Minimum uncertainty slant angle for trihedral pyramid targets

Abstract

Trihedral pyramid targets are used for scanning laser radar measurement surveys and range testing, and may be appropriate for testing optical line scanners. The intersection of the three faces at the pyramid apex provides an easily calculable coordinate. This paper examines the measurement uncertainty for the apex of trihedral pyramid targets as a function of slant angles, the goal being to ascertain a slant angle for the pyramid faces with minimum apex uncertainty. The technique calculates the trihedral apex with respect to the face angles, then examines the derivatives (i.e. sensitivities) of the apex with respect to slant angle. From the calculation, the slant angle with minimum apex uncertainty is about 41°. Noise in the reflected signal increases rapidly as the incidence angle goes beyond 50° resulting in a usable conic field-of-view (FOV) of about 9°, which may be insufficient for most metrology applications except range testing. Compromise between reduced slant angle, which increases apex uncertainty, and increased trihedral FOV is necessary.