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

Gaussian Elimination: Problem Solving

Gaussian Elimination: Problem Solving

Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...

$Interference and Diffraction$ 02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

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.

Calibration Curves: Linear Least Squares

Calibration Curves: Linear Least Squares

A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...

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...

Linear Approximation in Time Domain

Linear Approximation in Time Domain

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, the...

You might also read

Related Articles

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

Sort by

Same author

Symmetric gradient-index media reconstruction.

Optics express·2023

Same author

Testing lenses and reflecting concave surfaces using a knife-edge interferometer.

Applied optics·2019

Same author

Measurement of three-dimensional wavefronts using the Ichikawa-Lohmann-Takeda solution to the irradiance transport equation.

Applied optics·2018

Same author

Chalmers interferometric test using a reflective spatial light modulator.

Optics express·2012

Same author

Inclined toroidal surface that fits an off-axis conic section.

Applied optics·2010

Same author

Polynomial fitting of interferograms with Gaussian errors on fringe coordinates. 1: Computer simulations.

Applied optics·2010

Search research articles

Related Experiment Video

Updated: Jul 7, 2026

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

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

Published on: August 12, 2013

Polynomial Fitting of Interferograms with Gaussian Errors on Fringe Coordinates. III. Nonlinear Solution.

A Cordero-Dávila, O Cardona-Nuñez, A Cornejo-Rodríguez

|February 28, 2008

Summary

This study introduces a new algorithm for analyzing interferogram fringe data with random errors. The method refines fringe coefficient estimation, improving accuracy over traditional techniques.

More Related Videos

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Published on: April 4, 2017

Related Experiment Videos

Last Updated: Jul 7, 2026

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

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

Published on: August 12, 2013

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Published on: April 4, 2017

Area of Science:

Optics and Metrology
Data Analysis and Computational Science

Background:

Interferogram analysis often involves processing fringe data with random, Gaussian errors.
The standard least-squares method can lead to nonlinear systems of equations.
Accurate fringe coefficient estimation is crucial for precise measurements.

Purpose of the Study:

To develop and present an algorithm for estimating coefficients in nonlinear systems derived from interferogram analysis.
To improve upon the classic least-squares method for fringe data processing.
To validate the algorithm's performance on straight, equally spaced fringe patterns.

Main Methods:

The study converts the normal equations from the least-squares method into a nonlinear system.
It employs the Newton-Raphson method for coefficient estimation, initiating iterations from a classic solution.
The algorithm is applied to simulated data of straight and equally spaced fringes.

Main Results:

The algorithm successfully estimates the correct coefficients for the nonlinear system.
It aids in selecting appropriate terms for the mathematical model.
Results demonstrate a contrast and potential improvement compared to the classic method.

Conclusions:

The proposed Newton-Raphson based algorithm offers a robust approach to interferogram analysis with random errors.
This method enhances the accuracy of fringe coefficient estimation and model selection.
It provides a valuable alternative for precise optical metrology applications.