ABSTRACT
Interferometric tomography can reconstruct 3D refractive-index distributions through phase-shift measurements for different beam angles. To reconstruct a complex refractive-index distribution, many projections along different directions are required. For the purpose of increasing the number of the projections, we earlier proposed a beam-angle-controllable interferometer with mechanical stages; however, the quality of reconstructed distribution by conventional algorithms was poor because the background fringes cannot be precisely controlled. To improve the quality, we propose a weighted reconstruction algorithm that can consider projection errors. We demonstrate the validity of the weighted reconstruction through simulations and a reconstruction from experimental data for three candle flames.
ABSTRACT
This paper presents a new method to obtain a wrapped phase distribution from a single interferogram with a spatial carrier modulation. The Fourier transform of the interferogram has three peaks: one is a dc peak around the origin in the Fourier domain, and the other two are carrier peaks that have information of phase modulation by an object placed in the interferometer. Since the wrapped phase can be evaluated by one of the two carrier peaks, the dc peak and the adjoint peak that is the other peak of two carrier peaks should be removed by filters. The proposed filtering process consists of two stages: dc peak filtering and adjoint peak filtering. A spectrum shift filter based on symmetrical characteristics of the spectrum is applied in both stages as a basic filter that can remove most of the undesired spectrum. An additional two filters are applied to remove the remaining spectrum. The new method can automatically isolate the carrier peak, even when the boundary of peaks is not very clear. Numerical evaluations of simulation data and experimental data demonstrate that the proposed method can successfully isolate the carrier peak.
ABSTRACT
Phase unwrapping for a noisy image suffers from many singular points. Singularity-spreading methods are useful for the noisy image to regularize the singularity. However, the methods have a drawback of distorting phase distribution in a regular area that contains no singular points. When the singular points are confined in some local areas, the regular region is not distorted. This paper proposes a new phase unwrapping algorithm that uses a localized compensator obtained by clustering and by solving Poisson's equation for the localized areas. The numerical results demonstrate that the proposed method can improve the accuracy compared with other singularity-spreading methods.
ABSTRACT
Phase unwrapping still plays an important role in many data-processing chains based on phase information. Here, we introduce a new phase unwrapping approach for noisy wrapped phase maps of continuous objects to improve the accuracy and computational time requirements of phase unwrapping using a rotational compensator (RC) method. The proposed algorithm is based on compensating the singularity of discontinuity sources. It uses direct compensation for adjoining singular point (SP) pairs and uses RC for other SP pairs. The performance of the proposed method is tested through both simulated and real wrapped phase data. The proposed algorithm is faster than the original algorithm with the RC and has proved efficiency compared to other phase unwrapping methods.
ABSTRACT
In the process of phase unwrapping for an image obtained by an interferometer or in-line holography, noisy image data may pose difficulties. Traditional phase unwrapping algorithms used to estimate a two-dimensional phase distribution include much estimation error, due to the effect of singular points. This paper introduces an accurate phase-unwrapping algorithm based on three techniques: a rotational compensator, unconstrained singular point positioning, and virtual singular points. The new algorithm can confine the effect of singularities to the local region around each singular point. The phase-unwrapped result demonstrates that accuracy is improved, compared with past methods based on the least-squares approach.