UNIFORM FRONTAL ILLUMINATION OF PLANAR SURFACES - WHERE TO PLACE THE LAMPS

A method is presented for placing line, point, and ring light sources to produce uniform illumination of planar surfaces. Optimization consi sts in setting to zero as many terms as possible in a two-dimensional Taylor series expansion of the surface illumination. We analyze severa l practical lighting arrangements and discuss the significance of symm etry in lighting design. Four conditions are sufficient to produce opt imal illumination: (1) place all lamps in a single plane parallel to t he illuminated surface; (2) arrange linear sources in parallel pairs; (3) arrange point-source lamps to achieve fourfold symmetry with respe ct to any two orthogonal axes lying in the surface, this requires a mi nimum of four lamps; and (4) select lamp heights so that a line connec ting each lamp to the center of the illuminated surface forms specific angles with the surface normal: 30 deg for line sources and approxima tely 39 deg for point and ring sources. Any lamp arrangement meeting t hese conditions produces an illumination function in which at least th ree orders of terms of the Taylor series expansion are zero. We also d iscuss circumstances under which some of these conditions can be relax ed.