Some developments in Grating Transducer Systems

Abstract

In 1874 Lord Rayleigh 1 outlined some of the scientific possibilities of patterns formed by overlaid diffraction gratings. The patterns were named 'moire' after the techniques used by French silk weavers to produce decorative designs from overlapped layers of fine fabric. Although Righi 2 and later Giambiasi each contributed to the sum of knowledge en route, i t was to take the simult,~neous arrival in the early 1950's of the scientific definition of the technique by Roberts 4, the development of practical means for producing accurate gratings by NPL (based on a method suggested by Merton=), and the commercial requirement for optical grating transducers within a radically new concept of machine tool control by Williamson, Sheppard and Walker 6 , to end the gestation period and herald the birth of modern linear and rotary grating transducers. The technique relies on a 'magnification' of the spacing of ruled lines on two transparent gratings such that the spacing can be readily perceived by the eye or by optical instrumentation. Many methods exist to produce moir6 fringe patterns. For a simple explanation of the technique, consider two identical gratings with equi-spaced vertical rulings superimposed at a slight angle. Ignoring for the moment the effects of diffraction, it will be seen that the lines of one grating will cross the other at a vertical separation equal to the spacing of the lines on the grating, divided by the sine of the angle between them. The total effect of all the lines crossing at the same pitch height is to produce horizontal bands of light and dark, or transparency and opacity, along the grating representing a magnified horizontal version of the vertical grating (Fig 1). Horizontal movement of one grating relative to the other causes these bands to move in the vertical direction, where one vertical pitch movement is e.quivalent to a horizontal movement of one pitch of the grating. Diffraction effects can be utilized as a means of artificially improving contrast and sharpness by adjustment of the spacing between the gratings ~ . By interposing the gratings between a lamp and a photocell detector, the periodic variations in light intensity caused by movement of one grating relative to the other can be measured and counted. For gratings v~ith one hundred lines per millimeter the technique provides a direct measurement resolution of ten #m. Since the bands are produced by the effects of many lines on the gratings, small imperfections, blemishes, or random pitch errors in the rulings do not affect the accuracy of the measurements: indeed this improvement, by averaging, makes measurement by band-counting more accurate than the grating itself. Pressures induced by a need for greater accuracy and resolution prompted developments in electronic sub-division of the wave form out of the photocell to divide-byfour, by ten and then divide-by-twenty levels, the latter