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

Intensity Of Electromagnetic Waves01:22

Intensity Of Electromagnetic Waves

The energy transport per unit area per unit time, or the Poynting vector, gives the energy flux of an electromagnetic wave at any specific time. For a plane electromagnetic wave with E0 and B0 as the peak electric and magnetic fields and traveling along the x-axis, the time-varying energy flux can be given by the following equation:
Carrier Transport01:21

Carrier Transport

The generation of electrical current in semiconductors is fundamentally driven by two mechanisms: drift and diffusion. These processes are essential for the functionality and performance of semiconductor-based devices.
Drift Current:
The drift of charge carriers is started by an external electric field (E). Charged particles, such as electrons and holes, experience an acceleration between collisions with lattice atoms. For electrons, this results in a drift velocity (vd) given by:
Propagation Speed of Electromagnetic Waves01:30

Propagation Speed of Electromagnetic Waves

Electromagnetic waves are consistent with Ampere's law. Assuming there is no conduction current Ampere's law is given as:
Reynolds Transport Theorem01:24

Reynolds Transport Theorem

The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit mass.
Velocity and Acceleration of a Wave00:51

Velocity and Acceleration of a Wave

A wave propagates through a medium with a constant speed, known as a wave velocity. It is different from the speed of the particles of the medium, which is not constant. In addition, the velocity of the medium is perpendicular to the velocity of the wave. The variable speed of the particles of the medium implies that there must be acceleration associated with it. 
The velocity of the particles can be obtained by taking the partial derivative of the position equation with respect to time. We can...
UV–Vis Spectroscopy: Beer–Lambert Law01:09

UV–Vis Spectroscopy: Beer–Lambert Law

The Beer-Lambert law describes the relationship between absorbance and concentration, which combines the principles established by scientists Johann Heinrich Lambert and August Beer. Lambert's law states that when light passes through a medium, the loss in intensity is directly proportional to the original intensity and the path length of the light. Beer's law proposed that the transmittance of a solution remains constant if the product of concentration and path length is constant. The modern...

You might also read

Related Articles

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

Sort by
Same author

Rapidly tunable ultrabroadband flying focus using adaptive optics and an axiparabola.

Optics letters·2026
Same author

Parametric amplification of angularly multiplexed waves for application to beam smoothing.

Optics express·2025
Same author

Scalable waveplate for ultraviolet applications using laser-imprinted birefringence in silica.

Optics express·2025
Same author

Demonstration of controlled spatial incoherence for beam smoothing.

Optics express·2025
Same author

Degradation of temporal contrast from post-pedestal interference with a chirped pulse in an optical parametric amplifier.

Optics express·2024
Same author

Achievement of Target Gain Larger than Unity in an Inertial Fusion Experiment.

Physical review letters·2024

Related Experiment Video

Updated: Jun 22, 2026

Evanescent Field Based Photoacoustics: Optical Property Evaluation at Surfaces
10:21

Evanescent Field Based Photoacoustics: Optical Property Evaluation at Surfaces

Published on: July 26, 2016

Optical testing using the transport-of-intensity equation.

C Dorrer, J D Zuegel

    Optics Express
    |June 24, 2009
    PubMed
    Summary

    The transport-of-intensity equation offers a simple method for optical testing by linking light intensity and phase. This technique accurately measures surface variations, demonstrated on laser rods after finishing.

    Area of Science:

    • Optics
    • Optical Metrology
    • Surface Characterization

    Background:

    • The transport-of-intensity equation (TIE) relates the intensity distribution of an optical field to its phase.
    • Accurate phase retrieval is crucial for optical testing and surface metrology.
    • Fresnel diffraction effects are inherent in optical propagation and must be accounted for.

    Purpose of the Study:

    • To derive and validate the properties of the transport-of-intensity equation for spatial-phase measurement.
    • To demonstrate a simple and accurate method for optical testing of flat surfaces using TIE.
    • To experimentally quantify surface variations induced by magnetorheological finishing on laser rods.

    Main Methods:

    • Theoretical derivation of the transport-of-intensity equation and its implications for phase retrieval.

    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

    Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
    09:19

    Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

    Published on: July 29, 2013

    Related Experiment Videos

    Last Updated: Jun 22, 2026

    Evanescent Field Based Photoacoustics: Optical Property Evaluation at Surfaces
    10:21

    Evanescent Field Based Photoacoustics: Optical Property Evaluation at Surfaces

    Published on: July 26, 2016

    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

    Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
    09:19

    Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

    Published on: July 29, 2013

  • Development of a spatial-phase measurement technique based on TIE.
  • Experimental setup for optical testing and surface profile measurement.
  • Application of the technique to analyze surface modifications on laser rods.
  • Main Results:

    • The transport-of-intensity equation provides a robust framework for phase retrieval from intensity measurements.
    • The developed method enables simple and accurate spatial-phase measurements for optical surface testing.
    • Quantifiable surface variations on laser rods, resulting from magnetorheological finishing, were successfully measured.

    Conclusions:

    • The transport-of-intensity equation is a valuable tool for non-interferometric phase measurement in optical testing.
    • The demonstrated technique offers a practical approach for characterizing surface modifications in optical components.
    • Magnetorheological finishing process effects on laser rod surfaces can be effectively assessed using TIE-based methods.