Array Transducers

Question 1

How are the far-field directivity, and distance tot he axial maxima and minima related to the frequency?

Answer 1

Far field directivity is inversely proportional to frequency.
Axial max and min a directly proportional to frequency.

Question 2

After the last axial maxima, how does the axial pressure profile change?

Answer 2

Drops off as 1/wavelength.

Question 3

What is the equation for the axial pressure?

Answer 3

p=2p_0*|sin{(k/2)*(sqrt(z^2+a^2)-z)}|
where p0 is the pressure at z=0,
z is the depth in tissue,
a is the radius of the transducer,
k is the wavenumber.

Question 4

What is the equation for the location os the last axial maxima and minima?

Answer 4

z=a^2/(n*lambda)
n=odd, max
n=even, min

Question 5

What is the equation for the far-field directivity of a circular transducer?

Answer 5

D(0,k)=|[2J_1(kasin0)]/kasin0|
where k is the wavenumber,
a is the half aperture, and
J_1 is a first order Bessel function.

Question 6

How does the axial profile of a pulsed wave differ from that of a continuous wave?

Answer 6

• The final axial maximum is further out.
• Fewer axial minima
• Shallower minima.

Question 7

How does the axial profile of a square transducer differ from that of a circular one?

Answer 7

• The final axial maximum is shifted outwards.

- Incomplete destructive interference (non-zero minima)

Question 8

What is the equation for the far-field directivity of a square transducer?

Answer 8

D(0, phi, k)=|sinc{0.5kL_xsin(0}sinc{0.5kL_ysin(phi)}|

Question 9

What is the equation for the axial pressure of a circular focused transducer?

Answer 9

p=2p_0*(A/A-z)*|sin{(k/2)*(B(z)-z)}|
Where B(z)=sqrt(z^2+2b(A-z)),
and b = A-sqrt(A^2-a^2)
A is the radisu of curvature of the spherical trnasducer.

Question 10

What is the equation for the focal gain?

Answer 10

G=(pia^2)/Flambda

Question 11

How does the last axial maxim change with increased focal length?

Answer 11

Gets further out and lower in amplitude.

Question 12

What is the equation for the -6dB beam width at the focus?

Answer 12

w=0.7F*lambda/a

Question 13

Describe the construction of a mechanical sector transducer?

Answer 13

• Mechanically scanned single element transducer.
• The element is on a motor and is waggled side-to-side to produce the image.
• Only used in simple devices today (e.g. bladder scanners)

Question 14

Describe the construction of an annular array transducer?

Answer 14

• Mechanically scanned annular array transducers.
• Typically 4-8 equal area, concentric, ring-shaped elements.
• One electrical connection for each element.

Question 15

What are the advantages and disadvantages of an annular array transducer?

Answer 15

+ Beam is radially symmetrical.
+ Scan plane focusing and slice thickness focusing are identical.
- Moving parts make them less reliable.

Question 16

Describe the construction of a simple linear array transducer.

Answer 16

• Flexible printed circuit attaches to lower surface of the crystal.
• Flexible ground plate bonded to the upper surface.
• Backing material pedestal with crystal and matching layers bonded to it.
• Cut into a row of individual elements leaving air kerfs.
• Cylindrical silicone rubber lens bonded on top.

Question 17

What is the ideal array geometry?

Answer 17

• The pitch should be lambda/2 in tissue.
• The thickness should be lambda/2 in the crystal.
• w/d should be 0.7 for “width expanders”.

Question 18

What are the properties of a mechanically scanned array?

Answer 18

• Curved array with a silicone rubber lens in an oil bath.
• Used in private clinics for antenatal “bonding” scanning.
• 4D frame rate limited to about 4Hz due to sweep speed.

Question 19

What are the properties of a biplane transrectal transducer?

Answer 19

• Two separate curved arrays for sagittal and transverse views.
• Used widely in urology clinics for prostate biopsies.

Question 20

What are the properties of a radial transrectal transducer?

Answer 20

• Aperture size is limited by the array diameter (11mm).

- Used in some urology clinics to endoanal scanning.

Question 21

What are the properties of an intravascular transducer?

Answer 21

• Two types rotating a single element, and radial arrays.

- The diameter must be less than 8mm to fit in a 10mm trocar or less than 1mm for intracoronary imaging.