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。     

Measurement of wedge angle of a transparent parallel plate using quasi-monochromatic light source and phase shifting interferometry

A new technique (to our knowledge), for the measurement of residual wedge angle (RWA) of high optical quality transparent nearly parallel plate (PP), using a quasi-monochromatic light source, is presented. Advantages and drawbacks of the technique and the results obtained for a PP, using a filtered white light source, is discussed. A slightly modified optical setup for accurate determination of RWA, using phase shifting interferometry (PSI), has been described. Results obtained, applying PSI, for a validation experiment and for the determination of RWA of a quasi-PP is presented. The PSI based technique does not suffer from any measurement ambiguities due to limitation in effective beam aperture. Hence the technique is suitable for high accuracy measurement of RWA of PP. In both the optical setups, presented in this paper, the respective interfering beams travel the same optical circuit and are thus subject to same perturbation in optical path, due to external mechanical vibration, which finally cancels out. Thus the measurements are much less affected by external vibrations. Since the respective interfering beams undergo identical reflections and transmissions, the visibility or contrast of the interference fringes is very good.     

Lensmeter using a lateral shearing interferometer

The use of a laser shear interferometer for checking the collimation condition within a lensmeter is proposed. The interferometer consist of a wedged glass plate which produces a shear along the orthogonal direction to the wedge; when the fringes at the center of the pattern are parallel to the shear, the collimation condition is attained. The feasibility of the proposal for measuring the vertex power is experimentally shown and the accuracy of the method is under 5% of the measured value being an improvement to the commercial instruments based on the focusing of a reticule.     

Optical refractometry based on Fresnel diffraction from a phase wedge

A method that utilizes the Fresnel diffraction of light from the phase step formed by a transparent wedge is introduced for measuring the refractive indices of transparent solids, liquids, and solutions. It is shown that, as a transparent wedge of small apex angle is illuminated perpendicular to its surface by a monochromatic parallel beam of light, the Fresnel fringes, caused by abrupt change in refractive index at the wedge lateral boundary, are formed on a screen held perpendicular to the beam propagation direction. The visibility of the fringes varies periodically between zero and 1 in the direction normal to the wedge apex. For a known or measured apex angle, the wedge refractive index is obtained by measuring the period length by a CCD. To measure the refractive index of a transparent liquid or solution, the wedge is installed in a transparent rectangle cell containing the sample. Then, the cell is illuminated perpendicularly and the visibility period is measured. By using modest optics, one can measure the refractive index at a relative uncertainty level of 10(-5). There is no limitation on the refractive index range. The method can be applied easily with no mechanical manipulation. The measuring apparatus can be very compact with low mechanical and optical noises.     

Parallel Plate Interferometer with a Reflecting Mirror for Measuring Angular Displacement

A parallel plate interferometer with a reflecting mirror for measuring angular displacement is proposed. A deflection angle of a beam caused by an angular displacement is amplified by use of a reflecting mirror to increase the optical path difference (OPD) in the plane-parallel plate, which provides high sensitivity of the phase measurement. Detection of light transmitted through the plane-parallel plate with a position sensitive detector (PSD) enables high accurate measurement of the initial angle of incidence to the plane-parallel plate with insensitivity to stray light. The improved parallel plate interferometer achieves a measurement repeatability of 10⁻⁸ rad.     

Improvement of accuracy of interferometric measurement of wedge angle of plates

A method is proposed for improving the accuracy of measuring the wedge angle of transparent plates using a lateral-shear holographic interferometer. Consecutive processing of a pair of interferograms with doubled number of interference fringes leads to reduction of the observational error by a factor of two compared to traditional interferometric methods. Data on the experimental validation of the method are presented.     

Multi-frequency lateral shear interferometer system for simultaneous measurement of thickness and three-dimensional shape

This Letter demonstrates a novel lateral shear interferometer system for simultaneous measurement of three-dimensional(3D) shape and thickness of transparent objects. Multi-frequency fringe patterns can be created by tilting mirrors at different inclination angles. With a single camera, the multi-frequency fringes are recorded in one image. The phase-shift of the fringes can be generated synchronously only by moving a plane-parallel plate along an in-plane parallel direction. According to the feature of transparent materials, the thickness and 3D shape can be reconstructed simultaneously based on the relationship between the in-plane displacement and their characteristics. The experiment was conducted on a thin transparent film subjected to a shearing force,which verifies the feasibility of the proposed system.     

Direct measurement on transparent plates by using Fizeau interferometry

It is shown that Fizeau interferometry provides an accurate optical method to measure the refractive index and wedge angle of transparent plates used as optical components in different experiments. A near IR external cavity diode laser having spectral resolution up to 10⁻⁷ has been employed to measure the refractive index of the test plates by introducing amplitude modulation technique in the detection system of our phase shifting Fizeau interferometry. Detection of spatial fringes has been performed to find out the wedge angles of the plates by using a He–Ne laser along with the CCD-image sensor.     

等光程干涉仪中参考镜楔角最优补偿方式研究北大核心CSCD

在测量多表面平行样品时,多面干涉会影响测量结果。为了能改善多面干涉问题,介绍了等光程干涉仪,并研究了参考镜楔角的最佳补偿方式。在等光程干涉仪中,由于参考镜和分光镜的楔角和倾角的存在,测量结果中会带有回程误差。根据参考镜楔角的不同情况采用了不同的补偿,理论分析并确定了各种补偿的放置方式和补偿量,同时研究了倾角和楔角的大小对于要被遮拦光束高度和像方数值孔径NA的影响。再利用Zemax进行不同补偿方式下的干涉仪仿真,并根据仿真得到的干涉图PV值分析回程误差的大小。分析表明:选用最佳补偿方式,参考镜楔角为1′,回程误差优于0.003个波长。     

Demonstration for a two-axis interferometric tilt sensor in KAGRA

Recently, a folded Mach–Zehnder interferometer with homodyne in- and quadrature-phase detection was proposed as a high-precision, wide-dynamic range tilt sensor. By way of a practical application and to validate actual performance, two-axis tilt sensors were developed and installed for one mirror of the input mode cleaner cavity in KAGRA, the large-scale cryogenic gravitational-wave telescope in Kamioka, Gifu, Japan. Building on previous work, we have demonstrated that the two-axis tilt sensor has properly sensed the tilt angle changes of the mirror motion with high precision and without calibration. Compared with our initial angular sensor, an optical lever, which is calibrated by using the interferometer tilt sensor, we found that both sensors showed actual tilt motions of the mirror at low frequencies, and the two-axis interferometer sensor has a better sensitivity at higher frequencies.     

非接触法自动测量薄膜厚度

根据白光等厚干涉原理,基于单片机改造的迈氏干涉仪用于自动测量透明薄膜厚度,采用非接触性测量法。当迈克尔逊干涉仪静镜形成的虚像与动镜相交所成的夹角很小时,在光屏上看到彩色干涉条纹,插入薄膜后,光程差改变,彩纹消失。步进电机带动微调手轮转动,当彩纹再次出现,即可得出透明薄膜厚度。     

Measurement of tilt of a diffuse object by double-exposure speckle photography using speckle fanning in a photorefractive BaTiO3 crystal

A technique has been proposed for the measurement of tilt of a diffuse object using speckle fanning in a photorefractive BaTiO₃ crystal. Free space geometry has been used for recording in which the axis of rotation of the object lies away in three-dimensional space. The method is based on recording of two exposures, one before- and another after the tilt, thus producing speckle correlation fringes due to overlapping of two speckle fans. We consider a generalized case of tilt, generating curved fringes with center shifted in the transverse direction. The axis of rotation lies perpendicular to the optical axis in three-dimensional space having the transverse and axial components of the shift in the center of rotation with respect to the diffuser plane. Fourier transform of the curved fringes produces correlation output. Measure of separation between the correlation peaks in transverse and axial directions provides information about the tilt angle, the direction of tilt, and the distance of rotation axis from the optical axis. Experimental results have been presented to validate the theoretical predictions.     

Effect of decoherence of optical field with broad angular spectrum upon propagation through transparent media interfaces

The effects of the decoherence of a narrow-band optical field with a broad angular spectrum upon propagation through a plate of a transparent medium placed in one of the arms of the Michelson interferometer are established.     

Determination of ordinary and extraordinary refractive indices of nematic liquid crystals by using wedge cells

A new accurate and fast interference method for determining ordinary and extraordinary refractive indices of nematic liquid crystals is presented and discussed. The method relies on microscopic measurements of distances between interference fringes appearing in polarised parallel coherent monochromatic light beam transmitted normally to the surfaces through a wedge cell filled with a nematic. Both glass plates confining the cell are coated with a partly transparent thin film of metal which is deposited by evaporation in vacuum. Owing to the multiple reflections between the surfaces and a small edge angle, the interference fringes observed near the wedge apex edge are sharp and equidistant. To apply this method one needs only small amount of an investigated liquid crystal. Basic mathematical formulae and results of an experiment are briefly discussed.     

卡塞格林系统装调过程中高精度测角方法

为了能够准确测量同轴三反相机中次镜的倾斜量变化,提出一种新的角度测量方法,即用大口径干涉仪与经纬仪相结合进行测量。以主镜为测量基准,两镜相对倾角较小时,使用大口径干涉仪同时测量两镜的干涉条纹,相对倾斜角度过大时次镜无干涉条纹,加入一台经纬仪分别自准直于干涉仪和次镜,间接测量两镜相对夹角。通过模拟计算与实验验证表明,对于次镜组件倾角测量误差可以控制在0.5″以内。结果表明,该检测方法具有通用性强,测量精度高等特点,克服了传统检测方法测量精度不足的问题。     

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.     

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.     

Simultaneous measurement of surface shape and absolute optical thickness of a glass plate by wavelength tuning phase-shifting interferometry

The absolute optical thickness and the surface shape of a glass plate of 7-in. square and 3.1mm thick was simultaneously measured by three-surface interferometry using a wavelength tuning Fizeau interferometer. The wavelength of a tunable diode laser is scanned linearly from 632 to 642 nm, at which the initial and the final phases of the interference fringes for the surface shape and for the optical thickness were separated and measured by a tunable phase-shifting technique. The number of phase variations in the interference fringes during the scanning is counted by discrete Fourier analysis, in which systematic errors caused by a nonlinearity in the wavelength scanning is corrected by a correlation analysis between the observed and theoretical interference fringes. Experimental results demonstrate that the systematic errors in the measured value were 15 nm for the surface shape and 0.6 μm for the absolute optical thickness.     

Theory of the Fabry-Perot interferometer with nonparallel reflectors

Taking into account the wave structure of the light beam, determined by diffraction theory, we consider the harmful effect of the inclination of the mirrors of a Fabry-Perot interferometer when fringes of equal inclination are being observed. It is found that the contrast and resolution of the fringes of equal inclination are reduced as the angle of the wedge so formed is increased, and the interferometer (resonator) completely loses its high-resolution capability (Q-factor) when the mirrors deviate from parallelism by an angle equal to half the diffraction angle at its aperture. The advantages of stopping down both the incoming and outgoing beams in improving the contrast and increasing the resolution of the fringes of equal inclination are pointed out.The author thanks Professor F. A. Korolev for his interest.     

一种用激光干涉测量光波波长的新方法

提出了一种利用激光干涉仪测量光波波长的方法。通过改变在光的传播路径上垂直放置的透明玻璃与光传播方向的角度,使相干光的光程差发生变化;利用干涉条纹与转过角度、透明玻璃厚度之间的关系,通过激光干涉实验能准确测量出光波的波长。