Fourier analysis

Fraunhofer diffraction equation

In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the diffracting object, and also when it is viewed at the focal plane of an imaging lens. The equation was named in honour of Joseph von Fraunhofer although he was not actually involved in the development of the theory. This article gives the equation in various mathematical forms, and provides detailed calculations of the Fraunhofer diffraction pattern for several different forms of diffracting apertures, specially for normally incident monochromatic plane wave. A qualitative discussion of Fraunhofer diffraction can be found elsewhere. (Wikipedia).

Fraunhofer diffraction equation
Video thumbnail

Solve a Bernoulli Differential Equation (Part 2)

This video provides an example of how to solve an Bernoulli Differential Equation. The solution is verified graphically. Library: http://mathispower4u.com

From playlist Bernoulli Differential Equations

Video thumbnail

Solve a Bernoulli Differential Equation Initial Value Problem

This video provides an example of how to solve an Bernoulli Differential Equations Initial Value Problem. The solution is verified graphically. Library: http://mathispower4u.com

From playlist Bernoulli Differential Equations

Video thumbnail

C73 Introducing the theorem of Frobenius

The theorem of Frobenius allows us to calculate a solution around a regular singular point.

From playlist Differential Equations

Video thumbnail

Ex: Solve a Bernoulli Differential Equation Using an Integrating Factor

This video explains how to solve a Bernoulli differential equation. http://mathispower4u.com

From playlist Bernoulli Differential Equations

Video thumbnail

B24 Introduction to the Bernoulli Equation

The Bernoulli equation follows from a linear equation in standard form.

From playlist Differential Equations

Video thumbnail

Fraunhofer Diffraction Explained

https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. In this video

From playlist Fourier Optics

Video thumbnail

Separation of variables and the Schrodinger equation

A brief explanation of separation of variables, application to the time-dependent Schrodinger equation, and the solution to the time part. (This lecture is part of a series for a course based on Griffiths' Introduction to Quantum Mechanics. The Full playlist is at http://www.youtube.com/

From playlist Mathematical Physics II - Youtube

Video thumbnail

Single-Slit Fraunhofer Diffraction

https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. In this video

From playlist Fourier Optics

Video thumbnail

Joseph Fraunhofer Biography: The Father of Modern Astronomy [CC]

How did Joseph Fraunhofer, a poor glassmaker, get saved from poverty by a prince and then discover spectroscopy (Fraunhofer lines), single slit diffraction AND the diffraction grating? I use primary sources to discover the background and the physics of this epoch making discovery. Links:

From playlist Early History of Spectroscopy: Astronomy

Video thumbnail

C35 The Cauchy Euler Equation

I continue the look at higher-order, linear, ordinary differential equations. This time, though, they have variable coefficients and of a very special kind.

From playlist Differential Equations

Video thumbnail

How to determine if an equation is a linear relation

👉 Learn how to determine if an equation is a linear equation. A linear equation is an equation whose highest exponent on its variable(s) is 1. The variables do not have negative or fractional, or exponents other than one. Variables must not be in the denominator of any rational term and c

From playlist Write Linear Equations

Video thumbnail

Optics: Fraunhofer diffraction - adjustable slit | MIT Video Demonstrations in Lasers and Optics

Optics: Fraunhofer diffraction - adjustable slit Instructor: Shaoul Ezekiel View the complete course: http://ocw.mit.edu/RES-6-006S08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT RES.6-006 Video Demonstrations in Lasers and Optics

Video thumbnail

PHYS 201 | Slit Diffraction 3 - Fraunhofer Diffraction

Now we set up the mathematical calculation of diffraction with Huygens-Fresnel wavelets, including the confusing concept of "field amplitude". Diffraction will be calculated in the "far field". This means we make several approximations as we set up the diffraction integral. Diffraction

From playlist PHYS 201 | Diffraction

Video thumbnail

Optics: Fraunhofer diffraction - rectangular aperture

Optics: Fraunhofer diffraction - rectangular aperture Instructor: Shaoul Ezekiel View the complete course: http://ocw.mit.edu/RES-6-006S08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT RES.6-006 Video Demonstrations in Lasers and Optics

Video thumbnail

Fresnel Diffraction Explained

https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. In this video

From playlist Fourier Optics

Video thumbnail

Optics: Fraunhofer diffraction - circular apertures | MIT Video Demonstrations in Lasers and Optics

Optics: Fraunhofer diffraction - circular apertures Instructor: Shaoul Ezekiel View the complete course: http://ocw.mit.edu/RES-6-006S08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT RES.6-006 Video Demonstrations in Lasers and Optics

Video thumbnail

A09 The Hamiltonian

Moving on from Lagrange's equation, I show you how to derive Hamilton's equation.

From playlist Physics ONE

Video thumbnail

Quantum Transport, Lecture 15: Superconducting Interference

Instructor: Sergey Frolov, University of Pittsburgh, Spring 2013 http://sergeyfrolov.wordpress.com/ Summary: flux quantization, SQUIDs, pi-junctions, Fraunhofer diffraction in Josephson junctions. Quantum Transport course development supported in part by the National Science Foundation und

From playlist Quantum Transport

Video thumbnail

Solve a Bernoulli Differential Equation (Part 1)

This video provides an example of how to solve an Bernoulli Differential Equation. The solution is verified graphically. Library: http://mathispower4u.com

From playlist Bernoulli Differential Equations

Video thumbnail

Optics: Fraunhofer diffraction - thin wires | MIT Video Demonstrations in Lasers and Optics

Optics: Fraunhofer diffraction - thin wires Instructor: Shaoul Ezekiel View the complete course: http://ocw.mit.edu/RES-6-006S08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT RES.6-006 Video Demonstrations in Lasers and Optics

Related pages

Complex conjugate | Wavenumber | Polar coordinate system | Geometric series | Cartesian coordinate system | Dirac delta function | Bessel function | Wave vector | Euclidean vector | Step function | Fourier optics | Fourier transform | Hankel transform | Apodization | Wave equation | Euler's formula | Wavelength