Optical Mo<spacing diaeresis>bius transformation module for expanding beam-steering dimensions

Beam-steering dimension expansion can map a one-dimensional (1D) array with N2 points to a 2D array with N x N points. The scanning mode of existing expansion systems is limited to raster scan, therefore a new beamsteering dimension expansion module with advanced scanning mode is high desirable for easy integration with light detection and ranging (LiDAR) system. We propose an optical Mo<spacing diaeresis>bius transformation (OMT) module that can enable any single 1D scanning to 2D scanning. We experimentally demonstrate the transformation of a 1D static strip into 2D linear and radial fields utilizing specified OMT phase plates. We further realize the dynamic process of converting 1D steering spots into 2D steering array. The OMT module can achieve 2D beamsteering over a 15 degrees field of view with an angular resolution of 0.5 degrees combined with a Fourier transform lens. A LiDAR system that is capable of 3D imaging (with a resolution of 30 x 30 pixels) have been implemented by combing our OMT module with a simple Time-of-Flight (TOF) sensor. This scheme provides a simple and costeffective solution to generate 2D static and dynamic structured light fields from a 1D strip or scanning spots, which can facilitate applications such as LiDAR, laser processing, 2D display and illumination.