Shearing interferometry is well suited for short/partially coherent light sources. Moreover, the robustness of the interferometric setup is increased due to the common path arrangement. Various different shearing setups exist such as lateral shearing, longitudinal, rotational and radial shearing. Our setup relies on radial shearing, which furthermore enables the recovery of 3D spatial information. Besides, its decreased demand on the coherence properties of the light source employed and its increased environmental stability, the speckle noise of the reconstructed incoherent hologram is greatly reduced, resulting in an improved imaging performance. Moreover, all advantages known from quantitative phase imaging, such as numerical refocusing, are available to modify the reconstructed incoherent hologram.
Incoherent holography is applicable to both, spatially and temporally incoherent light.
The underlying working principle addressing the spatial incoherence is based on the analogy of the diffraction integral with the van Cittert-Zernike theorem. The van Cittert-Zernike theorem states that the Fourier transform of an incoherent source’s planar intensity is proportional to the spatial coherence function measured in the far field. The temporal incoherence is addressed via the Wiener-Khintchine theorem, which refers to the Fourier transform relation between the spectral density function and real correlation function. The underlying experimental principle is based on the combination of radial-shearing and phase shifting interferometry into a single optical system.
A flowchart how to obtain the incoherent holographic reconstructions is schematically displayed in Fig. 1.
Figure 1 Flowchart diagramm displaying the different image processing steps applied to the recorded phase stepped shearing interferograms
- D. N. Naik, G. Pedrini, W. Osten, ”Recording of incoherent-object hologram as complex spatial coherence function using Sagnac radial shearing interferometer and a Pockels cell,” Opt. Express, 21, 3990-3996 (2013)
- D. N. Naik, G.Pedrini, M.Takeda, W.Osten, “Spectrally resolved incoherent holography: 3D spatial and spectral imaging using a Mach-Zehnder radial-shearing interferometer,” Opt. Lett. 39:1857-1860 (2014)