Piezoelectric Effect Sound waves striking a PZ material produce an electrical signal Can be used to detect sound (and echoes)! Pierre Curie 1880. Piezoelectric Effect Sound waves striking a PZ material produce an electrical signal Can be used to detect sound (and echoes)! Reverse Piezoelectric Effect Applying an electrical signal causes the PZ element to vibrate Produces a sound wave Transducer Device that converts signals, or energy, from one form to another Many types of transducers exist – Pressure transducers – Air flow transducers, etc. Ultrasound transducers convert electrical signals to sound waves, and vice versa. Ultrasound Transducer Materials Quartz (naturally piezoelectric) – First used as a stable resonator in time measurement devices – Used in some laboratory ultrasound applications Most current applications use piezoelectric ceramics (ie, lead zirconate titanate; barium titanate) – Lower “Q” (good for short pulses) – Good sensitivity – Many shapes are possible Miniature quartz tuning fork; 32,768 Hz. Polarizing a Piezoelectric Element Most ultrasound transducer materials are not ‘naturally’ piezoelectric – Lead zirconate titanate – Microscopic crystals, randomly oriented Must be polarized – Heat to ~350oC (Curie Temperature) – Apply strong voltage across crystal – Cool while voltage is still applied Polarization Single Element Transducers Uses – Simple A-mode machines – Mechanical scanning transducers The design serves as a useful example of general construction methods Single element transducer construction Matching layers, lens Ultrasound Transducers Piezoelectric (PZT) ceramic elements Backing layer ½ wavelength resonance d Resonance frequency corresponds to the thickness = ½ wavelength Speed of sound in Piezoelectric material ~ 4,620 m/s What thickness is required for a 3 MHz frequency transducer? c 4,620m / s 0.00154m 1.54m m f 3,000,000/ s / 2 0.77m m ½ wavelength resonance d Resonance frequency corresponds to the thickness = ½ wavelength Speed of sound in Piezoelectric material ~ 4,620 m/s What thickness is required for a 3 MHz frequency transducer? c 4,620m / s 0.00154m 1.54m m f 3,000,000/ s / 2 0.77m m ½ wavelength resonance d Resonance frequency corresponds to the thickness = ½ wavelength Speed of sound in Piezoelectric material ~ 4,620 m/s What thickness is required for a 5 MHz frequency transducer? c 4,620m / s 0.000924m 0.924m m f 5,000,000/ s / 2 0.462m m Resonance Frequency PZT (c=4620m/s) Thickness vs 5 Frequency Element Thickness (mm) 4.5 4 3.5 3 2.5 2 Series1 1.5 1 0.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Frequency (MHz) Backing (Damping) Layer Need short duration pulses for decent axial resolution (we will discuss this later) Backing layer helps to reduce vibrations of the element following excitation – Like placing your hand on a bell to stop the ringing! Pulse Bandwidth • A pulse of sound contains many frequencies (analogous to white light consisting of many colors) • Range of frequencies quantified by the frequency “bandwidth” of the pulse • Short pulses, very broad bandwidths • Longer pulses, narrower bandwidths Multi Herz Matching Layers Thin layer of material – ¼ wavelength thick – Impedance is between that of the element (quite high) and that of tissue Provides better sound transmission from the transducer-patient-transducer Improves sensitivity Center Freq: - 8 MHz Bandwidth: - 6.5 MHz - 82% Broadband Transducers Multiple matching layers (analogous to coatings on optical lenses) STI-Ultrasound.com Pulsed Spectra vs transducer bandwidth 2.5 5 Multi-herz The transducer design enables operation at various frequencies. Each pulse is associated with a range of frequencies. Multi-frequency operation Modern transducers can operate over a range of frequencies (sort of like the speakers of a stereo sound system) By changing the frequency of the signal applied to the transducer, and by tuning the receiver, the center frequency can be changed Modern, broad bandwidth Multi-Hertz Spatial Detail in Ultrasound - depends on beam width, focus (lens); - depends on pulse duration (axially); - depends on slice thickness. Axial Resolution Defined as the minimum distance between 2 reflectors along the beam direction, such that the reflectors can be distinguished on the display. Beam Direction Axial Resolution Beam Direction Axial Resolution Axial resolution depends on the “pulse duration” Pulse duration is the amount of time the transducer oscillates during each transmit pulse The shorter the pulse duration, the better the axial resolution Axial Resolution 2 Axial vs Freq GE Logiq 700 Horizontal spacing: 2 mm, 1 mm, 0.5 mm, 0.25 mm Vertical Spacing: 2 mm, 1 mm, 0.5 mm, 0.25 mm 4 MHz 12 MHz 27. Axial resolution is determined by: A. pulse duration B. beam width C. beam diameter D. pulse repetition period 28. Axial resolution is most affected by changes in: A. beam frequency and beam diameter B. beam intensity and beam focusing C. beam frequency and pulse damping D. beam focusing and beam diameter 29. A decrease in pulse duration results in ________ frequency bandwidth. A. a wider B. a narrower C. an equivalent D. elimination of Lateral Resolution and Beam Width Linear Array Poor Lateral Resolution and Beam Width Linear Array Excellent Lateral resolution depends on the “beam width” Lateral resolution is how closely spaced 2 reflectors can be, along a line perpendicular to the ultrasound beam, and still be distinguished on the display It depends of the beam width at depth considered The narrower the beam, the better the lateral resolution Beam Physics Huygen’s Principle – “All points on a propagating sound wave serve as the source of spherical wavelets; the total wave at any location (and time) is the sum of these wavelets.” “Point sources” Christian Huygens (1629-1695) Dutch Physicist Interference 2 sources: – Final signal can be large or small, depending on the relative phase of the waves. Many sources – Final signal can be large or small, depending on relative phases of all waves. Huygens's Principle: all points on a propagating wavefront serve as the source of spherical secondary wavelets, such that the total wave at any location (and time) is the sum of these wavelets. 1 point source; spherical wave “Point sources” Huygens's Principle: all points on a propagating wavefront serve as the source of spherical secondary wavelets, such that the total wave at any location (and time) is the sum of these wavelets. 2 point sources; wave interference Interference creates minima and maxima Unfocused Transducer Beam 10 mm Beam properties depend on width of aperture and the wavelength (frequency); 2.5 MHz 10 mm NFL NFL 5.0 MHz Unfocused Transducer Beam a2 d2 NFL 4 a= transducer radius d=2a=transducer diameter Unfocused Transducer Beam NFL=D_squared over 4 lambda NFL for 2 MHz (=0.77 mm) Diameter NFL 1 cm 3.2 cm 2 cm 13 cm 4 cm 52 cm Assume D = 1 cm=10mm D 2 (10m m) 2 NFL 4 4 x 0 .7 m m 100m m2 3.08m m 32.4m m 3.2cm If the diameter doubles, NFL increases by 4. NFL for 2 MHz (=0.77 mm) NFL for 4 MHz (=0.385 mm) Diameter NFL Diameter NFL 1 cm 3.2 cm 1 cm 6.4 cm 2 cm 13 cm 2 cm 26 cm 4 cm 52 cm 4 cm 104 cm If the diameter doubles, NFL increases by 4. If the frequency doubles, NFL doubles. Divergence in far field (The ‘sin’ is a function of the angle) Larger diameter diverges less Higher frequency (smaller wavelength) diverges less What is the divergence angle for a 2 cm diameter, 3 MHz transducer? 1.2 sin d c 1540m / s 1,540,000m m/ s 0.51m m f 3,000,000/ s 3,000,000/ s 1.2 0.51m m sin 0.036 20m m sin 1 0.036 1.75o What is the divergence angle for a 2 cm diameter, 6 MHz transducer? 1.2 sin d c 1540m / s 1,540,000m m/ s 0.256m m f 6,000,000/ s 6,000,000/ s 1.2 0.256m m sin 0.01536 20m m sin 1 0.01536 0.88o Dependence on frequency Dependence on diameter Focusing, Methods Focusing reduces the beam width in the focal zone Methods – Lens – Curved element – Electronic Focal Definitions 2.5 MHz 20 mm 20 mm In Most Applications, Beams Are Focused - curved element - lens - electronic (arrays) Improves lateral resolution near the focal distance Higher frequencies produce narrower beams 5.0 MHz Short pulse (50% bw) 2.5 MHz 5.0 MHz CW 5.0 MHz 20 mm 10 mm - Previous diagrams exhibit sidelobes - Must be eliminated for good image quality - Pulsing reduces (or even eliminates) side lobes 2.5 MHz d F 1.2 F Beam width d 24. In order to focus a sound beam relatively far away from the transducer, it is advantageous to ______ of the element. A. increase the thickness B. increase the diameter C. increase the temperature D. decrease the diameter 25. Lateral resolution is determined by: A. beam length B. pulse duration C. pulse length D. beam width Array Transducer “Scanhead” containing many small PZT elements Element, along with a transmit-receive circuit in the machine is a channel. 128 channels are common. Beam Forming (Transmit) Group also permits electronic beam steering and electronic focusing. Curvilinear Phased Array Linear-Phased (“Virtual Convex”) Linear array – Rectangular FOV, defined by transducer footprint VC adds beam steering to expand imaged region at edges Annular Multiple Tx Focus Multiple Tx Focus 4 Tx focal zones 12 Hz frame rate Focus During Reception Dynamic Receive Focusing Focusing delays change in real time. (Not adjusted by the sonographer.) Dynamic Aperture Side Lobes, Grating Lobes - Both are forms of off axis sound transmission - Both lead to undesirable effects Side Lobes: part of the beam pattern from any transducer (single element, array) – Reduce using short duration, broad band pulses – Reduce using apodization Grating Lobes: result from having the transducer surface cut into small elements (think of grating cheese) – Reduce using very closely spaced elements Spatial Resolution Typical values Axial: 0.1 to 1 mm Lateral: 0.2mm to 10mm Spatial Pulse Length Transducer “Q” Q stands for “quality factor” A high Q system is one that rings at a pure tone A low Q system is well damped Low Q is needed for short duration pulses Miniature quartz tuning fork; 32,768 Hz. Slice Thickness (Conventional) Spherical Lesion Phantom 2 and 4 mm diameter spherical targets; Low scatter level; Target centers are co planar. Conventional Transducer Conventional Phased and linear Electronic focusing applies to lateral only. Annular Image-plane beam width = slice thickness Electronic focusing applies to both dimensions. 1 ½ D Probe (matrix probe) 100 – 200 elements in lateral direction 5 – 7 rows Matrix Transducer 1 ½ D (Matrix) Transducer Matrix Conventional Use of “Matrix” or “1 ½ D” Arrays Advantages: – Better control of slice thickness Disadvantages – Size (older models) – Cost – Complexity 2-D Array One of the transducer types used in 3-D imaging Volumetrics - Image Formats “Traditional” “C-scans” (constant depth) Use in 2-D arrays (Phillips) 2400 element 2-D array Possible Scan Planes Use in 2-D arrays (Phillips) 2400 element 2-D array Applications of 3-D Visualization of coronal planes Volume calculations OB Imaging – facial and other anatomical anomalies – detailed information on orientation Improved visualization of vasculature with 3-D color flow Important features of arrays Enable electronic scanning – Time delays between elements (phased arrays) – Electronic switching groups of elements (linear and curvilinear) Enable electronic focusing Type of transducer Linear array Method used for Method used beam focusing for scanning Electronic Electronic Curvilinear array Electronic Electronic Phased array Electronic Electronic Annular array Electronic Mechanical Single element Mechanical lens Mechanical Homework Calculate the NFL for a 3 cm diameter transducer operating at 5 MHz. Assume c=1540 m/s. Calculate the resonance frequency of a piezoelectric ceramic material whose thickness is 0.25mm.