Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Rectangular and Triangular Pulse Function01:19

Rectangular and Triangular Pulse Function

The unit rectangular pulse function is mathematically represented by a rectangular function centered at the origin with a height of one unit. This function is defined by two parameters: T, which specifies the center location of the pulse along the time axis, and τ, which determines the pulse duration.
For example, consider a rectangular pulse with a 5V amplitude, a 3-second duration, and centered at t=2 seconds. This pulse can be expressed using the rectangular function, written as,
Impulse Response01:17

Impulse Response

The impulse response is the system's reaction to an input impulse. In an RC circuit, the voltage source is the input, and the capacitor's voltage is the output. The system's state and output response before and after input excitation are distinctly defined.
Kirchhoff's law forms an input signal equation, with the capacitor's current and voltage providing the output. Substituting the current and dividing by RC yields a differential equation. The output for an impulse input is the impulse...
Convolution Properties II01:17

Convolution Properties II

The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
Deformations in a Transverse Cross Section01:21

Deformations in a Transverse Cross Section

When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...
Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the time...
Simpson's Rule II01:28

Simpson's Rule II

In warehouse roofing applications, corrugated or curved metal sheets are commonly used to improve structural strength, water drainage, and ventilation efficiency. To accurately estimate material requirements and optimize design parameters, engineers must determine the curved surface area of these sheets. Because the sheet profiles often repeat smoothly along their length, they can be effectively approximated by parabolic curves, enabling the use of numerical integration techniques for area...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

A triboelectric radical generation route to chlorine disinfectants from brine.

Nature communications·2026
Same author

Ultrasound-Based Techniques for Visualization of Dermal Microvasculature: A Scoping Review.

Diagnostics (Basel, Switzerland)·2026
Same author

Largely Enhanced Photocatalysis Process by Contact-Electro-Catalysis for Efficient and Eco-Friendly Recovery of Gold.

Advanced materials (Deerfield Beach, Fla.)·2025
Same author

Human lymph node microvascular imaging using a fast contrast-free super-resolution ultrasound technique.

Scientific reports·2025
Same author

Analysing the Renal Vasculature Using Super-Resolution Ultrasound Imaging: Considerations for Clinical and Research Applications.

Diagnostics (Basel, Switzerland)·2025
Same author

The Zucker Diabetic Fatty Rat as a Model for Vascular Changes in Diabetic Kidney Disease: Characterising Hydronephrosis.

Diagnostics (Basel, Switzerland)·2025

Related Experiment Video

Updated: May 23, 2026

Investigating the Potential of Singly Curved Thin Piezoelectric Transducers for Energy Harvesting and Structural Health Monitoring
07:02

Investigating the Potential of Singly Curved Thin Piezoelectric Transducers for Energy Harvesting and Structural Health Monitoring

Published on: November 14, 2025

̀Spatial impulse response of a rectangular double curved transducer.

David Böttcher Bæk1, Jørgen Arendt Jensen, Morten Willatzen

  • 1Center for Fast Ultrasound Imaging, Department of Electrical Engineering, Technical University of Denmark, Orsteds Plads Building 349, 2800 Kgs Lyngby, Denmark.

The Journal of the Acoustical Society of America
|April 17, 2012
PubMed
Summary
This summary is machine-generated.

A new semi-analytical algorithm precisely calculates the spatial impulse response for double-curved transducers. This method offers a computationally efficient and accurate alternative to traditional numerical approximations for ultrasound transducer modeling.

More Related Videos

A Stable Phantom Material for Optical and Acoustic Imaging
04:54

A Stable Phantom Material for Optical and Acoustic Imaging

Published on: June 16, 2023

Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy
07:44

Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy

Published on: April 27, 2016

Related Experiment Videos

Last Updated: May 23, 2026

Investigating the Potential of Singly Curved Thin Piezoelectric Transducers for Energy Harvesting and Structural Health Monitoring
07:02

Investigating the Potential of Singly Curved Thin Piezoelectric Transducers for Energy Harvesting and Structural Health Monitoring

Published on: November 14, 2025

A Stable Phantom Material for Optical and Acoustic Imaging
04:54

A Stable Phantom Material for Optical and Acoustic Imaging

Published on: June 16, 2023

Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy
07:44

Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy

Published on: April 27, 2016

Area of Science:

  • Acoustics
  • Ultrasound Technology
  • Computational Physics

Background:

  • Calculating the pressure field from curved transducers is complex due to the lack of analytical solutions.
  • Current methods often approximate curved surfaces with smaller flat elements, introducing potential inaccuracies.
  • The spatial impulse response (SIR) is crucial for accurate ultrasound field prediction.

Purpose of the Study:

  • To develop a semi-analytical algorithm for the exact solution of the SIR for rectangular-shaped double-curved transducers.
  • To investigate an approximation of the solution for computational efficiency.
  • To validate the algorithm's accuracy and consistency against established simulation tools.

Main Methods:

  • Development of a semi-analytical algorithm for the first-order diffraction effect of the SIR.
  • Reformulation of the solution into an analytically integrable expression for efficient computation.
  • Comparison of simulation results with FIELD II, a widely used ultrasound simulation software.
  • Utilized a three-point Taylor expansion for the approximation.

Main Results:

  • The semi-analytical algorithm provides an exact solution for the SIR of double-curved transducers.
  • An approximation yields a computationally efficient solution with a mean error ranging from 0.03% to 0.8% compared to numerical solutions.
  • The algorithm demonstrated consistent results with FIELD II simulations for various transducer geometries (linear flat, linear focused, convex nonfocused).
  • The three-point Taylor expansion approximation achieved an accuracy of 0.01%.

Conclusions:

  • The presented semi-analytical algorithm offers an accurate and efficient method for calculating the spatial impulse response of double-curved transducers.
  • The computationally efficient approximation is suitable for practical applications where speed is essential.
  • The algorithm's consistency with FIELD II validates its reliability for ultrasound transducer modeling.