Problem 3 (Ultrasound imaging) (15 points)

1. Assume you have a 11-element linear array transducer, with 0.75 mm spacing between the center of the elements, and a 3-channel transmit and receive beamformer (i.e. each focused scan line is produced using an aperture consisting of 3 elements).

a. Assume that the aperture is translated laterally by two elements at a time to create a B- mode image. Calculate the number of focused scan lines you can reconstruct to create one frame of a B-mode image.

b. Calculate the frame rate you can achieve when imaging up to a depth of 10 cm. Assume you have a single transmit focal point. Assume that the speed of sound is 1540 m/s.

2. By putting curvature in the phase delay pattern as shown below, a pulse can be focused. Which delay mode places the focus closer to the transducer? Please explain. Hint: focus on the curvature of the phase delay or time delay.

6 (Optical imaging) (15 points)

A.

a. List two different optical imaging modalities.

b. List two advantages and one limitation of optical imaging when compared to MRI, X- ray imaging and ultrasound. M S M2 M (movable) Laser di M M2 (fixed) d2 M

Laser (bending of rays exaggerated) (a) (b)

B. A red laser light of wavelength 630 nm is used in a Michelson interferometer. While keeping the mirror Mi fixed, mirror M2 is moved. From the zero-distance alignment, how much do we need to move M2 to have only one fringe pass by the eye (detector)?

Problem 7 (Nuclear Imaging) (10 points):

A. Pharmaceutical company X is developing a new nuclear imaging compound Y.

a. Given that the half-life of Y is 300 minutes, what is the decay constant? (Hint: half-life is the time required for the amount to fall to half its initial value.)

b. After taking the compound Y, how long will it take for a patient to have 0.01% the amount of the original compound?

B. Consider nine 1 x 1 cm photomultiplier tubes arranged in 3 x 3 array. The output of each photomultiplier tube to a scintillation event is shown below: 2 2 of 2 5 2 AL k cm, 2 2 2 1 cm

What is the estimated position of the scintillation event?