Filters and signal bandwidth for 3-D shape measurement using structured light

There are several ways in which light may be projected onto a surface so that the shape of the surface can be determined. There appears to be a basic problem with many methods which have been developed because of a lack of reference to the underlying properties of the signals produced. We examine the properties of light which is structured in the form of stripes, also referred to as fringes, and is projected onto a surface to be contoured. Due to interaction between the surface and the structure of the incident light, an observer will see curves in the light structure, these curves clearly displaying the shape of the surface to be imagined even though it is viewed in only two dimensions. A typical observed fringe pattern, is shown. It is also shown that the light structure is phase modulated, and the properties of the resulting signal are investigated. For theoretical compactness the signal is considered to be one dimensional, equivalent to taking a vertical section through the image. This approach is perfectly valid if the image is processed as columns one pixel wide, and the general conclusions may be extended into two dimensions for more complex arrangements of images and processing.