Single-shot phase-shifting radial-shearing digital holography with Fibonacci-sieve array irrespective of initial phases

We present a kind of single-shot common-path phase-shifting digital holography realized by both a holographic grating and a Fibonacci-sieve array. A test object wave is first split into multiple image copies by the holographic grating placed at the Fourier plane in a Kepler telescope. Then, the image copies are directed onto their own sieves, which can generate a pair of axial foci with customized phase shifts. This way, three phase-shifting sub-holograms are captured by a single exposure and extracted to reconstruct the original complex amplitude of the test object. The proposed method is free of pre-calibration and mechanical movement during the measuring process, so the imaging speed and robustness are significantly improved. The common path is less sensitive to external interference than an in-line system. A measurement of a USAF1951 test target is presented, and the results show the high resolution and stability over 24 h at least, which gives it potential in application to high-resolution dynamic measurements, such as biological microscopy.