Thickness and Surface Profile Measurement by a Sinusoidal Wavelength-Scanning Interferometer

We propose a sinusoidal wavelength-scanning interferometer for measuring thickness and surface profile of a thin film. The interference signal contains phase modulation amplitude Z and phase $aL which are related to the positions and profiles of the reflecting surfaces, respectively. By reducing the difference between the detected signal and the estimated signal using the multidimensional nonlinear least-squares algorithm, we estimate values of Z and $aL. Experimental results show that the front and rear surfaces of a silica glass plate of 20 $mUm-thickness could be measured with an error less than 10 nm.     

Multiple-surface testing by a wavelength-scanning interferometer for refractive index inhomogeneity measurement

Wavelength-scanning interferometers can separate the multiple interference signals generated by several reflecting surfaces in the frequency space. Optical thickness variations of a three-layer object and its top surface shape were measured simultaneously by a wavelength-scanning Fizeau interferometer. An efficient sampling window for the phase detection has been derived that can compensate for the frequency detuning of the interference signal and suppress the cross talk from noise components in other frequencies. From the experimental results, the refractive index variation of a glass plate was calculated with an accuracy of ∼1 ppm, which is equivalent to several tens of nanometers in optical thickness variations. The text was submitted by the authors in English.     

Test of a four plate neutron interferometer

A monolithically designed four plate perfect crystal interferometer was tested. The experimental results were compared to calculated interference patterns based on plane wave theory. Inside the four plate system are three independent interferometer loops which permit the definition of three effective phase shifts and determine the intensity modulation behind the interferometer crystal. Absorbing phase shifters cause a partial beam path detection and, therefore, influence the interference pattern by their individual location. Several features of multiplate interferometry and a modified phase echo system are discussed.Dedicated to Professor Dr. Ulrich Bonse on the occasion of his 60^th birthday     

Phase-Measuring Algorithms to Suppress Spatially Nonuniform Phase Modulation in a Two-Beam Interferometer

Phase modulation of presently used phase-shifting interferometers is assumed to be spatially uniform across the observing aperture. However, calibration errors or the configuration of an interferometer can cause a spatial nonuniformity in the phase modulation. Spatial nonuniformity causes a significant error in the measured phase when the phase modulator has nonlinear sensitivity. An even-order nonlinearity in the phase modulation in particular contributes to the errors. Lowest-order errors can be suppressed by adding a new symmetry to the sampling functions of the phase-shifting algorithm, however the algorithm suffers from large random noise. The random noise is shown to be decreased substantially by applying one more sampled frame to the algorithm. We derive new seven-sample and eight-sample algorithms that can compensate for a nonuniform phase shift and has much less random noise than the previous algorithm we proposed.     

Double sinusoidal phase modulating laser diode interferometer for thickness measurements of transparent plates

A double sinusoidal phase modulating (SPM) laser diode interferometer for thickness measurements of a transparent plate is presented. A carrier signal is given to the interference signal by using a piezoelectric transducer, and the SPM interferometry is applied to measure the thickness of a transparent plate. By combining the double-modulation technique with the Bessel function ratio method, the measurement error originating from light intensity fluctuations caused by the modulation current can be decreased greatly.The thicknesses of a glass parallel plate and a quartz glass are measured in real time, and the corresponding experimental results are also given.     

点衍射干涉检测技术

本文介绍了点衍射干涉仪不同发展阶段的特点和应用。点衍射干涉仪由波长量级的针孔产生高质量的球面波作为参考波前,能够得到衍射极限性能的分辨率。按照不同的光路特点,点衍射干涉仪可分为点衍射共路干涉和点衍射非共路干涉两种结构,主要应用于高精度波前检测和面形检测。共路干涉结构简单紧凑,对环境振动不敏感,对光源相干度要求不高,可利用光束偏振态及光栅衍射分束的特性对传统点衍射板进行改造,在全共路点衍射干涉仪中引入时间相位调制技术和干涉对比度可调技术,可进一步提高波前检测精度。采用反射式针孔和各种光纤结构发展了非共路点衍射干涉仪,实现了大口径、高精度球面反射镜面形的测量。本文重点阐述了用于极紫外光刻投影物镜中高精度球面反射镜面形检测的反射式针孔点衍射干涉仪,并展望了点衍射检测技术在生物检测等领域的应用前景和发展趋势。     

Phase synthesis of a holographic metrological diffraction grating of unlimited length

A breakthrough in the technology of measuring systems of submicrometre and subsecond precision was made possible by the invention of holographic phase aperture synthesis of highly regular interference structures. The practical fulfilment of holographic phase aperture synthesis requires development of the following new optical methods: (1) synthesis of the aperture by out of phase auxiliary holographic diffraction gratings; (2) high-precision analysis of the phase structure of the interference field; (3) automatic control of the aperture synthesis process using two-frequency modulation of the interference field; (4) an adaptive interferometer for aperture synthesis. This paper is devoted to the above methods.     

Noise immune unwrapping based on phase statistics and self-calibration

Unwrapping is an important step for precise phase measurement in an interferometric technique. Due to the effects of noises and speckles, an accurate unwrapping has been quite difficult. To address this issue, a new phase unwrapping method is proposed. The new method uses the wrapped phase statistics together with the limited smoothness characteristics of the interference phase. In this method, statistical parameters of the wrapped phase are firstly obtained. The step is then followed by a self-calibration process to identify and correct corrupted data points to obtain preliminary unwrapped phases. Finally, a phase revision step is taken to remove the effects of the residual errors. A computational testing was carried out to demonstrate the performance of the proposed method at six different levels of noise injection. An experimental test was also carried out using a lateral shearing interferometer. The success and the precision achieved using the proposed algorithm show that the method is quite effective and accurate for phase recovery under the condition of noise contaminations.     

Fizeau型偏振移相干涉仪的实验研究

研究了一种Fizeau型偏振移相干涉仪。以中心波长为650nm的多纵模半导体激光器作为光源,利用光源的短相干特性和一套偏振延迟装置分出一对偏振方向正交的参考光和测试光,采用巴比涅-索列尔补偿器作为偏振移相器。测试了一块平行平板的前表面面形,面形PV值为0.0682λ,RMS值为0.0127λ。该方法的优点是移相精度高,移相时无须推动参考镜,适用于大口径光学系统的干涉测试,可消除多表面干涉杂散条纹的影响。     

Properties of a dielectric plate using entangled two-photon states

We theoretically study the properties of a dielectric plate with a modified Hong-Ou-Mandel interferometer. The fourth-order correlation functions are calculated in two regimes, which are divided depending on the relative size between the thickness of the dielectric plate and the one-photon coherence length. When the thickness of the dielectric plate is less than the one-photon coherence length, a novel modulation behavior of the coincidence rate is observed, which has not been discussed before. If the thickness of the dielectric plate is larger than the one-photon coherence length, coalescence and anti-coalescence are observed. The obtained results highlight the effects of a linear optical element on fourth-order interference.     

大剪切实时干涉系统的火焰条纹分析

使用平行平晶做分光元件建立了剪切量随平行平晶偏转角可调的横向剪切实时干涉系统,该系统在最佳偏转角下所得最大剪切量与平行平晶的厚度成正比。实验表明,当系统的横向剪切量大于被测火焰畸变波面宽度的一半时,剪切域中的非核心剪切区将出现半幅以上的双曝光条纹,以之进行干涉测温处理可以避开传统剪切干涉测量技术所必需的剪切相位还原算法。这意味着实时双曝光条纹可以简单地通过大剪切量横向剪切干涉系统得到。     

斩波式自适应移相干涉技术

研究对环境振动和空气扰动所造成的两相干光束间常数项光程变化不敏感的自适应移相干涉系统，利用偏振分光技术，采用闭环控制，并将高频振幅调制与锁相技术相结合，建立一斩波式自适应移相干涉系统，可对环境振动引起的干涉条纹的抖动进行实时探测并予以光程补偿，将干涉条纹依次锁定在与任意相位差相对应的位置,该方法不受两相干光束间光程差大小的限制且具有高信噪比，阐述了该方法的原理，描述了所建立的系统，并给出了实验结果。     

基于等厚干涉的环形子孔径检测中环带参数的计算方法

环形子孔径拼接检测技术是一种利用小口径干涉仪实现对大口径非球面检测的有效方法。检测过程中,需要多次改变干涉仪同非球面镜之间的距离,以得到不同环带的干涉条纹。以等厚干涉为基础,建立了环带数学模型,仿真分析了各个环带的理论参数,以及干涉仪同非球面之间的理论距离。结果表明,该模型可用于环形子孔径拼接的仿真计算,对实际检测过程具有很好的指导作用。     

Real time phase modulation measurements in liquid crystals

We propose real time phase measurements in liquid crystals cells using Young's interferometer constructed with a new principle with possibility to control the distance between two point sources. The optical interference optical pattern is detected by a bicell photo-detector in a back Fourier focal plane. A phase modulation controlled by a monopixel liquid crystals’ cell placed in a reference arm of interferometer is observed as a dynamic shift of the fringes’ pattern in spatial domain. Concept of signals’ demodulation in the Fourier focal plane will be described using a new approach to the demodulation signals. In this work we evaluate the demodulation condition of our setup and we present measurements of a dynamic phase response for nematic liquid crystals and antiferroelectric liquid crystals cells.     

High angle phase modulated low coherence interferometry for path length resolved Doppler measurements of multiply scattered light

We describe an improved method for coherence domain path length resolved measurements of multiply scattered photons in turbid media. An electro-optic phase modulator sinusoidally modulates the phase in the reference arm of a low coherence fiber optic Mach-Zehnder interferometer, at a high phase modulation angle. For dynamic turbid media this results in Doppler broadened phase modulation interference peaks at the modulation frequency and its multiples. The signal to noise ratio is increased by almost one order or magnitude for large modulation angles and the shape of the spectral peaks resulting from the interference of Doppler shifted sample waves and reference light is not changed. The path length dependent Doppler broadening is compared with the theoretical predictions in the single scattered and diffusive regimes. The experimentally measured optical path lengths are validated with the Monte Carlo technique.     

差分相移键控色散管理孤子多扰动系统的相位抖动

差分相移键控(DPSK)调制方式和色散管理孤子传输方式的结合能抵制噪声和非线性损伤,在高速(40 Gbit/s以上)多信道系统中具有突出的优点。采用变分法分析了多波长信道的放大自发辐射(ASE)噪声、信号间的非线性串扰(ISI)等多种扰动因素引起差分相移键控色散管理孤子系统的均方根相位抖动,给出了扰动的作用区域以及各扰动的大小。研究发现,放大自发辐射引起的抖动与传输距离成三次方的关系,而交叉相位调制(XPM)引起的抖动与距离近似成线性关系。通过优化选择色散管理图强度范围1.5~3.5,各种扰动得到了抑制,而以放大自发辐射扰动抑制为最大,此时要远低于交叉相位调制引起的抖动,然后分别是交叉相位调制-放大自发辐射扰动和交叉相位调制,从而波分复用系统主要来自于增加信道数这一客观限制。     

Sinusoidal phase-modulating laser diode interferometer insensitive to intensity modulation for real-time displacement measurement with feedback control system

In sinusoidal phase modulating laser diode (LD) interferometer, the injection current of the LD is sinusoidally modulated to realize the modulation of the wavelength. However, the light intensity of LD is also modulated, which affects the measurement accuracy. An all-fiber sinusoidal phase modulating LD interferometer for real-time displacement measurement is proposed where the influence of the intensity modulation is eliminated with a new algorithm. It is made clear that an optimal depth of the sinusoidal phase modulation (SPM) exists in the algorithm. Moreover, the SPM depth is locked at the optimal value by controlling the injection current with a feedback control system. The feasibility of the proposed interferometer for displacement measurement is verified by experiments.     

Small Deformation Measurements of Diffuse Objects: Phase Stepping by Frequency Drift of a He-Ne Laser

We describe a simple phase-stepping speckle interferometer with large path difference, in which phase modulation is achieved by thermal frequency drift of the He-Ne light source. This system is easy to set up, requires no specialised components, is immune from the effects of piezo actuator hysteresis, and is capable of producing phase maps in which the noise is less than 1/20λ.Presented at 1996 International Workshop on Interferometry (IWI ‘96), August 27-29, Saitama, Japan.     

Phase Measurement Algorithm in Wavelength Scanned Fizeau Interferometer

Wavelength scanned interferometry allows the simultaneous measurement of top surface shape and optical thickness variation of a transparent object consisting of several parallel surfaces. Interference signals from these surfaces can be separated in frequency space, and their phases are detected by discrete Fourier analysis. However, these signal frequencies are shifted from the detection frequency by the refractive index dispersion of the object and a nonlinearity of the wavelength scanning. The Fourier analysis is sensitive to the detuning of the signal frequency and suffers from the multiple-beam interference noise. Conventional error-compensating algorithms cannot be applied to an object consisting of more than three reflecting surfaces. We derive a new 2N-1 sample error-compensating algorithm, which allows the phase detection of any order of harmonic frequency among the interference signals. The new algorithm suppresses the effect of signal frequency detuning as well as the multiple-beam interference noise and can be applied to the measurement of complex objects consisting of more than three reflecting surfaces.     

透镜初级球差的横向剪切干涉条纹研究

利用玻璃平行平板构成简单的横向剪切干涉仪可以观察到单薄透镜形成的准直光束的剪切干涉条纹,由干涉条纹分布求出对应的几何像差和离焦量.用焦距为190 mm的单薄透镜做实验,实验结果与计算机模拟结果符合,说明可以从剪切干涉条纹的分布求出透镜的轴向调整误差和初级球差.