  We propose a method of complex-amplitude Fourier single-pixel imaging (CFSI)
with coherent structured illumination to acquire both the amplitude and phase
of an object. In the proposed method, an object is illustrated by a series of
coherent structured light fields which are generated by a phase-only spatial
light modulator, the complex Fourier spectrum of the object can be acquired
sequentially by a single-pixel photodetector. Then the desired
complex-amplitude image can be retrieved directly by applying an inverse
Fourier transform. We experimentally implemented this CFSI with several
different types of objects. The experimental results show that the proposed
method provides a promising complex-amplitude imaging approach with high
quality and a stable configuration. Thus, it might find broad applications in
optical metrology and biomedical science.
