Focal depth localization for highly focused transducers in isotropic materials

Area of Science:

• Ultrasonic testing
• Acoustic focusing
• Non-destructive evaluation

Background:

• Conventional focusing equations for ultrasonic transducers rely on small-angle approximations.
• These approximations limit their accuracy for sharply focused transducers with significant curvature.
• Accurate focusing is crucial for effective non-destructive testing and material characterization.

Purpose of the Study:

• To develop a revised focusing equation applicable to sharply focused transducers.
• To extend the applicability of focusing equations beyond the paraxial approximation.
• To compare the performance of the revised equation against the conventional one.

Main Methods:

• Derivation of a closed-form focusing equation using ray tracing.
• Circumvention of the paraxial approximation in the new equation.
• Comparison of conventional and modified equations via ray diagrams for normal and oblique incidence.

Main Results:

• The revised focusing equation provides a closer approximation to the geometric focus.
• It achieves a smaller ultrasonic beam cross section.
• Enhanced time convergence is observed with the modified equation compared to the conventional one.

Conclusions:

• The proposed focusing equation enhances accuracy for sharply focused transducers.
• It offers improved performance in terms of focus proximity and beam convergence.
• This advancement is beneficial for applications requiring precise ultrasonic beam control.