What are Lambda and Z Parameters in Ultrasound B-mode Imaging?

AI Thread Summary
Lambda in ultrasound B-mode imaging is defined as 513 x 10^-6 m, with ZR values of 1.2 cm and 1 cm, leading to different calculations for LR based on whether Z is less than or greater than ZR. When Z is less than ZR, LR equals D, which is 0.5 cm; when Z exceeds ZR, LR is calculated using the formula involving the tangent function. The discussion also touches on the time calculation t = Z/c, resulting in 77.9 x 10^-6 s. Participants emphasize the importance of clarifying the variables used in the equations for better understanding. Overall, the conversation highlights the mathematical relationships in ultrasound imaging parameters.
nao113
Messages
68
Reaction score
13
Homework Statement
1. The transducer array of a linear-array real-time imaging instrument has 32 unfocused elements. Each element is 0.5 cm wide, and there is a nonradiating gap of 0.5 cm between neighboring elements. Only one element at a time is excited.
a) At a frequency of 3 MHz, find the lateral resolution of this instrument at a depth of 1 cm and a depth of 8 cm. The lateral resolution of a linear- array imager is given by the beam size or the line spacing, whichever is larger.
Use relationship:
c = 1540 m/s, c =frequency x l
b) If echo information out to a depth of 12 cm is desired, calculate the minimum time required to scan the entire array.
Relevant Equations
Z < ZR => LR = D
Z > ZR => LR = 2 tan(sin-1 lambda/D) x Z
Screen Shot 2022-05-26 at 19.16.11.png


a. lambda = 513 X 10^-6 m
ZR = 1, 2 cm
Z = 1 cm => Z < ZR => LR = D = 0.5 cm
Z = 8 cm => Z > ZR => LR = 2 tan(sin^-1 (lambda/D)) x Z
= 2 tan(sin^-1 (513 x 10^-6 m/0.005 m)) x 0.08
= 1.65 cm

b. t = Z/c => 0.12/1540 = 77.9 x 10^-6 s
 
Physics news on Phys.org
It won't hurt to actually explain what all these letters mean in your equations. This in case you have some question, eventually. So far I don't see the purpose of your post.
 
nasu said:
It won't hurt to actually explain what all these letters mean in your equations. This in case you have some question, eventually. So far I don't see the purpose of your post.
Hello, thank you for the advice, I already changed it, I wonder whether I answered them correctly or not.
 
Last edited:
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top