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

Triple Integrals in Spherical Coordinates

Triple Integrals in Spherical Coordinates

Triple integrals in spherical coordinates provide an efficient method for evaluating volumes over regions with central symmetry, such as spheres. Instead of describing points by rectangular coordinates, spherical coordinates use three variables: 𝜌, 𝜃, and 𝜑. Here, 𝜌 is the distance from the origin, 𝜃 is the angle in the xy-plane measured from the positive x-axis, and 𝜑 is the angle measured downward from the positive z-axis.To derive the volume of a sphere, the solid region can be divided...

The Principle of Superposition and the Gravitational Field

The Principle of Superposition and the Gravitational Field

The principle of superposition applies to gravitational forces of objects that are sufficiently far apart. It states that the net gravitational force on a point object is the vector sum of the gravitational forces on it due to various objects. The principle helps calculate the force by listing the individual forces and then vectorially summing them up. However, it should be noted that the principle of superposition is not always apparent. In the presence of a second force, the first force could...

Triple Integrals over General Regions

Triple Integrals over General Regions

Triple integrals over general bounded regions extend the concept of double integrals from planar domains to three-dimensional solids. A solid region E in space is commonly enclosed within a rectangular box B, and a continuous function f(x, y, z) is integrated over the region by defining F such that it coincides with f on E and is zero outside the solid. The triple integral is therefore expressed as\begin{equation*}\iiint_E f(x,y,z) dV \end{equation*}The existence of the integral requires that f...

Gauss's Law: Spherical Symmetry

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...

Electric Field of a Non Uniformly Charged Sphere

Electric Field of a Non Uniformly Charged Sphere

Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...

Integration Applied to Polar Coordinates to Find Areas

Integration Applied to Polar Coordinates to Find Areas

A rotating lawn sprinkler with an uneven spray pattern produces a variable reach as it distributes water in different directions. This directional variation in spray distance can be effectively described using polar coordinates, where the distance from the center is represented as a function of the angle of rotation. The path traced by the spray then forms a polar curve, which captures the irregularities in the sprinkler’s reach across the full rotation.To calculate the total area watered by...

You might also read

Related Articles

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

Sort by

Same author

Instrument for measuring phototube spectral response.

Applied optics·2010

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 17, 2026

Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects

Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects

Published on: May 10, 2019

Generalized integrating-sphere theory.

¹Colorimetry and Spectrophotometry Section, National Bureau of Standards, Washington, DC 20234, USA.

|January 9, 2010

Summary

This summary is machine-generated.

A new equation models integrating sphere efficiency with non-uniform coatings, assuming a perfect sphere and diffuse reflection. This helps improve reflectance measurements and absolute techniques.

More Related Videos

Studying the Integration of Adult-born Neurons

Studying the Integration of Adult-born Neurons

Published on: March 25, 2011

Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps

Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps

Published on: October 28, 2018

Related Experiment Videos

Last Updated: Jun 17, 2026

Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects

Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects

Published on: May 10, 2019

Studying the Integration of Adult-born Neurons

Studying the Integration of Adult-born Neurons

Published on: March 25, 2011

Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps

Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps

Published on: October 28, 2018

Area of Science:

Optical physics
Metrology

Background:

Integrating spheres are crucial optical instruments.
Nonuniform coatings can affect their performance.
Accurate modeling is needed for reliable measurements.

Purpose of the Study:

Develop a general equation for integrating sphere efficiency.
Account for nonuniform coating effects.
Analyze applications in reflectance measurements.

Main Methods:

Derived a general equation for integrating sphere efficiency.
Assumed a perfect spherical interior.
Assumed perfectly diffuse reflection from all interior surfaces.

Main Results:

The general equation applies to spheres with nonuniform coatings.
Three special cases were examined.
The equation is applicable to hemispherical reflectance and absolute reflectance techniques.

Conclusions:

The developed equation provides a framework for understanding integrating sphere efficiency.
It accounts for variations in coating properties.
This enhances the accuracy of optical measurements using integrating spheres.