05.10.2020
An interactive software package which includes a tutorial and example measurement data has been developed to demonstrate how the deconvolution method can be used to subsequently correct measured ultrasonic signals. This program can also be applied to evaluate one's own measurement data [1]. The intention is to make the technique of signal deconvolution accessible to a broader group of users as a basis for more common usage and inclusion in the relevant standards.
The ultrasonic signals which are emitted by medical ultrasound equipment need to be characterized before a device can be placed on the market. A technical challenge regarding the measurements often exists in the – frequently large – bandwidths of the acoustic waveforms to be measured. The hydrophones used for the measurement should therefore have a large bandwidth with – ideally – a frequency-independent sensitivity so that the signals can be detected without distortions. Real hydrophones, however, usually show a non-ideal, varying frequency response, which leads to an inhomogeneous weighting of the measured spectral components. The frequency response of a hydrophone is determined by individual calibration and is accessible to the user as a dataset. Today, it is possible to calibrate the modulus and phase responses of hydrophones in a frequency range up to 100 MHz [2]. Using such calibration data, signal deconvolution can be applied in order to compensate for the distortions which have been introduced by the measurement and to reconstruct the original ultrasonic pressure waveform in this way.
Figure 1: Schematic workflow of signal deconvolution, with an ultrasonic measurement taken as an example. The starting point is the measured frequency response of the hydrophone, which is available through calibration data, as well as the ultrasonic signal which is measured by the hydrophone and is available as the voltage signal. The deconvolution procedure is now carried out via several different steps so that at the end, the ultrasonic pressure waveform is reconstructed. A regularization is performed by applying a low-pass filter. The uncertainty contribution which arises in addition due to this is calculated by means of an estimation method that has been developed at PTB [3]. In each step of the procedure, both the signal data and the uncertainties are considered [4], so that the final result can be specified with the associated uncertainty.
To be able to perform the deconvolution procedure in practice, an interactive Python program was developed in the form of a Jupyter Notebook [1]. The basis for this is the Python package PyDynamic [5] which has been established and is maintained by PTB staff. The tutorial focuses on questions which are particularly relevant in the area of ultrasonic measurements. Thus, example calibration data of different hydrophones as well as real data which have been obtained with these hydrophones during acoustic output measurements come with the script. Many explanations were added to the Notebook so that the users are able to follow the procedure in the sense of a tutorial and to apply the knowledge obtained in this way to their own applications (see Figure 2). In addition, the reference data sets which are provided can also be applied by users to validate their own deconvolution routines, and they can also be transferred to other signal deconvolution applications outside the area of ultrasonic exposimetry.
The software can be tested 
online directly with a browser free of charge. It can also be downloaded and be used on one's own computer free of charge. The latter is recommended in particular if a user’s own measurement data is to be evaluated or individual adjustments of the software are intended.
Figure 2: Screenshot from tutorial and script. The excerpt shows a plot of a deconvolved ultrasonic waveform including measurement uncertainty as well as the results of the output parameters obtained.
Literature:
[1] Martin Weber, Volker Wilkens, Sascha Eichstädt, Tutorial for the deconvolution of hydrophone measurement data, DOI: 10.5281/zenodo.4012242
[2] Martin Weber, Volker Wilkens, Using a heterodyne vibrometer in combination with pulse excitation for primary calibration of ultrasonic hydrophones in amplitude and phase, 2017, Metrologia 54: 432, DOI: 10.1088/1681-7575/aa72ba
[3] Sascha Eichstädt, Volker Wilkens, Evaluation of uncertainty for regularized deconvolution: A case study in hydrophone measurements, 2017, The Journal of the Acoustical Society of America 141:6, 4155-4167, DOI: 10.1121/1.4983827
[4] Sascha Eichstädt, Volker Wilkens, GUM2DFT – A software tool for uncertainty evaluation of transient signals in the frequency domain, 2016, Meas. Sci. Technol. 27:5, 055001-1-055001-12, DOI: 10.1088/0957-0233/27/5/055001
[5] Björn Ludwig et al., PyDynamic: v1.4.4, DOI: 10.5281/zenodo.1489877
Contact:
Volker Wilkens, FB 1.6, AG 1.62, E-Mail: 
volker.wilkens(at)ptb.de