Phase estimation from digital holograms without unwrapping

Robust phase unwrapping for phase images in Fourier domain Doppler optical coherence tomography

To solve the 2 ? phase ambiguity for phase-resolved Doppler images in Doppler optical coherence tomography, we present a modified network programming technique for the first time to the best of our knowledge. The proposed method assumes that error of the discrete derivatives between unwrapped phase image and wrapped phase image can be arbitrary values instead of integer-multiple of 2 ? , which makes the real-phase restoration accurate and robust against noise. We compared our proposed method with the network programming method. Parameters including root-mean-square-error and noise amplification degree were adopted for comparison. The experimental study on simulated images, phantom, and real-vessel OCT images were performed. The proposed method consistently achieves optimal results.

Phase estimation using phase gradients obtained through Hilbert transform

An algorithm to extract phase in its unwrapped form from an interferogram having perturbed straight line fringes is proposed and studied. Phase gradients are extracted from an interferogram using the Hilbert transform, and the phase is then estimated from their gradients using the method of least squares for the Hudgin geometry. The matrix inversion required in implementing the method of least squares for the Hudgin geometry is carried out analytically by exploiting the additional symmetries available in the Hudgin matrix. The consistency of the proposed algorithm is demonstrated through its implementation, both on numerically generated interferograms, as well as on interferograms measured in a Mach-Zehnder interferometric setup, where the respective imparted phases were random, and corresponded to atmospheric turbulence-like models.

Local orientation coherence based segmentation and boundary-aware diffusion for discontinuous fringe patterns

Fringe patterns with noise and discontinuity are often encountered but difficult to analyze. Discontinuity-detectable and boundary-aware processing techniques are demanded. A local orientation coherence based fringe segmentation (LOCS) method and its cooperation with boundary-aware coherence enhancing diffusion (BCED) for discontinuous fringe pattern denoising are proposed in this paper. The LOCS method has three steps. First, as orientation coherence indicated by structure tensors is informative to describe fringe structures, it is selected for discontinuity recognition. Due to the complexity of the discontinuity problem, the detected boundary often has missing parts and is not very accurate. Boundary completion by cubic splines and boundary refinement based on partial structure tensors are further performed as the second and third steps, respectively. Subsequently, the BCED method is developed to adapt the original CED to fringe segments with irregular boundaries. Simulated and experimental fringe patterns are tested and successful results have been obtained.

Two-dimensional phase unwrapping using the transport of intensity equation

We report a method for two-dimensional phase unwrapping based on the transport of intensity equation (TIE). Given a wrapped phase profile, we generate an auxiliary complex field and propagate it to small distances to simulate two intensity images on closely spaced planes. Using the longitudinal intensity derivative of the auxiliary field as an input, the TIE is solved by employing the regularized Fourier-transform-based approach. The resultant phase profile is automatically in the unwrapped form, as it has been obtained as a solution of a partial differential equation rather than as an argument of a complex-valued function. Our simulations and experimental results suggest that this approach is fast and accurate and provides a simple and practical solution for routine phase unwrapping tasks in interferometry and digital holography.

Phase unwrapping with a virtual Hartmann-Shack wavefront sensor

The use of a spatial light modulator for implementing a digital phase-shifting (PS) point diffraction interferometer (PDI) allows tunability in fringe spacing and in achieving PS without the need for mechanically moving parts. However, a small amount of detector or scatter noise could affect the accuracy of wavefront sensing. Here, a novel method of wavefront reconstruction incorporating a virtual Hartmann-Shack (HS) wavefront sensor is proposed that allows easy tuning of several wavefront sensor parameters. The proposed method was tested and compared with a Fourier unwrapping method implemented on a digital PS PDI. The rewrapping of the Fourier reconstructed wavefronts resulted in phase maps that matched well the original wrapped phase and the performance was found to be more stable and accurate than conventional methods. Through simulation studies, the superiority of the proposed virtual HS phase unwrapping method is shown in comparison with the Fourier unwrapping method in the presence of noise. Further, combining the two methods could improve accuracy when the signal-to-noise ratio is sufficiently high.