A closed-form field analysis of a broad-band annular array

Area of Science:

• Acoustics
• Ultrasonics
• Wave propagation

Background:

• Understanding transient ultrasonic fields is crucial for medical imaging and non-destructive testing.
• Accurate modeling of transducer response is essential for precise focusing and signal interpretation.

Purpose of the Study:

• To derive a closed-form transient field response for impulse waves from circularly symmetric ultrasonic transducers.
• To analyze the focusing characteristics of phased annular arrays, including delay and apodization errors.

Main Methods:

• Linear transform techniques were employed to derive the impulse response.
• The paraxial approximation was used, with a closed-form solution for focal plane response.
• A solution without the paraxial approximation, including the obliquity factor, was also derived for planar annular transducers.

Main Results:

• A closed-form transient field response was obtained for various transducer types (disk, annulus).
• The focal plane response for nonuniform apertures with polynomial apodization was solved.
• Impulse responses for phased annular arrays were calculated by convolution and summation.

Conclusions:

• The derived solutions offer an effective method for studying phased annular array focusing.
• The results facilitate the analysis of focusing delay and apodizing quantization errors in ultrasonic systems.