The unrectified (RF) A-scan contains additional information in the phase component compared to its envelope-detected equivalent, but requires higher temporal sampling rates for accurate representation and measurement. The same is true for the pixel density in images reconstructed by the Total Focusing Method (TFM). However the time to calculate each pixel means there is a drive to minimise the total number of pixels for faster real-time imaging rates. This conflicts with the ASME V requirement for the amplitude measurement error, usually a result of under-sampling, to be less than 2dB \[1, 2\]. There is therefore a need to model the process and to optimise the pixel density trade-off.  
Quadrature-sampling is a standard approach for optimised representation of band-limited signals \[3-6\] and is a suitable candidate for ultrasound A-scans. This greatly reduces the size of the Full Matrix Capture (FMC) data set and hence the data transfer rate and storage requirements. A parametric analysis model of the FMC and TFM processes has been created. This has been used to evaluate the amplitude fidelity on both A-scans and TFM images as the fractional bandwidth of the transducer increases and as the pixel density reduces. The results from quadrature-sampling are compared with those using conventional high temporal sampling rates.  
Results from the parametric analysis modelling are presented for targets at varying scan angles and depths into the material. These show that, for typical transducer fractional bandwidths (up to 75%), quadrature-sampling of the FMC A-scans gives the required amplitude fidelity with TFM image resolutions of around 4 pixels/wavelength. This is a similar result to those reported for conventional FMC acquisition and envelope detection TFM \[7\]. Extensions of the quadrature-sampling approach for higher fractional bandwidth are also presented. These results are currently being compared with those from real data acquired from Side-Drilled Hole (SDH) targets in a calibration block.  
An advantage of the FMC+TFM approach is the separation of the acquisition and reconstruction processes. This allows the latter to be redone at higher pixel resolutions for better human interpretation when an indication is observed in the lower pixel resolution images. High resolution TFM reconstructions have been performed on the quadrature-sampled data to confirm that this capability is still possible.   
A key outcome from this work is the range of optimised pixel resolution values that are safe to use for fast FMC+TFM imaging, as well as the supporting evidence needed to justify them.

References  
\[1\]     ASME Committee, ASME BPVC.V Article 4 Mandatory Appendix XI Full Matric Capture, ASME, 2019.   
\[2\]     ASME Committee, ASME BPVC.V Article 4 Nonmandatory Appendix F - Examination of Welds Using Full Matric Capture., ASME, 2019.   
\[3\]     C. E. Shannon, “Communication in the presence of noise,” Proceedings of the Institute of Radio Engineers, vol. 37, no. 1, p. 10–21, Jan 1949.   
\[4\]     J. L. Brown Jnr., “On Quadrature Sampling of Bandpass Signals,” IEEE Transactions on Aerospace and Electronic Systems, Vols. AES-15, no. 3, pp. 366-371, May 1979.   
\[5\]     J. L. Brown Jnr., “A simplified approach to optimum quadrature sampling,” The Journal of the Acoustical Society of America, vol. 67, no. 5, pp. 1659-1662, May 1980.   
\[6\]     C. M. Rader, “A Simple Method for Sampling In-Phase and Quadrature Components,” IEEE Transactions on Aerospace and Electronic Systems, Vols. AES-20, no. 6, pp. 821-824, Nov 1984.   
\[7\]     N. Badeau, G. Painchaud-April and A. Le Duff, “Use of the Total Focusing Method with the Envelope Feature,” Olympus NDT Canada, 30 March 2020. \[Online\]. Available: https://www.olympus-ims.com/en/resources/white-papers/use-of-the-total-focusing-method-with-the-envelope-feature/. \[Accessed 30 March 2020\].  
 


Modelling of Echo Amplitude Fidelity for Transducer Bandwidth and Tfm Pixel Resolution

No proceedings papers in 2020. Video only.

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