Two-step Phase-shifting Method Research Articles

Leveraging the depolarization of scattered light for holography with the Stokes correlation

A correlation holography technique for quantitative phase imaging from scattered depolarized light is proposed and experimentally demonstrated. To implement this technique, we exploit the depolarization of scattered light with the higher-order Stokes correlation. The higher-order Stokes correlation along with the two-step phase-shifting method is utilized to retrieve the complex Fourier coefficient, this subsequently supports the recovery of the phase in the correlation holography with the fourth-order correlation. A detailed theoretical framework is developed and is also supported by numerical simulation and experimental tests. The applicability of the proposed technique is experimentally demonstrated by quantitatively reconstructing different phase objects from the scattered depolarized light.

Spatially divided two-step phase-shifting method for computational optical scanning holography

Computational optical scanning holography (COSH) is one of the single-pixel incoherent digital holographic techniques; therefore, three-dimensional fluorescent objects can be measured as a digital hologram with a single-pixel detector. However, due to the requirement of a phase-shifting method to remove unnecessary components from holograms, the number of measurements of COSH is larger than the number of pixels. To reduce the number of measurements, the spatially divided phase-shifting method has been proposed. Similar to the parallel four-step phase-shifting digital holography, the spatially divided phase-shifting method can obtain four phase-shifted holograms simultaneously. However, the spatially divided phase-shifting method has a problem in that the spatial resolution is lower than the original COSH. In this paper, a spatially divided two-step phase-shifting method is proposed to improve spatial resolution. The numerical evaluation results indicate the feasibility of the proposed method. In addition, the proposed method is applied to microscopy for proof of principle experiment. The experimental results indicate the proposed method improves the image quality compared with the conventional spatially divided four-step phase shifting method.

Fast two-step phase-shifting method for measuring the three-dimensional contour of objects

A two-step phase-shifting method is proposed. The method realized the rapid measurement of the three-dimensional (3D) contour of some objects using mean envelope denoising based on the striped structured light. First, Butterworth low-pass pre-filtering in the frequency domain was performed on the two deformed fringe images containing the height information of the objects. It reduced the influence of higher harmonics. Then the peak and valley values of fringes with sub-pixel accuracy were obtained through numerical interpolation and point-by-point comparison. Furthermore, the mean envelope was accurately obtained and removed. After removing the mean envelope, the rectangular low-pass filtering was used to thoroughly filter out the remaining background signal. Finally, the fast reconstructions of the 3D contour of the objects were realized. The 3D contour reconstructions of the objects were simulated and experimentally measured using the method proposed. The calculation speed and accuracy were compared with the traditional four-step phase-shifting method and other two-step phase-shifting methods. The method has the advantages of fast calculation speed and high calculation accuracy. It is a valuable method for quickly measuring the 3D contour of some objects.

Generalized 2-step phase-shifting algorithm for fringe projection

Fringe projection profilometry using the phase-shifting technique enables high-precision, high-speed and flexible measurements. Among them, the two-step phase-shifting method has become an important approach to coordinate the accuracy and measurement speed; methods especially based on the amount of phase-shift of π/2, π or 3π/2 can improve time efficiency by reducing steps in unique way. In this paper, a phase iterative technique is proposed and established for two-step phase-shifting with arbitrary phase shift. The general mathematical scheme and parameters linear and nonlinear optimization of the proposed method are described in detail. The simulational and experimental results show that the proposed technique is an effective and precise phase detection method for two-step phase-shifting profilometry.

任意步长两步相移法的鲁棒高精度相位解算方法

任意步长两步相移法的鲁棒高精度相位解算方法

Two-step method for fast phase-shifting digital holography using ferroelectric liquid crystal retarder

The phase-shifting method is widely used in digital holography (DH) to extract object light from interference fringes. We propose a fast phase-shifting DH that uses a ferroelectric liquid crystal (FLC) as a phase retarder. The FLC with its spontaneous polarization has a response speed of $< {1}\,{\textrm{ms}}$<1ms and can perform phase modulation faster than conventionally used nematic liquid crystals (NLCs). However, because the FLC cannot perform continuous phase modulation, the conventional phase-shifting method cannot be used. We propose a novel two-step phase-shifting method for DH using the FLC retarder and evaluate this method’s accuracy and effectiveness experimentally. The experimental results show that the proposed method can measure wavefronts at high speed with high accuracy, and it is also effective for measurement of biological samples.

Spatially incoherent Fourier digital holography by four-step phase-shifting rotational shearing interferometer and its image quality

Spatially incoherent Fourier digital holography using a rotational shearing interferometer for four-step phase-shifting method is proposed. The previous incoherent Fourier holography using a rotational shearing interferometer [Watanabe and Nomura (Appl. Opt. 54:A18, 2015)] employs the two-step phase-shifting method in the vertical and horizontal polarizations. The reconstructed image contains a large bias term. This paper proposes introduction of two kinds of wave plates in one path of a rotational shearing interferometer for a four-step phase-shifting method. A Fourier hologram is obtained from the four recorded holograms for eliminating the bias term and the twin image. The numerical simulation and the optical experiment demonstrate improvement of the image quality of reconstructed image by the twin image and bias level reduction. Furthermore, the effect of the size of an image sensor on the image quality in rotational shearing interferometer is also investigated by the numerical simulations.

Error analysis in parallel two-step phase-shifting method

This paper presents an analysis of error in parallel two-step phase-shifting method. From the analysis, it is clarified that the maximum bandwidth of the object that this technique can capture is a half bandwidth of recording devices. Also, the recording distance must be two times longer than the conventional method to have a good reconstruction image. The analysis was verified by simulations and experimental results.

Two-step interferometry by a regularized optical flow algorithm

A two-step phase-shifting method, that can demodulate open- and closed-fringed patterns without local sign ambiguity is presented. The proposed method only requires a constant phase-shift between the two interferograms. This phase-shift does not need to be known and can take any value inside the range (0, 2π), excluding the singular case where it corresponds to π. The proposed method is based on determining first the fringe direction map by a regularized optical flow algorithm. After that, we apply the spiral phase transform (SPT) to one of the fringe patterns and we determine its quadrature signal using the previously determined direction. The proposed technique has been applied to simulated and experimental interferograms obtaining satisfactory results. A complete MATLAB software package is provided in [http://goo.gl/Snnz7].

Study on the simplified phase-shifting digital holographic microscopy

In this paper, a new simplified technique for effectively eliminating the zero order and the conjugate virtual image in digital holographic microcopy, which makes use of two-step phase-shifting method of just recording two holograms and an intensity image of object wave, is proposed. Meanwhile, combined with the principle of making full use of spatial bandwidth of the CCD sensor by in-line lens-less Fourier holographic recording geometry, the theory and experimental methods to increase the resolution of the reconstructed image in digital holography by using phase-shifting technique are detailedly analyzed. At end, the validity and availability of this technique has been demonstrated through the off-axis and in-line Fourier transform recording geometry. The study provides some theoretical and experimental guidance for the design and operation of a digital holographic microscopy system.

Optical encryption of gray-level image using on-axis and 2-f digital holography with two-step phase-shifting method

In this paper we propose an encryption/decryption technique of gray-level image information using an on-axis 2-f digital holographic optical encrypting system with two-step phase-shifting method. This technique reduces the number of holograms in phase-shifting digital holography and minimizes the setup of the encryption system more than multistep phase-shifting technique. We are able to get the complete decrypted image by controlling the K-ratio which is defined as the reference beam intensity versus the object beam intensity. We remove the DC-term of the phase-shifting digital hologram to reconstruct and decrypt the original image information. Simulation results show that the proposed method can be used for encryption and decryption of a 256 gray-level image. Also, the result shows some errors of the decrypted image according to K-ratio.

Parallel two-step phase-shifting digital holography

We propose a parallel two-step phase-shifting digital holography technique capable of instantaneous measurement of three-dimensional objects, with a view toward measurement of dynamically moving objects. The technique is based on phase-shifting interferometry. The proposed technique carries out the two-step phase-shifting method at one time and can be optically implemented by using a phase-shifting array device located in the reference beam. The array device has a periodic two-step phase distribution, and its configuration is simplified compared with that required for three-step and four-step parallel phase-shifting digital holographies. Therefore the optical system of the proposed technique is more suitable for the realization of a parallel phase-shifting digital holography system. We conduct both a numerical simulation and a preliminary experiment in the proposed technique. The results of the simulation and the experiment agree well with those of sequential phase-shifting digital holography, and results are superior to those obtained by conventional digital holography using the Fresnel transform alone. Thus the effectiveness of the proposed technique is verified.