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

Linearization and Approximation01:26

Linearization and Approximation

59
Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
59
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

90
A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
90
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

378
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
378
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

372
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
372
Approximate Integration01:24

Approximate Integration

50
In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...
50
Accuracy, limits, and approximation01:28

Accuracy, limits, and approximation

1.3K
Accuracy, limits, and approximations are common in many fields, especially in engineering calculations. These concepts are imperative for ensuring that a given value is as close as possible to its true value.
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
1.3K

You might also read

Related Articles

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

Sort by
Same author

A method to efficiently and rapidly approximate the vectorial fields generated by large area metasurfaces.

Optics express·2024
Same author

Flexible gauge length intrinsic fiber-optic strain sensor using broadband interferometry [Invited].

Journal of the Optical Society of America. A, Optics, image science, and vision·2020
Same author

Improved description of the signal formation in grating generated-optical coherence tomography.

Optics express·2019
Same author

Considerations on the proposed linear theory of surface measurement for coherence scanning interferometers.

Applied optics·2017
Same author

Obtaining the Transfer Function of optical instruments using large calibrated reference objects.

Optics express·2015
Same author

Using dynamical barriers to control the transmission of light through slowly varying photonic crystals.

Physical review. E, Statistical, nonlinear, and soft matter physics·2011
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

Related Experiment Video

Updated: Jan 30, 2026

Implementation of a Reference Interferometer for Nanodetection
16:11

Implementation of a Reference Interferometer for Nanodetection

Published on: April 26, 2014

9.8K

Improvements to dispersed reference interferometry: beyond the linear approximation.

A J Henning, J Williamson, H Martin

    Applied Optics
    |January 16, 2019
    PubMed
    Summary
    This summary is machine-generated.

    Dispersion interferometry uses controlled dispersion to locate scattering surfaces. Linear approximations cause errors; including second-order terms is crucial for accurate metrology.

    More Related Videos

    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
    12:14

    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

    Published on: August 12, 2013

    22.5K
    Analyzing DNA-Protein Interactions with Streptavidin-Based Biolayer Interferometry
    08:07

    Analyzing DNA-Protein Interactions with Streptavidin-Based Biolayer Interferometry

    Published on: January 17, 2025

    2.2K

    Related Experiment Videos

    Last Updated: Jan 30, 2026

    Implementation of a Reference Interferometer for Nanodetection
    16:11

    Implementation of a Reference Interferometer for Nanodetection

    Published on: April 26, 2014

    9.8K
    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
    12:14

    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

    Published on: August 12, 2013

    22.5K
    Analyzing DNA-Protein Interactions with Streptavidin-Based Biolayer Interferometry
    08:07

    Analyzing DNA-Protein Interactions with Streptavidin-Based Biolayer Interferometry

    Published on: January 17, 2025

    2.2K

    Area of Science:

    • Optical Metrology
    • Interferometry
    • Spectroscopy

    Background:

    • Interferometric instruments utilize controlled dispersion in the reference arm.
    • This dispersion generates a signal with a distinct point related to scattering surface position.

    Purpose of the Study:

    • To demonstrate errors arising from linear approximations in dispersion interferometry.
    • To highlight the necessity of including second-order terms for metrological accuracy.

    Main Methods:

    • Analysis of dispersion-based interferometric signal generation.
    • Inclusion and evaluation of second-order terms in the theoretical model.

    Main Results:

    • Linear approximations in dispersion interferometry can introduce significant errors.
    • Second-order terms are essential for correcting these errors and improving precision.

    Conclusions:

    • Accurate metrological applications of dispersion interferometry require the inclusion of second-order terms.
    • The study corrects previous approximations, enhancing the reliability of these instruments.