Effects of a Local Atmospheric Temperature Gradient on Optical Measurement for the Active Control of a Segmented-Ring Telescope

A proposed segmented-ring telescope is a unique solution for giant telescopes. Because a ring configuration can cover baselines smaller than its outer diameter in all directions, such a telescope can have a complete interferomometry imaging capability, and it is named as a Ring Interferomety Telescope. Due to the absence of reflection in the circular region enclosed by the inner rim of the ring, additional tip-tilt sensing is needed for the closed-loop active control of the telescope. For realizing diffraction-limited imaging in the visible wavelength range, tip-tilt sensing of extremely high accuracies is needed for the active control of the system. We hereby propose an optical-metrology method using classical Shack-Hartmann wavefront sensors and reference light sources inside the telescope for accurate tip-tilt sensing. Theoretically the proposed method has a very high accuracy, but it is very sensitive to environmental disturbance. The refractive-index gradient caused by a local atmospheric temperature gradient is among the most important error sources of the method. It contributes to the systematic measurement error by causing low-order aberrations on the primary-mirror surface. Starting from the equation of optical path in non-uniform media, we derived the theoretical dependence of the systematic measurement error on the temperature gradient and the attitude of the telescope. We have found that theoretically the error is anisotropic if the temperature gradient is in the vertical direction. Using the theoretical analysis we propose a method of compensating or reducing the error by controlling the environmental temperature. Our results show that for an 30m Ring Interferometry Telescope to achieve diffraction-limited imaging by using the error compensating/reducing method, the temperature gradient must be controlled within 0.003K/m and the precision of temperature measurement needed for the control must be better than 0.1K.