The use of unwrapped phase in MR image segmentation: A preliminary study

This paper considers the problem of tissue classification in 3D MRI. More specifically, a new set of texture features, based on phase information, is used to perform the segmentation of the bones of the knee. The phase information provides a very good discrimination between the bone and the surrounding tissues, but is usually not used due to phase unwrapping problems. We present a method to extract textural information from the phase that does not require phase unwrapping. The textural information extracted from the magnitude and the phase can be combined to perform tissue classification, and used to initialise an active shape model, leading to a more precise segmentation.

A new approach for simple and rapid shape measurement of objects with surface discontinuities

A new approach for unwrapping phase maps, obtained during the measurement of 3-D surfaces using sinusoidal structured light projection technique, is proposed. "Takeda's method" is used to obtain the wrapped phase map. Proposed method of unwrapping makes use of an additional image of the object captured under the illumination of a specifically designed color-coded pattern. The new approach demonstrates, for the first time, a method of producing reliable unwrapping of objects even with surface discontinuities from a single-phase map. It is shown to be significantly faster and reliable than temporal phase unwrapping procedure that uses a complete exponential sequence. For example, if a measurement with the accuracy obtained by interrogating the object with S fringes in the projected pattern is carried out with both the methods, new method requires only 2 frames as compared to (log(2)S +1) frames required by the later method.

Three-dimensional profiling using a still shot

A method to reliably extract object profiles even with surface discontinuities that leads to 2n pi phase jumps is proposed. The proposed method uses an amplitude-modulated Ronchi grating, which allows one to extract phase and unwrap the same with a single image. Ronchi equivalent image can be derived from modified grating image, which aids in extracting wrapped phase using Fourier transform profilometry. The amplitude of the modified grating aids in phase unwrapping. As we only need a projector that projects an amplitude-modulated grating, the proposed method allows one to extract three-dimensional profile without using full video projectors. This article also deals with noise reduction algorithms for fringe projection techniques. (C) 2014 Society of Photo-Optical Instrumentation Engineers (SPIE)

Quantitative estimation of density variation in high-speed flows through inversion of the measured wavefront distortion

A simple method employing an optical probe is presented to measure density variations in a hypersonic flow obstructed by a test model in a typical shock tunnel. The probe has a plane light wave trans-illuminating the flow and casting a shadow of a random dot pattern. Local slopes of the distorted wavefront are obtained from shifts of the dots in the pattern. Local shifts in the dots are accurately measured by cross-correlating local shifted shadows with the corresponding unshifted originals. The measured slopes are suitably unwrapped by using a discrete cosine transform based phase unwrapping procedure and also through iterative procedures. The unwrapped phase information is used in an iterative scheme for a full quantitative recovery of density distribution in the shock around the model through refraction tomographic inversion. Hypersonic flow field parameters around a missile shaped body at a free-stream Mach number of 5.8 measured using this technique are compared with the numerically estimated values. (C) 2014 Society of Photo-Optical Instrumentation Engineers (SPIE)

用于大范围高精度实时位移测量的半导体激光干涉仪

现有的半导体激光干涉仪存在测量精度与测量范围的矛盾。本文提出一种新的实时位移测量半导体激光干涉仪，并分析了干涉仪的测量原理。首先提出一种新的解相算法，它通过两路实时相位探测电路从干涉信号中得到待测量相位，消除了光强波动、初始光程差、电路放大倍数、调制深度、Bessel函数等参数对测量精度的影响，提高了测量精度。其次，提出一种扩大测量范围的技术，并用解包裹电路得到真实相位和待测量的位移, 将测量范围从半个波长提高到几个波长。在实验中，测得喇叭的峰峰值为2361.7nm，重复测量精度为2.56nm，测量时间为

基于3×3耦合器的马赫-曾德尔干涉仪的光纤光栅波长解调技术

介绍了一种基于3×3和2×2光纤耦合器构成的非平衡马赫-曾德尔干涉仪的波长解调方案。理论分析和数据对比表明，相对于由两个2×2光纤耦合器构成的马赫-曾德尔干涉仪，本干涉仪具有宽谱的灵敏度、能跟踪波长的变化方向和相位展开的优点，实验方案用于测量固定在悬臂梁上的传感光纤布拉格光栅（FBG）的峰值波长变化，获得了±1pm的静态波长解调精度，在10Hz处的动态分辨率为27nε/√Hz。相位展开算法使得应变测量范围达到了2014με，对应的相位变化为3．22π。

相位解包裹算法中基于调制度的新质量图

在移相法测量光学波面或物体形貌过程中。相位解包裹是条纹自动分析中的关键技术，而质量图对解包裹相位算法起着至关重要的作用。用计算机模拟干涉图获得相位导数偏差质量图，指出其在标识相位数据质量方面的不足，并根据调制度结合相位梯度构造出新的质量图（称之为调制度相位梯度偏差质量图）来弥补此缺陷。再以新质量图数据为权值，采用加权最小二乘解包裹算法验证新质量图的可靠性。最后通过实验数据，比较新质量图和相位导数偏差质量图在解包裹相位算法中的作用，得到新质量图的解相结果均方根（RMS）值为2．652rad，而相位导数偏差质

基于分支设置的质量导引相位展开算法

二维相位展开方法是近年来较为活跃、引起关注的一个研究课题，它在许多测量应用中有着重要的作用。尽管掩膜阻断算法在多个领域都有成功应用实例，该算法存在着固有的缺陷。为了克服掩膜阻断算法的缺陷，综合分支阻断方法和质量导引方法的优点，提出一种基于分支设置的质量导引相位展开新算法。它先以一个初始质量图来引导分支的设置，然后把分支对应的相位质量设置为最低，从而产生一个新的质量图，最后按新质量图来引导相位展开，并使用几个包裹相位图来验证此方法的有效性。计算机模拟相位图和实际相位图的相位展开结果表明，在存在复杂轮廓不连续

光学干涉图像处理中基于质量权值的离散余弦变换解包裹相位

为减少噪声对相位恢复过程的影响,快速得到正确的解包裹相位,提出了一种改进的相位解包裹方法——加权离散余弦变换解包裹算法。该方法把离散余弦变换和标识相位数据好坏的质量权值结合起来,兼有速度快和可靠度高的优势。为验证此算法,对模拟和实验得到的包裹相位图添加随机噪声和散粒噪声,同时采用加权与非加权离散余弦变换算法进行处理,所得到的解包裹结果与未加噪声的解包裹相位值进行比较,结果表明,通过加权离散余弦变换算法恢复的相位图比非加权离散余弦变换算法所恢复的相位图更接近于理想值,而且两种算法的运行速度基本相同,这证明提

Multi-wavelength holographic profilometry - art. no. 60272L

A novel method for surface profilometry by holography is presented. We used a diode laser emitting at many wavelengths simultaneously as the light source and a Bi12TiO20 (BTO) crystal as the holographic medium in single exposure processes. The employ of multi-wavelength, large free spectral range (FSR) lasers leads to holographic images covered of interference fringes corresponding to the contour lines of the studied surface. In order to obtain the relief of the studied surface, the fringe analysis was performed by the phase stepping technique (PST) and the phase unwrapping was carried out by the Cellular-automata method. We analysed the relief of a tilted flat metallic bar and a tooth prosthesis.

Refractive and geometric lens characterization through multi-wavelength digital speckle pattern interferometry

Physical parameters of different types of lenses were measured through digital speckle pattern interferometry (DSPI) using a multimode diode laser as light source. When such lasers emit two or more longitudinal modes simultaneously the speckle image of an object appears covered of contour fringes. By performing the quantitative fringe evaluation the radii of curvature as well as the refractive indexes of the lenses were determined. The fringe quantitative evaluation was carried out through the four- and the eight-stepping techniques and the branch-cut method was employed for phase unwrapping. With all these parameters the focal length was calculated. This whole-field multi-wavelength method does enable the characterization of spherical and aspherical lenses and of positive and negative ones as well. (C) 2007 Elsevier B.V. All rights reserved.

Measurement of low-derivative surface lenses by two-laser holography with Bi12TiO20 crystals

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Profilometry of semiconductor components by two-colour holography with Bi12TiO20 crystals

We studied the shape measurement of semiconductor components by holography with photorefractive Bi12TiO20 crystal as holographic medium and two diode lasers emitting in the red region as light sources. By properly tuning and aligning the lasers a synthetic wavelength was generated and the resulting holographic image of the studied object appears modulated by cos2-contour fringes which correspond to the intersection of the object surface with planes of constant elevation. The position of such planes as a function of the illuminating beam angle and the tuning of the lasers was studied, as well as the fringe visibility. The fringe evaluation was performed by the four stepping technique for phase mapping and through the branch-cut method for phase unwrapping. A damage in an integrated circuit was analysed as well as the relief of a coin was measured, and a precision up to 10 μm was estimated. © 2009 SPIE.

Progressive power lens measurement by low coherence speckle interferometry

This work proposes a method for dioptric power mapping of progressive lenses through dual wavelength, low-coherence digital speckle pattern interferometry. Lens characterization finds several applications and is extremely useful in the fields of ophthalmology and astronomy, among others. The optical setup employs two red diode lasers which are conveniently aligned and tuned in order to generate a synthetic wavelength. The resulting speckle image formed onto a diffusive glass plate positioned behind the test lens appears covered of contour interference fringes describing the deformation on the light wavefront due to the analyzed lens. By employing phase stepping and phase unwrapping methods the wavefront phase was retrieved and then expressed in terms of a Zernike series. From this series, expressions for the dioptric power and astigmatic power were derived as a function of the x- and y-coordinates of the lens aperture. One spherical and two progressive lenses were measured. The experimental results presented a good agreement with those obtained through a commercial lensometer, showing the potentialities of the method. © 2013 Elsevier Ltd.

Lensometry by two-laser holography with photorefractive Bi12TiO20

Refractive and profilometric measurements of lenses were performed through holography with a photorefractive Bi12TiO20 crystal as the recording medium. Two properly aligned diode lasers emitting in the red region were employed as light sources. Both lasers were tuned in order to provide millimetric and sub-millimetric synthetic wavelengths. The surfaces of the test lens were covered by a 25-μm opaque plastic tape in order to allow the lens profilometry upon illuminating them with a collimated beam. The resulting holographic images appear covered by interference fringes corresponding to the wavefront geometry of the wave scattered by the lens. For refractive index measurement a diffusely scattering flat surface was positioned behind the uncovered lens which was also illuminated by a plane wave. The resulting contour interferogram describes the form of the wavefront after the beam traveled back and forth through the lens. The fringe quantitative evaluation was carried out through the four-stepping technique and the resulting phase map and the Branch-cut method was employed for phase unwrapping. The only non-optical procedure for lens characterization was the thickness measurement, made by a dial caliper. Exact ray tracing calculation was performed in order to establish a relation between the output wavefront geometry and the lens parameters like radii of curvature, thickness and refractive index. By quantitatively comparing the theoretical wavefront geometry with the experimental results relative uncertainties bellow 3% for refractive index and 1 % for focal length were obtained. © 2008 American Institute of Physics.