Calculate the PRP, PRF, PD, DF, SPL, wavelength, period, and Axial Resolution if a 2 cycle pulse emitted from a 10 MHz transducer if the echo time received was 0.26 ms in soft tissue.
To calculate the PRP (Pulse Repetition Period), PRF (Pulse Repetition Frequency), PD (Pulse Duration), DF (Duty Factor), SPL (Spatial Pulse Length), wavelength, period, and Axial Resolution, we can use the following formulas:
1. PRP (Pulse Repetition Period) = 1 / PRF
2. PRF (Pulse Repetition Frequency) = 1 / PRP
3. PD (Pulse Duration) = Number of cycles / Frequency
4. DF (Duty Factor) = PD / PRP
5. SPL (Spatial Pulse Length) = Number of cycles * Wavelength
6. Wavelength = Propagation Speed / Frequency
7. Period = 1 / Frequency
8. Axial Resolution = SPL / 2
Given information:
- Number of cycles = 2
- Frequency = 10 MHz = 10 million Hz
- Echo time received = 0.26 ms = 0.00026 s
- Propagation Speed in soft tissue = 1540 m/s
Let's calculate each parameter step-by-step:
1. PRP (Pulse Repetition Period):
PRP = 1 / PRF
PRF = 1 / PRP
Substituting PRF = 10 MHz into the formula, we get:
PRP = 1 / (10 * 10^6 Hz) = 1 * 10^-8 s = 10 ns
2. PRF (Pulse Repetition Frequency):
PRF = 1 / PRP
PRF = 1 / (10 ns) = 100 million Hz = 100 MHz
3. PD (Pulse Duration):
PD = Number of cycles / Frequency
PD = 2 / (10 * 10^6 Hz) = 2 * 10^-7 s = 0.2 µs
4. DF (Duty Factor):
DF = PD / PRP
DF = (0.2 µs) / (10 ns) = 20
5. SPL (Spatial Pulse Length):
SPL = Number of cycles * Wavelength
To calculate the wavelength, we need the propagation speed, which is 1540 m/s:
Wavelength = Propagation Speed / Frequency
Wavelength = (1540 m/s) / (10 * 10^6 Hz) = 0.154 mm
SPL = 2 cycles * 0.154 mm = 0.308 mm
6. Wavelength:
Wavelength = Propagation Speed / Frequency
Wavelength = (1540 m/s) / (10 * 10^6 Hz) = 0.154 mm
7. Period:
Period = 1 / Frequency
Period = 1 / (10 * 10^6 Hz) = 0.1 µs
8. Axial Resolution:
Axial Resolution = SPL / 2
Axial Resolution = 0.308 mm / 2 = 0.154 mm
Therefore, the calculated values are as follows:
- PRP (Pulse Repetition Period) = 10 ns
- PRF (Pulse Repetition Frequency) = 100 MHz
- PD (Pulse Duration) = 0.2 µs
- DF (Duty Factor) = 20
- SPL (Spatial Pulse Length) = 0.308 mm
- Wavelength = 0.154 mm
- Period = 0.1 µs
- Axial Resolution = 0.154 mm