Low-cost capacitive sensing for precision alignment of mirrors

Piezoelectric actuators are often used to align mirrors in high-precision optical systems; however they are highly hysteretic and are therefore not repeatable. Closed-loop control is a reliable way to correct for this, but requires an accurate position sensor for feedback. We present a capacitive sensor that is capable of measuring the tilt of a mirror with a noise density of 10 milliarcsec Hz^-1/2 and repeatability of better than 17 milliarcsec (corresponding to a distance of 4 nm) over a range of more than 6 arcmin. This enables the correction of hysteresis with much better performance at low frequencies than feedforward algorithms or charge controllers. Low cost (a hundredth of the cost of similar systems) and ease of construction and integration with commercially available mirror mounts are its primary advantages. The effect of temperature on the mirror mount was significant, with a change of several arcsec per degree Celsius. However, it was possible to obtain stable performance over periods of several hours in a lab without sophisticated temperature control.