Distance displaying on US images for ultrasound array probes with different scanning. A point reflector in (x, z) position from probe surface is displayed in (ξ, ζ) position on the scanner monitor, where ξ ≠ x and ζ ≠ z. Difference between real and displayed distances depends also on scanning geometry of the ultrasound probe and on difference between the effective acoustic velocities of the medium cm and the acoustic velocity ct used to calibrate the scanner.
On the left: a probe scanning an ultrasound phantom made by tissue-mimicking material. On the right: the corresponding ultrasound image, vertical and horizontal test objects are visible on the background. The LSM is performed on the known distances along vertical and horizontal distances: for each direction, firstly the distance error |Δd k | = |d k − d rk | is evaluated between the measured value of distance d k and a reference value d rk , where d rk is the kth nominal distance between test objects within USPh (nominal distances are claimed in the USPh data sheet), then from Δd k values of different distances the LSM calculates the relative error e by means of a last square fit on (d rk , Δd k ) points.
Plot diagrams from LSM and SDM. Both methods are applied on the same ultrasound system. In (a) vertical and horizontal error in distance measurements Δd evaluated with the LSM (the least squares fit is the solid line) versus nominal distance d r . In (b) vertical and horizontal error in distance measurements Δd versus target position, evaluated with the SDM method for a 2 cm distance. For vertical distances e = 0.70 ± 0.11 mm/cm with LSM (z axis diagram in the (a) plot) and e = 0.66 ± 0.07 mm/cm with the SDM (z axis diagram in the (b) plot), while for horizontal distances e = 0.49 ± 0.14 mm/cm with the LSM (x axis diagram in the (a) plot) and e = 0.51 ± 0.07 mm/cm with the SDM (x axis diagram in the (b) plot). Evaluations by means of a CIRS54 ultrasound phantom (cm = 1540 ± 3 m/s) at 4 MHz working frequency, 170 mm FoV, and 24 °C room temperature.
Distance relative error e in vertical and horizontal measurements for different probes models and subgroups. Hatched bars and gray bars refer to LSM and SDM, respectively. (a) Vertical and (b) horizontal measurements for convex array probes. (c) Vertical and (d) horizontal measurements for phased array probes. (e) Vertical and (f) horizontal measurements for linear array probes. Each plot shows the mean values of e among the probes of the group both for LSM (continuous line, LSMMV) and SDM (dotted line, SDMMV). Suffixes “a” and “b” in each probe label refer to advanced and intermediate technology level, respectively.
Difference between nominal and measured vertical distances for a probe phased array. In (a), from the LSM plot a nonlinear behaviour of the diagnostic system can be noticed (Rsquare = 0.4533), while in (b) the SDM plot is shown for a 20 mm distance evaluated at different depths. (a) e = 0.08 ± 0.14 mm/cm and (b) e = 0.13 ± 0.11 mm/cm. As the image spatial resolution is about 0.39 mm/pixel, the peak in (b) is due to a 1 pixel variation on 2 cm distance measurement (about 2% difference from nominal length).
Speed of sound cm for human tissues and percentage error referring to ultrasound scanner setting speed ct = 1540 m/s. Adapted from Ref. 14.
Experimental results on distance relative error e evaluation for four probes (LSM).
Experimental results on distance relative error evaluation for four probes (SDM).
Ultrasound phantoms characteristic.
Experimental settings adopted in the present study. FOV: field of view, DR: dynamic range, FZN: focal zones number, FZD: focal zone depth, OG: overall gain, PP: post-processing, FZ: focal zone.
Test range of distances for LSM and SDM evaluation.
Averages on e values among three groups of probes.
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