Hello everyone,
I’m doing some experimental measurements of ultrasound in a water tank. The goal is to get the pressure distributions in the water and on the surface, where the ultrasonic transducer is attached. All measurements are done with a Brüel & Kjaer 8103 hydrophone. I have an established workflow but I’m unsure whether all processing steps are correct. Most of the equations I found in the B&K technical documentation that came with the hydrophone (unfortunately very outdated, from 1992, even though the hydrophone was purchased recently). Do you think the steps below are correct?
Firstly, the hydrophone is connected to an amplifier and oscilloscope. The data is obtained as a time wave with 10000 data points, in mV. Sampling frequency is around 10 MHz (the frequency range that I’m interested in is between 20-60 kHz). Then, the correction of the amplifier is applied, by calculating the gain. This is done by dividing the output sensitivity (mV/Pa) by the transducer sensitivity (mV/Pa), resulting in values between 4-40 depending on the amplifier settings. Then the raw amplitude values are divided by 10^(gain/20).
I then carry a Fast Fourier transform on a window correction using the Hanning window. I do the FFT in R, using the fft() function. To get the amplitude I use 4* absolute values after the FFT divide by the total number of data points. After having frequency resolved data (which I ensured is correct by running it with a signal of known frequency) I correct for the sensitivity of the hydrophone, obtained by the manufacturer. I do this by calculating a transfer factor:
10e8*10^(sensitivity/20). The values in Pa are obtained by dividing the amplitude (after FFT) by the aforementioned transfer factor.
Final values are around 80 KPa. Unfortunately I have no exact expectation of the range of the pressure I would expect with ultrasound transducer powers that I use. Any suggestions/recommendations are very welcomed. There are many questions asked that I have come across on how to transform the raw voltage signal in pressure but this only leads to more confusion.
Transfer factor formula obtained from here: https://www.translatorscafe.com/unit-converter/de-DE/microphone-sensitivity/
Thanks a lot
Your hydrophone should be provided by the manufacturer with a calibration curve that represents its sensitivity (in V/Pa, or any sub-unit of this) as a function of frequency.
Note that in some cases, hydrophones are provided by the manufacturer to be attached to a specific preamplifier. In these cases, the calibration curve is the calibration curve of the hydrophone+preamplifier ensemble.
The hydrophone converts pressure to voltage, which one can (must) amplify before digitization (in your case by the scope).
All components in the receive path (from the hydrophone onward) are assumed to be linear, but most of them have a frequency dependent transfer function.
So, in order to get the pressure waveform collected at the hydrophone from the voltage waveform digitized by the scope, one need to compensate for the transfer functions of all the electronic component in the frequency domain.
The Fourier transform S(f) of the signal collected by the scope s(t) can then expressed as :
S(f)=P(f)*H(f)*G(f) with
P(f) : the Fourier transform of pressure waveform collected at the hydrophone,
H(f) : the frequency dependent sensitivity of the hydrophone (or hydrophone+preamp ensemble) provided by the manufacturer and,
G(f) : the transfer function of all other components positioned between the hydrophone and the scope, on the receive path.
One can then rewrite P(f)=S(f) / (H(f)*G(f), which one can inverse Fourier transform to get the p(t), the pressure waveform in the time domain.
If you have more questions don't hesitate to contact me.
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