We use calculation and simulation to characterize an all-reflective monolit
hic gyroscopic structure that supports 3 sets of orthogonal, spatially dens
e and continuous helical optical paths. This gyroscope differs from current
fiber optic and ring laser gyroscopes primarily in the free space multi-tu
rn nature of the optical path. The design also creates opportunities for in
troducing gain while minimizing spontaneous emission noise from those gain
regions. The achievable angular measurement precision for each axis, given
ideal components and no gain, is calculated to be similar to 0.001 degrees/
hr for a structure of similar to 6.5 cm diameter, similar to 1 watt average
optical power, and a wavelength of 0.5 mu m. For fixed power, the uncertai
nty scales as the reciprocal cube of the diameter of the structure. While t
he fabrication and implementation requirements are challenging, the needed
reflectivities and optical surface quality have been demonstrated in more c
onventional optics. In particular, the low mass, compact character, and all
reflective optics offer advantages for applications in space. (C) 2000 Opt
ical Society of America.