Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Traveling Waves: Lossless Lines

Traveling Waves: Lossless Lines

The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx and a shunt capacitance CΔx.

Kirchhoff's Voltage Law

Kirchhoff's Voltage Law

Kirchhoff's Voltage Law (KVL) is another fundamental principle in electrical engineering, introduced by physicist Gustav Robert Kirchhoff. This law is rooted in the principle of energy conservation, which states that energy can neither be created nor destroyed, only transferred or converted from one form to another.
KVL states that the algebraic sum of all voltages around a closed path or loop within a circuit is zero. This means that the total voltage supplied in a loop is equal to the total...

Surface Integrals

Surface Integrals

A curved roof has a surface area that is generally larger than its flat projection. To estimate the cost of painting it, the curved surface area must first be calculated. If the roof is represented parametrically by a vector-valued function r(u,v), then each point in a parameter domain D corresponds to a point on the surface S. This connection allows the curved surface to be studied through a two-dimensional parameter region.The parameter domain D is divided into many small rectangles. A...

Simpson's Rule II

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...

Kirchhoff's Current Law

Kirchhoff's Current Law

In the realm of electrical engineering, physicist Gustav Robert Kirchhoff made a significant contribution in 1847 by introducing Kirchhoff's laws for electric circuit analysis. These laws, particularly Kirchhoff's Current Law (KCL), have become foundational principles in understanding and analyzing electrical circuits.
Kirchhoff's Current Law is based on the principle of charge conservation. It states that at any node (a point where two or more circuit elements meet) in an electrical circuit,...

Tangent Planes to Level Surfaces

Tangent Planes to Level Surfaces

A level surface consists of all points in space where a function of three variables takes the same fixed value. If a point lies on this surface, understanding the surface’s geometry there requires more than just knowing the point’s coordinates; it requires describing how the surface is oriented, or how it tilts, near that point.To probe this local geometry, imagine tracing a path that stays entirely on the level surface and passes through the point of interest. This path can be described as a...

You might also read

Related Articles

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

Sort by

Same author

Simple calibration procedure for a full-Stokes imaging polarimeter using a polarized camera.

Applied optics·2026

Same author

Calibration of Stokes polarimeters with liquid-crystal variable retarders using the measured intensities.

The Review of scientific instruments·2026

Same author

Comparative exo-proteomics of solid and submerged state fermentation using the lignocellulose degrading Ascomycete Parascedosporium putredinis NO1.

Bioresource technology·2025

Same author

New weapons explosive exhibits persistent toxicity in plants.

Nature plants·2024

Same author

Controlling <i>In Planta</i> Gold Nanoparticle Synthesis and Size for Catalysis.

Environmental science & technology·2024

Same author

<i>Parascedosporium putredinis</i> NO1 tailors its secretome for different lignocellulosic substrates.

Microbiology spectrum·2024

Search research articles

Related Experiment Video

Updated: Jul 3, 2026

Scattering And Absorption of Light in Planetary Regoliths

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Single-scatter vector-wave scattering from surfaces with infinite slopes using the Kirchhoff approximation.

¹Centro de Ciencias Aplicadas y Desarrollo Tecnologico, Universidad Nacional Autonoma de Mexico, Mexico. neil.bruce@ccadet.unam.mx

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

|August 5, 2008

Summary

This summary is machine-generated.

This study introduces an improved 3D Kirchhoff approximation for calculating vector wave scattering from 2D rough surfaces, including those with infinite slopes. Results show good agreement with other methods for printed circuit board imaging applications.

More Related Videos

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation

Published on: March 2, 2021

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Published on: September 8, 2016

Related Experiment Videos

Last Updated: Jul 3, 2026

Scattering And Absorption of Light in Planetary Regoliths

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation

Published on: March 2, 2021

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Published on: September 8, 2016

Area of Science:

Electromagnetics and Wave Scattering
Computational Physics
Surface Metrology

Background:

Accurate modeling of wave scattering from rough surfaces is crucial for applications like remote sensing and printed circuit testing.
Existing methods may face limitations with surfaces exhibiting complex structures, such as infinite slopes.

Purpose of the Study:

To present a novel formulation of the 3D Kirchhoff approximation capable of handling 2D rough surfaces with infinite slopes.
To validate the new formulation through preliminary calculations and comparisons with established methods.

Main Methods:

Development of a new 3D Kirchhoff approximation formulation.
Calculation of vector wave scattering from 2D surfaces with infinite slopes.
Comparison of results with 1D surface calculations using Kirchhoff and integral equation methods.

Main Results:

The new 3D Kirchhoff approximation successfully calculates vector wave scattering from 2D surfaces with infinite slopes.
Preliminary calculations for rectangular grooves show good agreement between the 2D surface method and 1D surface methods.
Validation of the enhanced Kirchhoff approximation against integral equation methods.

Conclusions:

The proposed 3D Kirchhoff approximation formulation is effective for analyzing scattering from complex 2D rough surfaces.
This advancement has potential applications in remote sensing and the characterization of printed electronic circuits.
The method provides a reliable alternative for electromagnetic scattering calculations on challenging surface topographies.