Display of tilt information of vibrating object in time average mode using lateral shearing interferometry and interferometric grating

We have experimentally demonstrated vibration analysis of a reflecting object in time-average mode using shearing interferometry and interferometric grating. Experimental results show that time-average moiré fringes, formed between fringe pattern reflected from object and sinusoidal grating are modulated spatially by the amplitude of vibrating tilt. From the experimental results, information regarding tilt of vibrating objects can be determined.     

Speckle-pattern interferometry applied to the study of phase objects

If a speckle pattern is photographed through a phase object, the individual speckles are displaced over varying distances depending upon the phase irregularities in the object. A double exposure is made, the object being present during one of the two exposures only. When the processed photographic plate is observed through an aperture stop in the Fourier transform plane, interference fringes representing contours of the optical path gradient are obtained. The sensitivity of the method and the direction along which the gradient is measured can be varied by modifying, respectively, the distance of the Fourier-plane aperture from the optical axis and its azimuth.     

一种新的数字散斑振动定量分析系统

在数字散斑干涉(DSPI)测量方法中，数字散斑时间平均法测量振动时得到的是贝塞尔条纹，其定量分析比较困难。该文采用贝塞尔条纹准相移技术进行数字散斑振动定量分析，即在参考光路中引入和物体同频率的偏置参考振动,当参考振动的相位改变时,振动条纹会产生移动,这相当于静态余弦条纹的相移,可以采用相移算法对数字散斑振动测量的贝塞尔条纹进行定量分析。文中开发了一种新的数字散斑振动定量分析系统，研制了一种低压光学相移器和测量控制电路，给出了圆周固定圆片和四周固定方铜板的振动测量结果。实验结果表明：采用本系统可以方便地定量测出物体的振动模态。     

Optimization of recording process in laser irradiance modulated time-average holography of sinusoidally vibrating objects

The beam ratio during modulation of laser irradiance in time-average hologram interferometry of a sinusoidally vibrating object, is discussed for retaining the exposure time, and reducing it if the normal brightness of the higher order J₀ fringes is tolerable. It is assumed that a variable ratio lossless beam splitter is used for the beam division process.     

Talbot interferometry with a vibrating phase object

We describe a Talbot interferometer for measuring a vibrating phase object. The time-average fringes are moiré patterns modulated by the zeroth-order Bessel function. They provide information about the tilt at every point of a vibrating plate, for example. The Talbot interferometer is robust (common path) and cheap (printers grids as beam-splitters). The experiments can be performed with laser illumination or with a collimated beam of white light. Some experimental results are shown.     

Simplified interpretation of interference fringes obtained by time-average holography

A method of evaluating time-average holograms which gives the vibration amplitudes of an object is described. The method is based on the holodiagram, from which a value of sensitivity (k value) is obtained. For sinusoidal vibrations of an object, a_k values are calculated from the roots of the zero order Bessel function; these give the values of the vibration amplitude at the dark interface fringes directly by multiplication with the wave-lenght of the laser light and appropriate k value. a_k values are tabulated for the first twenty fringes. a_He values which incorporate the wavelenght of the commonly used He-Ne laser are also tabulated. The evaluation of a hologram of a metal sheet is described. Finally the difference between the position of fringes obtained from objects with sinusoidal and square-wave amplitudes of vibration is shown.     

Time-average holographic interferometry with a sinusoidally modulated laser diode

Laser diodes have the features of a single-mode operation and a frequency tunability. Holographic interferometry is described for investigating the vibrating amplitude and phase with a frequency-modulated laser diode. Sinusoidal wavelength change by varying laser injection current produces the sinusoidal phase modulation of relative phase difference between the reference and vibrating object paths. Holograms are made by time-average exposure of three-type recording modes with a laser diode. The phase of vibrating object is extracted from the measurements of Bessel-type fringe irradiances in three kinds of time-average holographic reconstruction. Experimental results of phase and amplitude for a vibrating cantilever object are shown.     

Optimization of interference fringe tuning by improving the sensitivity of measurements of the phase step height

The condition for obtaining optimal tuning of interference fringes, which correspond to their perpendicular direction to the phase step interface, are considered. Optimal tuning is attained when the sensitivity of measurements increases due to the overlap of a pair of holographic interferograms. It is noted that this method can be implemented most easily when a copy of the first interferogram rotated relative to the interface of the phase step is used as the second interferogram.     

Vibration analysis and non-destructive testing with real-time shearography

Real-time laser speckle shearography coupled with vibration stressing is shown to be an effective means of vibration analysis and non-destructive testing. The shearograms are modulated by a system of live fringes. These fringes are shown to be described by the zeroth-order Bessel function of the first kind and their visibility decreases with increasing fringe order. In vibration analysis, the instantaneous fringe pattern depicts the out-of-plane surface displacement gradient of the object surface at various resonance modes. In non-destructive testing, the flaw depth in a component can be determined without having to determine fringe orders. There is good agreement between the results obtained using the method and those from theory and time-average holography. A major advantage of real-time shearography is its facility for continuous assessment of a vibrating object without the need for secondary shearogram reconstruction.     

光学综合孔径成像中的傅里叶相位研究

傅里叶相位是光学综合孔径成像的重要信息,观测目标的傅里叶相位包含于干涉条纹中。从像平面干涉条纹形成原理出发,推导出大气扰动、星光方向与基线方向不垂直和望远镜系统机械误差等因素是影响干涉条纹初始相位的主要因素。利用条纹原点值和峰值位移从条纹中提取初始相位,采用闭合相位法从条纹初始相位中去除其它因素的影响,从而最终获取目标傅里叶相位：结合计算机模拟对噪声给条纹峰值位置的影响进行分析,模拟结果表明在频域中对条纹能量谱进行阈值处理有较好的去噪效果。最后结合目标重构迭代法阐述了闭合相位在像重构中的作用。     

Conditions for the translational vibratory motion of small objects under the action of pulses of various shapes

It is theoretically shown that the translational wave-induced movement of a small (compared to the wavelength) object is possible even when the time-average force on it is zero. In this case, the object moves, oscillating in the forward and backward directions. The predominant motion of the object in a given direction is found to require the optimum choice of a carrier-wave phase with respect to the leading edge of the wave pulses. A substantial feature of this wave transport mechanism is the possibility of inversion of the object motion direction by merely changing the phase shift and retaining the previous direction of wave propagation. The transport of an object under the action of pulses with various envelope shapes is studied. The undesirable backward motion of the object with respect to the main forward direction is found to decrease for an exponential envelope; when this envelope is optimized, the backward motion is completely eliminated.     

Calibration of a low-cost piezoelectrical mirror for DSPI

A cheap piezoelectrically driven mirror can be easily constructed in the laboratory. It can be located in one arm of a DSPI interferometer in order to introduce a controlled phase step. A procedure to calibrate this device is shown, that is based on the evaluation of the fringes obtained with the interferometer, by mean of the cross-correlation between profiles of the fringes. To evaluate the performance of the calibrated device, the phase map of a simulated plane object is calculated, using the four-step algorithm for the images of a speckle interferogram.     

Holographic reverse shearing interferometry with high measurement sensitivity

The possibility of studying phase objects by reverse shearing interferometry with high measurement sensitivity is demonstrated. Phase objects are studied in two stages. In the first stage, holographic reverse shear interferograms are measured with and without an object under nonlinear conditions with tuning to frequent reference fringes. In the next stage, these interferograms are optically processed to obtain two interference patterns. The behavior of the interference fringes is the same as in the case of conventional double-beam interferometry with a standard reference wave. The increase in the measurement sensitivity in the thus-obtained interference patterns is due to the use of higher diffraction orders reconstructed from the holographic interferograms. A possibility of controlling the width of interference fringes is considered. The results of experimental approval of this technique are presented.     

Position Sensing Grating Interferometer for a Specular Object

A position sensing interferometer is described which is able to sense the position of a specular object from a normal distance. The interferometer consists basically of a diffraction grating, a focusing lens and two plane mirrors. The grating acts as a tool to divide the incident beam and also to combine the reflected beams from an object so that they interfere with each other. An experiment was carried out to verify the principle. Interference fringe patterns caused by variation in the object position were obtained. The sensitivity obtained theoretically was confirmed by measuring the width of the fringes. As a result of theoretical comparison with conventional techniques, it was determined that this interferometric method has the advantage of the high sensitivity and the wide dynamic range being compatible with each other. The setting for sensing is simple and the analysis of the fringe patterns is easy.     

Phase-unwrapping algorithm for the measurement of 3D object

The phase unwrapping is a significant and difficult procedure for profilometry based on fringe. A new algorithm based on coded phase is proposed in this paper. It identifies the order of the fringe by projecting fringes with coded phase onto the object and performs fast phase unwrapping. The computer simulation and the experiment are presented to prove the feasibility and validity of the new algorithm.     

Fast Computation of Fresnel Holograms Employing Difference

We propose an approximation method that can calculate the Fresnel hologram 16 times faster than the conventional method. To compute the hologram, an object is assumed to be a collection of self-illuminated points and the fringes from each object point are superposed. The distance between object point and sampling point on the hologram is used to obtain the phase of the light. Since a sampled hologram usually has small pixel intervals, the difference of the distance values between adjacent pixels is also small and its n-th order difference can be assumed to be constant. Therefore, the distance value at a certain pixel can be obtained from its neighbor with simple additions. The distance error can be reduced less that one wavelength with practical parameters. A hologram, which has a horizontal parallax only, 1.3 Mega-pixels and 1,000 object points, can be calculated in less than one second with a personal computer.     

Passive ranging and three-dimensional imaging through chiral phase coding

We present a method for single-image passive ranging and three-dimensional (3D) imaging in incoherent light based on chiral phase coding. A chiral linear phase variation across the aperture of an optical system results in a frequency response with a characteristic pattern of fringes such that the spatial period and inclination of the pattern depend on the focusing error. From this dependency, the absolute focusing error and, hence, the distance to the object can be found. In the experiments a resolution of ~1.4 μm is achieved with a 20 mm aperture lens in a 4 mm interval at a distance of 140 mm from the lens. A resolution of ~0.7 mm is obtained at a distance of ~11 m with the range finder employing two 25.4 mm spherical mirrors spaced apart by ~140 mm. We also demonstrate 3D imaging of weakly textured objects.     

Photorefractive shearing interferometer

A novel method of obtaining shearing interferogram by slightly moving the crystal in a photorefractive interferometer is proposed. This method can measure the phase of an object itself instead of its diffraction field, and it is easy to realize continuously changeable shearing distance in any lateral direction and introduce carrier fringes at the same time. Both the theoretical analysis and experimental verification are given.