  Ophthalmic microsurgery is known to be a challenging operation, which
requires very precise and dexterous manipulation. Image guided robot-assisted
surgery (RAS) is a promising solution that brings significant improvements in
outcomes and reduces the physical limitations of human surgeons. However, this
technology must be further developed before it can be routinely used in
clinics. One of the problems is the lack of proper calibration between the
robotic manipulator and appropriate imaging device. In this work, we developed
a flexible framework for hand-eye calibration of an ophthalmic robot with a
microscope-integrated Optical Coherence Tomography (MIOCT) without any markers.
The proposed method consists of three main steps: a) we estimate the OCT
calibration parameters; b) with micro-scale displacements controlled by the
robot, we detect and segment the needle tip in 3D-OCT volume; c) we find the
transformation between the coordinate system of the OCT camera and the
coordinate system of the robot. We verified the capability of our framework in
ex-vivo pig eye experiments and compared the results with a reference method
(marker-based). In all experiments, our method showed a small difference from
the marker based method, with a mean calibration error of 9.2 $\mu$m and 7.0
$\mu$m, respectively. Additionally, the noise test shows the robustness of the
proposed method.
