
                           ξ 
                           y 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     Equation (13) can be simplified into the summation of two separate functions applying the Fourier Transform identity for a Dirac delta function (e.g., identity 2 in Table 2): 
     
       
         
           
             
               
                 
                   
                     G 
                     ⁡ 
                     ( 
                     
                       
                         ξ 
                         x 
                       
                       , 
                       
                         ξ 
                         y 
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           F 
                           ⁡ 
                           ( 
                           
                             
                               
                                 ξ 
                                 x 
                               
                               - 
                               
                                 c 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                             , 
                             
                               ξ 
                               y 
                             
                           
                           ) 
                         
                         + 
                         
                           F 
                           ⁡ 
                           ( 
                           
                             
                               
                                 ξ 
                                 x 
                               
                               + 
                               
                                 c 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                             , 
                             
                               ξ 
                               y 
                             
                           
                           ) 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     Equation (14) shows that two beams appearing at the focus are spatially shifted 
     
       
         
           
             
               b 
               ⁢ 
               y 
             
             ± 
             
               c 
               
                 2 
                 ⁢ 
                 π 
               
             
           
         
       
     
     compared to the original, non-modulated beam. In several embodiments, one or more other modulation functions, such as sine function, can be used to achieve a desired beam response. In several embodiments, aperture can be modulated such that more than two foci are created. For example, three, four, five, etc. foci can be created. In several embodiments, aperture can be modulated such that foci are created sequentially or substantially sequentially rather than simultaneously. 
     In several embodiments, therapy transducer modules comprise movement mechanisms configured to direct ultrasonic treatment in a linear or substantial liner sequence of individual TCPs with a treatment spacing between individual TCPs. For example, treatment spacing can be about 1.1 mm, 1.5 mm, etc. In several embodiments, transducer modules can further comprise movement mechanisms configured to direct ultrasonic treatment in a sequence so that TCPs are formed in linear or substantially linear sequences separated by a treatment spacing. For example, a transducer module can be configured to form TCPs along a first linear sequence and a second linear sequence separated by treatment spacing between about 2 mm and 3 mm from the first linear sequence. According to equation (14), a simultaneous or substantially simultaneous split in the ultrasonic beam may be achieved at the focus (or before the focus) if the aperture is modulated by a cosine and/or sine function of a desired spatial frequency. In one embodiment, two simultaneous or nearly simultaneous focused beams separated by about 1.1 mm treatment spacing can be created in a linear or substantially linear sequence. At 7 MHz frequency of ultrasound, the wavelength λ of ultrasound wave in water is approximately 0.220 mm. Accordingly, spatial frequencies ξ x  and ξ y  at the focus are represented as: 
     
       
         
           
             
               
                 
                   
                     ξ 
                     x 
                   
                   = 
                   
                     
                       
                         x 
                         0 
                       
                       
                         15 
                         * 
                         0.22 
                       
                     
                     = 
                     
                       
                         x 
                         0 
                       
                       3.3 
                     
                   
                 
               
               
                 
                   ( 
                   
                     15 
                     ⁢ 
                         
                     a 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     ξ 
                     y 
                   
                   = 
                   
                     
                       
                         y 
                         0 
                       
                       
                         15 
                         * 
                         0.22 
                       
                     
                     = 
                     
                       
                         y 
                         0 
                       
                       3.3 
                     
                   
                 
               
               
                 
                   ( 
                   
                     15 
                     ⁢ 
                         
                     b 
                   
                   ) 
                 
               
             
           
         
       
     
     In order to place two foci separated by about 1.1 mm, then the spatial frequency for modulating the aperture is calculated as follows. Using identities 3 and 4 in Table 2, the Fourier transformation of a sine or cosine function is a Dirac delta function with the argument: 
     
       
         
           
             
               
                 
                   arg 
                   = 
                   
                     
                       
                         x 
                         0 
                       
                       3.3 
                     
                     - 
                     
                       
                         k 
                         x 
                       
                       
                         2 
                         ⁢ 
                         π 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     16 
                     ⁢ 
                         
                     a 
                   
                   ) 
                 
               
             
           
         
       
     
     In one embodiment, equation (16a) can solved for k x  when argument is 0: 
     
       
         
           
             
               k 
               x 
             
             = 
             
               
                 2 
                 ⁢ 
                 π 
                 ⁢ 
                 
                   x 
                   0 
                 
               
               3.3 
             
           
         
       
     
     Further, x o  can be replaced by half of the separation distance (e.g., 1.1 mm): 
     
       
         
           
             
               
                 
                   
                     h 
                     ⁡ 
                     ( 
                     
                       
                         P 
                         o 
                       
                       , 
                       
                         P 
                         1 
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         1 
                         
                           j 
                           ⁢ 
                           λ 
                         
                       
                       ⁢ 
                       
                         
                           e 
                           
                             ( 
                             
                               jkr 
                               01 
                             
                             ) 
                           
                         
                         
                           r 
                           
                             0 
                             ⁢ 
                             1 
                           
                         
                       
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         ( 
                         
                           
                             n 
                             → 
                           
                           , 
                             
                           
                             
                               r 
                               
                                 0 
                                 ⁢ 
                                 1 
                               
                             
                             → 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         k 
                         x 
                       
                     
                     = 
                     
                       
                         
                           2 
                           ⁢ 
                           π 
                           ⁢ 
                           
                             s 
                             2 
                           
                         
                         
                           
                             z 
                             f 
                           
                           ⁢ 
                           λ 
                         
                       
                       = 
                       
                         
                           
                             2 
                             ⁢ 
                             π 
                             
                               1.1 
                               2 
                             
                           
                           3.3 
                         
                         = 
                         
                           1 
                           .04 
                             
                           
                             mm 
                             
                               - 
                               1 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     16 
                     ⁢ 
                     c 
                   
                   ) 
                 
               
             
           
         
       
     
     In several embodiments, a transducer with circular aperture emitting ultrasonic energy at various operating frequencies can be modulated by a sine and/or cosine functions at spatial frequencies listed in Table 3. Modulated aperture of the transducer can produce a simultaneously or substantially simultaneously split beam with two foci having different separation distances, as is indicated in Table 3. In one embodiment, the transducer can have OD of about 19 mm and a focal length of about 15 mm. 
     
       
         
           
               
               
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Ultrasound 
                 Separation Distance Between Foci 
                   
               
            
           
           
               
               
               
               
               
            
               
                 Frequency 
                 1.1 mm 
                 1.5 mm 
                 2 mm 
                 3 mm 
               
               
                   
               
               
                 4 MHz 
                 0.60 
                 0.82 
                 1.09 
                 1.63 
               
               
                 7 MHz 
                 1.04 
                 1.43 
                 1.90 
                 2.86 
               
               
                 10 MHz  
                 1.50 
                 2.04 
                 2.72 
                 3.08 
               
               
                   
               
            
           
         
       
     
     As is shown in Table 3, in several embodiments, a spatial frequency of an aperture modulation function increases as the ultrasonic operating frequency increases for a given foci separation distance. In addition, the spatial frequency increases as the desired foci separation distance increases. 
     In one embodiment, higher spatial frequency can result in amplitude transitions in the aperture occurring more rapidly. Due to transducer processing limitations, rapid amplitude variations in the aperture can make the aperture less efficient as there may be a variance in an amount of sound pressure produced by different parts of the aperture. In one embodiment, using spatial frequencies to simultaneously or nearly simultaneously split the beam can reduce the overall focal gain of each beam. As is shown in equation (14), a field pressure at the focus of each beam is reduced by a factor of two in comparison with an unmodulated beam. In one embodiment, the sound pressure or ultrasound intensity from the aperture can be increased to obtain similar or substantially similar intensities at the focal plane. However, in one embodiment, increasing the pressure at the aperture may not be limited by system and/or transducer processing limitations. In one embodiment, an increase in the pressure at the aperture can increase the overall intensity in the near field, which may increase the possibility of excessively heating treatment area tissue(s) that is located before focus. In one embodiment, the possibility of additional heating of the pre-focal tissue(s) may be limited or eliminated by using a lower ultrasound treatment frequency. 
     In one embodiment, applying aperture modulation function as is shown in equation (12) results in two simultaneous or substantially simultaneous ultrasound beams at the focus. In various embodiments, ultrasound beam can be split multiple times, such as three, four, five, etc. times, such that multiple simultaneous or nearly simultaneous beams are created. In one embodiment, four equally spaced beams along one dimension can be generated by modulating or multiplying the aperture by two separate spatial frequencies: 
     
       
         
           
             
               
                 
                                    
                   
                     
                       g 
                       ⁡ 
                       ( 
                       
                         x 
                         , 
                         y 
                       
                       ) 
                     
                     = 
                     
                       
                         ( 
                         
                           
                             cos 
                             ⁡ 
                             ( 
                             
                               c 
                               ⁢ 
                               x 
                             
                             ) 
                           
                           + 
                           
                             cos 
                             ⁡ 
                             ( 
                             
                               d 
                               ⁢ 
                               x 
                             
                             ) 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             circ 
                             ⁢ 
                             
                               ( 
                               
                                 r 
                                 a 
                               
                               ) 
                             
                           
                           - 
                           
                             circ 
                             ⁡ 
                             ( 
                             
                               r 
                               b 
                             
                             ) 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     17 
                     ⁢ 
                     a 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     G 
                     ⁡ 
                     ( 
                     
                       
                         ξ 
                         x 
                       
                       , 
                       
                         ξ 
                         y 
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           F 
                             
                           ( 
                           
                             
                               
                                 ξ 
                                 x 
                               
                               - 
                               
                                 c 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                             , 
                             
                               ξ 
                               y 
                             
                           
                           ) 
                         
                         + 
                         
                           F 
                           ⁡ 
                           ( 
                           
                             
                               
                                 ξ 
                                 x 
                               
                               + 
                               
                                 c 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                             , 
                             
                               ξ 
                               y 
                             
                           
                           ) 
                         
                         + 
                         
                           F 
                           ⁡ 
                           ( 
                           
                             
                               
                                 ξ 
                                 x 
                               
                               - 
                               
                                 d 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                             , 
                               
                             
                               ξ 
                               y 
                             
                           
                           ) 
                         
                         + 
                         
                           F 
                           ⁡ 
                           ( 
                           
                             
                               
                                 ξ 
                                 x 
                               
                               + 
                               
                                 d 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                             , 
                             
                               ξ 
                               y 
                             
                           
                           ) 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     17 
                     ⁢ 
                     b 
                   
                   ) 
                 
               
             
           
         
       
     
     As is shown in equation (17b), unmodulated beam at the focus can be created at four different locations along the x-axis. In one embodiment, a constant or DC term, C1, may be added to the amplitude modulation function to maintain placement of energy at the original focal location: 
     
       
         
           
             
               
                 
                                    
                   
                     
                       g 
                       ⁡ 
                       ( 
                       
                         x 
                         , 
                         y 
                       
                       ) 
                     
                     = 
                     
                       
                         ( 
                         
                           
                             cos 
                             ⁡ 
                             ( 
                             
                               c 
                               ⁢ 
                               x 
                             
                             ) 
                           
                           + 
                           
                             cos 
                             ⁡ 
                             ( 
                             
                               d 
                               ⁢ 
                               x 
                             
                             ) 
                           
                           + 
                           
                             C 
                             1 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             circ 
                             ⁡ 
                             ( 
                             
                               r 
                               a 
                             
                             ) 
                           
                           - 
                           
                             c 
                             ⁢ 
                             i 
                             ⁢ 
                             r 
                             ⁢ 
                             
                               c 
                               ⁡ 
                               ( 
                               
                                 r 
                                 b 
                               
                               ) 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     18 
                     ⁢ 
                     a 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     G 
                     ⁡ 
                     ( 
                     
                       
                         ξ 
                         x 
                       
                       , 
                       
                         ξ 
                         y 
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         1 
                         2 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             F 
                             ⁡ 
                             ( 
                             
                               
                                 
                                   ξ 
                                   x 
                                 
                                 - 
                                 
                                   c 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                   
                                 
                               
                               , 
                               
                                 ξ 
                                 y 
                               
                             
                             ) 
                           
                           + 
                           
                             F 
                             ⁡ 
                             ( 
                             
                               
                                 
                                   ξ 
                                   x 
                                 
                                 + 
                                 
                                   c 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                   
                                 
                               
                               , 
                               
                                 ξ 
                                 y 
                               
                             
                             ) 
                           
                           + 
                           
                             F 
                             ⁡ 
                             ( 
                             
                               
                                 
                                   ξ 
                                   x 
                                 
                                 - 
                                 
                                   d 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                   
                                 
                               
                               , 
                                 
                               
                                 ξ 
                                 y 
                               
                             
                             ) 
                           
                           + 
                           
                             F 
                             ⁡ 
                             ( 
                             
                               
                                 
                                   ξ 
                                   x 
                                 
                                 + 
                                 
                                   d 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                   
                                 
                               
                               , 
                                 
                               
                                 ξ 
                                 y 
                               
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         C 
                         1 
                       
                       ⁢ 
                       
                         F 
                         ⁡ 
                         ( 
                         
                           
                             ξ 
                             x 
                           
                           , 
                           
                             ξ 
                             y 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     18 
                     ⁢ 
                     b 
                   
                   ) 
                 
               
             
           
         
       
     
     In one embodiment, aperture modulation of equations (17) and (18), whereby the beam can be placed at multiple locations simultaneously or nearly simultaneously, may be have limited applicability due to system, material, and/or tissue limitations. In one embodiment, due to the possibility of heating treatment area tissue(s) located before focus, the frequency of ultrasound therapy may be adjusted, such as lowered, in order to limit and/or eliminate such possibility. In one embodiment, nonlinear techniques can be applied at the focus in order to limit and/or eliminate the possibility of heating of the pre-focal tissue(s). In one embodiment, the sound pressure or ultrasound intensity from the aperture can be increased to obtain similar or substantially similar intensities at the focal plane. 
     In various embodiments, as is shown in equation (7), if the amplitude and phase functions at the aperture are separable, the two-dimensional Fourier transform of a sound pressure function U(x 1 , y 1 ) can be expressed as a product of one-dimensional dimensional Fourier transform of two functions in x and y, which is shown in equation (8). In various embodiments, it may be advantageous to create multiple TCPs in a linear or substantially linear sequence as well as to create multiple linear sequences simultaneously or nearly simultaneously. As is shown in Table 1, in one embodiment, if two TCPs are created simultaneously or substantially simultaneously in a linear sequence, but linear sequences are created sequentially, overall treatment time may be reduced by about 24%. In one embodiment, if four TCPs are created simultaneously or substantially simultaneously in a linear sequence, but linear sequences are created sequentially, overall treatment time may be reduced by about 39%. In one embodiment, if two TCPs are created simultaneously or substantially simultaneously along with two linear sequences, overall treatment time may be reduced by about 50%. 
     Multiple Beam Splitting in Two Dimensions 
     In several embodiments, four TCPs can be created, such as two each in two linear or substantially linear sequences, using the following aperture amplitude modulation function: 
     
       
         
           
             
               
                 
                   
                     g 
                     ⁡ 
                     ( 
                     
                       x 
                       , 
                       y 
                     
                     ) 
                   
                   = 
                   
                     
                       cos 
                       ⁡ 
                       ( 
                       
                         c 
                         ⁢ 
                         x 
                       
                       ) 
                     
                     ⁢ 
                     
                       cos 
                       ⁡ 
                       ( 
                       
                         d 
                         ⁢ 
                         y 
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           circ 
                           ⁡ 
                           ( 
                           
                             r 
                             a 
                           
                           ) 
                         
                         - 
                         
                           c 
                           ⁢ 
                           i 
                           ⁢ 
                           r 
                           ⁢ 
                           
                             c 
                             ⁡ 
                             ( 
                             
                               r 
                               b 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     19 
                     ⁢ 
                     a 
                   
                   ) 
                 
               
             
           
         
       
     
     The Fourier transform of this function is: 
     
       
         
           
             
               
                 
                   
                     G 
                     ⁡ 
                     ( 
                     
                       
                         ξ 
                         x 
                       
                       , 
                       
                         ξ 
                         y 
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       4 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           F 
                           ⁡ 
                           ( 
                           
                             
                               
                                 ξ 
                                 x 
                               
                               - 
                               
                                 c 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                             , 
                               
                             
                               
                                 ξ 
                                 y 
                               
                               - 
                               
                                 d 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           ) 
                         
                         + 
                         
                           F 
                           ⁡ 
                           ( 
                           
                             
                               
                                 ξ 
                                 x 
                               
                               + 
                               
                                 c 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                             , 
                             
                               
                                 ξ 
                                 y 
                               
                               - 
                               
                                 d 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           ) 
                         
                         + 
                         
                           F 
                           ⁡ 
                           ( 
                           
                             
                               
                                 ξ 
                                 x 
                               
                               - 
                               
                                 c 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                             , 
                             
                               
                                 ξ 
                                 y 
                               
                               + 
                               
                                 d 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           ) 
                         
                         + 
                         
                           F 
                           ⁡ 
                           ( 
                           
                             
                               
                                 ξ 
                                 x 
                               
                               + 
                               
                                 c 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                             , 
                               
                             
                               
                                 ξ 
                                 y 
                               
                               + 
                               
                                 d 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           ) 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     19 
                     ⁢ 
                     b 
                   
                   ) 
                 
               
             
           
         
       
     
     As is shown in equations (19a) and (19b), the beam can be modulated into two linear sequences, with each sequence having two foci. In one embodiment, the linear sequences may be orthogonal. In one embodiment, the linear sequences may not be orthogonal. Because the Fourier transform is multiplied by ¼ in equation (19b), the amplitude of the beam or the intensity is further reduced as compared with beam split in into two foci (e.g., as is shown in equation (14)). In one embodiment, due to the possibility of heating treatment area tissue(s) that is located before focus, the frequency of ultrasound therapy may be adjusted, such as lowered, in order to limit and/or eliminate possibility of excessive heating of tissue(s) located before the focus. In several embodiments, modulation can be applied so that linear or substantially linear sequences of TCPs are created sequentially or substantially sequentially. 
     In various embodiments, as is shown in equations (12) through (14), cosine and/or sine amplitude modulation across a transducer with having a circular aperture creates two separate beams shifted by a spatial frequency of the cosine and/or sine modulation function. In various embodiments, modulation function can be spatially or phase shifted as follows: 
     
       
         
           
             
               
                 
                   
                     
                       g 
                       shift 
                     
                     ( 
                     
                       x 
                       , 
                       y 
                     
                     ) 
                   
                   = 
                   
                     
                       cos 
                       ⁡ 
                       ( 
                       
                         
                           c 
                           ⁢ 
                           x 
                         
                         - 
                         θ 
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           circ 
                           ⁡ 
                           ( 
                           
                             r 
                             a 
                           
                           ) 
                         
                         - 
                         
                           c 
                           ⁢ 
                           i 
                           ⁢ 
                           r 
                           ⁢ 
                           
                             c 
                             ⁡ 
                             ( 
                             
                               r 
                               b 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     20 
                     ⁢ 
                     a 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     
                       G 
                       shift 
                     
                     ( 
                     
                       
                         ξ 
                         x 
                       
                       , 
                       
                         ξ 
                         y 
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           2 
                           ⁢ 
                           π 
                           ⁢ 
                           
                             ξ 
                             x 
                           
                           ⁢ 
                           θ 
                         
                       
                       ( 
                       
                         
                           F 
                           ⁡ 
                           ( 
                           
                             
                               
                                 ξ 
                                 x 
                               
                               - 
                               
                                 c 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                             , 
                             
                               ξ 
                               y 
                             
                           
                           ) 
                         
                         + 
                         
                           F 
                           ⁡ 
                           ( 
                           
                             
                               
                                 ξ 
                                 x 
                               
                               + 
                               
                                 c 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                 
                               
                             
                             , 
                             
                               ξ 
                               y 
                             
                           
                           ) 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     20 
                     ⁢ 
                     a 
                   
                   ) 
                 
               
             
           
         
       
     
     In one embodiment, the amplitude caused by the shift is the same as that in equation (14). In one embodiment, although spatial shift (e.g., by angle θ) does not change the overall amplitude at the focus, the phase is modified. In several embodiments, modification of the phase may be advantageous for reducing a peak intensity before the focus. In several embodiments, an aperture can be designed so that near field or pre-focal heating of the tissue(s) is substantially minimized while intensity at the focus or focal gain is substantially maximized. 
     Therapy Delivery Using Phase Shifting 
     In various embodiments, the beam may be split axially. It may be advantageous to analyze such axial split through an analysis of time delays and application of discrete phasing. In several embodiments, splitting the beam axially in x and/or y direction can be combined with planar or two-dimensional amplitude modulation of the aperture (e.g., such as that shown in equations (19a) and (19b)), which may result in splitting the beam in two or three dimensions. In several embodiments, beam can be shifted by using phase tilting at the aperture, which can be substantially equivalent to spatial shifting. In several embodiments, phase tilting can be performed using the following Fourier transform pair: 
     
       
         
           
             
               
                 
                   
                     e 
                     
                       j 
                       ⁢ 
                       a 
                       ⁢ 
                       x 
                     
                   
                   = 
                   
                     
                       cos 
                       ⁡ 
                       ( 
                       
                         a 
                         ⁢ 
                         x 
                       
                       ) 
                     
                     + 
                     
                       j 
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         ( 
                         ax 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     21 
                     ⁢ 
                     a 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     ⁡ 
                     ( 
                     
                       e 
                       
                         j 
                         ⁢ 
                         a 
                         ⁢ 
                         x 
                       
                     
                     ) 
                   
                   = 
                   
                     δ 
                     ⁡ 
                     ( 
                     
                       ξ 
                       - 
                       
                         a 
                         
                           2 
                           ⁢ 
                           π 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   
                     21 
                     ⁢ 
                     b 
                   
                   ) 
                 
               
             
           
         
       
     
     In one embodiment, this function describes an aperture which is only phase modulated since the magnitude of the exponential term is one. In one embodiment, each spatial location has an element that is under a different phase which can be expressed as the ratio of the imaginary (sine) and real (cosine) parts as follows: 
     
       
         
           
             
               
                 
                   
                     
                       θ 
                       ⁡ 
                       ( 
                       i 
                       ) 
                     
                     = 
                     
                       
                         tan 
                         
                           - 
                           1 
                         
                       
                       ( 
                       
                         
                           sin 
                           ⁡ 
                           ( 
                           
                             a 
                             ⁢ 
                             x 
                           
                           ) 
                         
                         
                           cos 
                           ⁡ 
                           ( 
                           
                             a 
                             ⁢ 
                             x 
                           
                           ) 
                         
                       
                       ) 
                     
                   
                   ) 
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     Equation (22) expresses the phase differences spatially. 
     In various embodiments, time delays associated with the propagation of ultrasound waves can be used to describe the phase shift or tilt for focusing the beam. In one embodiment, a transducer aperture can be a focused circular bowl having the following geometry: 
         r   2 +( z−z   f ) 2   =z   f   2   (23a)
 
         r   2   =x   2   +y   2   (23b)
 
     Equations (23a) and (23b) describe a circular bowl that is centered at the bowl apex with a focal length zf. In one embodiment, the focus can be moved from (0, 0, zf) to a spatial point P0 which is located at (x0, y0, z0). The distance to this new spatial point P0 from any point on the bowl can be expressed as: 
         d =( x   1   −x   0 ) 2 +( y   1   −y   0 ) 2 +( z   1   −z   0 ) 2   (24)
 
     where (x1, y1, z1) are points on the bowl aperture that is defined by equations (23a) and (23b). In one embodiment, in order to determine the actual time to the target P0, then the speed of sound c (343.2 m/s) can be divided into a propagation distance d as follows: 
     
       
         
           
             
               
                 
                   t 
                   = 
                   
                     
                       
                         
                           
                             ( 
                             
                               
                                 x 
                                 1 
                               
                               - 
                               
                                 x 
                                 0 
                               
                             
                             ) 
                           
                           2 
                         
                         + 
                         
                           
                             ( 
                             
                               
                                 y 
                                 1 
                               
                               - 
                               
                                 y 
                                 0 
                               
                             
                             ) 
                           
                           2 
                         
                         + 
                         
                           
                             ( 
                             
                               
                                 z 
                                 1 
                               
                               - 
                               
                                 z 
                                 0 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                     c 
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
           
         
       
     
     In one embodiment, in order to obtain a desired constructive interference associated with propagation of delayed ultrasound waves at the focus, equation (25) can be used to calculate the relative time delay to another part of the aperture. In one embodiment, this can be accomplished by subtracting equation (25) by the minimum time delay. The remaining time is the extra time for ultrasound waves emitted by other parts of the aperture to arrive at the new spatial point P 0 . 
     In several embodiments, a focus point of (0, 0, 15 mm) can be moved to a different focus point P 0 . Relative time delays to new focus points P 0  relative to the center or apex of the aperture bowl (as expressed in radial distance) can be calculated using equation (25) and are illustrated in  FIGS.  5 A- 5 D  for a transducer having geometry of outer diameter (OD)=19 mm, inner diameter (ID)=4 mm, and distance to focus (F L )=15 mm. Other embodiments can use other dimensions, the present examples illustrate one non-limiting embodiment. Other dimensions are contemplated.  FIG.  5 A  illustrates the relative time delay  1002   a  (in microseconds) for sound energy travelling from a spatial point on the aperture to reach a target focus point P 0 =(0, 0, 15 mm) in relation to varying radial locations on the bowl aperture according to one embodiment. As expected, the delay illustrated in  FIG.  5 A  is zero since the target point is the same as the focal point, and the focus point has not changed.  FIG.  5 B  illustrates the relative time delay  1002   b  (in microseconds) for sound energy travelling from a spatial point on the aperture to reach a target focus point P 0 =(0, 0, 10 mm) in relation to varying radial locations on the bowl aperture according to one embodiment. As is illustrated, the radial position starts at 2 mm due to a hole in the center of the transducer bowl. In one embodiment, an imaging element can be placed in the hole. Time to the target point P 0 =(0, 0, 10 mm) increases as the radial position on the bowl increases.  FIG.  5 C  illustrates the relative time delay  1002   c  (in microseconds) for sound energy travelling from a spatial point on the aperture to reach a target point P 0 =(0, 0, 20 mm) in relation to varying radial locations on the bowl aperture according to one embodiment. As is illustrated, if the focus is shifted to P 0 =(0, 0, 20) mm, time to the target decreases as the radial position on the bowl increases.  FIG.  5 D  illustrates the relative time delay  1002   d  (in microseconds) for sound energy travelling from a spatial point on the aperture to reach a target focus point P 0 =(2 mm, 0, 14.7 mm) in relation to varying radial locations on the bowl aperture according to one embodiment. In one embodiment, the total distance from the apex to the target point P 0 =(2 mm, 0, 14.7 mm) is about 15 mm. As is illustrated, if the focus is shifted to P 0 =(2 mm, 0, 14.7 mm), time to the target is linearly dependent on the x coordinate of the position on the bowl. Time to the target is less for positions having positive x relative to the apex and greater for positions having negative x relative to the apex. Positions having x coordinates between about −2 mm and about 2 mm occur outside of the inner diameter of the bowl (e.g., where an imaging element can be located). 
       FIGS.  5 A- 5 D  illustrate time delays for propagation of sound from various points on the aperture for constructively placing the sound energy at the focus according to several embodiments. A negative time relative to zero implies that it takes less time for energy from that point to reach a new focus point. A positive time relative to zero implies that it takes more time for energy to reach a new focus point. In one embodiment, if appropriate time delays could be placed on individual points of the bowl, the time delays can be controlled to obtain constructive interference at the new focus. In one embodiment, for transducers comprising piezoelectrically active material, moving the focus from a mechanical focus (0, 0, z f ) to a new focus point P 0  can changes the distances that resonators on the aperture should travel (due to expansion and/or contraction of the material) to create constructive interference at the focus P 0 . These distances can be converted to time delays by dividing by the distances by the speed of sound. In one embodiment, if time delays for the resonators on the surface of the aperture are known, additional time delays to reach the focus P 0  could be accounted for such that desired pressure intensity at the focus P 0  can be achieved. 
     In various embodiments, ultrasound wave of a suitable frequency can be directed to a target area. In one embodiment, a transducer comprising piezoelectrically active material can be electrically excited by a continuous wave signal of a suitable operational frequency to achieve a suitable therapy frequency. In various embodiments of transducers, the operational frequency can be about 4 MHz, about 7 MHz, about 10 MHz, less than about 4 MHz (e.g., between about 20 KHz and about 4 MHz), between about 4 MHz and about 7 MHz, greater than about 10 MHz, etc. In one embodiment, the continuous wave signal can be on or active for a period of between about 20 msec to 30 msec. This in turn can imply that the aperture is excited by between about 80,000 cycles to about 300,000 cycles of the excitation signal. In one embodiment, other suitable periods of the excitation signal being active can be used, such as for example, less than about 20 msec, greater than about 30 msec, and the like. In one embodiment, a short duration of the excitation signal being active can make it unnecessary to obtain constructive interference at the focus. This can be a result of time delays for propagation of an ultrasonic wave from different points of the aperture to a focus point P 0  being greater than the duration of the excitation signal being active. In one embodiment, it may be sufficient to modify phases corresponding to aperture locations based on the operational frequency without controlling the time delays for obtaining constructive interference. In one embodiment, phases corresponding to aperture locations may be modified and, additionally, time delays for obtaining constructive interference at a new focus point may be controlled. 
       FIGS.  6 A- 6 C  illustrate phase delays associated with propagation of sound to focus relative to the apex of an aperture according to several embodiments. In one embodiment, phase delays are associated with time delays.  FIG.  6 A  illustrates the relative phase delays  1012   a ,  1014   a , and  1016   a  (in degrees) for sound energy travelling from a spatial point on the aperture to reach a target focus point P 0 =(0, 0, 10 mm) in relation to varying radial locations on the bowl aperture according to one embodiment. Curve  1012   a  corresponds to an excitation signal of about 4 MHz, curve  1014   a  corresponds to an excitation signal of about 7 MHz, and curve  1016   a  corresponds to an excitation signal of about 10 MHz.  FIG.  6 B  illustrates the relative phase delays  1012   b ,  1014   b , and  1016   b  (in degrees) for sound energy travelling from a spatial point on the aperture to reach a target focus point P 0 =(0, 0, 20 mm) in relation to varying radial locations on the bowl aperture according to one embodiment. Curve  1012   b  corresponds to an excitation signal of about 4 MHz, curve  1014   b  corresponds to an excitation signal of about 7 MHz, and curve  1016   b  corresponds to an excitation signal of about 10 MHz.  FIG.  6 C  illustrates the relative phase delays  1012   c ,  1014   c , and  1016   c  (in degrees) for sound energy travelling from a spatial point on the aperture to reach a target focus point P 0 =(2 mm, 0, 14.7 mm) in relation to varying radial locations on the bowl aperture according to one embodiment. Curve  1012   c  corresponds to an excitation signal of about 4 MHz, curve  1014   c  corresponds to an excitation signal of about 7 MHz, and curve  1016   c  corresponds to an excitation signal of about 10 MHz. As is illustrated in  FIGS.  6 A- 6 C , in one embodiment, whether the aperture attempts to focus shallow, deep, or laterally, which can be related to the operational frequency, is related to a number of discontinuities in the phase delay. The number of discontinuities over a given length increases with the operational frequency of the excitation signal. In one embodiment, as is explained below, manufacturing and system limitations may increase the number of discontinuities. In one embodiment, as is illustrated in  FIG.  6 B , the rate of phase delay transitions increases toward the edge of the transducer (e.g., right part of the graph) regardless of whether the transducer is used to focus deep or shallow. In one embodiment, as is illustrated in  FIG.  6 C , the rate of phase delay transitions is substantially constant when a transducer is used to tilt the beam.  FIGS.  5 B- 5 D  and  FIGS.  6 A- 6 C  illustrate additional time and phase to a focus point from a point on a transducer bowl. In one embodiment, the additional time and/or phase can be reduced or eliminated by placing an opposite of the time and/or phase delay at appropriate transducer locations. 
     Therapy Delivery Using Discrete Phase Shifting 
     In one embodiment, delay and/or phase quantization can affect the precision that is used to represent time and/or phase delays. In other words, the discrete delay and/or discrete phase can be used. In one embodiment, a precision of time and/or phase delays can be limited by system parameters, such as a system clock and/or number of bits available for representing the delay. In one embodiment, other system parameters can instead or further limit the precision. In one embodiment, phase delays are equally spaced around the unit circle (360°). In one embodiment, phase delays can aperiodic or unequally spaced around the unit circle. Table 4 shows phase quantization levels according to several embodiments. Additional numbers of levels (greater than 8) can be used in several embodiments. As is shown in Table 4 two phases (N=2), 0° and 180°, can represent a minimum level of phase control for changing the focus point of an ultrasound beam according to one embodiment. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 4 
               
               
                   
                   
               
               
                   
                 Number of levels (N) 
                 Phases (degrees) 
               
               
                   
                   
               
             
            
               
                   
                 2 
                 0, 180 
               
               
                   
                 3 
                 0, 120, 240 
               
               
                   
                 4 
                 0, 90, 180, 270 
               
               
                   
                 5 
                 0, 72, 144, 216, 288 
               
               
                   
                 6 
                 0, 60, 120, 180, 240, 300 
               
               
                   
                 7 
                 0, 51, 103, 154, 206, 257, 309 
               
               
                   
                 8 
                 0, 45, 90, 135, 180, 225, 270, 315 
               
               
                   
                   
               
            
           
         
       
     
       FIGS.  7 A- 7 C  illustrate discrete or quantized phase delays for various quantization levels, where phase delays are associated with propagation of sound to focus relative to the apex of an aperture according to several embodiments.  FIGS.  7 A- 7 C  illustrate sound propagation at an operational frequency of about 7 MHz.  FIG.  7 A  illustrates the relative quantized phase delays  1022   a ,  1024   a , and  1026   a  (in degrees) for sound energy travelling from a spatial point on the aperture to reach a target focus point P0=(0, 0, 10 mm) in relation to varying radial locations on the bowl aperture according to one embodiment. Curve  1022   a  corresponds to two phase quantization levels, curve  1024   a  corresponds to three phase quantization levels, and curve  1026   a  corresponds to four phase quantization levels.  FIG.  7 B  illustrates the relative quantized phase delays  1022   b ,  1024   b , and  1026   b  (in degrees) for sound energy travelling from a spatial point on the aperture to reach a target focus point P0=(0, 0, 20 mm) in relation to varying radial locations on the bowl aperture according to one embodiment. Curve  1022   b  corresponds to two phase quantization levels, curve  1024   b  corresponds to three phase quantization levels, and curve  1026   b  corresponds to four phase quantization levels.  FIG.  7 C  illustrates the relative quantized phase delays  1022   c ,  1024   c , and  1026   c  (in degrees) for sound energy travelling from a spatial point on the aperture to reach a target focus point P0=(2 mm, 0, 14.7 mm) in relation to varying radial locations on the bowl aperture according to one embodiment. Curve  1022   c  corresponds to two phase quantization levels, curve  1024   c  corresponds to three phase quantization levels, and curve  1026   c  corresponds to four phase quantization levels. In several embodiments, as the number of quantization levels increases as is shown in  FIGS.  7 A- 7 C  (e.g., curves  1026   a ,  1026   b , and  1026   c ), quantized phase delay patterns in the one embodiment with a frequency of 7 MHz become substantially similar to unquantized phase delay patterns shown in  FIGS.  6 A- 6 C  (e.g., curves  1014   a ,  1014   b , and  1014   c ). 
     In one embodiment with reference to curve  1022   c  of  FIG.  7 C  (two-level phase quantization), demonstrates that when a focused beam is steered 2 mm and −2 mm, a resulting phase delay pattern is substantially similar with transition from 0° to 180° occurring at substantially same spatial frequency. There is a slight spatial shift in the phase delay pattern. Since the phase delay pattern is substantially similar at 2 mm and −2 mm, in one embodiment, acoustic intensity distribution at the focus may have a peak at both foci locations simultaneously. In one embodiment, if the phase quantization is two levels, a phase solution for a specific focus will also be a solution for another location. In one embodiment, this result can be similar for modification of the focus along the beam axis. If the phase quantization is two levels, then a solution for one focus can also be a solution for another focus. 
       FIG.  8 A  illustrates discrete or quantized phase delays associated with propagation of sound, at an operational frequency of about 7 MHz, to focus relative to the apex of an aperture according to several embodiments.  FIG.  8 A  illustrates the relative phase delays  1032   a  and  1034   a  (in degrees) for sound energy travelling from a spatial point on the aperture to reach target focus points (2 mm, 0, 14.7 mm) and (−2 mm, 0, 14.7 mm) respectively. Curves  1032   a  and  1034   a  are shown in relation to varying radial locations on the bowl aperture according to one embodiment. In one embodiment, the quantization level of two is shown in  FIG.  8 A . As shown in  FIG.  8 A , quantized phase delay patterns for the two foci are substantially similar. 
       FIG.  8 B  illustrates discrete or quantized phase delays associated with propagation of sound, at an operational frequency of about 7 MHz, to focus relative to the apex of an aperture according to several embodiments.  FIG.  8 B  illustrates the relative phase delays  1032   b  and  1034   b  (in degrees) for sound energy travelling from a spatial point on the aperture to reach target focus points (0, 0, 10.25 mm) and (0, 0, 27 mm) respectively. Curves  1032   b  and  1034   b  are shown in relation to varying radial locations on the bowl aperture according to one embodiment. In one embodiment, the quantization level of two is shown in  FIG.  8 B . As shown in  FIG.  8 B , quantized phase delay patterns for the two foci are substantially 180° out of phase. 
     In various embodiments, continuous or discrete amplitude modulation at an aperture and/or continuous or discrete phase delays to focus an ultrasound beam can be used. In one embodiment, it may be advantageous to provide a mechanical focal point rather than using aperture amplitude modulation and/or phase control in a flat aperture because the focal gain associated with mechanical focus may be preferable. In one embodiment, complexity of aperture or system design may be reduced if a mechanical focus can be created and modulation and/or phase delay techniques can be applied to the mechanical focus. One advantage can be a reduction in a number of discrete phase transitions for focusing the beam at a new focal point. Another advantage can be that a distance between different discrete phase levels can be increased when the aperture is already mechanical focused, which may result in using fewer quantization levels, such as two, three, four, etc. 
     In various embodiments, fabrication methods, including piezoelectric material poling and/or discrete system phasing, can be used to manufacture transducers configured to split or focus an ultrasound beam in two and/or three dimensions from a mechanical focus. The following lists several non-limiting examples of transducer designs. In various embodiments, other transducer designs can be manufactured using the disclosed methods. 
     Multi-Focal Energy Delivery Using Transducer Poling 
     In several embodiments, a transducer can comprise piezoelectric material. Piezoceramic material can be poled at elevated temperatures and high electric fields to create a net dipole moment in the material. A net dipole moment can allow the piezoceramic material to have a piezoelectric effect that causes either material contraction or expansion when an electric field is placed across a whole or part of the material in the direction of the dipole moment. In one embodiment, parts of a transducer, such as a transduction element, can be treated to have different poling moment features. In one embodiment, a single transduction element can be treated to have one, two, or more poling features. In one embodiment, a single transduction element can be treated to have one pole. In another embodiment, parts of an element can be treated with one pole, and non-treated parts of the element can have a second pole. In one embodiment, a poling treatment can be painted on a transduction element. 
       FIG.  9    shows a schematic diagram of a poled piezoceramic material and resulting behavior when a voltage is applied according to one embodiment. In one embodiment, a transducer can comprise PZT  1052  piezoceramic material. The arrow shown in the PZT material  1052  is a net dipole moment. In one embodiment, if a voltage is placed across the PZT material  1052  such that the electric field is in the opposite or substantially opposite direction of the dipole moment (as is shown in  1082 ), then the material contracts. In one embodiment, if a voltage is placed across the PZT material  1052  such that the electric field is in the same or substantially same direction as the dipole moment (as is shown in  1072 ), then the material expands. In one embodiment, the PZT material  1052  does not expand or contract when no voltage is applied across the material, as is shown in  1062 . 
     In several embodiments, piezoelectric material poling can be used to implement aperture amplitude modulation. In one embodiment, two level modulation can be equivalent to two level phase quantization. As is shown in equations (12)-(14), an ultrasonic beam emitted by a transducer aperture can be modulated to appear at two (or more) locations in a focal plane shifted by a distance that is related to the spatial frequency of a modulation function (e.g., cosine and/or sine function). In one embodiment, poling direction may be used to modify the amplitude modulation at the aperture, and to approximate cosine and/or sine amplitude modulation. As is shown in  FIG.  9   , in one embodiment, poling or applying voltage across the whole or part of the material can provide three levels of amplitude modulation: −1 (contraction of the material), 1 (expansion of the material), and 0 (no change to the shape of the material).  FIGS.  10 A- 10 B  illustrate approximations of amplitude modulation using two and three levels of poling according to several embodiments.  FIG.  10 A  illustrates approximations of amplitude modulation using a sine function according to one embodiment. The x-axis represents relative distance with respect to an apex of the aperture and the y-axis represents amplitude of the modulation function. Curve  1092   a  illustrates the modulation function (e.g., sine function), curve  1094   a  illustrates approximation using two levels of poling (e.g., ±1), and curve  1096   a  illustrates approximation using three levels of poling (e.g., ±1 and 0).  FIG.  10 B  illustrates approximations of amplitude modulation using a sine function with DC offset of 0.25 according to one embodiment. The x-axis represents relative distance with respect to an apex of the aperture and the y-axis represents amplitude of the modulation function. Curve  1092   b  illustrates the modulation function (e.g., sine function), curve  1094   b  illustrates approximation using two levels of poling (e.g., ±1), and curve  1096   b  illustrates approximation using three levels of poling (e.g., ±1 and 0). In one embodiment, as is illustrated in  FIGS.  10 B , the width of a positive poled region (having amplitude of 1) is greater than the width of a negative poled region (having amplitude of −1) so that a mean amplitude is substantially equal to the DC offset (e.g., 0.25). The limitation of two or three levels limits the achievable DC offset between −1 and 1. In several embodiments, more than three levels of poling can be used for amplitude modulation. 
     In one embodiment, in order to quantify the energy distribution at the focus, then the square wave can be represented in terms of a function that has a related Fourier transform pair. The Fourier series expansion for a square wave of period c is: 
     
       
         
           
             
               
                 
                   
                     
                       f 
                       
                         s 
                         ⁢ 
                         q 
                         ⁢ 
                         u 
                         ⁢ 
                         a 
                         ⁢ 
                         r 
                         ⁢ 
                         e 
                       
                     
                     ( 
                     
                       x 
                       c 
                     
                     ) 
                   
                   = 
                   
                     
                       
                         4 
                         π 
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             n 
                             = 
                             1 
                           
                           ∞ 
                         
                         
                           
                             sin 
                             ⁡ 
                             ( 
                             
                               2 
                               ⁢ 
                               
                                 π 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     n 
                                   
                                   - 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               c 
                               ⁢ 
                               t 
                             
                             ) 
                           
                           
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 n 
                               
                               - 
                               1 
                             
                             ) 
                           
                         
                       
                     
                     = 
                     
                       
                         4 
                         π 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             sin 
                             ⁡ 
                             ( 
                             
                               2 
                               ⁢ 
                               π 
                               ⁢ 
                               c 
                               ⁢ 
                               t 
                             
                             ) 
                           
                           + 
                           
                             
                               1 
                               3 
                             
                             ⁢ 
                             
                               sin 
                               ⁡ 
                               ( 
                               
                                 2 
                                 ⁢ 
                                 π 
                                 ⁢ 
                                 3 
                                 ⁢ 
                                 c 
                                 ⁢ 
                                 t 
                               
                               ) 
                             
                           
                           + 
                           
                             
                               1 
                               5 
                             
                             ⁢ 
                             
                               sin 
                               ⁡ 
                               ( 
                               
                                 2 
                                 ⁢ 
                                 π 
                                 ⁢ 
                                 5 
                                 ⁢ 
                                 c 
                                 ⁢ 
                                 t 
                               
                               ) 
                             
                           
                           + 
                           … 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
           
         
       
     
     In one embodiment, a circular aperture with amplitude modulation described in equation (25) can be described as: 
     
       
         
           
             
               
                 
                   
                     
                       f 
                       aperture 
                     
                     ( 
                     
                       x 
                       , 
                       y 
                     
                     ) 
                   
                   = 
                   
                     
                       
                         f 
                         
                           s 
                           ⁢ 
                           q 
                           ⁢ 
                           u 
                           ⁢ 
                           a 
                           ⁢ 
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                           ⁢ 
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                       ( 
                       
                         x 
                         c 
                       
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                     ⁢ 
                     
                       ( 
                       
                         
                           circ 
                           ⁡ 
                           ( 
                           
                             r 
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                             c 
                             ⁡ 
                             ( 
                             
                               r 
                               b 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     26 
                     ⁢ 
                     a 
                   
                   ) 
                 
               
             
           
         
       
     
     The Fourier transform of this function is: 
     
       
         
           
             
               
                 
                   
                     
                       F 
                       
                         x 
                         , 
                         y 
                       
                     
                     ( 
                     
                       
                         f 
                         aperture 
                       
                       ( 
                       
                         x 
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                       ) 
                     
                     ) 
                   
                   = 
                     
                   
                     
                       [ 
                       
                         
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                   ( 
                   
                     26 
                     ⁢ 
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     Equation (26b) may be simplified as follows: 
     
       
         
           
             
               
                 
                   
                     
                       F 
                       
                         x 
                         , 
                         y 
                       
                     
                     ( 
                     
                       
                         f 
                         aperture 
                       
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                   = 
                     
                   
                     [ 
                     
                       
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     In one embodiment, sound wave pressure in the focal plane includes repeating patterns of the main beam at multiple spatial locations separated by a distance of 2c between each beam. The repeating patterns can be decreasing in the amplitude. 
       FIGS.  11 A- 11 H  illustrate some embodiments of aperture modulation or apodization functions (using two-level poling or three-level poling) and some corresponding normalized intensity distributions of the sound wave pressure at the focus or foci for a transducer excited by a 7 MHz excitation signal according to several embodiments. In one embodiment, transducers illustrated in  FIGS.  11 A- 11 H  are configured a circular bowls with OD=19 mm and F L =15 mm.  FIGS.  11 A- 11 B  illustrate apodization profile without splitting the beam and a corresponding intensity distribution according to one embodiment.  FIG.  11 B  illustrates that intensity is concentrated at the focus  1108 .  FIGS.  11 C- 11 D  illustrate apodization profile with laterally splitting the beam by about 1.1 mm between the foci peaks and a corresponding intensity distribution according to one embodiment. As is illustrated by region  1104  in  FIG.  11 A  and region  1114  in  FIG.  11 C , in several embodiments, part of an aperture of the transducer has an apodization of zero, which represents an inner diameter (ID) of the bowl. In some embodiments, these regions  1104  and  1114 , which are illustrated as being about 4 mm in diameter, can correspond to regions where an imaging element can be located. In one embodiment, apodization of the imaging element can be represented by region  1106 . 
     With reference to  FIG.  11 C , in one embodiment, amplitude modulation for a 1.1 mm split between the foci peaks is illustrated. In one embodiment, if two poling or apodization levels are used, then 8 strips of substantially equal width (except at the edges) are defined on the aperture surface. For example, two such strips are labeled as  1112  and  1112 ′. In one embodiment, the polarization of the strips alternates from −1 to +1 across the transducer surface. The resulting beam pattern is shown in  FIG.  11 D . As expected, the ultrasonic beam appears at two foci  1120  and  1120 ′ are located at about −0.55 mm and 0.55 mm. Higher frequency components of the beam are visible in regions  1122  and  1122 ′ at a distance of about 1.65 mm from the beam axis. In one embodiment, these components have lower intensity than foci regions  1120  and  1120 ′. The higher frequency components can correspond to the third harmonic having a lower intensity, as is expressed in equation (26c). In various embodiments, such as illustrated in  FIGS.  11 E- 11 H , polarization of portions  1125 ,  1125 ′ of the transducer surface can include lines, curves, shapes, waves, patterns, etc. In one embodiment, features of a portions  1125 ,  1125 ′ can be used to maintain a foci split, and can redistribute energy pre-focally and/or post-focally for less heating. 
     In one embodiment, the split of the beam may occur in both x (azimuth) and y (elevation) dimensions. In one embodiment, x and y axis splits may be treated independently when performing the Fourier transform. In one embodiment, an aperture can be designed for splitting the beam in the x dimension by about 1.0 mm and in the y dimension by about 0.5 mm. The corresponding aperture modulation function can be represented as: 
     
       
         
           
             
               
                 
                   
                     
                       f 
                       aperture 
                     
                     ( 
                     
                       x 
                       , 
                       y 
                     
                     ) 
                   
                   = 
                   
                     
                       
                         f 
                         
                           s 
                           ⁢ 
                           q 
                           ⁢ 
                           u 
                           ⁢ 
                           a 
                           ⁢ 
                           r 
                           ⁢ 
                           e 
                         
                       
                       ( 
                       
                         y 
                         d 
                       
                       ) 
                     
                     ⁢ 
                     
                       
                         f 
                         
                           s 
                           ⁢ 
                           q 
                           ⁢ 
                           u 
                           ⁢ 
                           a 
                           ⁢ 
                           r 
                           ⁢ 
                           e 
                         
                       
                       ( 
                       
                         x 
                         c 
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           circ 
                           ⁡ 
                           ( 
                           
                             r 
                             a 
                           
                           ) 
                         
                         - 
                         
                           c 
                           ⁢ 
                           i 
                           ⁢ 
                           r 
                           ⁢ 
                           
                             c 
                             ⁡ 
                             ( 
                             
                               r 
                               b 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
     The spatial frequency for alternating amplitude modulation can be calculated as described above in connection with equations 26(a)-(c), with the exception that the calculation is performed for two dimensions.  FIGS.  12 A- 12 D  illustrate some embodiments of aperture modulation or apodization functions (using two-level poling) and a corresponding normalized intensity distributions of the sound wave pressure at the focus or foci for a transducer excited by a 7 MHz excitation signal according to several embodiments. In one embodiment, transducers illustrated in  FIGS.  12 A- 12 D  are configured a circular bowls with OD=19 mm and FL=15 mm.  FIG.  12 A  shows an apodization function for the aperture according to one embodiment. As is illustrated, the checkerboard pattern  1132  and  1136  is alternating in amplitude in both x and y directions. As is illustrated in  FIG.  12 B , the checkerboard pattern produces four substantially distinct ultrasound beams  1140 ,  1140 ′,  1142 , and  1142 ′ separated by the expected distances, namely by about 1.0 mm in x direction and by about 0.5 mm in y direction. In one embodiment, a five point pattern can be achieved by adding a constant to an apex of the aperture, which may have a corresponding intensity distribution at the origin. 
     In one embodiment, as is illustrated in  FIGS.  12 C- 12 D , a line of four peaks is obtained by placing multiple frequencies along the same dimension (e.g., x dimension). The modulation function can be expressed as: 
     
       
         
           
             
               
                 
                   
                     
                       f 
                       aperture 
                     
                     ( 
                     
                       x 
                       , 
                         
                       y 
                     
                     ) 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             f 
                             
                               s 
                               ⁢ 
                               q 
                               ⁢ 
                               u 
                               ⁢ 
                               a 
                               ⁢ 
                               r 
                               ⁢ 
                               e 
                             
                           
                           ( 
                           
                             x 
                             d 
                           
                           ) 
                         
                         + 
                         
                           
                             f 
                             
                               s 
                               ⁢ 
                               q 
                               ⁢ 
                               u 
                               ⁢ 
                               a 
                               ⁢ 
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                               ⁢ 
                               e 
                             
                           
                           ( 
                           
                             x 
                             c 
                           
                           ) 
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           circ 
                           ⁡ 
                           ( 
                           
                             r 
                             a 
                           
                           ) 
                         
                         - 
                         
                           c 
                           ⁢ 
                           i 
                           ⁢ 
                           r 
                           ⁢ 
                           
                             c 
                             ⁡ 
                             ( 
                             
                               r 
                               b 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
           
         
       
     
       FIG.  12 C  shows an apodization function for the aperture according to one embodiment. As is illustrated, the pattern  1142  and  1146 , the polarization of the strips alternates from −1 to +1 across the transducer surface. As is illustrated in  FIG.  12 D , in one embodiment, the pattern produces four substantially distinct ultrasound beams  1150 ,  1152 ,  1154 , and  1156  separated by about 1.0 mm and 3.0 mm in an x direction. 
     In one embodiment, an axial split of the beam or split along one dimension is achieved such that the beam remains axis symmetric. In one embodiment, splitting the beam axially using only two phases from poling can be more difficult than obtaining a lateral split. This can be due to the difficulty of obtaining intensity balance between the two or more peaks. In one embodiment, two phases may produce two simultaneous intensity peaks with one shallower than the other. The deeper intensity peak can be of lower intensity than the shallow peak due to additional diffraction and attenuation in tissue. In one embodiment, more than two phases may be used to achieve an axial split. 
     In several embodiments, splitting an ultrasonic beam simultaneously, nearly simultaneously, or sequentially into two or more foci points can be achieved through an application of discrete system phasing.  FIG.  13    is a schematic illustration of a two-phase system  1200  according to one embodiment. As is illustrated, block  1202  is a AC voltage (or current) source that drives the discrete phase shifters, blocks  1204  and  1206  are discrete phase shifters by 0° and 180° respectively, and blocks  1208  and  1210  are transducer portions that are phase shifted. In one embodiment, discrete phase shifters  1204  and  1206  can be configured to phase shift the AC voltage (or current) signal supplied by the source  1202 , so that the resulting signals are 180° out of phase. In one embodiment, discrete phase shifters  1204  and  1206  can be configured to excite different portions of the transducer. In one embodiment, the system  1200  is configured to mimic two levels of material poling. In one embodiment, it may be desirable to electrically isolate the transducer portions  1208  and  1210 . Electrical isolation and corresponding connection scheme can determine a resultant beam pattern at the focus according to one embodiment. In one embodiment, no electrical isolation may be performed. With reference to  FIG.  1   , in several embodiments, discrete phase shifters may be placed in or on the controller  300 , hand wand  100 , module  200 , and/or transducers of the ultrasound system  20 . In one embodiment, continuous phase shifting may be used. 
     In several embodiments, more than two discrete phase shifters can be used (e.g., as is shown in Table 4). The increase in the number of phases may result in an improved approximation of the phase delays for steering and/or focus the beam. In one embodiment, four discrete phase shifters can be used.  FIG.  14    is a schematic illustration of a selectable, four-phase system  1250  according to one embodiment. As is illustrated, blocks  1252 ,  1254 ,  1256 , and  1258  are AC voltage (or current) sources that drive the discrete phase shifters  1262 ,  1264 ,  1266 , and  1268 . Each discrete phase shifter block can be configured to provide four different phases 0°, 90°, 180°, and 270°. In one embodiment, multiplexers  1272 ,  1274 ,  1276 , and  1278  can be included to select a particular phase of a signal. Signal with selected phase can be applied to portions  1282 ,  1284 ,  1286 , and  1288  of a transducer  1280 . In one embodiment a portion is a part of a single transducer with a single transduction element. In one embodiment, a portion can be a transduction element. As is illustrated, each portion  1282 ,  1284 ,  1286 , and  1288  of the transducer  1280  has a selectable phase (e.g., 0°, 90°, 180°, or 270°). In one embodiment, portions  1282 ,  1284 ,  1286 , and  1288  can be electrically isolated (e.g., from each other). In one embodiment, if the transducer  1280  is divided or segmented into portions  1282 ,  1284 ,  1286 , and  1866 , the ultrasonic beam could be steered and focused to multiple foci locations. 
     In one embodiment, an advantage of providing more discrete phase shifters can be illustrated by considering a flat disc or ring transducer and a measured intensity at the focus as compared to a measured intensity at the focus of a substantially perfectly focused circular bowl transducer.  FIG.  15    illustrates performance of a discrete-phase system according to one embodiment. In one embodiment, the bowl transducer can be configured to have OD=19 mm and F L =15 mm, and its intensity (in dB) is illustrated by line  1302 . Intensity of the flat ring transducer is illustrated by line  1306 . As is illustrated, the improvement in the focal intensity produced by the flat ring transducer increases (e.g., exponentially) between about two and 5-6 discrete phase levels, but starts to level off after about 5-6 discrete phases. In one embodiment, the intensity asymptotically approaches about −2.3 dB (line  1304 ). As is illustrated, in one embodiment flat ring transducer (line  1306 ) produces a smaller focal gain than the bowl transducer (line  1302 ). As can be seen, in one embodiment, adding additional discrete phase levels can improve the intensity at the focus and, thereby, improve the transducer performance. 
     In one embodiment, a difference in intensity between a desired focus point and an ideal focus point can be changed by using a focused bowl. In one embodiment, a circular bowl transducer with OD=19 mm and F L =15 mm can be used initially. Subsequently, in one embodiment, discrete phasing techniques can be used to move the focus to depth of about 12 mm or 18 mm.  FIGS.  16 A- 16 B  are plots illustrating performance of discrete-phase systems at various foci points according to several embodiments.  FIG.  16 A  illustrates performance  1316  of a bowl transducer (OD=19 mm and F L =15 mm) when the focus is moved to 12 mm using discrete phasing when compared to performance  1312  of a bowl transducer (OD=19 mm bowl and F L =12 mm) according to one embodiment. As is illustrated, line  1316  asymptotically approaches about −1.3 dB (line  1314 ). In one embodiment, comparing line  1316  with performance of flat disc transducer, which is illustrated by line  1306  in  FIG.  15   , intensity produced by the bowl transducer has been improved.  FIG.  16 B  illustrates performance  1326  of a bowl transducer (OD=19 mm and F L =15 mm) when the focus is moved to 18 mm using discrete phasing when compared to performance  1322  of a bowl transducer (OD=19 mm bowl and F L =18 mm) according to one embodiment. As is illustrated, line  1326  asymptotically approaches about 0.5 dB (line  1324 ). As is illustrated, performance of the bowl transducer with discrete phasing (line  1326 ) can exceed performance of an ideal transducer (line  1322 ), such as when number of discrete phase levels exceeds about six. In one embodiment, it may be advantageous to use discrete phases to move the focus deeper. 
     Therapy Delivery Using Amplitude Modulation and Discrete Phase Shifting 
     In several embodiments, amplitude modulation (e.g., realized via material poling) can be used in addition to discrete phasing. In one embodiment, splitting of an ultrasound beam may cause an increase in transducer power that may be difficult to obtain due to, for example, system or transducer material limitations. It may be desirable to phase shift or tilt the ultrasound beam from one focal position to another focal position. In one embodiment, split of the ultrasound beam may be difficult to achieve due to a possibility of excessive heating of tissue before focus. In one embodiment, linear sequences of TCPs may be created sequentially or substantially sequentially without moving a transducer, which can result in reduction of therapy time. In one embodiment, the transducer can be moved to further distribute treatment points. In one embodiment, a transducer can be a circular bowl transducer excited by 7 MHz excitation signal and having OD of about 19 mm, ID of about 4 mm, and F L  of about 15 mm. Linear TCP sequences can be spaced about 1.0 mm apart. It may be desirable to split the ultrasound beam so two linear TCP sequences are created simultaneously or substantially simultaneously about 1.0 mm apart from each other. However, in one embodiment, as compared to intensity of a beam that is not split, each of the split beams can have intensity that is approximately 2.4 times lower. Due to a potential for excessive heating of tissue located before focus, power delivered to the transducer may not be increased by about 2.4 times to compensate for the reduction in intensity. In one embodiment, quadrature phasing may be used to create linear TCP sequences one at a time. Quadrature phasing can be accomplished by combining material poling with discrete system phasing. In one embodiment, using quadrature phasing may relate to an increase in power of approximately 1.2 times when quadrature phasing is applied to a focused bowl transducer. In one embodiment, such slight increase in power may be desirable. 
       FIGS.  17 A- 17 B  illustrate quadrature control of a transducer by combining poling and discrete system phasing according to one embodiment.  FIG.  17 A  illustrates, in one embodiment, individual strips (e.g.,  1402 ,  1404 , etc.) defined across a focused circular bowl transducer  1400  at a pitch configured to achieve an about 1.0 mm in the ultrasonic beam produced by the transducer. The focus of the transducer is a single beam  1408  in the plane parallel to the transducer face. Transducer  1400  is not configured with discrete phasing. In one embodiment, as is illustrated in  FIG.  17 B , strips of transducer  1410  are poled by alternating the phasing direction. For example, strip  1412  has a phase of 0° and strip  1414  has a phase of 180°. As is shown in the intensity plot, two intensity peaks  1418  and  1418 ′ appear substantially along a line at a focal depth. 
     In one embodiment, creating two intensity peaks  1430  and  1432  may be undesirable due to limitations of the system (e.g., power supply) and/or transducer materials. For example, more power may need to be supplied to the transducer to create two TCPs simultaneously or nearly simultaneously.  FIG.  17 C  illustrates modulation of an aperture of a transducer  1420  using an additional phase shift (by 90°) according to one embodiment. As is illustrated, strip  1422  has a phase of 0°, and is further divided into a region or sub-strip  1426  having a phase of 90° and sub-strip  1428  having a phase of 0°. Further, strip  1424  has a phase of 180° (e.g., alternating phase with respect to strip  1422 ), and is further divided into a region or sub-strip  1430  having a phase of 270° and sub-strip  1432  having a phase of 180°. In one embodiment, these two additional phases (e.g.,  1426  and  1428 ) can be electrically connected to the transducer  1420  through a conductive bond and, optionally, a switch or flex circuit configured to separate the two phases. Similar to the embodiments illustrated in  FIGS.  17 A- 17 B , transducer  1420  is poled so that the phase alternates between 0° and 180° between adjacent strips. In one embodiment, one half of the transducer  1420  is excited with 0° phase excitation signal and the other half is excited with 180° phase excitation signal. In one embodiment, a pitch of the phase variation is decreased by two with the additional phasing (e.g., sub-strips  1426  and  1428 ). In one embodiment, when discrete phasing is combined with poling (e.g., alternating the phase between 0° and 180° between adjacent strips  1422  and  1424 ), four distinct phases can be provided, namely 0°, 90°, 180°, and 270°. As is illustrated in  FIG.  17 C , the repeating phase pattern applied across the transducer  1420  from left to right can be 90°, 0°, 270°, and 180°. As is illustrated in the intensity plot, in one embodiment, a peak  1438  about −1 mm away from a beam axis at a focal depth can be created. In one embodiment, as is illustrated in  FIG.  17 D , if the phase pattern has a reversed order of 0° (sub-strip  1446 ), 90° (sub-strip  1448 ), 180° (sub-strip  1450 ), and 270° (sub-strip  1452 ), then a peak  1458  moves about +1 mm away from a beam axis. As is illustrated in  FIG.  17 D , strip  1442  has a phase of 0° and strip  1444  has a phase of 180° (e.g., alternating phase with respect to strip  1442 ). 
       FIG.  18    is a schematic illustration of a two-phase switchable system  1500  according to one embodiment. As is illustrated, the system  1500  includes an AC voltage (or current) source  1502  that drives the discrete phase shifters  1504  (0° phase shifter) and  1506  (90° phase shifter), switches  1508  and  1510 , and transducer portions  1512  and  1514 . In one embodiment, discrete phase shifters  1504  and  1506  can be configured to phase shift the AC voltage (or current) signal supplied by the source  1502 , so that the resulting signals are 90° out of phase. In one embodiment, discrete phase shifters  1504  and  1506  can be configured to excite different portions (e.g., strips) of the transducer. Output of discrete phase shifters  1504  and  1506  can be connected to switches  1508  and  1510  that are connected to different portions  1512  and  1514  of the transducer. On one embodiment, the switches  1508  and  1510  cause the phase of the voltage (or current) signal provided by the source  1502  to toggle between 0° and 90° such that the phase pattern at the transducer reverses the order and causes a focal point to move from one side of the beam axis to another side of the beam axis, as is illustrated in  FIGS.  17 C- 17 D . In one embodiment, phase shifters  1504  and  1506  can shift the phase by any suitable value, such as 30°, 45°, 120°, 145°, 180°, etc. 
     Therapy Delivery Using Amplitude Modulation With Walking 
     In one embodiment, modulating or splitting an ultrasound beam axially and/or laterally, for example so that multiple linear sequences of TCPs are created simultaneously, substantially simultaneously, or sequentially may necessitate supply of additional power to a transducer in order to achieve substantially same intensity at focal point(s) as an unmodulated beam. In one embodiment, such increase in power can cause a possibility of excessive heating in tissue proximal (pre-focal) and/or distal (post-focal) to the focus. For example, for a given transducer configuration, splitting an ultrasound beam from a focal position of about (0, 0, 15 mm) to focal positions of about (−0.55 mm, 0, 15 mm) and (0.55 mm, 0, 15 mm) may necessitate increasing the supply of power by about 2.2 times in order to produce substantially same intensity at the two focal positions as the intensity in the unmodulated focal position. In one embodiment, such an increase in power may be undesirable. In various embodiments, amplitude modulation can be combined with walking aperture techniques in order to reduce the possibility of excessive heating of tissues in pre-focal and post-focal regions. For example, the maximum intensity measured in the pre-focal and post focal regions may be reduced. 
       FIGS.  19 A- 19 C  are plots of an intensity distribution  1600  in an x-y plane at about 2 mm before focus according to one embodiment. No modulation has been applied to a transducer. The plot  1600  illustrates that the acoustic intensity distribution is axis symmetric about a beam axis. In one embodiment, the symmetry is caused by a circular aperture of the transducer (e.g., a focused circular bowl transducer). The regions of highest intensity  1601 ,  1602 , and  1604  occur along the beam axis at a radius of approximately 0 mm (region  1601 ), 0.75 mm (region  1602 ) and 1.0 mm (region  1604 ). In one embodiment, the maximum intensity is about 101 W/cm 2  in the plane provided that the intensity at the aperture is about 1 W/cm 2 . 
       FIGS.  20 A- 20 C  are plots of an intensity distribution  1620  in an x-y plane at focal depth according to one embodiment. In one embodiment, the focal depth can be about 15 mm.  FIGS.  20 A- 20 C  show a significant concentration  1622  in acoustic intensity at a focal plane. In one embodiment, the diameter of the acoustic distribution has decreased from an OD of about 3 mm in  FIGS.  20 A- 20 C  to a diameter of less than about 0.3 mm at a focal depth. The maximum intensity has increased to about 7.73 kW/cm 2 , which is approximately 77.3 times greater than the maximum intensity about 2 mm before focus. 
       FIG.  21    is a schematic illustration of an amplitude modulation aperture pattern  1630  according to one embodiment. The amplitude modulation pattern  1630  can be placed across an aperture. Groups of transducer strips or portions  1632  can represent an amplitude of +1 (e.g., due to expansion of transducer material). Groups of transducer strips or portions  1634  can represent an amplitude of −1 (e.g., due to contraction of transducer material). As is shown, groups  1632  and  1634  can alternate across the aperture. Pitch distance  1640  can correspond to a spatial period of transitions between +1 and −1 transducer material across the aperture. In one embodiment, the pitch distance  1640  along with a focal depth and operating frequency may determine the distance of the split beams in the focal plane. In one embodiment, any number of transducer portions can be grouped into groups  1632  and  1634 . In one embodiment, the number of portions in groups  1632  and  1634  may be the same. In one embodiment, the number of portions in groups  1632  and  1634  may be different. In one embodiment, amplitude modulation can include more than two levels, such as three (0 and ±1) or more levels. 
       FIGS.  22 A- 22 C  are plots of an intensity distribution  1650  in an x-y plane from an amplitude modulated aperture pattern of  FIG.  21    about 2 mm before focus according to one embodiment. In one embodiment, the pitch distance is approximately 6 mm for an excitation signal frequency of about 7 MHz. In one embodiment, the amplitude modulation pattern  1630  is placed along the y-axis to split the beam by about 1.1 mm, as is demonstrated by foci points  1652  and  1654 . In one embodiment, although the energy distribution has an OD of approximately 3 mm in the x-direction, it is increased in the y-direction to about 4 mm. As compared with  FIGS.  19 A-C , the maximum intensity of intensity distribution  1650  is increased by about 20% to 112 W/cm 2 , provided that 1 W/cm 2  of intensity is placed at the unmodulated focal point. In one embodiment, the amount of power from a split aperture may need to be increased by a factor of about 2.2 to achieve substantially similar intensity at two foci points. At a depth of about 2 mm before focus, the maximum intensity may be about 246 W/cm 2  due to the increase in power. However, because in one embodiment temperature increases in a tissue are proportional to increases in intensity, the temperature rise in a pre-focal region can be more than double for a split beam design. 
       FIGS.  23 A- 23 C  are plots of an intensity distribution  1670  in an x-y plane from an amplitude modulated aperture pattern of  FIG.  21    at focal depth according to one embodiment. In one embodiment, the focal depth can be about 15 mm. In one embodiment, the intensity of each of the foci  1672  and  1674  can be about 3.45 kW/cm 2 , provided that 1 W/cm 2  of intensity is placed at the unmodulated focal point. As is illustrated, two symmetric beams occur at focal positions  1672  (0.55 mm, 0, 15 mm) and  1674  (−0.55 mm, 0, 15 mm) mm. In one embodiment, the intensity distribution at the focal positions  1672  and  1674  is substantially similar to the intensity distribution illustrated in  FIG.  20   . 
       FIG.  24    is a schematic illustration of an amplitude modulation aperture pattern  1680  with walking or changing states according to one embodiment. In one embodiment, the pattern  1680  is the same as the amplitude modulation function  1630  illustrated in  FIG.  21    with the exception of state changes. In one embodiment, the amplitude modulation pattern  1680  can be placed across an aperture as follows. Pitch distance  1688  can comprise a plurality of transducer strips or portions. Although eight such portions are shown in  FIG.  24   , the number of portions can be any suitable number such as less than eight or more than eight. The transducer portions can be individually addressable, and can be configured to represent an amplitude state of −1 and/or +1. As voltage or current is supplied to the transducer, the aperture can change states (or walk) from S1 to S2, then S2 to S3, then S3 to S4, and so on. As is illustrated, in state S1 the plurality of portions across the pitch distance  1688  are divided into two groups  1682  (+1 modulation) and  1684  (−1 modulation). When transition is made from state S1 to state S2, the plurality of portions across the pitch distance  1688  are divided into groups  1692  (+1 modulation) and  1690  and  1694  (−1 modulation). As is illustrated, portion  1681  in state S1 has corresponds to +1 and in state S2 corresponds to −1. When transition is made from state S2 to state S3, the plurality of portions across the pitch distance  1688  are divided into groups  1702  (+1 modulation) and  1700  and  1704  (−1 modulation). When transition is made from state S3 to state S4, the plurality of portions across the pitch distance  1688  are divided into groups  1712  (+1 modulation) and  1710  and  1711  (−1 modulation). Accordingly, the modulation pattern shifts (or walks) across the aperture over time. In one embodiment, there are eight unique states if the aperture walks with the same amplitude modulation pattern across the aperture. In one embodiment, the effective intensity can be determined as a weighted time average of the acoustic intensity distribution from each aperture state. In one embodiment, the aperture changes state (or walks) at a rate sufficient to reduce the possibility of excessive heating of tissues pre-focally and/or post focally. In one embodiment, pitch distance  1688  can include any suitable number of transducer portions. In one embodiment, the number of portions in groups corresponding to modulation of +1 and −1 may be the same. In one embodiment, the number of portions in groups corresponding to modulation of +1 and −1 may be different. In one embodiment, amplitude modulation can include more than two levels, such as three (0 and ±1) or more levels. 
       FIGS.  25 A- 25 D  are plots of an intensity distribution  1730  in an x-y plane from an amplitude modulated aperture pattern with walking of  FIG.  24    about 2 mm before focus according to one embodiment. In one embodiment, the maximum intensity is about 71 W/cm 2  which is about 37% lower than the maximum intensity from an amplitude modulated aperture pattern without walking (e.g., shown in  FIG.  22   ). In one embodiment, this reduction may be significant.  FIGS.  25 A- 25 D  illustrate that a number and area of regions experiencing high intensity have been reduced as compared with  FIG.  22   . Regions receiving significant amount of energy are localized to approximately six locations  1731 - 1736 . Intensity distribution plot  1730  illustrates that the extent of the energy distribution is reduced, as compared to  FIG.  22   , to about 2 mm OD in the x-dimension and about 3 mm OD in the y-dimension. In one embodiment, this reduction may be significant. In one embodiment, the intensity distribution  1730  appears as acoustic power being emanated from two apertures as the intensity distribution  1730  appears to be a spatially offset summation of the distribution  1600  of  FIG.  19   . In one embodiment, as is illustrated in  FIG.  25   , the possibility of excessive heating of tissues located before and after the focus is significantly reduced. 
       FIGS.  26 A- 26 C  are plots of an intensity distribution  1750  in an x-y plane from an amplitude modulated aperture pattern with walking of  FIG.  24    at focal depth according to one embodiment. In one embodiment, the focal depth can be about 15 mm. In one embodiment, although intensity distribution before focus changes substantially (compare  FIGS.  25    with  FIG.  22   ), intensity distribution  1750  at focal is substantially similar to the intensity distribution  1670  at focal depth for amplitude modulated aperture pattern without walking illustrated in  FIG.  23   . In one embodiment, peak intensity of the intensity distribution  1750  is reduced (e.g., compare 3.34 W/cm 2  with 3.45 W/cm 2 ). In one embodiment, to order to get the same intensity at the focal depth, supplied power may need to be increased by a factor of 2.3. The maximum intensity about 2 mm before focus would be 163 W/cm 2 , which is a substantial reduction over the prediction of 246 W/cm 2  ( FIG.  22   ) if the amplitude modulation pattern is not walked across the aperture. In one embodiment, acoustic intensity maximums at foci  1752  and  1754  are substantially concentrated as compared to the intensity distribution  1650  in  FIG.  22   . 
       FIG.  27 A  is a schematic illustration of an amplitude modulated aperture with walking (two levels ±1) 180° according to one embodiment. In one embodiment, the schematic  1800  corresponds to the pattern  1680  illustrated in  FIG.  24   .  FIG.  27 B  is a state transition table  1850  of the two-state schematic  1800  according to one embodiment. 
       FIG.  28 A  is a schematic illustration of an amplitude modulated aperture with walking (three levels)  1900  according to one embodiment. Schematic  1900  includes a 0 level  1952 . In one embodiment, 0 level  1952  can be realized by using a ground terminal or a connecting a resistor to the ground terminal. In one embodiment, 0 level  1952  can reduce an amount of high frequency spatial components in a focal zone (e.g., these components can correspond to grating lobes). In one embodiment, 0 level  1952  can reduces spatial frequency transitions in pre-focal and post focal zones.  FIG.  28 B  is a state transition table  1950  of the three-state schematic  1900  according to one embodiment. 
       FIG.  29 A  is a schematic illustration of an amplitude modulated aperture with walking (four levels)  2000  according to one embodiment. Schematic  2000  includes two additional levels +0.5  2002  and −0.5  2004 . In one embodiment, doing so can provide the similar advantages as adding a 0 level. In one embodiment, amplitude modulation across the aperture provided by schematic  2000  can better approximate a sine wave, such that high frequency spatial components do not occur in the focal plan.  FIG.  29 B  is a state transition table  2050  of the three-state schematic  1900  according to one embodiment. 
     In several embodiments, number of transducer strips and/or portions in a pitch distance can be less than or greater than eight. The number of portions selected can depend on an amount of heating reduction desired for tissues located before and/or after the focus. In several embodiments, number of amplitude modulation levels can be greater than four, such as six, eight, ten, etc. 
     There are several advantages to use of embodiments of the systems and methods disclosed herein. In one embodiment, amplitude modulation, particularly with walking, and/or phase shifting techniques can reduce a possibility of excessive pre-focal and post-focal heating. In one embodiment, amplitude modulation, particularly with walking, and/or phase shifting techniques can allow splitting an ultrasound beam into two or more beams. In one embodiment, amplitude modulation, particularly with walking, and/or phase shifting techniques can approximate two or more ultrasound sources by placing ultrasonic energy at two or more foci locations. In one embodiment, amplitude modulation, particularly with walking, and/or phase shifting techniques can reduce pain or discomfort experienced by a patient during ultrasound therapy by redistributing acoustic energy away from a focal point. In one embodiment, amplitude modulation, particularly with walking, and/or phase shifting techniques can reduce therapy time due to the production of multiple TCPs. 
     Imaging Systems 
     In one embodiment, a receive ultrasound beamformer can be used as part of an ultrasound imaging system. In one embodiment, an ultrasound imaging system uses a transmit and a receive event to create one line of an ultrasound image. The transmit typically focuses at one location and then the receive processing of the imaging system focuses on the same location. In this case, the response of the imaging system is described as: 
         h ( t )=( Tx )* Rx ( t )  (29)
 
     where h(t) is the spatial response of both the transmit and receive apertures, Tx(t) is the response of the transmit aperture, and Rx(t) is the response of the receive aperture. 
     In one embodiment, an ultrasound imaging systems uses dynamic receive focusing. In this case, although the transmit ultrasound beam focused on one spatial location, the receive system could ‘dynamically’ change the focus along the beam axis so each spatial location in depth was focused. This system response is represented as: 
         h ( t −δ)= Tx ( t )* Rx ( t −δ)  (30)
 
     The δ represents the time delay between received signals which suggests how the focusing can change for the receive aperture as the signals come from deeper depths. 
     In one embodiment, a technique to split a transmit therapy beam into multiple foci through aperture amplitude manipulation can include receiving beam(s) as well. In one embodiment, a system can include two transmit foci (or more), and it is possible to focus on either spatial aperture using a receive aperture such as a linear array where delays may be used to steer and focus the received beam along different axes. This method allows the system to obtain two receive beams with just one transmit. This reduces the required time to visually observe the two beam axes from the receive aperture. This system is described as: 
         h   1 ( t −δ)= Tx ( t )* Rx   1 ( t −δ)  (31a)
 
         h   2 ( t −δ)= Tx ( t )* Rx   2 ( t −δ)  (31b)
 
     For example, suppose the system produces two foci, one at a distance 1.0 mm away from the center axis of the therapy transducer and another −1.0 mm away from the center axis of the therapy transducer each at a depth of 15 mm. The ultrasound receiver would be able to create two receive lines, one constantly focused on the 1.0 mm peak and one constantly focused on the −1.0 mm peak. In one embodiment, a receiver can create two receive lines, one constantly focused on the 1.0 mm peak and one constantly focused on the −1.0 mm peak simultaneously. 
     In one embodiment, a method  2100  comprises the steps of: 
     transmitting multiple foci with a therapy aperture 
     gathering a signal from each portion of a receive aperture array 
     creating multiple receive vectors based on the multiple foci, and 
     utilizing the receive vectors to speed up an algorithm for imaging. 
     In some embodiments, the transmission of multiple foci can be simultaneous or sequential. In some embodiments, the receive vectors can be simultaneously or sequentially utilized. 
     Some embodiments and the examples described herein are examples and not intended to be limiting in describing the full scope of compositions and methods of these invention. Equivalent changes, modifications and variations of some embodiments, materials, compositions and methods can be made within the scope of the present invention, with substantially similar results. 
     While the invention is susceptible to various modifications, and alternative forms, specific examples thereof have been shown in the drawings and are herein described in detail. It should be understood, however, that the invention is not to be limited to the particular forms or methods disclosed, but to the contrary, the invention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the various embodiments described and the appended claims. Any methods disclosed herein need not be performed in the order recited. The methods disclosed herein include certain actions taken by a practitioner; however, they can also include any third-party instruction of those actions, either expressly or by implication. For example, actions such as “coupling a transducer module with an ultrasonic probe” include “instructing the coupling of a transducer module with an ultrasonic probe.” The ranges disclosed herein also encompass any and all overlap, sub-ranges, and combinations thereof. Language such as “up to,” “at least,” “greater than,” “less than,” “between,” and the like includes the number recited. Numbers preceded by a term such as “about” or “approximately” include the recited numbers. For example, “about 25 mm” includes “25 mm.”