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BME/ECE 487 HW4 Solutions Ultrasound Imaging
PROBLEM 8: TIME GAIN COMPENSATION
a) Two figures from MiniLab 4b.
Fig. 1: B-mode image without TGC. Fig. 2: B-mode image with TGC.
b)
The effects of attenuation are clearly seen in Fig. 1, where the bottom of the image appears dark. The ultrasound must travel further, resulting in more attenuation.
The ultrasound beam width causes the point targets to appear smeared. This is a natural result of convolution (see right)! The unfocused transducer has a width of 5 mm, so the beam width is about 5 mm. The Fresnel region of the transducer is about zF = D2/0 = 83 mm, so the resolution is expected to be roughly the same throughout the image. In reality, it turns out that the ultrasound beam pattern is not perfectly constant as it propagates within zF. This is why the resolution is not the same throughout the depth of the image.
The slightly narrow appearance of the cysts is a natural effect due to convolution (see right). However, the resulting image of the cyst is actually NARROWER than the cyst itself. This is different from the point targets. Why? Remember that a cyst is an ANECHOIC region, meaning it does NOT produce echoes. However, the tissue surrounding the cyst does produce echoes. As the ultrasound beam is scanned across the cyst, part of the beam collects signal from the surrounding tissue, while other parts collect no signal from the cyst. Therefore, the image of the cyst is slightly filled in.
c) Any measurement has some NOISE. Attenuation, particularly from large depths, can cause the received ultrasound signal to be weaker than the noise floor of the receiving electronics. Applying TGC will simply result in amplified noise without any distinguishable echoes from the object itself.
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BME/ECE 487 HW4 Solutions Ultrasound Imaging
PROBLEM 9: Linear Array Beamforming
a) Four figures from MiniLab4c.
Fig. 9.1: Array data Fig. 9.2: Beamformed image with Msub = 64
Fig. 9.3: Beamformed image with Msub = 16 Fig. 9.4: Grating lobes from undersampled array.
b) The five “arcs” in the original RF data suggest there are five point targets.
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BME/ECE 487 HW4 Solutions Ultrasound Imaging
c) Recall that an array is focused at ALL values of z. However, the focused beam width varies with z according to w =
(z/D)0, where D is the subarray width. The ratio (z/D) is the “f#” of the sub-array aperture. Smaller f#’s produce tighter focal spots. In Fig. 9, the top point target appears sharpest while the bottom target is the broadest. The top target has the smallest “z”, so the sub-array can produce a very tight focal spot. The bottom target has the largest “z”, so this produces a larger sub-array f# and therefore a broader focal spot.
d) The array is still focused at ALL values of z. For any value of z, the focal width is w = (z/D)0. The subarray width D is now 4 time smaller, leading to a focused beam width that is four times larger. This leads to point target images that are four times wider, and therefore produces worse lateral resolution.
NOTE: The depth resolution is the SAME when using 64 or 16 sub-array elements. This is because depth resolution depends on pulse duration, not the sub-array aperture.
e) Grating lobes occur at: sinm = m∙/d = m∙/1.2 = m∙ (0.428).
Therefore, the grating lobe angles are 1= 25.3° and -1 = -25.3°.
For the point target at z = 40 mm, the ghost images should occur at x = 40 ∙ tan(°) = 19 mm and x = -19 mm. This is indeed consistent with the reconstructed image, where the center of the smudges occur at roughly x = +20 mm and x = -20 mm. NOTE: At the focus (e.g. the main image), pulses from each element overlap at the same spot to produce a nice tight image. In theory, grating lobes occur when the pulses have a path length difference equal to a multiple of a wavelength
(e.g. m ∙ ). This constructive interference is NOT abrupt, meaning “partial” constructive interference occurs at image points slightly away from the “ideal” grating lobe location. This “walk off” between pulses results in the smeared out appearance of the grating lobes.
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