Common-path interferometer with a tri-window

A common-path interferometer is proposed with a tri-window. It is built using a 4f optical system with Ronchi ruling as a spatial filter. The input rectangular aperture is formed by three windows; the central window supports a phase object, and the other two are used for reference beams. Using an appropriate grating period relative to input aperture size, an interferogram containing three patterns can be obtained in the output plane. The object phase can then be reconstructed from the three patterns using just one interferogram. The experiments are carried out to demonstrate the feasibility and reliability of the proposed scheme.     

Digital phase-shifting interferometer with an electrically addressed liquid-crystal spatial light modulator

A digital phase-shifting interferometer with a liquid-crystal-display coupled, parallel aligned, nematic liquid-crystal spatial light modulator is developed. The optical phase shift in the Michelson-type polarization interferometer is achieved by a digital phase shift of a grating displayed on the spatial light modulator. Accurate experimental results of using the heterodyne system for pi/2 phase steps were demonstrated. A phase-shifting interferometer with no moving parts and no requirement for calibration of the value of the phase shift was achieved.     

Phase-shifting interferometry with four interferograms using linear polarization modulation and a Ronchi grating displaced by only a small unknown amount

A method to reduce the number of captures needed in phase-shifting interferometry is proposed on the basis of grating interferometry and modulation of linear polarization. The case of four interferograms is considered. A common-path interferometer is used with two windows in the object plane and a Ronchi grating as the pupil, thus forming several replicated images of each window over the image plane. The replicated images, under proper matching conditions, superpose in such a way so that they produce interference patterns. Orders 0 and +1 and −1 and 0 form useful patterns to extract the optical phase differences associated to the windows. A phase of π is introduced between these orders using linear polarizing filters placed in the windows and also in the replicated windows, so two π-shifted patterns can be captured in one shot. An unknown translation is then applied to the grating in order to produce another shift in the each pattern. A second and final shot captures these last patterns. The actual grating displacement and the phase shift can be determined according to the method proposed by Kreis before applying proper phase-shifting techniques to finally calculate the phase difference distribution between windows. Related simulations and experimental results are given.     

Common-path interferometry with one-dimensional periodic filters

We discuss a spatial filtering interferometry setup that employs a periodic spatial filter with either cosine transmittance or binary phase modulation. The setup's input plane is formed by two separate windows, one of which supports a phase object and the other, a reference beam. Using the appropriate frequency and orientation of the filter produces an interference pattern of the two input fields at the output plane of the system. The main attributes and advantages of the setup are discussed and experimentally illustrated with the example of a binary phase periodic filter implemented with a spatial light modulator.     

Phase profile analysis of transparent objects through the use of a two windows interferometer based on a one beam splitter configuration

In this research we implemented a two windows interferometer based on polarization phase shifting and grating interferometry techniques in order to retrieve the phase data profile of the object in a single capture. The optical configuration has two optical beams with circular polarization in opposite directions, and it is coupled with a 4-f system. An amplitude grid is used as a filter which is placed at the Fourier plane to obtain replicas of each beam which can properly interfere, depending on the separation between beams. The interferometer presents the capability of changing the beam separation in order to make different orders interfere properly. The interference patterns produced can be separately modulated through the operation of linear polarizer's placed on each interference replica. In order to present the capabilities of the system we will select four interferograms result of contiguous orders interference.     

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.     

用3×3耦合器的干涉仪直接解调光纤光栅传感器的信号

为了简单直接地解调出光纤光栅的波长移动 ,提出了另外一种非平衡马赫曾德尔干涉仪的直接解调技术。用一只 2× 2耦合器和一只 3× 3耦合器组成非平衡的马赫曾德尔光纤干涉仪 ,作为光纤光栅的波长移动解调器。解调器输出的 3路信号 ,互成 12 0°相位差。通过对 3路输出信号计算的方法 ,就可以直接解调出光纤光栅的波长移动。将 3路信号采集送入计算机 ,用软件实现了信号的解调。测量结果表明 ,在干涉仪两臂长度相关 5mm时 ,测量动态应变的分辨率达到了 0 5 1nε/Hz1/2 。还得到了输出信号的频谱和输入输出信号的关系。     

Fabry-Perot interferometer with diffraction-scattered reflection of light

The incorporation of a phase grating into the optical system of a Fabry-Perot interferometer makes it possible to transform the incident beam of light so that the major part of energy in the reflected wave is contained in the side lobes in the far-field diffraction pattern and radiation in the zero order of diffraction along the optical axis is suppressed. Experimental results are presented, which are obtained with a grating produced by evaporating a thin-layer dielectric coating onto the input mirror of the interferometer.     

Grating Interferometer Using ± 1st Order Beams for Step-Profile Altitude Difference Measurement

We propose a grating interferometer for step-profile altitude difference measurement. There are two main characteristics in this interferometer. The first is that the intensity distribution of the interference pattern is independent of the wavelength of the laser-diode used. No change of the intensity distribution occurs when the wavelength fluctuates. The second is that the measuring range is much larger than the wavelength of the light source because the spatial period of the grating is much larger than the wavelength. Sinusoidal phase modulating interferometry is easily applied to detect the phase variation of the interference pattern by vibrating the grating sinusoidally. The thickness of a 3.5-inch disk is measured with an accuracy of less than 0.5 μm.     

Optical Logic Gates Using Grating Interferometers

We describe two-input optical logic gates implemented using grating interferometrers. AND, OR, and XOR logic functions are easily implemented with the same optical system, simply by changing the relative spatial phase of the gratings. We also describe an extension of this idea in which a four-grating interferometer is used as an optical half-adder, and demonstrate its operation with experimental results.     

Shifting curves based on the detector integration effect for x-ray phase contrast imaging

In theory, we find that the actual function of the analyzer grating in the Talbot–Lau interferometer is segmenting the self-images of the phase grating and choosing integral areas, which make sure that each period of self-images in one detector pixel contributes the same signal to the detector. Furthermore, in the case of the lack of an analyzer grating, the shifting curves are still existent in theory as long as the number of fringes is non-integral in a detector pixel, which is a sufficient condition for creating shifting curve. The sufficient condition is available for not only the Talbot–Lau interferometer and the inverse geometry of Talbot–Lau interferometer, but also the x-ray phase contrast imaging system based on geometrical optics. In practical applications, we propose a method to improve the performances of the existing systems by employing the sufficient condition. This method can shorten the system length, is applicable to large period gratings, and can use the detectors with large pixels and large field of view. In addition, the experimental arrangement can be simplified due to the lack of an analyzer grating. In order to improve detection sensitivity and resolution, we also give an optimal fringe period.We believe that the theory and method proposed here is a step forward for x-ray phase contrast imaging.     

Characteristics of a three-mirror interference system with a noninverted response function in reflected light

It is demonstrated that a reflection interferometer with optical properties of a three-mirror system in transmitted light can be created by including a phase grating in the structure of an input mirror. The response function is determined, a technique for the selection of parameters for the formation of spectral characteristics of the reflection coefficient is considered, and results of calculations are presented.     

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     

A reflection interferometer with a noninverted response function based on a phase grating

It is shown that the inclusion of a simple phase grating in the optical scheme of a resonator provides the possibility of performing spectral investigations in reflected light with characteristics of a Fabry-Perot interferometer. The response function of the interferometer is examined, and experimental results are presented.     

Phase-difference amplification using a Sagnac interferometer

In this paper, we describe a new method for achieving phase-difference amplification, which is quick and convenient, operates in real time, and requires no photographic steps. Magnification factors of 2, 4 or 6 are achieved easily in one step. Because the system operates in real time, phase stepping may be applied to extract the amplified phase distributions. Our method is a variation on longitudinally reversed shearing interferometry, using first- or higher-order diffraction from a grating (hologram) which is in fact the interferogram of the wavefront under test. The grating is derived from a standard two-beam interferometer which is phase-stepped, and displayed in real time on a spatial light modulator in the phase-difference amplification setup. It is illuminated by the two output beams from a Sagnac interferometer, similar to the set up used by (Barnes et al. Barnes TH, Eiju T, Matsuda K. Appl Opt 1986; 25:1864). for spectral resolution enhancement, and a phase-amplified fringe pattern is obtained by spatial filtering using a Fourier transform lens. We demonstrate operation of the phase amplifier and show amplified phase maps retrieved by phase-stepping. We believe this is the first time that real-time phase amplification without photographic steps and with phase stepping has been demonstrated.     

一种用于动态过程测量的实时偏振相移方法

利用一种特殊的相位龙基光栅和偏振相移技术,可同时获得四幅具有不同相移的干涉图,由此可计算出被测物体的全场相位分布,从而实现对支态过程相位的测量。将该方法应用于马赫－曾德尔干涉系统的散斑干涉系统,分别测量了液体的折射率变化和固体的离面位移,给出了实验结果。     

带有对称啁啾光纤光栅的Sagnac环滤波器

通过在光纤Sagnac环中引入对称啁啾光纤光栅,对带有光纤光栅的Sagnac环梳状滤波器进行了改进,克服了原有滤波器工作带宽小、通带间隔不等的缺点.通过对光栅参量进行适当设计,在中等折射率调制度下,可使光栅同时具有高反射率和大反射带宽,结合Sagnac环可得到大带宽、等间隔梳状滤波器.     

In-plane ESPI using an achromatic interferometer with low-coherence laser source

The use of an achromatic interferometer is explored as a means of doing in-plane ESPI measurements using a laser diode as the light source. This interferometer type, which uses a diffraction grating in place of the conventional beamsplitter, has two features that make it suitable for making ESPI measurements over extended areas, even when using a low-coherence laser diode source. First, the parallelogram optical geometry of the interferometer causes all rays passing through to have the same optical path lengths. Second, the interferometer is achromatic, whereby the piezo-actuated mirror that steps the illumination light does so by the same phase angle, independent of wavelength. This latter feature accommodates the spectral impurity of a laser diode source. A periodic variation of fringe visibility is observed in experiments, where narrow ranges of high visibility occur at regular spatial intervals. This behavior derives from the clustered discrete spectral character of laser diode light output. A method to “tune” the interferometer by slightly rotating the diffraction grating is described so as to achieve consistent high fringe visibility throughout the measured images.     

空域移相偏振点衍射波前检测技术

点衍射干涉仪结构简单、共光路、测量精度高, 空域移相干涉仪抗振性能优越, 两者在波前检测领域获得了广泛的应用. 本文采用激光打孔技术, 通过在金属纳米线栅偏振片上制备小孔, 制作了偏振点衍射板; 结合分光结构的空域移相技术, 搭建了空域移相偏振点衍射干涉仪, 并对一焦距为550 mm, F_#10的平行光管准直物镜透射波前进行测量, 与法国Phasics公司生产的商业化波前传感器SID4的测量结果相比较, 两者峰谷值相差0.09λ, 均方根值相差0.012λ ; 利用35项Zernike多项式拟合两者的测量结果, 将拟合得到的系数在同一坐标轴下绘制成两条曲线, 两者基本重合, 从而验证了所搭建的空域移相偏振点衍射波前检测装置的测试精度. 从而在传统点衍射干涉仪的基础上引入了空域移相技术, 实现了波前的高分辨率、高精度、实时检测, 并且提高了对振动、气流等环境因素的抗干扰能力.     

Diffraction grating interferometers for mechanical characterisations of advanced fabric laminates

It is demonstrated that two grating interferometers with high spatial resolutions can successfully be applied for the mechanical characterisation of the advanced fabric composite materials. Based on these two techniques, the mechanical properties of two kinds of fabric laminates are obtained without assumption of uniform strain fields to be used in the characterisation approaches using the local strain sensors. The degree of the yarn crimp effects of the two laminates is compared in terms of the out-of-plane displacement derivatives. Especially, it is shown that the grating shearing interferometer is appropriate for the crimped fabric structure requiring a three-dimensional analysis. The modification from moiré interferometer to grating shearing interferometer is performed by introducing a Michelson interferometer modified for image shearing.