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

Partial Fractions

Partial Fractions

A partial fraction is a component of a rational expression represented as the sum of simpler fractions. When a rational function is expressed as a ratio of two polynomials, it can often be decomposed into a sum of fractions whose denominators are simpler polynomials, typically linear or irreducible quadratic factors. This process is called partial fraction decomposition, and it is used to simplify complex expressions for integration, solving equations, or analysis.Partial fraction decomposition...

Complex Zeros

Complex Zeros

Complex zeros are the solutions to polynomial equations that include imaginary numbers, specifically, numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit defined by i2=-1. These zeros satisfy the equation P(x) = 0, where P(x) is a polynomial with real or complex coefficients. Since the complex number system includes all real numbers, it provides a complete framework for analyzing all possible roots of a polynomial.Every polynomial of degree n≥1 can be...

Fundamental Theorem of Algebra

Fundamental Theorem of Algebra

The Fundamental Theorem of Algebra is central to the study of polynomial equations, asserting that every non-constant polynomial with complex coefficients has at least one complex zero. This means that a polynomial of degree n ≥ 1, written as: with an ≠ 0, has at least one solution in the complex number system. Since the set of real numbers is a subset of complex numbers, this theorem applies equally to polynomials with real coefficients.Building on this result, the Complete Factorization...

Factorial Design

Factorial Design

Factorial Analysis is an experimental design that applies Analysis of Variance (ANOVA) statistical procedures to examine a change in a dependent variable due to more than one independent variable, also known as factors. Changes in worker productivity can be reasoned, for example, to be influenced by salary and other conditions, such as skill level. One way to test this hypothesis is by categorizing salary into three levels (low, moderate, and high) and skills sets into two levels (entry level...

Compacting Factor test

Compacting Factor test

The compacting factor test is a method used to assess the workability of concrete. It is especially suitable for concrete mixes containing aggregates up to one and a half inches in size. This test involves specialized equipment consisting of two truncated cone-shaped hoppers and a cylinder, all with polished interior surfaces to minimize friction.
The procedure begins by placing concrete into the upper hopper without any compaction. Once filled, the bottom door of this hopper is opened,...

Type IV Collagen of Basal Lamina

Type IV Collagen of Basal Lamina

Type IV collagen is a 400 nm long, network-forming collagen that acts as a barrier between the epithelial and endothelial cells. Type IV collagen forms the backbone of the basement membrane by scaffolding with laminin, entactin, proteoglycans, and fibronectin. Apart from rendering structural support to the basement membrane, it also helps entail signaling potentials necessary for both pathological and physiological functions.
A type IV collagen molecule has six alpha chains which can exist in...

You might also read

Related Articles

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

Sort by

Same author

Simple trace criterion for classification of multilayers.

Optics letters·2007

See all related articles

Search research articles

Related Experiment Video

Updated: Jul 9, 2026

Production of Single Tracks of Ti-6Al-4V by Directed Energy Deposition to Determine the Layer Thickness for Multilayer Deposition

Production of Single Tracks of Ti-6Al-4V by Directed Energy Deposition to Determine the Layer Thickness for Multilayer Deposition

Published on: March 13, 2018

Basic factorization for multilayers.

J J Monzãân, T Yonte, L L Sãânchez-Soto

|November 28, 2007

Summary

This study introduces a new factorization method for multilayer optics, simplifying their description using three fundamental matrices. This approach connects multilayer optical behavior to principles of geometrical optics.

Area of Science:

Optics
Materials Science

Background:

Multilayer optical systems are crucial in various technologies.
Describing their behavior can be complex due to multiple interfaces.

Purpose of the Study:

To develop a simplified and consistent mathematical framework for analyzing multilayer optical elements.
To establish a connection between the behavior of multilayer optics and established geometrical optics principles.

Main Methods:

A novel factorization scheme tailored for multilayer structures was developed.
The action of a multilayer was consistently described using three fundamental matrices derived from this scheme.

Main Results:

The factorization scheme effectively simplifies the analysis of multilayer optics.

Related Experiment Videos

Last Updated: Jul 9, 2026

Production of Single Tracks of Ti-6Al-4V by Directed Energy Deposition to Determine the Layer Thickness for Multilayer Deposition

Production of Single Tracks of Ti-6Al-4V by Directed Energy Deposition to Determine the Layer Thickness for Multilayer Deposition

Published on: March 13, 2018

A clear representation of multilayer optical action using three basic matrices was achieved.

Analogies between multilayer and geometrical optics behaviors were identified and discussed.

Conclusions:

The proposed factorization scheme offers a powerful tool for understanding and designing multilayer optical systems.
This work bridges the gap between complex multilayer optics and fundamental geometrical optics concepts.