Grating-based real-time polarization phase-shifting interferometry: error analysis

A phase Ronchi grating-based real-time polarization phase-shifting method can be efficiently used for dynamic phase measurement in optical interferometry. A thorough error analysis is required for exhibiting how error sources influence phase-measurement results. We analyze the phase-measurement errors that are induced by the retardation error and azimuth angle error of the quarter-wave plate, the azimuth angle error of polarizers, the phase and intensity aberrations of diffractive wave fronts, and pixel mismatch of the interferometric patterns. The results will also be useful for evaluating the phase-measurement accuracy of other similar systems.     

Differential Rayleigh scattering method for measurement of polarization and intermodal beat length in optical waveguides and fibers

We propose a modification of the Rayleigh scattering method, which allows for measurement of polarization and intermodal beat length in single-mode and few-mode channel waveguides and optical fibers. A significant sensitivity increase is achieved by taking two high-resolution photographs in oblique scattered light of π-shifted intensity distributions produced by interference of polarization or spatial modes and applying Fourier analysis to the differential image. In the case of polarization beat length measurements, the π-phase shift is obtained by switching the polarization state at the fiber input, while in intermodal measurements, the π-phase shifting is realized by changing the excitation conditions. The usefulness of the method for characterization of channel waveguides and optical fibers is demonstrated in several examples. Moreover, we show that the combination of the spectral interferometry method with the proposed method allows for broadband measurements of differential phase and group effective indices.     

Statistical properties of a radially polarized twisted Gaussian Schell-model beam in a uniaxial crystal

We derive the analytical formulas for the elements of the cross-spectral density matrix of a radially polarized partially coherent beam with a twist phase named radially polarized twisted Gaussian Schell-model (RPTGSM) beam propagating in a uniaxial crystal, and explore the statistical properties, such as the intensity distribution, the degree of polarization (DOP) and the state of polarization (SOP) of such beam in a uniaxial crystal with the help of the derived formulas. It is found that the statistical properties of a RPTGSM beam are closely related with the twist phase and the anisotropy of the uniaxial crystal, e.g. the twist phase leads to the rotation of the intensity, DOP and SOP distributions, and the anisotropy of the uniaxial crystal leads to the asymmetry distributions of these statistical properties. Our results will be useful for designing light field with prescribed intensity, DOP and SOP distributions, and may be useful in optical manipulations and free-space optical communications.     

Rician distribution to describe speckle statistics in adaptive optics

Adaptive optics systems allow us to retrieve high-spatial-frequency information that is preserved in the wave fronts distorted by the atmosphere. Although wave-front correction should be as complete as possible, only partial compensation is attainable in the visible. We provide a procedure that uses the Rician distribution to predict the intensity statistics of the light at the image center as a function of the number of corrected Zernike polynomials.     

Subsurface damage identification in optically transparent materials using a nondestructive method

Total internal reflection microscopy has been applied to image subsurface damage sites in conventionally polished fused-silica flats. This technique can differentiate between surface and subsurface features by changing the illuminating polarization. The method is nondestructive, and no surface preparation is required other than a thorough cleaning of the surface. The intensity distributions in the illuminated region of interest are discussed. The technique has been used successfully as an optical fabrication in-process diagnostic.     

Effects of phase shifts on four-beam interference patterns

An analysis of the effects of relative phase changes on the interference pattern formed by the coherent addition of four plane waves is presented. We focus on the configuration in which four plane waves converge at equal angles along two orthogonal planes, an arrangement that is potentially useful for printing arrays of microstructures in resist. We show that, depending on the set of polarization vectors chosen, the shape of the interference pattern is a strong function of the phase difference between each pair of beams. If all the beams have the same phase constant, an intensity distribution that is perfectly modulated and that exhibits strong contrast is produced. However, if the phase constant of any one of the beams is shifted by pi from this condition, a pattern with degraded modulation and significantly weaker contrast is formed. We discuss the implication of these results on lithographic applications of multiple-beam patterns. Further, we show that the sensitivity to phase is a general property of all interference patterns formed by four or more intersecting coherent wave fronts that have collinear electric-field components.     

Testing of refractive silicon microlenses by use of a lateral shearing interferometer in transmission

Wave aberrations of refractive photoresist microlenses and silicon microlenses were measured with a lateral shearing interferometer. Because of the silicon elements, a near-infrared working wavelength (lambda = 1.32 mum) was used. The wave front was evaluated by a phase step technique with four steps. Integration of the phase distributions was performed with a computationally efficient Fourier transformation algorithm. The influence of the detector vidicon nonlinearity on the measured wave front was calculated. The defocusing behavior of the interferometer was investigated by fitting the measured wave fronts with the help of Zernike circle polynomials. It is shown that the reproducibility can be kept below lambda/100 rms. Examples for the measured wave fronts of plano-convex silicon microlenses are discussed in detail.     

Intensity, polarization, and phase information in optical disk systems

Digital information in optical data storage systems can be encoded in the intensity, in the polarization state, or in the phase of a carrier laser beam. Intensity modulation is achieved at the surface of the storage medium either through destructive interference from surface-relief features (e.g., CD or DVD pits) or through reflectivity variations (e.g., alteration of optical constants of phase-change media). Magneto-optical materials make use of the polar magneto-optical Kerr effect to produce polarization modulations of the focused beam reflected from the storage medium. Both surface-relief structures and material-property variations can create, at the exit pupil of the objective lens of the optical pickup, a phase modulation (this, in addition to any intensity or polarization modulation or both). Current optical data storage systems do not make use of this phase information, whose recovery could potentially increase the strength of the readout signal. We show how all three mechanisms can be exploited in a scanning optical microscope to reconstruct the recorded (or embedded) data patterns on various types of optical disk.     

Probing the wave fronts based on autocorrelation

We proposed an easy method for probing the wave fronts via a typical Fourier transform system. An amplitude only spatial light modulator (SLM) was set on the front focal plane of a Fourier lens to control the wave front transmittance. A CCD was set on the back focal plane of the Fourier lens to record the intensity patterns. The Fourier transform of the intensity pattern is the autocorrelation of the wave front passing through the SLM. When we choose suitable pixels of the SLM to permit the wave front passing through, the information from the wave front illuminating the pixels can be directly extracted from the Fourier transform of the diffraction intensity pattern without complicated calculations. The complex amplitude of the wave front illuminated on the SLM can be probed using the above-mentioned method. The simulation results certifying our theory were also given.     

Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation

We present a procedure that compensates for phase aberrations in digital holographic microscopy by computing a polynomial phase mask directly from the hologram. The phase-mask parameters are computed automatically without knowledge of physical values such as wave vectors, focal lengths, or distances. This method enables one to reconstruct correct and accurate phase distributions, even in the presence of strong and high-order aberrations. Examples of applications are shown for microlens imaging and for compensating for the deformations associated with a tilted thick plate. Finally we show that this method allows compensation for the curvature of the specimen, revealing its surface defects and roughness. Examples of applications are shown for microlenses and metallic sphere imaging.     

Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator

We show how to two dimensionally encode the polarization state of an incident light beam using a parallel-aligned liquid-crystal spatial light modulator (LCSLM). Each pixel of the LCSLM acts as a voltage-controlled wave plate and can be programmed over a 2pi phase range at a wavelength of 514.5 nm. Techniques are reviewed for either rotating the major axis of elliptically polarized light or for converting an input linearly polarized beam into an arbitrary elliptically polarized beam. Experimental results are demonstrated in which we generate various two-dimensional spatial patterns of polarized light. Several potential applications are suggested. We also report an unexpected edge-enhancement effect that might be useful in image processing applications.     

Phase-space formulation for phase-contrast x-ray imaging

Phase-space formulation based on the Wigner distribution has been presented for analyzing phase-contrast image formation. Based on the statistical nature and affine canonical covariance of Wigner distributions in the phase space, we show that the partial coherence effects of incident x-ray wave field on image intensity are simply accounted for by a multiplication factor, which is the reduced complex degree of coherence of the incident x-ray wave field. We show especially that with the undulator sources one cannot obtain the phase-contrast intensity by summing over the contributions from all electron positions, since the van Cittert-Zernike theorem fails in general for undulators. We derive a comprehensive formula that quantifies the effects of partial spatial coherence, polychromatic spectrum, body attenuation, imaging-detector resolution, and radiation dose on phase-contrast visibility in clinical imaging. The results of our computer modeling and simulations show how the formula can provide design guidelines and optimal parameters for clinical x-ray phase-contrast imaging systems.     

Precision of moment-based estimation of the degree of polarization in coherent imagery without polarization device

We propose and analyze a statistical method to estimate the degree of polarization of light from a single speckle intensity image by analyzing the statistical distribution of the light intensity. The optimal precision of such an estimation method is evaluated by computing the Cramer-Rao bounds for several speckle degrees. Two moment-based estimators of the square degree of polarization are introduced and characterized. For the first time to our knowledge, it is shown theoretically and through simulations that the estimators are almost efficient for high orders of speckle. The robustness of the method is discussed for the case when the intensity fluctuations do not follow the standard speckle model.     

Digital-holographic interferometry with an image-intensifier system

A method for recording digital holograms on an image intensifier coupled with a CCD sensor is presented. The advantage of the image intensifier is that it can be gated (electronic shutter action produced by controlling of the image intensifier's photocathode voltage). This allows us to record holograms with a short exposure time. Two holograms of an object submitted to dynamical displacements (e.g., vibrations) are recorded by two short exposures. The phase of the wave front recorded at different times is calculated from the recorded intensity by use of a digital Fourier-transform method. By comparison of the phases recorded it is possible to get the displacement of the object during a short interval. Experimental results are presented, and the problems related to the noise and to the spatial resolution are discussed.     

Effect of crack curvature on stress intensity factors for ASTM standard compact tension specimens

The stress intensity factors (SIF) are calculated using the method of lines for the compact tension specimen in tensile and shear loading for curved crack fronts. For the purely elastic case, it was found that as the crack front curvature increases, the SIF value at the center of the specimen decreases while increasing at the surface. For higher values of crack front curvatures, the maximum value of the SIF occurs at an interior point located adjacent to the surface. A thickness average SIF was computed for parabolically applied shear loading. It is assumed that it reflects the average stress environment near the crack edge. These results were used to assess the requirements of ASTM standards E399-71 and E399-81 on the shape of crack fronts.     

新型偏振特性因子及其传递关系的研究

偏振遥感图像通常可以采用强度、偏振度、偏振角或HIS柱形彩色空间表征目标偏振特性.本文通过建立光束在多层介质中传递的简单模型,找到一种新型偏振特性因子.此偏振特性因子所成图像是偏振度图像和偏振角图像信息复合的结果,其实质反映了偏振光束中的线偏振光的光强相对含量及它的偏振角方向.对伪装过的车牌进行偏振成像,实验表明此偏振特性因子可以用于特定环境下的伪装辨别.     

利用非线性表面波评价材料疲劳损伤

采用非线性Rayleigh表面波检测方法,实现了不同疲劳阶段下钢试样拉伸和腐蚀疲劳损伤的测试与评价;基于楔块\换能器激发与接收声波方式,搭建非线性Rayleigh波检测系统,测量了不同激励水平下基波幅值平方与二次谐波幅值间的线性关系以及Rayleigh表面波二次谐波的累积效应;分别在拉伸载荷和腐蚀疲劳载荷下,采集非线性时域信号并进行频谱分析,测量声学非线性系数在不同疲劳阶段下变化趋势,并分析不同疲劳载荷对钢试样声学非线性系数的影响。实验结果表明:超声非线性系数与疲劳周期数呈单调递增关系,可以用声学非线性系数来表征材料的表面疲劳损伤程度;相比较周期性拉伸疲劳损伤,腐蚀疲劳试样的声学非线性系数会增大,是由于腐蚀环境会加重实验中钢试样的疲劳损伤程度。研究成果可为疲劳损伤无损检测与评价提供一定的指导意义。     

Iterative algorithm of phase determination in digital holography for real-time recording of real objects

We propose a numerical method to obtain complex amplitude distribution of a three-dimensional (3D) object from a digital hologram. The method consists of two processes. The first process is to measure simultaneously a hologram of the 3D object and an object intensity distribution by two image sensors. These intensity distributions give us the amplitude and absolute value of phase of the 3D object at the image sensor plane. The second process is the determination of phase distribution by a proposed iterative process based on the criterion that the reconstructed 3D object is in focus and its conjugate reconstruction is out of focus. Numerical and experimental results show the effectiveness of the proposed method.     

Identification of Specimen Position and Orientation Using Standard Deviation of Intensity in Phase‐Shifting Digital Holography1

Abstract: Phase‐shifting digital holography is a useful method to measure the displacement distribution and the strain distribution of an object surface. The complex amplitude distribution of an object surface is obtained as the complex amplitude distribution at a reconstruction distance. It is, however, difficult to measure the reconstruction distance by actual measurement. We discovered that the standard deviation of the intensity on the reconstructed image becomes the maximum value when the reconstruction distance is the same as the actual optical path length. The displacement distributions are obtained for the x‐, y‐ and z‐directions. When the normal direction of an object surface inclines from the z‐direction, the displacements defined on the xyz‐coordinate system should be transformed into the object coordinate system. It is, therefore, required to develop a measurement method of the orientation of the object to obtain the parameters for transforming from the xyz‐coordinate system into the object coordinate system. In this paper, the method to identify the position and the orientation of a specimen using the standard deviation of the intensity distribution is proposed.     

Intrinsic speckle noise in off-axis particle holography

In holographic imaging of particle fields, the interference among coherent wave fronts associated with particle scattering gives rise to intrinsic speckle noise, which sets a fundamental limit on the amount of information that particle holography can deliver. It has been established that the intrinsic speckle noise is especially severe in in-line holography because of superposition of virtual image waves, the direct transmitted wave, and the real image. However, at sufficiently high particle number densities, such as those typical in holographic particle image velocimetry (HPIV) applications, intrinsic speckle noise also arises in off-axis particle holography from self-interference among wave fronts that form the real image of particles. To overcome the latter problem we have constructed a mathematical model that relates the first- and second-order statistical properties of the intrinsic speckle noise to relevant holographic system parameters. Consistent with our experimental data, the model provides a direct estimate of the information capacity of particle holography. We show that the noise-limited information capacity can be expressed as the product of particle number density and the extent of the particle field along the optical axis. A large angular aperture of the hologram contributes directly to achievement of high information capacity. We also show that filtering in either digital or optical form is generally ineffective in removing the intrinsic speckle noise from the particle image as a result of the similar spectral properties of the two. These findings emphasize the importance of angular aperture in designing holographic particle imaging systems.