Spatial coherence wavelets and the phase-space representation of holography

Previous researches have shown that spatial coherence wavelets provide the phase-space representation for optical fields in any state of coherence and polarization and can represent the radiometric properties of optical sources. In this paper, we have developed a research about their holographic features and particularly we have found the cross-spectral density at the observation plane should be regarded as the second-order wave reconstructed from the Fourier hologram of the marginal power spectrum, where the power spectrum corresponds to the zeroth-order of the reconstruction and the characteristic hermiticity of the cross-spectral density determines the twin images. In a similar way, the holographic reconstruction of the cross-spectral density at the aperture plane has been stated, taking the marginal power spectrum as its Fourier hologram, the power spectrum at the aperture plane related to its zeroth-order, and its twin images determined by the hermiticity of the cross-spectral density at aperture plane. After realizing that spatial coherence wavelets can be regarded as Wigner distribution functions with similar morphology to the hologram diagrams recently proposed for formulating holography in the phase-space by Lohmann and Testorf, we recognized their power for providing a precise and wide physical interpretation of optical signals in phase space which enables us to apply these holographic features in many fields like optical coherence modulation and beam shaping.