Moire interferometry techniques have long been used to obtain contour measurements of surfaces of interest. A typical projection type moire fringe measurement system 10 is schematically depicted in FIG. 1. The system 10 includes light source 14, a plane 15 in which a first optical grating 16 and a second optical grating 17 are located, a first lens 18, located in plane 19, surface 20, second lens 24 located in plane 19, camera 26, electronic circuitry and computer 28, and motion device 34.
Optical grating 16 is made up of parallel dark lines on a transparent medium such as glass. Light source 14, grating 16, and lens 18 are arranged so as to project the image of grating 16 onto the surface 20. The image projected onto surface 20 is viewed using lens 24, optical grating 17, and some sort of camera with lens or viewing device, designated as item 26 in FIG. 1. Item 28 is the electronics or computer equipment used to analyze the image collected by item 26.
In order to simplify many things, the optical system 10 of projection type moire fringe systems is arranged so that the two lenses (items 18 and 24) lie in the same plane 19 and have their optical axes parallel to each other. Also, the two optical gratings 16 and 17 are both located in another plane 15 behind the lenses 18 and 24 and the lines on gratings 16 and 17 are oriented parallel to each other. The plane 15 containing the gratings is parallel to the plane 19 containing the lenses. The plane 19 containing the lenses is called the optical plane of the system. In most applications, the optical plane 19 is positioned approximately parallel to the surface to be viewed which is identified as item 20 in FIG. 1.
The image as viewed at the camera 26 looks like a number of bands of dark and light. These bands of light and dark are called moire fringes and are the result of an interference pattern between two grating patterns, grating 17 and the image of grating 16 projected onto surface 20 by lens 18, re-imaged through grating 17 by lens 24. One fringe consists of an adjacent light and dark area. In appearance, the fringes look like the lines on a topographic map. The spacing between the fringes conveys information about the slope of surface 20 in relation to the optical plane of the measurement system. Fringes close together represent a steep slope on surface 20; fringes farther apart represent areas nearly parallel to the optical plane of the system. The difference in distance between two areas of surface 20 and the optical plane can be measured by counting the total number of fringes between those areas. For a given fineness of optical gratings (designated 16 and 17 in FIG. 1), a given magnification of the lenses 18 and 24 and distance D between the optical axes of the projection and viewing devices, the number of fringes per unit of distance perpendicular to the optical plane 19 is inversely related to the distance from the optical plane 19.
The change in distance perpendicular to the optical axis which results in a one-fringe change is called the contour interval. As mentioned previously, the contour interval in the system depicted in FIG. 1 gets larger as the distance H from the optical plane increases (i.e., the number of fringes per unit of distance decreases). This is illustrated in FIG. 1 by the distances C1 and C2. Contour interval C1 is smaller than contour interval C2 because C1 lies closer to the optical plane 19 than does C2. Assuming identical gratings 16 and 17 and identical lenses 18 and 24 in the geometry of FIG. 1, the contour interval is equal to the pitch of the projected image of grating 16 times H divided by D. Thus, a "hill" rising from surface 20 a vertical distance C1 would span one contour interval (one complete fringe change). Similarly, a "valley" of depth C2 relative to surface 20 would also span a one-fringe change, even though vertical distances C1 and C2 are not the same.
A finer measurement of distance H is possible with the use of sinusoidal gratings for 16 and 17 in FIG. 1. In a sinusoidal grating, the variation in optical density between the dark lines and the interposing clear areas is not a sharp edge, but describes a sinusoidal function. Alternately, square wave gratings, similar to that depicted in FIG. 8 can be used if the resolution or focus of the lenses 18 and 24 is such that the image of the grating can be blurred. The blurring creates an approximation to a sinusoidal variation in optical density between the dark and clear areas of the grating.
With appropriate gratings and optics, the moire fringe patterns viewed by camera 26 will also be sinusoidal in light intensity variation between dark and light areas. The sinusoidal variation in light intensity allows phase information to be extracted from within a single fringe. This phase information relates directly to relative distance changes within a fringe and allows distance measurement on a fractional fringe basis to improve measurement resolution.
However, regardless of the above-described resolution improvements, the periodic nature of moire fringes allows only relative measurements of distance H in FIG. 1 to be taken. While counting the fringes and doing phase measurement within fringes allows the changes in distance H across surface 20 to be determined, there is no way to tell with certainty whether the distance is increasing or decreasing as fringes are counted. Thus, study of the moire fringe image of a "hill" is ambiguous; using the topographic map analogy, one is unable to discern a "hill" from a "valley." The measurement system 10 depicted in FIG. 1 is incapable of absolute measurements of distance H because the fringes convey only relative distance information. In a mathematical sense, the fringes convey only the absolute value of the first derivative of the distance H as shown in FIG. 1. Also, variation in the reflectivity of surface 20 in FIG. 1 will distort the periodic nature of the moire fringes, causing measurement error.
To overcome the problem of sensitivity to reflectivity variation and improve measurement resolution, phase shifting techniques have been used. The typical moire system 10 establishes a fringe pattern in which the light intensity varies periodically with range, or, in other words, with changes in vertical distances. The full cycle or period of light variation with range is called the contour interval. The range information within the contour interval can be extracted using a phase shifting technique as described in "Adaption of a Parallel Architecture Computer to Phase Shifted Moire Interferometry" by A. J. Boehnlein, K. G. Harding, ref. SPIE vol. 728, Optics, Illumination and Image Sensing for Machine Vision, 1986, hereby incorporated by reference. This technique causes the phase to shift uniformly over the entire viewing volume and, using multiple images, intensity change during this phase shift is used to calculate the phase at each point in the moire image. The phase shift is created by moving either grating 16 or grating 17 with motion device 34. For the phase shifting technique, the measurement range is limited to the contour interval because phase cannot be calculated beyond a range of 2.pi. radians. This is referred to as the 2.pi. interval ambiguity. Thus, there is a need to provide an optical measuring system that eliminates or minimizes the above mentioned problems, including ambiguity limitation and which allows accurate absolute measurements of H to be taken.