The surface normal vector relates geometry to image irradiance because it determines the angles i and e appearing in the surface reflectance function . In an orthographic projection, the viewing direction and hence the phase angle is constant for all the surface elements. Thus for a fixed light source and geometry, the ratio of scene radiance to scene irradiance depends on the surface normal vector (i.e. on gradient co-ordinates p and q). If we suppose each surface element receives the same irradiance, then the scene radiance, and hence image intensity, depends only on the surface normal defined by p and q.

The reflectance map determines the proprtion of light reflected as a function of p and q. The viewed image intensity is directly proportional to the surface radiance. setting the proportional constant to one, by appropriate choice of optics, the image intensity and reflectance map are equivalent.

Expressions for , and can be derived using normalised dot products of the surface normal vector, , the vector , which points in the direction of the light source, and the vector = (0,0,-1) which points in the direction of the viewer. Recall, for two vectors, where is the angle between the vectors. Hence,

Equations 5, 6 and 7 are used to transform a surface reflectance function into a reflectance map . In the simplest case of a Lambertian surface