A 3.8 m segmented telescope is planned to be built at the Okayama Astrophysical Observatory by the joint
program among Kyoto university, Nagoya university, NAOJ, and Nano-Optonics Energy Inc. This is the world’s
first optical-infrared telescope whose primary mirror is composed of “petal-shaped” segment mirrors.
To investigate the best layout of the displacement sensors as well as to study the control algorithm, we have
developed a simulation software for the segmented petaloid mirrors. This simulator calculates the vertical position
differences between the segments at the 60 displacement sensors based on the three-dimensional movements of
the 54 actuators, and enables us to test the control algorithms under various conditions including random noise
on the displacement sensors, random movement errors of the actuators, and unexpected lateral shifts of the
segments. The outputs of the simulator are not only the phase error of the primary mirror but also the PSF
image, taking the structure function of the optical surfaces into account.
Using a singular value decomposition method, we found that the 18 petal-shaped segments are controllable
within the required displacement errors of 15 nm under the following three conditions: 1) the displacement
measurement sensors are placed in staggered fashion between segments, 2) the displacement measurement sensors
are axisymmetrically placed with respect to the optical axis, and 3) the relative lateral shift and rotation of each
segment are less than 500 μm and 0.05 degree, respectively.
In this report, the control algorithm, requirements for the layout of the displacement measurement sensors,
and the simulated performance will be presented.