Space-domain Kramers-Kronig relations and their applications to holographic imaging

Abstract

Holography is a powerful imaging modality that records waves without loss of information and has benefitedimaging science in visible, x-ray, and electron-wave regimes. Holographic images depict the propagation of wavesand visualize invisible light-matter interactions by quantifying the phase delays. In holography, the information ofa wave is recorded into a hologram based on various forms of wave interference. However, such recordingprocesses result in the ambiguity in information, which necessitates extra measures to retrieve correct holographicimages. Although several techniques, such as modulations of waves, approximations, and assumptions, wereintroduced, they lead to technical challenges that restrict the applicability of holographic imaging.Here, we demonstrate the space-domain Kramers-Kronig relations (KK) for holographic imaging. Unlikeexisting techniques that rely on different principles depending on the imaging system and measured signal, thespace-domain KK relations are proposed as a single governing principle to address the issues of holographicimaging. The dissertation is composed of two parts. In the first part, we develop the theory for the space-domainKK relations. We first review the conventional KK relations and required conditions. Then we discuss theirextension to different domains and formulate the space-domain KK relations for holographic imaging, where thephase image is obtained directly from the intensity measurement. In the second part, we demonstrate theapplications of the space-domain KK relations in interferometric and non-interferometric holographic imaging. Weprocess interferograms using the KK relations to maximize the information capacity of off-axis holography. Wealso achieve direct holography and diffraction tomography from intensity images without the help of interferometry.The proposed method does not require iterative processes nor strict constraints and opens up new opportunities forholographic imaging in various spectral regimes.