Fourier optics analysis of grating sensors with tilt errors

Dynamic diffraction gratings can be microfabricated with precision and offer extremely sensitive displacement measurements and light intensity modulation. The effect of pure translation of the moving part of the grating on diffracted order intensities is well known. This study focuses on the parameters that limit the intensity and the contrast of the interference. The effects of grating duty cycle, mirror reflectivities, sensor tilt and detector size are investigated using Fourier optics theory and Gaussian beam optics. Analytical findings reveal that fringe visibility becomes <0.3 when the optical path variation exceeds half the wavelength within the grating interferometer. The fringe visibility can be compensated by monitoring the interfering portion of the diffracted order light only through detector size reduction in the expense of optical power. Experiments were conducted with a grating interferometer that resulted in an eightfold increase in fringe visibility with reduced detector size, which is in agreement with theory. Findings show that diffraction grating readout principle is not limited to translating sensors but also can be used for sensors with tilt or other deflection modes.     

Quantitative coherence analysis of dual phase grating x-ray interferometry with source grating

Dual phase grating x-ray interferometry is compatible with common imaging detectors,and abandons the use of an absorption analyzer grating to reduce the radiation dose.When using x-ray tubes,an absorbing source grating must be introduced into the dual phase grating interferometer.In order to attain a high fringe visibility,in this work we conduct a quantitative coherence analysis of dual phase grating interferometry to find how the source grating affects the fringe visibility.Theoretical analysis shows that with the generalized Lau condition satisfied,the fringe visibility is influenced by the duty cycle of the source grating and the transmission through the grating bar.And the influence of the source grating profile on the fringe visibility is independent of the phase grating type.Numerical results illustrate that the maximum achievable fringe visibility decreases significantly with increasing transmission in the grating bar.Under a given transmission,one can always find an optimal duty cycle to maximize the fringe visibility.These results can be used as general guidelines for designing and optimizing dual phase grating x-ray interferometers for potential applications.     

Analysis of period and visibility of dual phase grating interferometer

Dual phase grating interferometer may simultaneously achieve large field of view and high x-ray dose efficiency. Here, we develop a simple theoretical method to better understand the imaging process of the dual phase grating interferometer. The derivation process of fringe period and the optimal visibility conditions of the dual phase grating interferometer are given in detail. Then, we theoretically prove that the fringe period and optimal visibility conditions of the dual phase grating interferometer include that of the Talbot interferometer. By comparing our experimental results with those of other researchers, we find that when the positions of phase gratings are far away from the positions where the fringe visibility is optimal, the fringe period of the dual π -phase grating interferometer is twice the theoretical results under the illumination of polychromatic x-ray. This conclusion may explain the contradictory research results of dual phase grating interferometer among different researchers.     

Achromatic stellar interferometry

One drawback of Michelson's stellar interferometer is due to the fact that the period of the interference fringes is proportional to the wavelength. Hence, in broadband light the fringe contrast is low, or in narrowband light (after filtering) the luminosity is low. We propose a modified stellar interferometer with perfectly achromatic fringes, that has better light efficiency and better signal to noise under most circumstances. To that end, two pieces of grating have to fill the two apertures of Michelson's setup. Achromatic interference fringes occur somewhere along the system axis, where the plus-first diffraction order from one aperture meets the minus-first diffraction order from the other aperture. Laboratory experiments confirm the predicted achromatic performance.     

Spectral-domain intermodal interference under general measurement conditions

Spectral-domain intermodal interference is analysed theoretically at the output of a few-mode optical fibre alone and at the output of the optical fibre in a tandem configuration with a Michelson interferometer. The theoretical analysis is performed under general measurement conditions when a light source of a given spectral bandwidth and a spectrometer of a given spectral bandpass are considered and when first- and second-order intermodal dispersion effects in the optical fibre are taken into account. Thus, the effect of a variable spectral bandpass of a low-resolution spectrometer on the spectral fringe visibility functions for a two-mode optical fibre of known intermodal dispersion is specified.     

基于衍射光栅的干涉式精密位移测量系统

介绍了基于几何莫尔条纹原理和衍射干涉原理的两种光栅精密位移测量系统及各自的特点。综述了国内外对光栅干涉式精密位移测量系统的研究进展,总结了系统存在的关键问题及发展趋势。光栅干涉式精密位移测量系统的优点是对环境要求小,测量分辨率和精度较高,结构紧凑,成本低。该系统需要解决的问题包括提高光栅以及光学元器件制造和安装精度;寻求一种更高精度的检测手段对光栅位移测量系统进行标定等。光栅干涉式精密位移测量系统的发展方向为更高测量分辨率和精度,大量程、多维度测量以及尺寸小巧。该系统在现代工业加工精密制造领域将具有更广阔的应用前景。     

Additive-subtractive phase-modulated speckle interferometry: Fringe visibility under partial decorrelation

Additive-subtractive phase modulated speckle interferometry (ASPMSI) is a technique that minimizes the susceptibility of speckle methods to environmental noise while providing fringes of good visibility. The method requires the acquisition of two consecutive video frames of additive-speckle images of the same two deformed states of an object at a rapid enough rate such that ambient noise is not a problem. The additive-speckle images as expected are of very poor visibility due to the presence of the self-interference term. An interframe phase-modulation is introduced and the two additive-speckle images are digitally subtracted to improve the fringe visibility by removing the self-interference term. The ASPM-SI method works with in-plane and out-of-plane deformation sensitive ESPI as well as with displacement-gradient sensitive speckle-shearing interferometry. It is shown that the ASPM-SI scheme has higher visibility than conventional additive-SI and performs consistently better than subtractive-SI schemes in the presence of partial interframe speckle decorrelating optical noise. Furthermore, it is shown that the fringe visibility of the out-of-plane displacement sensitive interferometer which uses a protected reference beam separate from the object beam can be made to be essentially unity even at complete interframe decorrelation.     

Novel achromatic distributed feedback dye laser for subpicosecond operation

The optical pump arrangement of distributed feedback dye lasers (DFDLs) having a grating beam splitter is analyzed in detail. The upper limit of the pump spectral bandwidth and beam divergence are given as a function of the length of the excited volume. A novel achromatic pump arrangement is reported which is capable of producing a short, high visibility interference pattern even if a divergent pump source of several nm bandwidth is used. The DFDL pulse duration has an estimated lower limit of 200 fs.     

物体表面形貌的正弦相位调制实时干涉测量技术研究

表面形貌干涉测量技术是一种高精度的非接触式测量技术,在工业生产和科学研究中具有广泛的应用。提出一种实时测量表面形貌的正弦相位调制干涉测量新技术。该技术用激光二极管作光源,用自制的高速图像传感器探测干涉信号,通过信号处理电路实时解相得到被测表面所对应的相位分布,实时分析相位获得物体表面形貌。该技术消除了光强和部分外界干扰的影响,提高了系统的测量精度。楔形光学平板表面形貌的测量结果表明,测量点为60×60个的情况下,测量时间小于8.2 ms,重复测量精度(RMS)为4.3 nm。     

The separation of out-of-plane displacement from in-plane components by fringe carrier method based on large image-shearing ESPI

A fringe carrier method for separating out-of-plane displacement from in-plane components based on large image-shearing electronic speckle pattern interferometry (ESPI) is presented. If the test object is respectively illuminated by two expanded symmetric illuminations in large image-shearing ESPI, two interferometers are formed. Carrier fringe patterns can be introduced by tilting reference surface a small angle. The carrier fringe patterns are demodulated after deformation of the object. Two phase maps, which include out-of-plane and in-plane displacement, can be obtained by using Fourier transform. Then out-of-plane displacement can be easily separated from in-plane displacement by simple operation between two unwrapped phase distributions. The principle of spatial carrier frequency modulation in large image-shearing ESPI is discussed. A typical three-point-bending experiment is completed. Experimental results are offered. The results show that the method offers high visibility of carrier fringes. And the system presented does not need a special beam as a reference light and has simple optical setup.     

Development of narrow-linewidth diode lasers by use of volume holographic transmission gratings

We present two diode laser setups that employ volume holographic transmission gratings to provide optical feedback. The advantage of this kind of grating is high diffraction efficiency and the possibility to place optical elements on both sides of the grating. This allows for advanced external cavities and adjustable feedback efficiency. The first setup is a diode laser in the Littman configuration with the transmission grating replacing the conventional reflection grating. The second setup improves the frequency selectivity by substituting the feedback mirror with a passive resonator. This grating-enhanced external cavity diode laser (GECDL) achieves excellent frequency stability. A prototype of the GECDL setup demonstrates an intrinsic linewidth of 7 kHz and an operation range that covers the full amplification profile of the laser diode.     

Variational denoising method for electronic speckle pattern interferometry

Traditional speckle fringe patterns by electronic speckle pattern interferometry (ESPI) are inherently noisy and of limited visibility, so denoising is the key problem in ESPI. We present the variational denoising method for ESPI. This method transforms the image denosing to minimizing an appropriate penalized energy function and solving a partial differential equation. We test the proposed method on computer-simulated and experimental speckle correlation fringes, respectively. The results show that this technique is capable of significantly improving the quality of fringe patterns. It works well as a pre-processing for the fringe patterns by ESPI.     

光热正弦相位调制干涉仪中相位的抗干扰测量

在正弦相位调制半导体激光干涉仪中,半导体激光波长随注入电流和温度漂移而产生相位测量误差,同时干涉仪的机械振动和干涉仪两臂中的空气扰动也会引入相位误差,在已有光热正弦相位调制干涉仪中引入反馈机制,有效地降低了上述误差,增强了干涉仪的抗干扰能力,使用此干涉仪测量了物体的位移,测量结果表明这种方法可以有效地提高相位的测量精度。     

An electronic fringe counter for interferometric applications

An electronic fringe counter for use with optical interferometers is described. Provision is made for automatic fringe counting and indication of change in the direction-of-motion of the interferometer flats. Two cadmium sulphide cells, with peak spectral response closely matched to the wavelength of the interferometer light source, serve as photosensors. Changes in cell resistance are measured with dc bridge circuits, the output of which is amplified and plotted on strip recorders. In this manner, a continuous display of fringe to fringe displacements is obtained. The system described here permits integral fringe counting accurate to ∼0.01 fringe.     

Symmetric Talbot bands experiment

By impinging a step phase-shifted white light beam on a grating-based interferometer, one of diffraction orders is modulated and interference bands so-called “Talbot bands” are formed. Here, classical Talbot bands set up is generalized to the symmetry configuration, in which two glass plates of the same thickness instead of one plate, are inserted halfway into the grating interferometer aperture. Formation of Talbot bands were studied theoretically and experimentally. Frequency impulse response of the new Talbot bands setup was, also presented. It was demonstrated that symmetric set-up causes modulation of both of two opposite orders, according to the theory. In this manner, their visibility is the same. As a result, this similarity of the visibility is reduced while the symmetric arrangement of the glass plates with respect to the optical axis, is broken.     

Polychromatic light interferometer for high-accuracy positioning

Superposition of different-wavelength, multimode- and single-mode laser diode beams is investigated to locate the fringe of zero interference order in a Twyman-Green interferometer. The possibility of central fringe detection using three multimode laser diodes or one single-mode together with a pair of multimode laser diodes is shown. If a single-mode laser diode is applied, a simultaneous fringe-counting technique for displacement measurement is available. The influence of the angle between wavefronts entering the interferometer is analyzed. A repeatability of about 5 nm is shown for surface position determination when using three-beam source.     

A comprehensive ESPI based system for combined measurement of shape and deformation of electronic components

This paper describes a very simple and reliable procedure for measuring shape and deformation of electronic components with a single experimental set-up. The procedure is based on two electronic speckle pattern interferometry (ESPI) techniques referred to as conventional ESPI and phase shifting ESPI (PS-ESPI). The present research is motivated by the fact that mismatch in thermal expansion coefficients of the different materials included in electronic packaging (EP) may cause mechanical failures since thermal stresses will change sharply through subsequent loading cycles. ESPI is particularly suitable for measurements on EP since it allows us to perform non–contact testing of non-planar heterogeneous surfaces. It is apparent that gathering detailed topographic information will certainly help us to measure accurately surface deformations of EP along with modeling correctly numerical analysis.As is known, the accuracy of results obtained with ESPI may be significantly improved by phase shifting techniques (PST). Therefore, this paper compares the relative merits of different phase-stepping strategies in order to find which strategy will perform the best for the optical set-up utilized in the experiments. Preliminary investigations on a standard specimen under three-point-bending served to choose properly the optical set-up and phase-stepping procedure which yield the best fringe visibility. Four-phases achieved the best fringe visibility and the minimum number of invalid pixels.These information have been utilized in the experimental campaign on standard and surface mounted technology (SMT) electronic components. ESPI and PS-ESPI have been used for analyzing the transient state and the steady state of devices, respectively. From the experimental results obtained here, it appears possible to measure strains induced by thermal loading cycles. The experimental set-up, based on the Lendeertz's interferometer, proved itself also able to contour specimen surface at a good level of detail. Remarkably, by using the same set-up for deformation and shape measurements we can preserve the pixel by pixel relationship between displacements and surface depth which will hold true if correlation between different exposures is not destroyed.The results obtained in this research justify using PS-ESPI in order to understand better failure mechanisms of electronic components. This fact along with the exact knowledge of object shape may be particularly useful in the different design stages (including FEM modeling and analysis) of electronics for special applications.     

Multiple-beam interferometric determination of the coherence length of spectral sources

A theoretical treatment for multiple-beam fringe visibility taking into consideration the profile of the spectral source is derived for (a) a Gaussian profile; and (b) a Lorentzian profile. A comparative study between the visibility of the two profiles is presented. Expressions for the intensity distribution for Doppler and Voigt cases are given. The fringe visibility dependence on the half-width of the spectral profile of the light illuminating the interferometer for the two cases, namely Lorentzian and Gaussian, is presented. This leads to the view that the coherence length for a Voigt profile is less than it is in the absence of Doppler or pressure broadening. Multiple-beam Fabry-Perot fringes in transmission have been utilized for the determination of the coherence length of the two spectral lines emitted from ¹⁹⁸Hg at wavelengths of 5461 Å and 4358 Å. The method for determination is based on the variation of the visibility of the recorded interference fringes with path difference.     

Nanometer-scale displacement sensing using self-mixing interferometry with a correlation-based signal processing technique

A self-mixing interferometer is proposed to measure nanometre-scale optical path length changes in the interferometer’s external cavity. As light source, the developed technique uses a blue emitting GaN laser diode. An external reflector, a silicon mirror, driven by a piezo nanopositioner is used to produce an interference signal which is detected with the monitor photodiode of the laser diode. Changing the optical path length of the external cavity introduces a phase difference to the interference signal. This phase difference is detected using a signal processing algorithm based on Pearson’s correlation coefficient and cubic spline interpolation techniques. The results show that the average deviation between the measured and actual displacements of the silicon mirror is 3.1 nm in the 0–110 nm displacement range. Moreover, the measured displacements follow linearly the actual displacement of the silicon mirror. Finally, the paper considers the effects produced by the temperature and current stability of the laser diode as well as dispersion effects in the external cavity of the interferometer. These reduce the sensor’s measurement accuracy especially in long-term measurements.     

Multi-wavelength,high spatial brightness operation of a phase-locked stripe-array diode laser

Stable continuous wave multi-wavelength operation of a stripe-array diode laser with an externalcavity spectral beam combining geometry is presented. In this setup each emitter of the stripe-array is forced to operate at a different wavelength, which leads to a decoupling between the usually phase-locked emitters. With a reflective diffraction grating with a period of 300 lines per mm, 33 equidistant laser lines around a center wavelength of 978 nm were realized, spanning a spectral range of 26 nm. With this novel approach near-diffraction limited emission with a beam quality of M ² < 1.2 and an output power of 450 mW was achieved. This laser light source can be used for applications requiring low temporal but high spatial coherence.