Non-iterative complex wave-field reconstruction based on Kramers-Kronig relations

Abstract: A new computational imaging method to reconstruct the complex wave-field is reported. Due to the existence of zero frequency component, the measured signal by amplitude modulation of pupil has a spectrum similar to the one of off-axis hologram. The mathematical analogy between them is established in this paper. Based on this observation and analyticity of band-limited signal under any diffraction-limited system, an algorithm from Kramers-Kronig (KK) relations is utilized to recover the phase information only from the intensity patterns. From the sensing side, only two measurements are required at least. From the reconstruction algorithm side, our method is iteration-free and parameter-free, also without any assumption on sample characteristics. It owns several advantages over existing phase imaging methods and could provide a unique perspective to understand current computational imaging methods.