We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 05 June 2012
Fraunhofer diffraction
The application of Fourier theory to Fraunhofer diffraction problems, and to interference phenomena generally, was hardly recognized before the late 1950s. Consequently, only textbooks written since then mention the technique. Diffraction theory, of which interference is only a special case, derives from Huygens' principle: that every point on a wavefront which has come from a source can be regarded as a secondary source; and that all the wave fronts from all these secondary sources combine and interfere to form a new wavefront.
Some precision can be added by using calculus. In Fig. 3.1, suppose that at O there is a source of ‘strength’ q, defined by the fact that at A, a distance r from O, there is a ‘field’, E, of strength E = q/r. Huygens' principle is now as follows:
If we consider an area dS on the surface S we can regard it as a source of strength E dS giving at B, a distance r′ from A, a field E′ = q dS/(rr′). All these elementary fields at B, summed over the transparent part of the surface S, each with its proper phase, give the resultant field at B. This is quite general – and vague.
In elementary Fraunhofer diffraction theory we simplify. We assume the following.
That only two dimensions need be considered. All apertures bounding the transparent part of the surface S are rectangular and of length unity perpendicular to the plane of the diagram.
[…]
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
