Dougmoire

Moire deflectometry

Moire patterns or fringes are the relatively thick lines produced when two patterns of thin lines overlap. The effect is noticeable when looking at overlapping folds in lace curtains: the comparatively fine structure of the curtains seem to have semi-regular thicker lines superimposed (like the grain in some kinds of wood, cut diagonally to the more regular natural "tree rings"). It can also be seen on television images when the regularities of a check fabric chance to coincide with some of the regularities in the pattern of pixels of the screen. The set of fairly thick, sometimes coloured, additional lines can be distracting.


The sketch opposite demonstrates the formation of moire fringes. One grid consists of equally space straight lines sloping upwards to the left. The grid sloping upwards to the right consists of straight lines whose spacing, which is the same at the left as that of the first grid, doubles going from left to right. The pattern is relatively bright around the points of intersection of the two grids. The loci of these points specify the positions of the moire fringes. The limiting slope, where the spacings are equal (on the left), is horizontal. Scanning from left to right the slope increases very quickly. It is the large change in slope from a relatively small change in spacing which makes moire deflectometry so useful in detecting and monitoring small changes in the value of some parameter which maps on to the small changes in one of the grids.

In optical moire, the fringes are produced typically when looking at (or otherwise imaging) one fine grid or grating illuminated from behind through, usually, an identical grid. What is imaged is the composite pattern of the nearer grid and the shadow on it of the grid upstream. The nearer grid is undistorted, but distortions of the light beam (such as its divergence or convergence) lead to distortions of the shadow component and corresponding distortions in the moire fringes from their normally regular appearance (parallel lines if the grids are linear). The distortions of the light beam could be produced by the presence of a simple lens (approximately constant power across its diameter) or – more interestingly – a phase object whose optical power varies with position in it, such as a liquid with density or temperature gradients within it. Refractive index variations map on to these gradients. The refractive index variations then determine the shape of the moire fringes.

Examples of moire fringes below are from moire deflectometry rig in the Third Year Physics Teaching Laboratory (see in the optics subsection).


Image 1: Unenhanced image from two linear grids, illuminated by an undistorted parallel (expanded laser) beam transmitted at right angles to the planes of the grids. Grids separation approximately 9 cm. See introductory paragraph above.

Image 2: Unenhanced image with now a segment of a varifocal spectacle lens upstream of the grids, distorting the beam. To provide the necessary low optical power for basic moire fringe production, a "thin lens" combination of spectacle lens and a negative (diverging) lens was used. Right to left across the image corresponds to "distance viewing" to "reading glasses" specification of the segment of spectacle lens investigated. For the distance viewing part, the moire fringes are nearly parallel to those in image 1 because the optical power of the thin lens combination there is close to zero, producing hardly any distortion of the illuminating beam.

(text still under development)

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Most recent update on Thursday 27 September 2001 RCD