Reflected wave-front sensing computation and experimental digital control of a cavity

We present a detailed numerical computation of the demodulated misalignment signal in the reflected wave-front sensing from a two-mirror plane-concave cavity. The results of the computation is experimentally checked on caviti es of a few cm length, high finesse and in the two possible mirror disposit ions (plane-concave and concave-plane). The longitudinal and transverse loc king of a 2 cm, high finesse (congruent to 2000) and small waist w(0) (80 m u m) plane-concave cavity is performed by entirely digital signal acquisiti on, processing and feedback generation. The RMS residual noise on the relat ive translation between beam direction and cavity axis is less than 10(-11) m (10(-7) x w(0)), and noise sources are briefly outlined.