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The programme extends the ides of Fourier series to Fourier transformations in order to cope with commonly encountered gratings such as the single slit.
Metadata describing this Open University video programme
Module code and title: ST291, Images and information
Item code: ST291; 04
First transmission date: 14-04-1977
Published: 1977
Rights Statement:
Restrictions on use:
Duration: 00:23:54
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Producer: Ted Smith
Contributors: Keith Hodgkinson; Barrie Jones
Publisher: BBC Open University
Keyword(s): Diffraction patterns; Fourier Series; Frequency spectra; Slit diffraction grating
Footage description: Keith Hodgkinson, with several graphic aids, briefly recaps the previous programme. Barrie Jones displays several laser diffraction patterns and poses the question of how one can account for diffraction patterns of gratings which cannot even approximately be considered infinite. Hodgkinson generates frequency spectra which are displayed together with their corresponding square wave forms in a computer animation. Jones, with computer animations and other graphics, shows how the shape of the frequency continuum is related to the shape of a single pulse in X-space when the two form a pair of Fourier mates. Hodgkinson takes this approach further. By showing computer animations, he explains how the amplitude of the frequency components is normalised and why this needs to be done. Hodgkinson then goes on to explain and demonstrate how to change a wave profile. The computer animation shows a Gaussian and its frequency spectrum. Hodgkinson examines another function, a spike and its Fourier transforming Q-space as a continuum. Hodgkinson shows a final profile, a spike expanding out as an exponential with its Fourier transform as a Lorentzian. Barrie Jones, using several graphic aids, summarises the results observed so far. Keith Hodgkinson considers the problem of the non-infinite repetitive waveform - the restricted width diffration grating. He explains how to construct a restricted grating by laying a simple slit over an infinite grating. Next, using a computer animation, he shows how a Fourier transform for a limited grating is obtained by the "convolution" operation. Barrie Jones sums up the above case in which one of the functions was infinite. He then considers a case in which a Lorentzian function is convoluted with a sine function (both functions are now continuous). Jones used an animation to illustrate. Keith Hodgkinson closes the programme by showing how the Fourier transform relationship between X-space and spatial frequencies can be paralleled by a similar Fourier transform relationship between time and temporal frequencies. Hodgkinson demonstrates by restricting a pure tone to smaller and smaller time intervals while the temporal frequency spectrum broadens out to include more and more frequency components.
Master spool number: HOU2263
Production number: 00525_1244
Videofinder number: 2115
Available to public: no