Phase-shift extraction for phase-shifting interferometry by histogram of phase difference

Sub-nanometer height sensitivity by phase shifting interference microscopy under environmental fluctuations

Phase shifting interferometric (PSI) techniques are among the most sensitive phase measurement methods. Owing to its high sensitivity, any minute phase change caused due to environmental instability results into, inaccurate phase measurement. Consequently, a well calibrated piezo electric transducer (PZT) and highly-stable environment is mandatory for measuring accurate phase map using PSI implementation. Here, we present an inverse approach, which can retrieve phase maps of the samples with negligible errors under environmental fluctuations. The method is implemented by recording a video of continuous temporally phase shifted interferograms and phase shifts were calculated between all the data frames using Fourier transform algorithm with a high accuracy ≤ 5.5 × 10^-4 π rad. To demonstrate the robustness of the proposed method, a manual translation of the stage was employed to introduce continuous temporal phase shift between data frames. The developed algorithm is first verified by performing quantitative phase imaging of optical waveguide and red blood cells using uncalibrated PZT under the influence of vibrations/air turbulence and compared with the well calibrated PZT results. Furthermore, we demonstrated the potential of the proposed approach by acquiring the quantitative phase imaging of an optical waveguide with a rib height of only 2 nm and liver sinusoidal endothelial cells (LSECs). By using 12-bit CMOS camera the height of shallow rib waveguide is measured with a height sensitivity of 4 Å without using PZT and in presence of environmental fluctuations.vn.

Universal phase reconstruction approach of self-calibrating phase-shifting interferometry

Self-calibrating phase-shifting interferometry (PSI) reconstructs the phase map from three-frame or more phase-shifting interferograms without the need for knowing accurate phase steps. The existing phase reconstruction methods for self-calibrating PSI still have many constraints in terms of the required number of interferograms, special usage preconditions, etc. In this Letter, a universal, accurate, and efficient phase reconstruction method for self-calibrating PSI is proposed. In this approach, we search the solution space of phase shifts to obtain the modulation amplitude of interferograms with the minimum coefficient of variation (CV). Then the phase is reconstructed through the searched phase shifts. Numerical and experimental studies demonstrate that this method can realize highly accurate phase reconstruction consistently, compared to the currently popular methods in their own usable ranges. We anticipate that this Letter may provide a universal and powerful solution for the phase reconstruction of self-calibrating PSI.

Phase retrieval in two-shot phase-shifting interferometry based on phase shift estimation in a local mask

Fringe analysis in two-shot phase-shifting interferometry is important but meets challenges due to a limited number of images, corrupting noise, and background modulation. Here we propose an effective algorithm for phase retrieval from two interferograms with unknown phase shifts. The algorithm first evaluates the phase shift in a local mask through phase fitting and global optimization and then computes a full-field phase map using an arctangent function. Since the phase shift evaluation is performed within a local mask, the algorithm is fast compared with conventional optimization-based algorithms and typically needs tens of seconds to complete the processing. Computer simulation and experimental results show that the proposed algorithm has excellent performance compared with state-of-the-art algorithms. A complete software package of the algorithm in MATLAB is available at http://two-shot.sourceforge.io/.

Phase shifting interferometry from two normalized interferograms with random tilt phase-shift

We propose a novel phase shifting interferometry from two normalized interferograms with random tilt phase-shift. The determination of tilt phase-shift is performed by extracting the tilted phase-shift plane from the phase difference of two normalized interferograms, and with the calculated tilt phase-shift value the phase distribution can be retrieved from the two normalized frames. By analyzing the distribution of phase difference and utilizing special points fitting method, the tilted phase-shift plane is extracted in three different cases, which relate to different magnitudes of tilts. Proposed method has been applied to simulations and experiments successfully and the satisfactory results manifest that proposed method is of high accuracy and high speed compared with the three step iterative method. Additionally, both open and closed fringe can be analyzed with proposed method. What's more, it cannot only eliminate the small tilt-shift error caused by slight vibration in phase-shifting interferometry, but also detect the large tilt phase-shift in phase-tilting interferometry. Thus, it will relaxes the requirements on the accuracy of phase shifter, and the costly phase shifter may even be useless by applying proposed method in high amplitude vibrated circumstance to achieve high-precision analysis.

High-resolution electronic interferometry for the measurement of in-plane vibration

This study proposes an algorithm based on the standard deviation in the temporal domain to remove influences from background noise and ambient disturbance and enhance the quality of images obtained using interferometric technology. From measurements of the first ten in-plane resonant frequencies and mode shapes of vibrating zirconate titanate (PZT) laminates, we investigated the resonant characteristics in both the U and V directions. The resulting interference fringes were used to quantify the vibration amplitude of PZT plates on a submicron scale. The resonant frequencies obtained using the proposed method are in excellent agreement with those obtained using the finite element method and an impedance analyzer.

Phase extraction from randomly phase-shifted interferograms by combining principal component analysis and least squares method

A method combining the principal component analysis (PCA) and the least squares method (LSM) is proposed to extract the phase from interferograms with random phase shifts. The method estimates the initial phase by PCA, and then determines the correct global phase sign and reduces the residual phase error by LSM. Some factors that may influence the performance of the proposed method are analyzed and discussed, such as the number of frames used, the number of fringes in interferogram and the amplitude of random phase shifts. Numerical simulations and optical experiments are implemented to verify the effectiveness of this method. The proposed method is suitable for randomly phase-shifted interferograms.

Principal component analysis of multiple-beam Fizeau interferograms with random phase shifts

A non-iterative method based on principal component analysis (PCA) is presented to directly extract the phase from multiple-beam Fizeau interferograms with random phase shifts. The PCA method is the approach that decomposes the multiple-beam Fizeau interferograms into many uncorrelated quadrature signals and then applies principal component analysis algorithm to extract the measured phase without any prior guess about the phase shifts. Some factors that affect the performance of the proposed method are analyzed and discussed. Numerical simulations and experiments demonstrate that the proposed method extracts phase fast and exhibits high precision. The method can be applied in high precision interferometry.