Single-pixel phase imaging by Fourier spectrum sampling

We present a single-pixel imaging technique that enables phase extraction from objects by complex Fourier spectrum sampling. The technique exploits a digital micromirror device to scan a wavevector-varying plane wave, which interferes with a stationary reference beam to produce time-varying spatial frequencies on the object. Synchronized intensity measurements are made using a single-pixel detector, and four-step phase-shifting is adopted in spectrum acquisition. Applying inverse Fourier transform to the obtained spectrum yields the desired image. The proposed technique is demonstrated by imaging two digital phase objects. Furthermore, we show that the image can be reconstructed from sub-Nyquist measurements via compressive sensing, considerably accelerating the acquisition process. As a particular application, we use the technique to characterize the orbital angular momentum of vortex beams, which could benefit multiplexing techniques in classical and quantum communications. This technique is readily integrated into commercial microscopes for quantitative phase microscopy.