Analysis of moire fringes by a solenoidal coil grating

We analyze the moire fringes by a solenoidal coil grating of which the properties depend upon the condition of light illumination. The moire fringes are observed on the surface of a stretched spring or on its projection screen when the spring is illuminated by a light bulb. We derive the indicial equations of the fringe shape, the fringe slope and the spacing between the neighboring fringes for both a line-type source and a point-like source. We show that the fringe spacing is enlarged by the ratio of the source-screen distance to the diameter of the grating. We also show that the sign of the fringe slope changes according to the helicity of the wound wires in the grating. The photographs of the moire patterns formed on the surface of a stretched spring are presented to confirm our theoretical analysis. The fringe slope can be used as a simple measure of the helicity of a solenoidal coil grating, and the fringe spacing large compared with the pitch between the wound wires can be used to precisely monitor the change of length in a spring balance. (C) 2001 Elsevier Science B.V. All rights reserved.