A Closed-Form Differential Formulation for Ultrasound Spatial Calibration: Single Wall Phantom

Calibration is essential in freehand 3-D ultrasound to find the spatial transformation from the image coordinates to the sensor coordinate system. Ease of use, simplicity, precision and accuracy are among the most important factors in ultrasound calibration, especially when aiming to make calibration more reliable for day-to-day clinical use. We introduce a new mathematical framework for the simple and popular single-wall calibration phantom with a plane equation pre-determination step and the use of differential measurements to obtain accurate measurements. The proposed method provides a novel solution for ultrasound calibration that is accurate and easy to perform. This method is applicable to both radiofrequency (RF) and B-mode data, and both linear and curvilinear transducers. For a linear L14-5 transducer, the point reconstruction accuracy (PRA) of reconstructing 370 points is 0.73 ± 0.23 mm using 100 RF images, whereas the triple N-wire PRA is 0.67 ± 0.20 mm using 100 B-mode images. For a curvilinear C5-2 transducer, the PRA using the proposed method is 0.86 ± 0.28 mm on 400 points using 100 RF images, whereas N-wire calibration gives a PRA of 0.80 ± 0.46 mm using 100 B-mode images. Therefore, the accuracy of the proposed variation of the single-wall method using RF data is practically similar to the N-wire method while offering a simpler phantom with no need for accurate design and construction.