Recording of incoherent vector holograms using elements of the spatial cross-spectral density matrix

We present an approach to record incoherent vector holograms using a highly stable field-based interferometer employing radial shearing. The vector holograms are recorded as the elements of the 2 x 2 cross-spectral den-sity (CSD) matrix and reconstruction of the object encoded into these holograms is demonstrated by digitally propagating the elements of the CSD matrix. The CSD matrix contains its elements in the form of a complex spatial coherence function and is connected with an incoherent vector source by the vectorial van Cittert-Zernike theorem. The experimental measurement of the two-dimensional distributions of the complex elements of the CSD matrix is realized by a Sagnac radial shearing interferometer with a phase-shifting approach. The five-step phase-shifting technique is used to measure the fringe visibility and corresponding phase which give the complex elements of the CSD matrix. Recording of incoherent vector holograms is demonstrated from the experimentally recovered elements of the CSD matrix and results are presented for two different incoherent sources, namely polarized and unpolarized. The complex nature of the CSD matrix elements helps in the digital reconstruction and focusing of the incoherent source.

Automated summary

We introduce a method of recording incoherent vector holograms using a stable field-based interferometer and radial shearing technique. The vector holograms are recorded as elements of the 2x2 cross-spectral density (CSD) matrix, and the object encoded into these holograms is digitally reconstructed by propagating the elements of the CSD matrix. The CSD matrix, containing complex spatial coherence function elements, is connected to an incoherent vector source through the vectorial van Cittert-Zernike theorem. We experimentally measure the two-dimensional distributions of the complex elements of the CSD matrix using a Sagnac radial shearing interferometer with a phase-shifting approach.