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"One common thread is apparent in the writings of all those who have published papers on the subject of optical transforms - the great power of visual presentation in teaching, in stimulating thought and in aiding the development of intuition, which still plays a major role in solving the more complex diffraction problems."
C. A. Taylor 1975

 Crystalline systems diffract X-rays which have a wavelength comparable to the distances between atoms (~1 angstrom). The principles of X-ray diffraction can be demonstrated by light diffraction from optical diffraction masks. These masks are 2D representations of physical systems "drawn" onto a transparency (slide) using a photomation apparatus. The image is on a fine scale so that a good sized diffraction pattern (Optical Transform) is formed when the transparency is illuminated with a standard low power HeNe laser (or similar).

 Optical Transforms are a very useful educational tool for illustrating a wide variety of diffraction phenomena from Bragg diffraction, through diffuse scattering from disordered and amorphous systems to diffraction from quasicrystals with non-crystallographic symmetry. The following figures demonstrate the use of a selection of these optical transforms for modelling the scattering patterns of amorphous and crystalline systems. (The full list of available diffraction masks is given below).

Powders and Liquids

powder transformsThis image shows diffraction from basic gratings, powder diffraction from different symmetry lattices, and diffraction from a liquid.


benzene transformsThis image shows diffraction from randomly distributed benzene molecules, from a lattice of benzene molecules, from randomly distributed pairs and quartets of molecules, and the effect of thermal diffuse scattering and lattice vacancies on diffraction patterns.

Quasicrystals and Paracrystals

powder transformsThis image shows the effect of space group symmetry on diffraction patterns, quasicrystal diffraction patterns with two ordering schemes and a distorted paracrystal diffraction pattern.

Simple Diffraction Apparatus

Some laser links

Some lens links
Edmund Scientific http://www.edmundscientific.com/scientifics/scientifics.cfm
Optosigma http://optics.org/optosigma/lenses/microobj.html


List of Optical diffraction masks available......

 August 1998

The slides are designed to demonstrate various diffraction effects encountered in crystallography, but some at least will have wider applicability.

The slides are in 35mm format and each contains a very fine-scale image of a computer-generated model. The scale is chosen to be small so that the optical diffraction pattern (Transform), which may be obtained using a laser and a simple arrangement of lenses, is of a large enough size that it may easily be viewed in a class-room with no further magnification required.

1a-f 1D gratings 3 different spacings, single or double slit 6

2a,b,c 2D powder patterns 3

3 2D liquid like structure 1

4a,b,c 2D Penrose tiling etc. 3

5 Various Molecular crystals (hypothetical) showing different symmetries. 4

6 Disordered Molecular crystal showing diffuse scattering. 3

7a,b,c Helical molecules, combinations of different pitches and radii. 3

8. Examples showing effect of molecular shape on transform of lattice. 10

c.f. Plates 11 & 12 of ' Atlas of Optical Transforms' by Harburn, Taylor & Welberry

9. Lattice modulations. 2

c.f. Plate 20 of ' Atlas of Optical Transforms' by Harburn, Taylor & Welberry

Updated  10.  Highly distorted lattices (Hosemann paracrystals). 6     Updated !

11a,b Novelty transforms 2

12. Various Lattice functions - demonstration multiplication/convolution. 6

c.f. Plates 10 &13 of ' Atlas of Optical Transforms' by Harburn, Taylor & Welberry

13. Development of 1D chain - multiplication/convolution - SINC function. 5

c.f. Plates 1 & 10 of ' Atlas of Optical Transforms' by Harburn, Taylor & Welberry

New  14. Atomic Size Effect -  4      New !

see  Welberry, T.R. (1986)  J. Appl. Cryst.  19, 382-389 Total number of slides.................. 58

Optical Diffraction Slides may be ordered by writing to:-

Dr. T.R.Welberry,
Research School of Chemistry,
Australian National University,
Canberra City, ACT 0200,


Cost of slides is A$20 per slide.

Overhead transparencies showing enlarged portions of each slide may be obtained for an extra A$5 per slide.

Web page maintained by T.R.Welberry | ANU | last update   August 2000 welberry@rsc.anu.edu.au