Simultaneous measurement with one-capture of the two in-plane components of displacement by electronic speckle pattern interferometry

We present the simultaneous measurement of the two in-plane displacement components by electronic speckle pattern interferometry with three object beams and without an in-line reference beam. Three interference fringe patterns, corresponding to three different sensitivity vectors, are recorded in a single interferogram and separated by means of the Fourier transform method. Then, two interference fringe patterns are selected to obtain the in-plane displacement components.     

Electronic speckle pattern interferometer design to get maximum sensitivity on the measurement of displacement vector fields

In the present work, different geometries of interferometers with three divergent illumination beams are discussed. It is shown that the sensitivity components for each source can be measured with a maximum weight factor. The three sources were placed respectively, on x, y and near to z axis of a coordinate system. Based on our theoretical calculations it is proposed an interferometer that uses ESPI technique. Experimental results of displacements and strains are presented for one elastic surface when a torsion load is applied near to the target centre.     

Inspection of a micro-cantilever’s opened and concealed profile using integrated vertical scanning interferometry

In this paper, we describe a method based on the proposed vertical scanning interferometry (VSI) for the measurement of both surface profile of the micro-cantilever and corresponding etching sacrificial layer beneath the cantilever by only one scanning. A white light source illuminates a micro-cantilever at a certain incident angle through a Mirau interference objective. With this arrangement the top surface of the cantilever and a normally obstructed surface profile beneath the cantilever can be assessed in the same system. A digital filtering technique based on Fourier transform and a Gaussian fit are implemented to simultaneously retrieve an envelope of two series of interferograms at the top surface of a cantilever and as well as area of interest underneath the cantilever. The retrieved envelope peaks, which represent the height information of points on the test surface, are plotted to show whole field surface contour and demonstrate its effectiveness as a means for micro-electro-mechanical systems (MEMS) dual/multi-layer inspection. Results obtained agree well with those of a commercial instrument and show that the proposed method is simple and accurate.     

Uncertainty analysis of whole-field phase-differences retrieved from ESPI fringe patterns by using the Fourier transform method (FTM)

We have evaluated the uncertainty associated with the whole-field phase-differences retrieved by using the Fourier transform method (FTM), from a fringe pattern generated by electronic speckle pattern interferometry (ESPI). The phase-differences were induced by applying load to an elastic sample. The FTM involved the Fourier transform application to the fringe pattern, the isolation of the term carrying the phase information by applying a band-pass filter in the spatial frequency domain, and then the inverse Fourier transform application. Since the fringes in the analyzed pattern were adequately open, the FTM outcomes were presumed to be mainly affected by errors in the determination of both the width and the location of the applied filter mask. The influence of these error sources was assessed by using a Monte Carlo-based computer simulation. It implied evaluating the phase-differences a large number of times under the influence of the involved error sources. We found that the phase uncertainty depends strongly on the width of the applied filter mask; the influence of the other error sources considered into the uncertainty propagation was significantly smaller.     

Consideration and compensation of calibration falloff for optical flying height measurement

In sub-10 nm low flying height (FH) region, system calibration is a significant challenge to achieve precise FH measurement. Unloading calibration mechanism is utilized for every FH measurement using three-wavelength interferometry. Our experiment has shown that the cutoff frequency of photodetectors and the bandwidth of optical filters induce calibration falloff during the calibration process. As a result, the FH measured is underestimated, i.e., the FH measured is lower than its true value. In this paper, mathematical models are proposed to eliminate the side effects due to the bandwidth of optical filters and the cutoff frequency of photodetectors. Results indicate that the proposed compensation schemes are effective in terms of improving the calibration accuracy.     

Determination of displacement derivative in digital holographic interferometry

Digital holography (DH) and digital shearography (DS) both play an important role in non-destructive evaluation. In this paper, a novel method based on digital holographic interferometry (DHI) and complex phasor (CP) is proposed to determine displacement derivative. An algorithm is employed to filter the imaginary and real parts of complex values without the need of direct phase manipulation. Two-dimensional short time Fourier transform (STFT) is employed subsequently to process wrapped phase maps. An experiment is conducted to demonstrate the validity of the proposed method.     

Generalization of Carré equation

The present work offers new equations for phase evaluation in measurements. Several phase shifting equations with an arbitrary but constant phase shift between captured intensity signs are proposed. The equations are similarly derived as the so-called Carré equation. The idea is to develop a generalization of Carré equation that is not restricted to four images. Errors and random noise in the images cannot be eliminated, but the uncertainty due to their effects can be reduced by increasing the number of observations. An experimental analysis of the mistakes of the technique was made, as well as a detailed analysis of mistakes of the measurement. The advantages of the proposed equation are its precision in the measures taken, speed of processing and the immunity to noise in signs and images.     

Measurement of Density Inhomogeneity for Glass Pendulum

The density inhomogeneity of a glass pendulum is determined by an optical interference method. The relative variations of the densities over a volume with sizes of 5 × 5×5 mm^3 are （0.64 ± 0.97） × 10^-5 and （0.99 ± 0.92） × 10^-5 for the K9 glass and silica glass pendulum, respectively. These variations of densities contributing to the relative uncertainties of the Newtonian gravitational constant G are 0.20 ppm and 0.21 ppm in our experiment on measurement of G.     

Estimation of the 2D measurement error introduced by in-plane and out-of-plane electronic speckle pattern interferometry instruments

Optical interferometric metrology techniques are being increasingly used in industry. These techniques assure a greater accuracy in measuring displacements caused by deformations. One such technique, electronic speckle pattern interferometry (ESPI), has been used successfully to measure in-plane and out-of-plane deformations. The usual model describing ESPI instruments behaviour is only valid in or near the centre of the illuminated surface. In general, this model is used as such for all the points on the surface creating thus an approximate figure of the reality. This study has led to an improved 3D vectorial model, allowing us to assess qualitatively and quantitatively what is actually measured throughout all the inspected surface. Calculations with practical parameters taken from real ESPI instruments designed in the Joint Research Centre of Ispra (Italy) were carried out. The results showing three-dimensional diagrams of the measurement errors are presented and discussed.     

High-resolution dynamic measurement using electronic speckle pattern interferometry based on multi-camera technology

The speckle interferometer based on multi-camera technologies using two cameras is applied to a dynamic measurement. The new speckle interferometer is constructed by a prism array and two cameras. A phenomenon, which a bearing-ball collides against a thin polymer film, is investigated by the proposed interferometer. Then, it is shown that the local maximum deformation of the thin film by the collision is about 1.0 μm. Such a deformation process can precisely be analyzed by this method without any troubles of optical dislocations. In the results, it is confirmed that a large deformation process can be analyzed by accumulating measured results of small deformation in every small continuous analysis. Furthermore, it is estimated that the measurement precision of this method is about 5 nm as experimental results.     

电子散斑干涉载频调制形貌测量方法的分析

根据电子散斑干涉载频调制测量物体形貌的基本原理,物体表面的微小偏转可引入包含物体高度信息的载波干涉条纹。将物体的偏转视为变形,对物体变形与载波干涉条纹之间的关系进行了讨论,得出了离面位移引入载波和面内位移引入含有物体高度信息相位的结论。发现利用典型电子散斑干涉系统测量物体形貌效果最好,并通过实验得到了验证。     

Phase measurement improvement in temporal speckle pattern interferometry using empirical mode decomposition

When the Hilbert transform method is used to recover the phase distribution in temporal speckle pattern interferometry, the influence of the fluctuations of the bias and the modulation intensities on the calculated phase must be driven heuristically. In this paper we show that the Empirical Mode Decomposition method can overcome these drawbacks and consequently introduces an improvement in the evaluation of the phase distribution. An example is used to illustrate the phase measurement improvement that can be obtained by the application of the proposed approach.     

Vibration mode analysis using electronic speckle pattern interferometry

The use of electronic speckle pattern interferometry as a non-destructive testing technique has been widely reported for measuring a variety of objects. When used for vibration mode analysis, the only information presented to the operator was at the nodal area. The instrument has been developed so that, with the use of a microcomputer, the operator can now produce an isometric view of an object vibrating in a resonant mode, making the results easier to interpret. The instrument provides a real-time, non-contact alternative to other mode analysis equipment and can detect high-order modes as easily as low-order modes.     

Disturbance-free laser diode Sagnac interferometer using direct phase modulation

We exploited the wavelength tunability of the laser diode of a phase-shifting Sagnac interferometer to realize disturbance-free measurements. The Sagnac interferometer is robust against mechanical disturbances because it has a common path configuration and requires no special references. An unbalanced optical path was introduced between p- and s-polarized beams to enable easy phase shifting by direct current modulation. The experimental results indicate that the proposed system is effective for performing precise disturbance-free measurements.     

Analysis of a loss-compensated recirculating delayed self-heterodyne interferometer for laser linewidth measurement

A loss-compensated recirculating delayed self-heterodyne interferometer (LC-RDSHI) for laser linewidth measurement is theoretically analyzed. An analytical result for the output spectrum of the LC-RDSHI is obtained. It is found that the spectrum from a LC-RDSHI is equivalent to a spectrum from a conventional delayed self-heterodyne interferometer with equivalent time delay and frequency shift, but modified by a periodical function, which could significantly influence the laser linewidth measurement. The parameters of a LC-RDSHI must be optimized to permit an accurate and direct measurement of laser linewidth from the output spectrum.     

Interference Diagnosis of the Initial Stage of Laser-Produced-Plasma in Air

By using a Q-switched YAG Laser and a optical path delay set-up, we study the process in whith a laser induces breakdown to produce plasma in air, and obtain time-resolved Mach-Zehnder interferograms and optical shadowgrams of the initial stage of the plasma and the expansion wave produced in the process for the first time     

Evaluation of impact-induced transient deformations using double-pulsed electronic speckle pattern interferometry and finite elements

Transient out-of-plane displacements generated in a steel cantilever beam by an impact load are measured using a double-pulsed electronic speckle pattern interferometry system. The state of deformation of the object is freezed using a ruby laser and the pulse emission is synchronised with the impact load. Correlation fringes for different times after the start of the impact are obtained using a digital image system. For each time, transient displacements are evaluated by digital analysis of the fringes. In order to test the experimental results, the time response of the beam subjected to the impact load is evaluated using a 3-D finite element analysis. A close agreement is found between the experimental and numerical results, which prove the reliability of the optical technique to measure high-speed transient deformations.     

New theoretical and experimental results in fresnel optics with applications to matter-wave and X-ray interferometry

We present new methods and formulae for calculating the image amplitude and image spatial power spectral density produced by monochromatic point-source illumination of a finite (and/or infinite) periodic complex transmission grating. At specific finite-width resonances the image amplitude is seen to display periodic complex amplitude self-imaging of the grating, with interlaced alias images. The finite width grating resonances (as a function of spatial frequency) are broadened (from zero width) and displaced in frequency relative to those produced by an infinite grating, although the finite resonance width relative to illumination wavelength variation persists with infinite gratings. In the Fresnel domain the self images are generalizations of the Talbot and von Lau effects, while in the Fraunhofer to Fresnel transition domain, our formulae demonstrate the formation of these structures from Fraunhofer diffraction order side-lobes. Using these results, design criteria are provided for constructing lens-free three-grating interferometers with spatially diffuse illumination and detection. Such interferometers have a wide variety of applications for both X-rays and matter-waves, including a phase sensitive imaging device and/or narrow-band interference filter. For wavelengths in the Ångstrom to sub-Ångstrom range they feature high throughput and ease of fabrication. Experimental results using light with such an interferometer are presented. Our results conclusively demonstrate interference and image aliasing in such a device with spatially diffuse illumination and detection. The experiment is readily reproducible in any undergraduate physics laboratory.Work supported by ONR Grant N00014-90-J-1475, by the firm J. F. Clauser & Assoc., and (MWR) by a U.S. Dept. of Education Fellowship     

Sound field monitoring by tomographic electronic speckle pattern interferometry

Time-averaging electronic speckle pattern interferometry (ESPI) allows to record the phase modulation of light that has propagated through a sound field. When such data are collected from different projection directions the three-dimensional spatial distribution of amplitude and phase of the sound are obtained by tomographic back projection. The performance of such a setup increases with the number of projection directions, the number of effective resolution elements in the detector, and the number of recordings taken in averaging. These efforts, however, compete with the need for acceptable recording and processing times. Recent improvements in time-averaging ESPI enable even demanding applications in sound field monitoring. This is demonstrated in the design of a 38.5 kHz ultrasound source composed of a large number of individual piezoelectric transducer elements and intended to generate highly directive audio sound by nonlinear mixing in air (parametric array). The success of this method relies essentially on a non-intrusive control of the spatial homogeneity of the ultrasound field. Tomographic ESPI data have guided in a delicate alignment of the transducer elements yielding the expected narrowing of the angular radiation of the audio sound.