Measurement of surface figure of plane optical surfaces using Fizeau interferometer with wedge phase-shifter

A Fizeau interferometer-based set-up for measurement of surface figure of plane optical surfaces has been discussed. Phase-shifting interferometry has been applied using wedge phase shifter. Technique for elimination of system aberrations has been described. Results are shown for a plane surface.     

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。     

System error removal and structure optimization based on Fizeau interferometer

In the process of interferometric testing, the measurement result is influenced by the system structure, which reduces the measurement accuracy. To obtain an accurate test result, it is necessary to analyze the test system, and build the relationship between the measurement error and the system parameters. In this paper, the influences of the system elements which include the collimated lens and the standard surface on the interferometric testing are analyzed, the expressions of phase distribution and wavefront error on the detector are obtained, the method to remove some element errors is introduced, and the optimization structure relationships are given.     

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.     

Wavefront measurement with a phase-shifting lateral-shearing Sagnac interferometer operating in broadband light

A phase-stepping lateral shearing Sagnac interferometer for wavefront measurement is described. Phase shifting is implemented using a polarisation modulator operating on the wavelength independent Pancharatnam's phase allowing accurate measurement of phase maps even with broadband light. We demonstrate the interferometer by measuring a range of different wavefront shapes using both laser and white light.     

Multiple beam Fizeau interferometer with filtered frequency comb illumination

Real wedge interferometers of the Fizeau-type do not allow for fringes in case of a spectral broadband source - or in short: for white light fringes. Here, the use of a suitable frequency comb source will help to overcome this limitation on the one hand and on the other will offer the capability for enhanced phase sensitivity in high precision measurements of surface deviations. Frequency combs can be produced either by using a pulse train from a fs-laser or by passive filtering of the light emitted by a broadband source as a superlum-diode or a fs-laser. The frequency comb produced by a common fs-laser is extremely fine, i.e., the frequency difference of consecutive peaks is very small or the distance of consecutive pulses of the pulse train might be of the order of 1 m. Therefore, the pulse train produced by passive filtering of a broadband source is better adapted to the needs of surface testing interferometers. White light fringes are either applied for the profiling of discontinuous surfaces and/or can serve as an indication for the correct choice of multiplication factors in superposition interferometry. During the last decennium it became more and more clear that spatially incoherent sources provide better measuring accuracy in surface measurements due to the reduced influence of dust diffraction patterns. The advantage of laser illumination can nevertheless be maintained if the laser light is made spatially incoherent through moving scatterers in the light path. Here, we will discuss the application of spatially incoherent broadband light frequency filtered through a Fabry-Perot filter. The main applications are in the following fields: (1) surface profiling applications using two-beam Fizeau interferometers, (2) selection of single cavities out of a series of interlaced cavities, and (3) sensitivity enhancement for multi-beam interferometers for planeness or sphericity measurements. Some of the discussed possibilities will be experimentally demonstrated.     

Double domain wavelength multiplexed Fizeau interferometer with high resolution dynamic sensing and absolute length detection

In this work, we present a simple photonic instrument that has the ability of measuring positions, distances and vibrations with very high resolution by means of two Fizeau interferometers (FI), both using the same optical fiber end as a probe tip itself. On the one hand we have a time domain FI powered with a 1310 nm laser and monitored by an InGaAs detector providing displacement information with resolution around a tenth of nm but regardless of the absolute position of object and of the displacement sense. On the other, a spectral domain FI version based on a super luminescent source (SLED) centred at 800 nm with bandwidth of nearly 40 nm is analysed in real time by means of a digital spectrometer. Each spectrum is acquired in a very small time interval and provides information of both length of the cavity as well as its correct sense of evolution. Resolution of this system is lower than its complementary temporal case, but distance and sense measurements are absolute and can be determined successfully by adequate processing of spectral signal.Both interferometers are optically coupled to a single fiber optic probe and are wavelength modulated.Therefore, combination of both sensors results in a new one which allows the correct knowledge of an object or surfaces under test, i.e. a high resolution of displacement data plus its absolute position and true sense of movement.     

菲索干涉仪中精确移相的实现

为了实现移相式菲索干涉仪对光学元件面形的高精度测量,建立了干涉仪同步采集移相系统,并对精确移相方法进行了研究。介绍了移相系统的构成和工作原理,计算了测量过程中移相器的速度。针对PZT移相器在移相过程中会引入离焦误差,并存在加速段和减速段的问题,详细设计了移相器的行进过程。最后,对移相器的性能进行了标定。在改造后的干涉仪上开展了重复性验证实验,结果表明：干涉仪可以获得λ/11 340的RMS测量重复性。对改造后干涉仪与Zygo公司生产的Verifire XP/D干涉仪的测量精度做了比对实验,结果显示：相同元件下两者测量结果的面形RMS之差约为0.9 nm,表明提出的移相系统及移相方法在重复性和准确度方面都能满足纳米级面形测量的要求,为研制高精度移相干涉仪奠定了基础。     

Heterodyne interferometer with two spatial-separated polarization beams for nanometrology

An interferometer having accuracy in displacement measurement of <1 nm is necessary in nanometrology. To meet the requirement, the periodic nonlinearity mainly caused by polarization and frequency mixings should be less than deep sub-nanometer. In this paper, two spatial-separated polarization beams are used to avoid mixings and then the periodic nonlinearity. The developed interferometer demonstrates a periodic nonlinearity of about 25 pm and a 2 pm/Hz in displacement noise level.     

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.     

迈克耳孙干涉仪中附加光程差对干涉图样影响的讨论

用迈克耳孙干涉仪做物理光学实验,教学中出现了在常规中不能出现的奇异现象,本通过分析仪器中的附加光程差,对干涉图样形成的原因作了定性解释,并得出结论。     

Error analysis for a Mach-Zehnder type speckle interferometer

A phase shifting speckle interferometer based on a Mach-Zehnder geometry is presented. The displacement field is measured using an electro-optic phase shifting technique. An analytical investigation of the accuracy of the interferometer is performed by considering the most contributing error sources. It is shown that in the case of the use of a low power laser source, the geometrical aberration of the optical component is the main contribution to the systematic errors. The case of the sampling of a full measurement is investigated. It is demonstrated that the systematic error of the full measurement has the same statistics as those given by a simple acquisition. Experimental results are reported in the case of the measurement of the deformation of industrial connectors submitted to a crushing test. It is found that for a peak to valley of 32 μm, the trueness of the measurement appears higher than 160 nm.     

Polarization phase-shifting interferometer by rotating azo-polymer film with photo-induced optical anisotropy

A new type of phase-shifting interferometer was presented by rotating an azo-polymer film with photo-induced optical anisotropy in the light path of orthogonal polarization interferometry. By changing the angle of the optical axis of the azo-polymer film, four phase-shifted fringe patterns were obtained, from which phase difference between orthogonal polarized light could be calculated. The polarization states and the formation of the interferograms were analyzed theoretically using Jones matrix calculations and the experimental verification of the proposed method was also given. This method has a simple optical configuration which utilizes commercially available polarization devices and anisotropic azo-polymer film of low cost. The phase-shifting interferometer also demonstrates a new application of azo-polymer film.     

Measurement of surface profile in vibrating environment with instantaneous phase shifting interferometry

In-process measurement has been the requirement of the precision industries, but due to vibrations while manufacturing, in-process measurement has been difficult to achieve. There is little work on in-process measurement using phase shifting interferometry, as phase shifting is extremely sensitive to vibrations. In this work, the advantage of the developed non-mechanical and instantaneous phase shifting interferometry is felt while measuring surface profile of large flat surfaces under vibrating conditions which can be extended for in-process measurement of surface profile. A near common path optical configuration is achieved and the effect of the environment is reduced. Moreover, the measurement of phase is instantaneous which increases the versatility of this technique for measuring vibrating objects. Profile measurements were carried out on a smooth mirror surface excited with vibrations of different frequencies and the technique was found to be immune to vibrations of up to 1000 Hz.     

Practical common-path heterodyne surface profiling interferometer with automatic focusing

In modern semiconductor and optics industries, there is a strong demand for a highly sensitive and non-contact surface profilometer. This paper describes a practical heterodyne surface profiling interferometer for on-line non-contact measurement which has been developed recently. The essential feature of the profilometer is a newly designed common-path configuration to minimize the effects caused by vibration, air turbulence and other environmental variations. A single-mode frequency-stabilized laser diode (780 nm) serves as the light source to make the whole system compact (total volume 250L×200W×100H mm). A powerful signal processing scheme is also developed, which includes three parts: automatic voltage control, phase measurement with wide range and automatic focusing control. All these make the repeatability and stability of the profiling interferometer greatly improved. The system has vertical resolution of 0.39 nm and lateral resolution of 0.73 μm. During approximately an hour, the stability is within 1.95 nm(3σ).     

Volume-grating phase-shifting digital speckle pattern interferometry used for measurement of out-of-plane displacement field

A new digital speckle pattern interferometry, called volume-grating phase-shifting digital speckle pattern interferometry, is discussed in this paper. The out-of-plane displacement field of a bent plate can be quantitatively measured using volume-grating phase-shifting digital speckle pattern interferometry proposed in this paper. Theoretical and experimental results, as well as absolute errors, are given.     

共光路外差干涉法精密测量光学表面

报道了光学外差法测量表面起伏精度及横向分辨精度达到０．１１ｎｍ及４μｍ。本文采用的是完全共光路外差干涉系统，阐述了它的原理、构造及噪声的影响，并将测量结果与其它商品仪器测量结果作了比较。     

Measurement of shock waves using phase shifting pulsed holographic interferometer

A phase shifting pulsed holographic interferometer was applied to the experimental study of the propagation of laser-induced shock waves over metal plates. A double-pulsed ruby laser was used to generate the shock waves and to make a holographic interferogram of the wave fields. The phase shifting method with a dual-reference beam solved the sign ambiguity problem in holographic fringe patterns and allowed a quantitative evaluation of the phase of the interference patterns. The transient surface profile and propagation behavior of the shock wave over plates were investigated from the holographic fringe patterns.     

Measurement of edge residual stresses in glass by the phase-shifting method

Control and measurement of residual stress in glass is of great importance in the industrial field. Since glass is a birefringent material, the residual stress analysis is based mainly on the photoelastic method. This paper considers two methods of automated analysis of membrane residual stress in glass sheets, based on the phase-shifting concept in monochromatic light. In particular these methods are the automated versions of goniometric compensation methods of Tardy and Sénarmont. The proposed methods can effectively replace manual methods of compensation (goniometric compensation of Tardy and Sénarmont, Babinet and Babinet-Soleil compensators) provided by current standards on the analysis of residual stresses in glasses.     

Instantaneous phase shifting arrangement for microsurface profiling of flat surfaces

Phase shifting interferometry is a well-established technique for non-contact surface profile measurement. Though phase shifting technique has many advantages, it is marred by a few inaccuracies due to the vibration and mechanical movement of the phase shifter itself. Significant amount of work is reported to theoretically compensate these error sources. But for a few works, prominent achievements have not been reported in eliminating these error sources in phase shifting interferometry. In this paper, a novel optical layout, in combination with instantaneous phase shifting interferometry is described. Experiments were carried out with this setup on a super mirror with a λ/20 surface roughness, to demonstrate the validity of the principle.