Tooth characterization using ultrasound with fractional Fourier transform

Ultrasound allows the internal tooth structure to be imaged non-destructively and has been demonstrated experimentally using the pulse-echo technique at different frequencies since the 1960s. For low frequencies the resolution is limited but changing to higher frequencies increases attenuation and decreases the penetration depth. The proposed solution in this paper is to use a long-duration, frequency modulated excitation signal in order to improve SNR and increase penetration depth. Although long-duration excitation provides a better penetration, the internal reflections inside the enamel and dentin layers make the received signal uninterpretable. The fractional Fourier transform (FrFT) allows frequency modulated signals overlapping in time and frequency to be separated. In this work, we present the application of the fractional Fourier technique to tooth imaging by analyzing and filtering chirp signals, overlapping in both the time and frequency domains, where the common time or frequency based filtering is not applicable. The intended application of the proposed technique is producing an image of tooth enamel and underlying dentino-enamel junction (DEJ).