Multi-directional lateral shearing interferometer based on rotatable prism pairs

The common camera lens usually includes the spherical glass/plastic lens and aspheric glass/plastic lens. However, spherical/aspheric shape measurement is still a key problem in the process of optical lens fabrication. At present, the in-process measurement of spherical/aspheric shape is conducted mainly by the probe-contacting method. But after a long time, its probe could be scratched severely and cause some big errors. Laser shearing interferometry is a good substitute to some degree. Nevertheless, it is not convenient for general shearing interferometer to carry out the in-process measurement because it is only suitable for certain kind of spherical/aspheric with respect to aperture or asperity. Here a new lateral shearing interferometer is proposed to solve the described problems. It is based on two Jamin plates and rotatable prism pairs which are used not only for shearing displacement and direction, but also for fringe period and tilt degree, in order to meet requirements of various spherical/aspheric shapes or asperities. The new interferometer features a simple optical structure and two symmetric light paths, which makes its system with minimal error. The relation between shearing displacement, fringe period and prism angle of rotation is given in this paper. And the error source is primarily from the manufacture errors of prisms and plates. The final experiments show that one can achieve good-quality fringe patterns according to the requirement of measurement, concerning the shearing direction, shearing displacement, fringe period, tilt degree, etc.     

A simple electronic speckle shearing interferometer

A new speckle shearing interferometer with simple setup is proposed. The interferometer can be converted easily from a speckle referenced speckle pattern interferometer into a speckle shearing interferometer and vice versa. A beamsplitter and a mirror are used to generate the shear. The amount of shear can be adjusted by simply rotating the mirror. The costs involved are low and it is particularly useful for fast inspection in non-destructive testing of structural integrity. Both the theoretical studies of the method of measurement and the experimental results are presented.     

A new lateral shearing interferometer for precision surface measurement

A new lateral shearing interferometer is proposed for precision surface measurement. In this shearing interferometer, a novel shear generator made of a single birefringence crystal plate is utilized. The shear adjustment is realized through the change of angle at which tested wavefront is incident into the crystal plate. By changing the orientation of the principal section of the plate, the generator can adjust the shearing direction. With the incident beam being circularly polarized, the generator can equalize the intensities of two shearing beams to make a good contrast interference pattern. The interferometer is simple and compact in terms of mechanism and has a complete common optical path structure. Phase shifting can be realized conveniently. The interferometer is insensitive to external vibrations and environmental disturbances, and hence has good stability and reliability with high measurement accuracy. To examine the performance of the proposed interferometer, experimental testing was conducted. High accuracy and repeatability are demonstrated.     

Simple versatile shearing interferometer suitable for measurements on a microscopic scale

Micro-electromechanical systems (MEMS) behave differently from massive samples. Conventional testing and inspection techniques usually fail at the microscale. Recently there has been an increasing interest in the application of optical techniques for microstructure testing, because they are high-resolution, non-contact, full-field, fast and relatively inexpensive. New interferometric systems, which are suitable for microscopic optical metrology, are of interest for engineering and industrial applications.A modified electronic speckle pattern shearing interferometer (ESPSI) with a very simple shearing device has been designed for metrology applications on the microscale. The shearing device consists of two partially reflective glass plates. The reflection coefficients of the coatings are 0.3 and 0.7, respectively. The distance and the tilt between the two glass plates control the size of the shear. A long working distance microscope objective is attached to the CCD camera to form a field of view variable over several millimetres in width. The suitability of the system for microscopic measurements is demonstrated. The capability of the system for phase shifting is also demonstrated. The results obtained are promising for future applications of the ESPSI system for testing and characterisation of MEMS.     

Polarization phase-shifting lateral shearing interferometer with two polarization beam splitter plates

We proposed a compact and simple polarization phase-shifting lateral shearing interferometer using two polarization beam splitter plates (PBSP). This interferometer is composed of two PBSP, a quarter-wave plate, an analyzer and a CCD camera. With the two PBSP positioned in appropriate spatial positions, optical path difference compensation is achieved, which allows for the implement of aplanatic and common-path shearing interferometer. Therefore, the system possesses significant advantages of simple structure, compact and strong anti-interference ability. The effectiveness of the interferometer is demonstrated by simulations and experiments.     

相干合成子光束一致性检测研究

分析了激光相干合成装置及其光路调整要求,提出利用剪切干涉检测合成光路中子光束一致性的方法。分析剪切干涉原理,建立了剪切板干涉物理模型,以相干合成中两路矩形光束拼接组束为例,数值模拟并研究了子光束的整体倾斜、离焦所对应的剪切干涉条纹,得到了条纹图像与子光束光轴误差、离焦误差之间的对应关系,用于相干合成光路中子光束光轴和发散角误差的判断。光轴倾斜大于5μrad时,可以直接观察互干涉和自干涉条纹变化,发散角在大于10μrad时,干涉条纹变化明显。此外,剪切干涉的自干涉条纹平移可用来检测子光束间的活塞误差,可作为光束拼接相干合成中闭环相位检测和控制的手段。     

Analysis of Digital Lateral Shearing Interferometer

A new method is proposed for reconstructing wavefront from discretely sampled interferogram data obtained by a digital lateral shearing interferometer. Assumptions applied in the conventional methods are not used and reconstruction error caused by the difference between the amount of shear and the sampling interval can be removed. System error and the influence of the discrete sampling, which limit accuracy of the tested results of the lateral shearing interferometer, are analyzed.     

Polarization phase-shifting Jamin shearing interferometer

The Jamin shearing interferometer is very useful in wavefront testing, especially for the low coherent light. Based on this interferometer, a polarization phase-shifting Jamin shearing interferometer is proposed to improve the performance. In the interferometer, two interference beams are linearly polarized and a polarization phase shifter is applied to realize the phase shifting. Different types of configurations of the interferometer are given. With phase-shifting interferograms, the precision of the interferometer can be improved. The interferometer is kept as an equal optical path system and its shearing amount remains changeable with simple structure and easy operation. In experiments, phase-shifting interferograms are obtained by rotating the analyzer. The usefulness of the interferometer is verified.     

马赫-曾德尔型相移矢量剪切干涉仪

为了实现对激光波面的等光程测试,设计了一个新颖的相移矢量剪切干涉仪。该干涉仪以马赫曾德尔结构为基础,为等光程干涉仪。通过在相干的两路光束中分别插入楔角方向正交放置的楔板实现矢量剪切;其中一块楔板分成两块(平板部分和楔板部分),楔板部分沿平板部分的表面移动,通过改变光程差来实现相移,2π相移所需的移动距离为几毫米的量级,该相移方法在相移精度控制上比较简单。文中还对楔板引入的横向剪切误差和相移误差进行了分析,最后给出了实验所得的一组相移干涉图。     

Spatially incoherent Fourier digital holography by four-step phase-shifting rotational shearing interferometer and its image quality

Spatially incoherent Fourier digital holography using a rotational shearing interferometer for four-step phase-shifting method is proposed. The previous incoherent Fourier holography using a rotational shearing interferometer [Watanabe and Nomura (Appl. Opt. 54:A18, 2015)] employs the two-step phase-shifting method in the vertical and horizontal polarizations. The reconstructed image contains a large bias term. This paper proposes introduction of two kinds of wave plates in one path of a rotational shearing interferometer for a four-step phase-shifting method. A Fourier hologram is obtained from the four recorded holograms for eliminating the bias term and the twin image. The numerical simulation and the optical experiment demonstrate improvement of the image quality of reconstructed image by the twin image and bias level reduction. Furthermore, the effect of the size of an image sensor on the image quality in rotational shearing interferometer is also investigated by the numerical simulations.     

Collimation testing of a CO2 laser beam with a shearing interferometer

A shearing interferometer based on a Michelson interferometer is proposed for collimation testing of a CO₂ laser beam. The shear and tilt between the interfering wavefronts is obtained by replacing one or both mirrors of the Michelson interferometer with double mirrors arranged to act as 90 ° or near 90 ° prisms in retroreflecting mode. Detailed analysis for two experimental configurations of this system are presented.     

Step index fibre using laser interferometer

A model is suggested to describe the fringe shift which occurs due to the phase variations of cladded glass fibre introduced between the two plates of the liquid wedge interferometer illuminated with a He–Ne laser. The fringe shift of the phase object which appears in the denominator of the Airy distribution formula of the multiple beam interference is represented in the harmonic term. An experiment is conducted using liquid wedge interferometer where the step index glass fibre of a nearly quadratic thickness variation is introduced between the two plates of the interferometer. The obtained fringe shift shows a good agreement with the proposed quadratic model. The Matlab code is written to plot the interferometer fringes comprising the shift of the step index fibre. Secondly, recognition of elliptical fibres is outlined using tomographic imaging. Finally, results and concluding remarks are given.     

基于波长移相剪切干涉的准直波前重构技术

为了实现干涉仪出射准直波前的重构，提出了基于波长调谐移相的横向剪切干涉技术。干涉仪出射波前分别经楔板的前后表面反射，通过角锥棱镜返回后在干涉仪CCD上形成剪切干涉条纹。采用波长移相方法提取剪切干涉条纹的相位信息从而实现准直波前重构。分析相对剪切比对波面重构精度的影响，推导相对剪切比和其影响因素间的关系公式，给出波长移相中光程差常数分量的估算方法。测量干涉仪的三组出射波前，波前的峰谷值分别为3.22λ、2.10λ、0.83λ。该方法简化了传统测量干涉仪准直波前的横向剪切干涉装置，提高了测量精度，特别适合于测量波长移相干涉仪的出射波前。     

Phase-shifting lateral shearing interferometer with two pairs of wedge plates

We present a compact and robust phase-shifting lateral shearing interferometer that produces shearing fringes in orthogonal directions without any mechanical rotation or precise alignment. It consists of two pairs of wedge plates, a beam splitter, and a single CCD camera. Both phase-shifting and tilt for lateral shearing are achieved with two pairs of wedge plates, which can reduce systematic errors caused by external vibration and atmospheric disturbance.     

Photopolymer diffractive optical elements in electronic speckle pattern shearing interferometry

In this paper we present an electronic speckle pattern shearing interferometer using a photopolymer diffractive optical element in the form of a holographic grating, in combination with a ground glass to shear the images. The sheared images on the ground glass are further imaged onto a CCD camera. The distance between the grating and the ground glass can be used to control the shear and to vary the sensitivity of the system. The direction of sensitivity is easily controlled by rotation of the diffraction grating around its normal.Introducing photopolymer holographic gratings in ESPSI gives the advantage of using high aperture optical elements at relatively low cost. The fact that the diffractive optical element is a photopolymer layer on glass substrate with thickness of 2 mm makes for a compact optical system.The system was successfully used for detection of the resonant frequencies of a vibrating object.Most of the published work on vibration analysis is analytical. Very few experimental results are available in the literature. The well known laser Doppler vibrometers (LDV) and accelerometers used for modal analysis are pointwise measurement techniques, although multipoint LDV is available at significant cost.Electronic speckle pattern techniques suitable for experimental detection of the resonant frequencies of vibrating objects are very promising for vibration analysis because they are whole field and non-contact.A finite element model is developed for prediction of the vibration modes of the object under test. Detection of vibrational modes of aluminium diaphragm is demonstrated and compared with the theoretical model. The results obtained are very promising for future application of ESPSI systems with HOEs, for modal analysis. A significant advantage of shearography over electronic speckle pattern interferometry is that ESPSI is relatively insensitive to external disturbances. Another advantage of the proposed system is that it could be easily converted to a phase-shifting electronic speckle shearing interferometer.     

软X射线双频光栅剪切干涉法研究

本文中设计了一种利用软X射线双频光栅作为剪切干涉元件的剪切系统, 使剪切干涉法在软X射线波段得到了应用. 介绍了软X射线双频光栅的结构及衍射特性, 在同步辐射光束线对双频光栅的效率分布进行了测试实验, 两个剪切级次的效率比值高于75%, 干扰级次效率低于5%. 利用软X射线双频光栅为剪切干涉光学元件, 对待测靶进行了静态检测, 得到了对比度高, 稳定的干涉条纹, 验证了该方法在软X射线等离子体密度诊断中的可行性. 关键词： 双频光栅 剪切干涉仪 软X射线 等离子体诊断     

Shearing interferometer using low-coherent light source and calcite prism

A shearing interferometer using a low-coherent light source and calcite prism is proposed in this paper. The calcite prism is the shear plate that generates sheared wavefronts with optical-path difference induced only by the contour of the specimen. Low-coherent light source is thus available while the interferometer is adopted for contour derivative determinations. The design of this interferometer is introduced, a setup constructed to realize the interferometer is described, and the experimental results from the uses of the setup are finally presented.     

A 180° rotation shearing interferometer with increased optical efficiency

Use of a rotating wedge-shaped mirror rather than a rotating prism gives a higher throughput rotation shearing interferometer. The new interferometer has polarization problems if the shear differs from 0° or 180°. However, for the commonly used 180° shear, the new interferometer offers a 4-fold reduction in time required for observations employing short-exposure sequences.     

大孔径静态干涉成像光谱仪中双通道Mach-Zehnder横向剪切干涉仪的设计

大孔径静态干涉成像光谱技术是一种时空联合调制的傅里叶变换成像光谱技术,其核心元件通常采用Sagnac横向剪切干涉仪。这种结构会使进入干涉仪的光线有一半沿原路返回,降低了能量利用率。文章提出一种改进型Mach-Zehnder横向剪切干涉仪结构,克服了能量利用率低的缺点,在实现横向剪切的同时,还具有双通道输出的优点。本文通过光线追迹的方法,得到剪切量的一般表达式,并分析了各种误差源对剪切量误差的贡献。为大孔径静态干涉成像光谱仪的设计提供了新思路,可为该类型的成像光谱仪的设计与优化提供理论指导。     

Broadband light source shearing interferometer using Savart plate and angular scanning technique

A shearing interferometer based on using broadband light source, Savart plate, and angular scanning technique is proposed for slope contour measurements in this Letter. Of which, the Savart plate divides the wavefront reflected from the detected surface into two laterally displaced ones, the interference pattern generated by the interference of the divided wavefronts is modulated by an envelope function, and the slope contour of the detected surface is determined by examining the shifting of the darkest fringe as the shear plate is angularly scanned. A setup for realizing the interferometer is constructed. The experimental results of using this setup agree the validity and feasibility of the proposed interferometer.