Automatic refractive index profiling of fibers by phase analysis method using Fourier transform

Automatic fringe pattern analysis is a powerful and inexpensive digital image-processing technique. It is used to analyze the fringe pattern obtained by different optical techniques, such as multiple-beam Fizeau fringes. To perform accurate and fast automatic measurement of fiber refractive index profile, phase analysis method has been used with the Fourier transform technique. In this paper, the refractive index profiles of polyethylene fibers with different draw ratios are presented by two methods, fringe shift method and phase analysis method. A comparison between the results obtained is presented.     

Quantitative vibration amplitude measurement with time-averaged digital speckle pattern interferometry

A new method of using time-averaged digital speckle pattern interferometry for the quantitative measurement of vibration amplitude was developed. Signal processing techniques especially the Hilbert transformation for quantitative evaluation of the Bessel fringes obtained in time-averaged digital speckle pattern interferometry were explored. The quadrature signal after Hilbert transformation is equivalent to a 90° phase-shifted interferogram for a monotonically increasing or decreasing phase function. An algorithm was developed for Bessel fringe contrast enhancement and phase extraction. The techniques were tested numerically and experimentally. Sub-fringe quantification of the time-averaged vibration fringes is realised with the proposed method. Compared with the commonly used phase shift method which requires a minimum of two images for image processing, this method requires only one fringe pattern for data extraction.     

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.     

A derivative based simplified phase tracker for a single fringe pattern demodulation

In this paper, a novel fringe demodulation method for the estimation of phase and its first-order derivative from a closed-fringe interferogram is proposed. The proposed method determines the phase derivatives in both x&y directions from fringe orientation and density. The phase derivatives are subsequently used to determine phase values using a novel simplified phase tracker. In the phase tracking model, the complexity of the cost function is reduced using predetermined derivatives so computation time required for phase tracking is reduced considerably. The proposed model is more robust while dealing with saddle points in fringes than the conventional phase tracker model. Hence it does not require any specialized scanning strategy. The proposed method is validated with simulated and experimental fringe patterns (obtained using electronic speckle pattern interferometry and optical holographic interferometry) and a comparison study is carried out with conventional regularized phase tracker. The simulation results show that the proposed method has good accuracy and requires less computation time than existing phase-tracking algorithms. The experimental results demonstrate the robustness of the proposed method against speckle noise and its practical applicability for static and dynamic applications.     

Shape identification using phase shifting interferometry and liquid-crystal phase modulator

A phase shifting technique using a Michelson interferometry system is presented and applied to surface contour measurement. Hyperbolic fringes are produced by the interference of two spherical wavefronts expanded from a beam expander. The fringe pattern is projected on an object surface and the deformed grating image is captured by a CCD camera for subsequent analysis by a PC. Phase variation is achieved by a liquid-crystal device incorporated in the Michelson interferometry system. Results obtained using the proposed method for objects of various shapes and sizes compared well with those from a conventional profilometer.     

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.     

Comparison of phase recovery methods in spiral speckle pattern interferometry correlation fringes

Spiral interferometry can be used as a solution to the problem of sign ambiguity presented in the conventional speckle pattern interferometric technique when the optical phase needs to be reconstructed from a single closed fringe system. Depressions and elevations of the topography corresponding to the object deformation are distinguished by the direction of rotation of the local spiral fringe pattern. In this work, we implement and compare several methods for optical phase reconstruction by analyzing a single image composed of spiral speckle pattern interferometry correlation fringes. The implemented methods are based on contour line demodulation, center line demodulation, Spiral Phase Quadrature Transform and the 2D Riesz transform with multivector structure. Contour line and center line demodulation approaches are exclusively dedicated to images containing a fringe system with spiral structure. The others are based on the 2D Riesz transform, these being well known approaches in conventional interferometry. We examine simulated experiments and analyze some of the emerging drawbacks for solving the phase reconstruction problem by using different mean values of speckle size and background noise levels. We also discuss several numerical procedures that may well improve the efficiency and robustness of the presented numerical implementations. The performance of the implemented demodulation methods is evaluated by using a universal image quality index and therefore a quantitative comparison is also presented.     

基于迈克尔逊干涉的傅里叶变换散斑形貌测量技术

提出了电子散斑干涉载频调制测量物体形貌的方法。采用典型的迈克尔逊干涉光路,将物体偏转一微小角度（等效为物面与参考面间形成空气楔）产生等厚干涉,可在物体的表面引入包含物体高度信息的载波干涉条纹。用CCD采集该载波条纹图,利用傅里叶变换法可解调出物体高度的位相信息,从而实现物体的形貌测量。介绍了电子散斑干涉载频调制测量物体形貌的原理,并进行了实物测量,给出了实验结果。由于该方法采用散斑干涉方法测量物体形貌,所以具有灵敏度高的优点。     

Parameter estimation of optical fringes with quadratic phase using the fractional Fourier transform

Optical fringes with a quadratic phase are often encountered in optical metrology. Parameter estimation of such fringes plays an important role in interferometric measurements. A novel method is proposed for accurate and direct parameter estimation using the fractional Fourier transform (FRFT), even in the presence of noise and obstacles. We take Newton׳s rings fringe patterns and electronic speckle pattern interferometry (ESPI) interferograms as classic examples of optical fringes that have a quadratic phase and present simulation and experimental results demonstrating the performance of the proposed method.     

Microscopic surface contouring by fringe projection method

This paper describes the use of optical fringe projection method for 3D surface profile and deformation measurement of micro-components. In this method, sinusoidal linear fringes are projected on a micro-component surface by a grating phase shifting projector and a long working distance microscope (LWDM). The image of the fringe pattern is captured by a high-resolution CCD camera and another LWDM and processed by phase-shifting technique. A simple procedure is described which enables calibration of the optical set-up for subsequent quantitative measurement of micro-components of unknown shapes. This method is relatively simple and accurate, and is capable of conducting fully automated measurements. In this paper, two micro-components, a micro-mirror (0.1 mm×0.1 mm) and a micro-electrode pad are used to demonstrate deformation measurement and microscopic surface contouring.     

Highly sensitive interferometric system for optical surface contouring

In the present work we demonstrate a highly sensitive system for optical surface contouring constructed by combining phase conjugation and digital phase shifting interferometry. The phase conjugating mirror in the modified phase conjugate Michelson interferometer is based on degenerate four wave mixing in a photorefractive BTO crystal. Digital phase shifting interferometry is used to decode the interference fringe pattern. An increase in sensitivity and high measurement accuracy are achieved through this new combination due to the interferometric scheme and the phase shifting. Experimental results are presented. The interferometric system is flexible and undergoes further improvement.     

Demodulation of a single interferogram based on continuous wavelet transform and phase derivative

A novel method based on continuous wavelet transform (CWT) and guidance of phase derivative is developed to measure the phase of a single fringe pattern which contains closed fringes. Wrapped phase values are retrieved by ridge extraction algorithms based on CWT which has the capability of better noise reduction and thus increases the resolution of measurement significantly. To further reduce the noise, the scales detected by maximum ridge algorithm are filtered iteratively before retrieval of wrapped phase. The proposed method also identifies any ambiguous point in a non-monotonous fringe pattern by directly tracking an inflexion point from an unwrapped phase map without the use of a carrier. The algorithm developed is validated by computer simulation and experimental results. Based on micro interferometry the experimental results for both static and dynamic deformations of a micro structure demonstrate that the proposed method is an effective tool for the analysis of closed fringe patterns and subsequent deformation measurement. However, the proposed technique is limited to measurement of surface which is relatively smooth compared to the mean wavelength of the light source. In addition, prior knowledge of the sign of surface slope is required in cases where a spatial carrier is not available or adaptable.     

云纹干涉载频调制技术及分析

在物体变形场的测量中,云纹干涉的载频调制技术有重要作用.在云纹干涉中,对称光照明产生的衍射光沿试件栅表面的法线传播并产生干涉.通过改变照明光的入射角度,可实现变形条纹场的空间调制.通过光程差的分析说明了载波条纹产生的机理,得出了载波频率与照明光入射角度变化之间的关系式.利用三点弯曲加载结合二维载频调制实验,给出了实验结果.证明了在初始条纹较少的情况下,载频调制技术能有效地测量物体的位移场.     

基于适度光反馈自混合干涉技术的振动测量

光反馈自混合干涉技术是一种新浮现的有别于传统双光束干涉的一类新的测试技术。为了在适度光反馈下进行振动的精密测量,提出了一种基于适度光反馈自混合干涉技术的振动测量方法。经对光反馈自混合干涉信号条纹分析,发现通过选定合适的光反馈水平及激光器线宽展宽因数,可以得到锯齿干涉条纹。这种干涉信号不仅包含振动幅度信息也包含振动方向信息。该振动测量方法利用锯齿干涉条纹的特点,首先通过条纹记数实现大范围振幅粗测,具有半波长位移分辨力;然后基于适度光反馈下小数条纹的特点,给出了小于半波长位移测量的线性表达式,从而实现位移的精测。仿真计算表明,该方法可以实现大量程高分辨力振动位移测量,在叠加20 dB的噪声下,振幅测量相对误差平均为0.5%。     

Mechanical characterization of unplasticised polyvinylchloride thick pipes by optical methods

In this work a number of techniques (electronic speckle pattern interferometry, holographic interferometry, strain gauge and finite element method) are brought to bear in order to establish consistency in the results of strain measurement. This is necessary if optical non-destructive testing methods, such as those used here, are to gain acceptance for routine industrial use. The FE model provides a useful check. Furthermore, ESPI fringe data facilitates the extension of FE models, an approach that is of growing importance in component testing.

The use of in-plane and out-of-plane sensitive electronic speckle pattern interferometry (ESPI) for non-destructive material characterization of thick unplasticised polyvinylchloride (uPVC) pipes is presented. A test rig has been designed for stressing pipes by internal pressure. ESPI gives a complete mapping of the displacement field over the area imaged by the video camera. The results for the strain of uPVC obtained from ESPI data and from strain gauges are in good agreement. The value of Young's modulus has been obtained from the fringe data and compared with results obtained using holographic interferometry and from strain gauge measurements. The FE model also produces fringe data that is consistent with the ESPI results.     

The separation of out-of-plane displacement from in-plane components by fringe carrier method based on large image-shearing ESPI

A fringe carrier method for separating out-of-plane displacement from in-plane components based on large image-shearing electronic speckle pattern interferometry (ESPI) is presented. If the test object is respectively illuminated by two expanded symmetric illuminations in large image-shearing ESPI, two interferometers are formed. Carrier fringe patterns can be introduced by tilting reference surface a small angle. The carrier fringe patterns are demodulated after deformation of the object. Two phase maps, which include out-of-plane and in-plane displacement, can be obtained by using Fourier transform. Then out-of-plane displacement can be easily separated from in-plane displacement by simple operation between two unwrapped phase distributions. The principle of spatial carrier frequency modulation in large image-shearing ESPI is discussed. A typical three-point-bending experiment is completed. Experimental results are offered. The results show that the method offers high visibility of carrier fringes. And the system presented does not need a special beam as a reference light and has simple optical setup.     

Nanoscale deformation measurement by using the hybrid method of gray-level and holographic interferometry

This study extends the use of holographic interferometry to measure the nanoscale out-of-plane displacement with high surface resolution. It is noted that if the deformation is less than half of the optical wavelength, it is hard to find an obvious fringe pattern. Under such a situation, in general, the phase shift method is used. However, it needs to take more than 3 images for phase shifting and phase reconstruction In this paper, a more simple hybrid method of gray-level and holographic interferometry is used to extract fringe skeletons, in which it just needs to take one or two images for the normal deformation measurement directly, even if there exists no obvious fringe pattern. The displacement field with high surface resolution can also be obtained. The proposed method yielded a theoretical precision of 0.15 nm for out-of-plane displacement with a monochromatic CCD camera of 10-bit gray scale (1024 gray scales) sensitivity and microscale surface resolution for millimeter scale object with 640×480 pixels image resolution by an He–Ne LASER (632.8 nm wavelength) light source. The gray-level method is proposed to calculate the non-obvious interferometry fringe by traditional holographic interferometry hologram, and the result showed that this method works for this purpose.     

Speckle correlation fringes denoising using stationary wavelet transform. Application in the wavelet phase evaluation technique

This paper presents a stationary wavelet transform (SWT) method for speckle noise reduction in digital speckle pattern interferometry fringes. The main advantage of SWT is its translation invariance, which makes it important in statistical image processing applications. This method was used to denoise a simulated speckle fringe patterns, a good fidelity value was obtained. Applied to the wavelet phase evaluation, it has provided a phase distribution with a good accuracy.     

Fringe pattern denoising via image decomposition

Filtering off noise from a fringe pattern is one of the key tasks in optical interferometry. In this Letter, using some suitable function spaces to model different components of a fringe pattern, we propose a new fringe pattern denoising method based on image decomposition. In our method, a fringe image is divided into three parts: low-frequency fringe, high-frequency fringe, and noise, which are processed in different spaces. An adaptive threshold in wavelet shrinkage involved in this algorithm improves its denoising performance. Simulation and experimental results show that our algorithm obtains smooth and clean fringes with different frequencies while preserving fringe features effectively.