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

Spherical Coordinates

Spherical Coordinates

Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...

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...

Surface Area Calculations

Surface Area Calculations

Surface area calculations for a graph z = f(x, y) are fundamental in engineering applications involving curved structures such as satellite dishes. A parabolic dish reflects communication signals efficiently, but engineers must determine its exact curved surface area to estimate coating materials, fabrication costs, and structural requirements. Since the rim of the dish forms a circular boundary, the surface area is calculated over a circular domain in the xy-plane.Parametric Representation of...

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...

Trigonometric Substitution

Trigonometric Substitution

Trigonometric substitution is a technique used to simplify integrals that contain square root expressions involving quadratic forms. It is particularly effective when the integrand includes terms resembling those found in standard geometric equations, such as circles or ellipses.Molniya satellites follow highly elliptical orbits, repeatedly sweeping out the same regions of space as they revolve around Earth. To estimate the area enclosed by such an orbit, the path is modeled as an ellipse...

Integration Applied to Polar Coordinates to Find Arc Lengths

Integration Applied to Polar Coordinates to Find Arc Lengths

In polar coordinates, a plane curve is described by a radial distance r from a fixed point, called the pole, and an angle θ measured from a reference direction. This system is especially useful for paths that naturally involve rotation, such as an expanding spiral followed by a search drone. If the hiker’s last known position is treated as the pole, then the drone’s location at any instant can be represented by the polar equation r = f(θ), where the distance from the pole changes as the drone...

You might also read

Related Articles

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

Sort by

Same author

Development of inverted pendulum thrust stand with spring-shaped wire for high power electric thrusters.

The Review of scientific instruments·2023

Same author

Machine learning algorithms predict experimental output of chaotic lasers.

Optics letters·2023

Same author

The association between <sup>11</sup>C-methionine uptake, IDH gene mutation, and MGMT promoter methylation in patients with grade II and III gliomas.

Clinical radiology·2020

Same author

Intratumoural immune cell landscape in germinoma reveals multipotent lineages and exhibits prognostic significance.

Neuropathology and applied neurobiology·2019

Same author

2D:4D and spatial abilities: From rats to humans.

Neurobiology of learning and memory·2018

Same author

Interactions of Dietary Fats and Proteins on Fatty Acid Composition of Immune Cells and LTB4 Production by Peritoneal Exudate Cells of Rats.

Bioscience, biotechnology, and biochemistry·2016

Same journal

Multifunctional reconfigurable terahertz metasurface based on vanadium dioxide phase transition: achieving broadband absorption and efficient polarization conversion.

Applied optics·2026

Same journal

High-Q-factor electromagnetically induced transparency utilizing quasi-bound states in the continuum in an all-dielectric terahertz metasurface.

Applied optics·2026

Same journal

Automated stitching interferometry for high-precision metrology of X-ray mirrors.

Applied optics·2026

Same journal

Experimental demonstration of an approach to designing a metal-dielectric DBR resonant cavity structure.

Applied optics·2026

Same journal

High-precision wavefront reconstruction from a single-shot interferogram using a physics-driven hybrid feature calibration network.

Applied optics·2026

Same journal

Ultra-high-Q Fano resonance based on coupled topological corner states in Kagome photonic crystals.

Applied optics·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 17, 2026

Near-Infrared Temperature Measurement Technique for Water Surrounding an Induction-heated Small Magnetic Sphere

Near-Infrared Temperature Measurement Technique for Water Surrounding an Induction-heated Small Magnetic Sphere

Published on: April 30, 2018

A 5-m integrating sphere.

M Nonaka¹, T Kashima, Y Kondo

¹Central Research Laboratory, Hitachi,Ltd., Kokubunji, Tokyo, Japan.

|January 9, 2010

Summary

This summary is machine-generated.

This study details the construction of a large, 5-meter integrating sphere, crucial for accurate optical measurements. The sphere achieved high spectral reflectance of 0.93-0.96 in the visible spectrum after barium sulfate coating.

More Related Videos

Indoor Experimental Assessment of the Efficiency and Irradiance Spot of the Achromatic Doublet on Glass (ADG) Fresnel Lens for Concentrating Photovoltaics

Indoor Experimental Assessment of the Efficiency and Irradiance Spot of the Achromatic Doublet on Glass (ADG) Fresnel Lens for Concentrating Photovoltaics

Published on: October 27, 2017

Scattering And Absorption of Light in Planetary Regoliths

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Related Experiment Videos

Last Updated: Jun 17, 2026

Near-Infrared Temperature Measurement Technique for Water Surrounding an Induction-heated Small Magnetic Sphere

Near-Infrared Temperature Measurement Technique for Water Surrounding an Induction-heated Small Magnetic Sphere

Published on: April 30, 2018

Indoor Experimental Assessment of the Efficiency and Irradiance Spot of the Achromatic Doublet on Glass (ADG) Fresnel Lens for Concentrating Photovoltaics

Indoor Experimental Assessment of the Efficiency and Irradiance Spot of the Achromatic Doublet on Glass (ADG) Fresnel Lens for Concentrating Photovoltaics

Published on: October 27, 2017

Scattering And Absorption of Light in Planetary Regoliths

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Area of Science:

Optical Engineering
Metrology

Background:

Accurate optical measurements require specialized equipment like integrating spheres.
Large-scale integrating spheres are essential for various photometric and radiometric applications.

Purpose of the Study:

To construct a large-diameter (5 m) integrating sphere with high geometric accuracy.
To characterize the spectral reflectance of the sphere's interior surface after coating.

Main Methods:

Construction involved welding 12 mm steel plates, achieving radii deviations within +/-0.3%.
A novel method involving substitution of a low-reflectance surface was used for spectral reflectance measurement.
Spectrophotometric measurements were conducted using a tungsten lamp and a measurement window.

Main Results:

The constructed integrating sphere demonstrated high geometric accuracy.
Spectral reflectance values ranged from 0.93 to 0.96 in the visible region.
These reflectance values were maintained ten months after the barium sulfate coating.

Conclusions:

The large integrating sphere meets stringent geometric requirements for accurate measurements.
The barium sulfate coating provides durable, high spectral reflectance suitable for optical applications.