Design and performance of a sub-nanoradian resolution autocollimating optical lever

Precision goniometry using optics has the advantage that it does not impose much stress on the object of investigation and, as such, is adopted extensively in gravitational wave detection, in torsion balances investigating fundamental forces, in specialized studies of biological samples, and it has potential applications in condensed matter physics. In this article we present the considerations that go into designing optical levers and discuss the performance of the instrument we have constructed. We motivate the design by considering an idealized setup and the limitations to the angular resolution induced by statistical fluctuations of the photon count rate and diffraction at the apertures. The effects of digitization of the count rate and of the spatial location of the photons on the image plane motivating the actual design are discussed next. Based on these considerations, we have developed an autocollimating optical lever which has a very high resolution and dynamic range. An array of 110 slits, of 90 microm width and a pitch of 182 microm, is located in the focal plane of a field lens, of focal length 1000 mm, and is illuminated by a CCFL tube. This array is imaged back onto the focal plane after retroreflection from a mirror placed just beyond the lens. The image is recorded on a linear charge-coupled device array at the rate of 1000 images/s and is processed through a special algorithm to obtain the centroid. The instrument has a centroid stability of approximately 3 x 10(-10) rad Hz(-1/2) and a dynamic range of approximately 10(7).