Consider a linear array of 100 flat, rectangular 3.0 MHz transducers, each 1.5 m

Question

Consider a linear array of 100 flat, rectangular 3.0 MHz transducers, each 1.5 mm wide and 2.1 cm deep. Assume for simplicity that they are packed tightly together so that the array is 15 cm long by 2.1 cm deep. The transducer array is tested in a medium having a speed of sound of 1500 m/s.

a. If 14 consecutive transducers on the transducer array are electronically grouped on each transmit and receive, what depths (ranges) are considered to be in the far field?

b. At what time interval after the transmit pulse will an echo from an object at range 7 cm arrive back at the transducer array?

c. A B-mode image is created by successively grouping 14 transducers on the array, sliding one transducer at a time down the length of the array. Suppose the depth of penetration is 20 cm. What is the frame rate for this linear array image?

Explanation / Answer

(a) Aperature D = 14*1.5 mm = 21 mm,

lamda = v/f = 1500/3e6 =0.0005 m or 0.5 mm

Rc > D2/lamda =21*21/0.5 =882 mm

alternatives D2/2*lamda =21*21/2*0.5 =441 mm

D2/4*lamda =21*21/4*0.5 =220.5 mm

(b) Travel Time = 2*d/c = 2*0.07/1500 =9.33x10^-5 sec

(c) Travel Time = 2*d/c = 2*0.2/1500 =267 micro seconds

PRF is the inverse =3750 Hz

No. of beams N = 100 -14 +1 =87

FR = PRF/N = 3750/87 =43.103 frames per second..........Ans.

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