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.     

Parallel three-step phase-shifting digital holography

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

Parallel phase-shifting interferometry based on Michelson-like architecture

In this paper, we present a new scheme for parallel phase-shifting interferometry that employs a Michelson-like architecture and a simple polarization unit to generate two phase-shifting interferograms with phase shift of π/2 at a single camera exposure. The parallel phase-shifting unit is built with simple optical components, and the distance between the parallel interferograms can be adjusted conveniently. Phase reconstruction is performed by using an algorithm developed for two-step phase-shifting interferometry. The practicability of the proposed configuration and the reconstruction method is demonstrated by experiments.     

Space-bandwidth conditions for efficient phase-shifting digital holographic microscopy

Microscopy by holographic means is attractive because it permits true three-dimensional (3D) visualization and 3D display of the objects. We investigate the necessary condition on the object size and spatial bandwidth for complete 3D microscopic imaging with phase-shifting digital holography with various common arrangements. The cases for which a Fresnel holographic arrangement is sufficient and those for which object magnification is necessary are defined. Limitations set by digital sensors are analyzed in the Wigner domain. The trade-offs between the various holographic arrangements in terms of conditions on the object size and bandwidth, recording conditions required for complete representation, and complexity are discussed.     

Image formation in phase-shifting digital holography and applications to microscopy

We discuss image formation in phase-shifting digital holography by developing an analytical formulation based on the Fresnel-Kirchhoff diffraction theory. Image-plane position and imaging magnification are derived for general configurations in which a spherical reference is employed. The influences of discrete sampling of the resulting interference patterns by a CCD and numerical reconstruction on qualities of point images are investigated. Dependence of the point images on the ratio of the minimum fringe spacing to pixel pitch of the CCD is numerically analyzed. Two-point resolution and magnification are also investigated as a function of pixel numbers by a simulation using a one-dimensional model. In experiments magnified images of biological objects and a resolution target were reconstructed with the same quality as by conventional microscopy.     

Compensation algorithm for the phase-shift error of polarization-based parallel two-step phase-shifting digital holography

We propose an algorithm for compensating the phase-shift error of polarization-based parallel two-step phase-shifting digital holography, which is a technique for recording a spatial two-step phase-shifted hologram. Although a polarization-based system of the technique has been experimentally demonstrated, there had been the problem that the phase difference of two phase-shifted holograms had been changed by the extinction ratio of the micropolarizer array attached to the image sensor used in the system. To improve the performance of the system, we established and formulated an algorithm for compensating the phase-shift error. Accurate spatial phase-shifting interferometry in the system can be conducted by the algorithm regardless of phase-shift error due to the extinction ratio. By the numerical simulation, the proposed algorithm was capable of reducing the root mean square errors of the reconstructed image by 1/4 and 1/5 in amplitude and phase, respectively. Also, the algorithm was experimentally demonstrated, and the experimental results showed that the system employing the proposed algorithm suppressed the conjugate image, which slightly appeared in the image reconstructed by the system not employing the algorithm, even when the extinction ratio was 10:1. Thus, the effectiveness of the proposed algorithm was numerically and experimentally verified.     

采用长工作距离物镜的低噪声相移数字全息显微研究

在数字全息显微技术中,为了提高测量精度,提出了一种利用长工作距离物镜的相移数字全息显微的测量装置和方法。该装置采用LED作为照明光源,可以有效地抑制相位噪声,提高了重建精度。通过在长工作距离物镜和样品之间加入分光棱镜的方法,构建了一种准物参共路的迈克尔逊干涉仪。该装置结构简单,调整方便,在部分相干光照明时,容易实现干涉。重建时,采用盲相移干涉技术,结合两步盲相移算法,重建出物体的表面相位分布。实验中,分别采用LED照明和He-Ne激光照明,测量了一个反射式USAF1951分辨率板的高度分布。结果表明,两者的测量结果相互吻合,但是LED照明时的噪声与激光照明时相比降低了70%。此外,为了进一步验证装置的有效性,使用该装置对刻于硅基底的微纳矩形台阶进行测量,测量结果与标称值具有良好的一致性,表明该装置在微结构的形貌测量方面有广阔的应用前景。     

Microscopic phase-shifting profilometry based on digital micromirror device technology

A microscopic three-dimensional (3-D) shape measurement system based on digital fringe projection has been developed and experimentally investigated. A Digital Micromirror Device along with its illumination optics is integrated into a stereomicroscope, which projects computer-generated fringe patterns with a sinusoidal intensity profile through the microscope objective onto the object surface being measured. The fringe patterns deformed by the object surface are recorded by a CCD camera. The microscopic 3-D shape of the object surface is measured and reconstructed by use of a phase-shifting technique. We discuss design considerations and error analysis of the system. Experimental results successfully demonstrate the capability of this technique for surface profile measurement of rough surfaces at the micrometer level.     

基于数字移相锁相技术的扬声器故障检测

该文为改善3种传统锁相检测法相位差不可控的缺点,通过对互相关锁相检测原理的改进,提出一种新型数字移相锁相检测法。在核电环境长距离传输条件下,结合对模拟前端电路的相位误差分析,该检测法将两路具有频率固定延时的数字移相信号代替两路正相关模拟信号,对强噪声中的微弱信号进行相敏检测,根据相关函数的差异性利用低通滤波器实现有用信号信息的提取。在核电厂区90 dB的强噪声环境中,对扬声器进行故障试验测试。结果表明:该数字移相锁相检测法可稳定检测的最低信噪比为-40 dB,最大检测误差为2.1%,可有效克服前端模拟移相误差不可控的缺点,完成扬声器工作状态的检测。     

Parallel phase-shifting digital holography with adaptive function using phase-mode spatial light modulator

Parallel phase-shifting digital holography using a phase-mode spatial light modulator (SLM) is proposed. The phase-mode SLM implements spatial distribution of phase retardation required in the parallel phase-shifting digital holography. This SLM can also compensate dynamically the phase distortion caused by optical elements such as beam splitters, lenses, and air fluctuation. Experimental demonstration using a static object is presented.     

Encryption of digital hologram based on phase-shifting interferometry and virtual optics

A new information encryption system is presented, based on phase-shifting interferometry and virtual optics. Three-step phase-shifting interferometry is used to record a digital hologram of the input data and a virtual optical system based on the scaled optical fractional Fourier transform is used for encryption of the recorded digital hologram. In the virtual optical system, the digital hologram to be encrypted is fractional Fourier transformed two times, and a random phase mask is placed at the output plane of the first fractional Fourier transform. Both the encryption and decryption processes are performed digitally. The encrypted data and the keys for decryption can be stored and transmitted in a conventional communication channel. Numerical simulations are presented to verify validity and efficiency.     

Dependence of fringe spacing on the grating separation in a long-period fiber grating pair

The spectral spacing of the interference fringes formed by a pair of long-period fiber gratings was investigated. The variation of the fringe spacing was measured while the separation between the gratings was changed from 22 to 500 mm. When the grating separation was much longer than the length of the individual grating, the inverse of the fringe spacing became linearly proportional to the grating separation and to the differential effective group index of the fiber. In the third stop band of the grating pair, made along a dispersion-shifted fiber centered at 1.55 mum, the differential effective group index was calculated to be ~6.4 x 10(-3), which is approximately twice the differential effective index of the fiber. The discrepancy between the two indices was observed to decrease with the band order, a phenomenon that is explained by the first-order dispersion of the fiber. The measured interference fringes were not regularly spaced in the frequency domain, but regular spacing is required in wavelength-division multiplexing communication systems. Analysis of the second-order dispersion of the fiber and the grating-induced nonlinear phase shift within grating regions as the factors that induce chirping on the fringe spacing is presented.     

Enhanced two-frequency phase-shifting method based on generalized phase-shifting algorithm

In this paper, we develop a novel dual-frequency pattern which not only releases the restriction of conventional two-frequency phase-shifting algorithm that at least six fringe patterns are needed, but reduces the noise impact by decreasing the frequency ratio between the high- and low-components. To decrease the number of necessary patterns to five, a novel composite dual-frequency pattern scheme combining together a high- with a low-frequency pattern is employed. To make the algorithm less sensitivity to noise, the low-frequency component is with more than one period fringes, which is relatively prone to recover the continuous result by simple spatial phase unwrapping approach. Besides, the restriction of special phase shifts between two-frequency components in conventional methods is released by the generalized phase-shifting algorithm. Simulations and experiments are conducted to demonstrate that in addition to maintaining the minimum number of patterns, the proposed method reveals higher accuracy of phase retrieval.     

Optical sectioning with a low-coherence phase-shifting digital holographic microscope

The properties of a low-coherence phase-shifting digital holographic microscope are first studied and analyzed. We then demonstrate en face imaging with transverse resolution of 3 μm and axial resolution of 10 μm through a thickness of 300 μm onion membrane. In addition, with the above said resolutions, optical sectioning of the eye and spine of a live zebra fish has been demonstrated. To the best of our knowledge, this is the first time that a short coherence phase-shifting holographic microscope has been applied to the internal structure visualization of a biological specimen under an in vivo environment.     

Spectrally resolved phase-shifting interference microscopy: technique based on optical coherence tomography for profiling a transparent film on a patterned substrate

Spectrally resolved white-light phase-shifting interference microscopy has been used for measurements of the thickness profile of a transparent thin-film layer deposited upon a patterned structure exhibiting steps and discontinuities. We describe a simple technique, using an approach based on spectrally resolved optical coherence tomography, that makes it possible to obtain directly a thickness profile along a line by inverse Fourier transformation of the complex spectral interference function.     

Slope measurement of a phase object using a polarizing phase-shifting high-frequency Ronchi grating interferometer

An interferometric method to measure the slope of phase objects is presented. The analysis was performed by implementing a polarizing phase-shifting cyclic shear interferometer coupled to a 4-f Fourier imaging system with crossed high-frequency Ronchi gratings. This system can obtain nine interference patterns with adjustable phase shifts and variable lateral shear. In order to extract the slope of a phase object, it is only analyzed using four patterns obtained in a single shot, and applying the classical method of phase extraction.     

Two-wavelength phase-shifting interferometry with a superimposed grating displayed on an electrically addressed spatial light modulator

A two-wavelength moire phase-shifting interferometer that uses a superimposed grating has been developed. The optical phase shifts for the two wavelengths are given by digital phase shifts of a superimposed grating displayed on a liquid-crystal spatial light modulator. A phase shift of the moire fringe is achieved by equal phase shifts with opposite signs in the two gratings. A moire phase-shifting interferometer with no moving parts and no requirement for calibration of the value of the phase shifts was obtained. Our experimental result shows measurements of the profile of a step object with a 2.65-microm synthetic wavelength.     

Surface shape measurement by phase-shifting digital holography with a wavelength shift

Surface contouring by phase-shifting digital holography is proposed and verified by experiments and numerical simulations. Digital holograms are recorded before and after mode hopping of a laser diode subject to current tuning, and the difference of the reconstructed phases at each wavelength is computed to deliver surface contours of a diffusely reflecting surface. Since normal incidence on the object is employed, the method does not need the removal of the tilt component and is free from the shadowing effect as advantages over the dual-incidence method proposed before by the first author.     

Spatial carrier phase-shifting algorithm based on least-squares iteration

An advanced spatial carrier phase-shifting (SCPS) algorithm based on least-squares iteration is proposed to extract the phase distribution from a single spatial carrier interferogram. The proposed algorithm divides the spatial carrier interferogram into four phase-shifted interferograms. By compensating for the effects of the variations of phase shifts between pixels and the variations of background and contrast, the proposed algorithm determines the local phase shifts and phase distribution simultaneously and accurately. Numerical simulations show that the accuracy of the proposed algorithm is obviously improved by compensating for the effects of background and contrast variations. The peak to valley of the residual phase error remains less than 0.002 rad when the magnitude of spatial carrier is in the range from pi/5 to pi/2 and the direction of the spatial carrier is in the range from 25 degrees to 65 degrees. Numerical simulations and experiments demonstrate that the proposed algorithm exhibits higher precision than the existing SCPS algorithms. The proposed algorithm is sensitive to random noise, but the error can be reduced by N times if N measurements are taken and averaged.     

Phase-only encryption and watermarking based on phase-shifting interferometry

Generally, the reconstruction of an object image from its diffraction field requires both the amplitude and the phase information of this field. We systematically investigated the effects of using only the real part, the imaginary part, or the phase information of the diffraction field to reconstruct the original image for both the binary and the gray-level images. We show that the phase information can yield a better result of image retrieval than the real or imaginary part and that the recovered image from the phase information is satisfactory especially for binary input. On the basis of this idea, a new technique of image encryption and watermarking by use of only one delivered image-the phase map of the diffraction field of the original image-through double random-phase encoding is proposed and verified by computer simulations with phase-shifting interferometry. This method can greatly cut down the communication load and is suitable for Internet transmission.