In practice, this coefficient varies somewhat randomly with the cleanness of the surface, and it may not be relevant to determine it accurately. If four or more images are obtained using further illumination sources, more information can be obtained-for example, the coefficient of specular reflectance, R 1. This itself ensures that ambiguities are resolved over most of the surface. Another possibility is to assume that the surface is reasonably smooth, so that p and q vary continuously over it. This method is prone to difficulty, however, since it means that parts of the surface could be in shadow, thereby preventing the gradient for these parts of the surface from being measured. If a third source of illumination cannot be used, it is sometimes possible to arrange that the inclination of each of the sources is so high that (p 2 + q 2) 1/2 on the surface is always lower than ( p s 2 + q s 2) 1/2 for each of the sources, so that only one interpretation of the data is possible. To resolve this ambiguity, a third source of illumination can be employed (this must not be in the plane containing the first two and the surface point being examined), and the third image gives another curve in gradient space that should pass through the appropriate crossing point of the first two curves ( Fig.

In general, two such conic curves meet in two points, so there is now only a single ambiguity in the gradient of the surface at any given point in the image. This would also be true for a second such image, the curve being a new one if the illuminating source is different.

It has already been seen that, for known absolute reflectance R 0, a constant brightness in one image permits the surface orientation to be limited to a curve of conic cross section in gradient space. The basic idea of photometric stereo is that of cutting down the number of possible positions in gradient space for a given point on the surface of an object.

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