Fourier transform profilometry using single-pixel detection based on two-dimensional discrete cosine transform

Abstract

We present a single-pixel Fourier transform profilometry (FTP) for obtaining three-dimensional (3D) maps with few measurements. Two digital micromirror devices were employed to generate a two-dimensional (2D) sinusoidal illumination pattern and a series of specified sampling patterns, respectively, coupled with a single-pixel detector to sequentially collect spatially light field from an object surface. The reflectance image at the object surface was recovered with single-pixel imaging (SPI) scheme, 3D map of the object surface was reconstructed with FTP from the recovered reflectance image. We incorporated the 2D discrete cosine transform into the SPI scheme to reduce the number of sampling patterns, where only a few sampling patterns whose spatial frequencies around the illumination frequency were required for the measurement. We experimentally reconstructed acceptable 3D maps, the ratios of the number of measurements to the number of pixels of 3D maps were determined to be 1.04% and 1.79% for the 3D reconstructions of simple and complex objects, respectively. This significantly reduces the number of measurements that is necessary for the current 3D reconstruction based on SPI scheme.