Wavefront restoration from lateral shearing data using spectral interpolation.

Although a lateral-shear interferometer is robust against optical component vibrations, its interferogram provides information about differential wavefronts rather than the wavefronts themselves, resulting in the loss of specific frequency components. Previous studies have addressed this limitation by measuring four interferograms with different shear amounts to accurately restore the two-dimensional wavefront. This study proposes a technique that employs spectral interpolation to reduce the number of required interferograms. The proposed approach introduces an origin-shift technique for accurate spectral interpolation, which in turn is implemented by combining two methods: natural extension and least-squares determination of ambiguities in uniform biases. Numerical simulations confirmed that the proposed method accurately restored a two-dimensional wavefront from just two interferograms, thereby indicating its potential to address the limitations of the lateral-shear interferometer.

Weighted reconstruction of three-dimensional refractive index in interferometric tomography.

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.

Carrier peak isolation from single interferogram using spectrum shift technique.

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.

Reliable phase unwrapping algorithm based on rotational and direct compensators.

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.

Phase unwrapping for noisy phase maps using rotational compensator with virtual singular points.

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.