Spatial-carrier phase-shifting digital holography utilizing spatial frequency analysis for the correction of the phase-shift error

We propose a single-shot digital holography in which the complex amplitude distribution is obtained by spatial-carrier phase-shifting (SCPS) interferometry and the correction of the inherent phase-shift error occurred in this interferometry. The 0th order diffraction wave and the conjugate image are removed by phase-shifting interferometry and Fourier transform technique, respectively. The inherent error is corrected in the spatial frequency domain. The proposed technique does not require an iteration process to remove the unwanted images and has an advantage in the field of view in comparison to a conventional SCPS technique.     

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.     

Parallel two-step phase-shifting digital holography using polarization

We propose an optical implementation of a parallel two-step phase-shifting digital holography that utilizes a polarization technique. The implementation uses a phase-shifting array device consisting of a retarder array attached to an image sensor, and does not require the optical system to image the phase-shifting array device onto the image sensor required for the previously reported optical implementation of the parallel two-step phase-shifting digital holography. Then, the proposed implementation is essentially simple to align and compose. A preliminary experiment showed that the parallel two-step phase-shifting digital holography based on the proposed implementation can remove the conjugate image clinging to the image reconstructed by Fresnel transform alone with DC term suppression. Also, when the reconstruction distance was changed, the qualities of the reconstructed images were quantitatively evaluated by using normalized root-mean-square error. It was clarified that the proposed implementation was superior to other parallel phase-shifting digital holographies and Fresnel transform alone. Thus, the validity of the proposed implementation was confirmed.     

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.     

Four-step spatial phase-shifting shearing interferometry from moiré configuration by triple gratings

A spatial phase-shifting shearing interferometry is presented in this paper. The whole optical configuration is simple and consists of three Ronchi gratings. Four phase-shifted shearing interferograms can be obtained simultaneously. The explicit intensity distributions of shearing interferograms are given and a corresponding four-step spatial phase-shifting algorithm is proposed to extract phase information from the new interferometry. This spatial phase-shifting configuration is applied to extract phase projection of a propane flame and a mathematical error analysis is presented.     

Simulation study on the quantitative phase retrieval method under two-step phase-shifting technique

Based on two-step phase-shifting technique, we present a new derivative method for phase information extraction in quantitative phase imaging (QPI). By acquiring two phase-shifted interferograms and numerically calculating their 1st order derivatives, one can directly obtain the quantitative phase information. We demonstrate the proposed method by comparing our simulated results with the experimental results of the red blood cell and the HeLa cell, respectively. It shows that our method can be generally applied to any QPI, such as on-axis and off-axis interferometry, especially for slightly off-axis interferometry, and it has the feature of efficient utility of camera spatial bandwidth and the ability of fast data processing.     

提高数字全息再现像像质的两步相移迭代算法

在两步相移数字全息术中,相移误差直接影响着零级像和共轭像的消除.为了消除相移误差,获得实际相移值,提出了一种基于相位统计特性的两步相移迭代算法.首先利用全息图的相位统计特性计算出初始相移值,然后用数字全息图再现像抽样点强度偏差之和作为评价标准,通过迭代计算寻找参考光的真正相移值.该算法能对任意未知相移量进行提取,从而有效地消除零级像和共轭像,提高了再现像质量.理论分析和光学实验结果证明了该方法的可行性和有效性.     

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.     

Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography

Phase-shifting digital holographic technique is a powerful tool for the measurement of various physical parameters, such as object deformation and liquid or cell’s refractive index change. However, for an accurate measurement, phase-shifting error in the reference wave path is still a major issue. In this paper, three novel and simple algorithms are proposed to quantitatively detect and correct phase-shifting error for a pure phase object in two-step phase-shifting digital holography. Influence of phase-shifting error is illustrated, and the effectiveness of the proposed algorithms is demonstrated by numerical simulation results.     

优化的两步相移算法在图像加密中的应用研究

优化了此前提出的两步相移算法,仅通过两幅去除背景光强(或抑制直流分量)后的干涉图数据和一个(0,π)区间的相移值,就可以成功再现出原始物波场信息,无需借助于物光光强、参考光光强等其他辅助测量信息.与菲涅耳域的双随机相位编码技术结合,该优化算法可以应用于图像加密方案中,通过计算机仿真实验验证了所提方案的可行性,并对几何密钥的灵敏度进行了测试分析.     

四步相移数字全息中随机误差的抑制方法

提出一种在四步相移数字全息中消除随机相移误差及CCD噪声的方法。通过多次重复四步相移数字全息的实验过程,使得每一步的相移都有多幅全息图像与之对应,把每一步对应的多幅全息图像进行数学平均就会得到4幅全息均值图像。理论分析表明,使用这4幅全息均值图像进行数字全息的重建,可以得到精确的物光波的分布,有效地消除随机相移误差及CCD噪声的影响。计算机模拟结果表明:该方法有助于提高数字全息重建光场质量。     

两步广义相移干涉术的光学实验验证

提出了一种基于两步广义相移干涉术的波前再现技术以及基于衍射场统计特性的未知相移值提取算法,并且进行了光学实验验证.该方法中可仅利用两幅干涉图及一次不需精确预设的未知相移,参照物光光强和参考光光强,即可通过计算提取真实的相移量,进而恢复出物波波前复振幅,而无需借助傅里叶谱分析或数字滤波等操作.在光学实验中,对借助于空间光调制器（SLM）的间接输入和三维漫反射物体直接输入两种情况进行了详细地研究,得到的光学实验结果验证了所提方案的有效性和可行性. 关键词： 信息光学 相移干涉术 波前再现 数字图像处理     

Multi-frequency inverse-phase fringe projection profilometry for nonlinear phase error compensation

A new multi-frequency inverse-phase method was proposed to compensate for nonlinear phase errors in fringe projection profilometry and to measure the three-dimensional shape of discontinuous objects. After introducing a phase offset of π/4 into the multi-frequency four-step phase-shifting method the corresponding nonlinear phase error reversed its sign, which allowed the addition of unwrapped phases before and after the phase-offset operation to compensate for the error. For the four-step phase-shifting method, simulation analysis showed that the nonlinear phase error had quadrupled the fringe frequency. Moreover, experimental results verified the feasibility and applicability of the proposed method.     

Conceptual design of a phase-shifting telescope-interferometer

This paper deals with the theoretical principle and optical design of a phase-shifting telescope-interferometer. What is called a “telescope-interferometer” (T-I) is indeed a novel, recently proposed wavefront error (WFE) sensing technique, whose basic idea consists in combining the main pupil of a telescope with a second, off-axis reference arm. Then a weak modulation of the point spread function (PSF) is generated at the focal plane, allowing for direct phase measurements. We propose a notable improvement of the method, inspired from classical principles of phase-shifting interferometry. Herein are presented the alternative principle and its achievable measurement accuracy. The technique shows high performance excepted on narrow areas located near the pupil boundary. It is applicable to both ground or space telescopes and is suitable for the co-phasing of segmented mirrors, which is of prime importance in view of future giant telescope projects.     

Parallel two-step phase-shifting microscopic interferometry based on a cube beamsplitter

Parallel two-step phase-shifting interferometry for microscopy is presented, and the recording condition for generalized two-step phase-shifting interferometry is discussed. A 45° tilted cube beamsplitter enables to replicate the orthogonally linear polarized object and reference waves into two parallel beams, respectively. As a consequence, two interferograms with quadrature phase shift are obtained along the two beams, and phase reconstructed with an improved algorithm. To reconstruct the phase distribution from the two-step phase-shifting interferograms, a certain recording condition should be satisfied. However, the recording condition has not ever been discussed before. In this paper, the recording condition for the two-step phase-shifting interferometry is derived and that is: the intensity of reference wave should be no less than two times object wave intensity.     

同轴相移数字全息中相移角的选取及相移误差的消除

基于两步同轴相移数字全息,首先从理论上分析了记录时不同相移角的选取及相移误差对再现像的影响,并给出了一种利用再现像所有抽样点的强度偏差之和作为评价标准,通过逐步改变理论设定相移角值来寻找实际相移角的相移误差消除新方法;其次对二步相移数字全息中记录时参考光波最佳相移角的选取作了计算机模拟,发现只有将参考光波的相移角选择在一定范围内,再现像的噪声较小;最后利用计算机模拟了相移误差消除,验证了所提方法的可行性.     

空域移相偏振点衍射波前检测技术

点衍射干涉仪结构简单、共光路、测量精度高, 空域移相干涉仪抗振性能优越, 两者在波前检测领域获得了广泛的应用. 本文采用激光打孔技术, 通过在金属纳米线栅偏振片上制备小孔, 制作了偏振点衍射板; 结合分光结构的空域移相技术, 搭建了空域移相偏振点衍射干涉仪, 并对一焦距为550 mm, F_#10的平行光管准直物镜透射波前进行测量, 与法国Phasics公司生产的商业化波前传感器SID4的测量结果相比较, 两者峰谷值相差0.09λ, 均方根值相差0.012λ ; 利用35项Zernike多项式拟合两者的测量结果, 将拟合得到的系数在同一坐标轴下绘制成两条曲线, 两者基本重合, 从而验证了所搭建的空域移相偏振点衍射波前检测装置的测试精度. 从而在传统点衍射干涉仪的基础上引入了空域移相技术, 实现了波前的高分辨率、高精度、实时检测, 并且提高了对振动、气流等环境因素的抗干扰能力.     

Error compensation in two-step triangular-pattern phase-shifting profilometry

This paper presents an analysis of error compensation using a newly modified two-step triangular-pattern phase-shifting measurement method, developed to reduce periodic measurement errors due to gamma nonlinearity and defocus of the projector and camera. Experimental analysis revealed that a trade-off is necessary in choosing a higher minimum projector input intensity to use the more linear region of input-to-output intensity mapping, and a lower minimum input intensity for greater dynamic range of input intensity. The modified two-step triangular-pattern phase-shifting method performs two-step triangular-pattern phase-shifting twice, the second time with an initial phase offset of one-eighth of the pitch, and generates the three-dimensional object height distribution by averaging the two obtained object-height distributions. The modified two-step triangular-pattern phase-shifting method consistently had higher measurement accuracy than the unmodified method. Errors were reduced by 23.4% at the midrange of depth using an input intensity value of 40, which yielded the highest measurement accuracy and up to 64% and 54% at small and large depths, respectively.     

一种提高干涉相位识别精度的方法

针对开环相移驱动下的单色光干涉测量,提出一种满足四步法的高精度相位识别的方法。首先选取干涉场中存在适当相位差的两像素点,建立相移驱动单周期内两像素点灰度序列值之间的干涉方程组。运用椭圆拟合获取相应干涉方程组参数,然后通过反算序列相位确定逐点驱动步长或序列相位信息。结合序列相位信息,运用Lagrange抛物插值算法,设计计算满足四步法的4幅干涉图,并计算各像素点的初相位。最后,运用多波长算法计算表面形貌并进行误差分析。实验表明:计算得到的方波多刻线样板的Ra值为0.439 0 m,测量误差为0.23%,此方法降低了对测量条件的硬件与环境要求,满足表面形貌高精度测量的要求。     

A method for measuring two-dimensional refractive index distribution with the total internal reflection of p-polarized light and the phase-shifting interferometry

Based on the total internal reflection of p-polarized light and the phase-shifting interferometry, an alternative method for measuring the two-dimensional refractive index distribution of a material is presented. The p-polarized light is incident on the boundary between a right-angle prism and a tested material. When the total internal reflection occurs at the boundary, and the p-polarized light has a phase variation. It depends on the refractive index of the tested material. Firstly, the two-dimensional phase variation distribution of the p-polarized light at the boundary is measured by the four-step phase shifting interferometric technique. Then, substituting the data into the special equations derived from Fresnel equations, the two-dimensional refractive index distribution of the tested material can be obtained.