The determination of material parameters of microcomponents using digital holography

Progresses in microsystem technology promise a lot of new applications in industry and research. However, the increased complexity of the microsystems demand sensitive and robust measurement techniques. Fullfield and non invasive methods are desirable to get access to spatially resolved material properties and parameters.This contribution describes a simple and fast interferometric method for the analysis of shape and deformation of small objects by optical means. These quantities together with a well defined loading of the components can be the starting point for the determination of material parameters like Poisson-ratio, Young's modulus or the thermal expansion coefficient. Holographic interferometry and multiple wavelength contouring as well as multiple source point contouring are precise enough to fulfill the requests for precision and resolution in microsystem technology even on complex shaped structures with steps or gapsA new adaptive, iterative algorithm is developed and applied to the measured results that allows the numerical evaluation of the phase data to get absolute shape and deformation information in Cartesian coordinates. Surfaces with holes, gaps and steps can be registered without any ambiguities. Digital holography as the underlying holographic recording mechanism is extremely suitable for small objects and lead to simple and compact setups in which the objects’ shape as well as their deformation behavior can be recorded. Experiments using silicon microbeams and an object from fine mechanics are described to show the great potential of these fast and robust measurement techniques with respect to the determination of material parameters.     

Digital color holography applied to fluid and structural mechanics

In various domains such as acoustics, vibrations or fluid mechanics, non-invasive metrological tools, giving full-field measurements with very high spatial and temporal resolutions, need to be developed to validate the models and/or numerical simulations of the studied phenomena. In this way, ONERA and LAUM have developed optical real-time methods based on three-wavelength digital holographic interferometry to analyze either unsteady wake flows or vibrating kinematics or complex fields. These digital color holographic methods aim at avoiding panchromatic holographic plates and their related constraints. In the domain of fluids mechanics, an interferometric set-up is presented to generate micro fringes from the observed area. The data are processed thanks to direct and inverse Fourier transforms to obtain a gas density field and to study its evolution in time. In structural mechanics, a versatile interferometric imaging set-up, based on digital Fresnel holography, is presented. These new optical imaging methods result in full-field measurements with a high spatial resolution. This research ultimately aims at analyzing, in time, unsteady complex wake flows, vibrating kinematics and acoustic fields. A few examples are given and the possibilities and limits of these methods are discussed.     

Quasi-common path three-wavelength holographic interferometer based on Wollaston prisms

This article presents a digital three-wavelength holographic interferometer based on the use of two Wollaston prisms. This provides an in-line setup with quasi common-path and as a consequence there is no additional independent reference wave to be added. Thus, immunity to external perturbations such as vibrations or thermal perturbations is achieved. Furthermore, the set-up exhibits a single shot and real time capability which is very useful to study dynamic events. By using the two Wollaston prisms in an astigmatic configuration, spatial carrier frequencies can be adjusted both in amplitude and orientation. The digital hologram processing is based on Fourier processing and filtering around the carrier spatial frequency so that phase shifting is not required. The use of three wavelengths leads to visualizing directly the zero order fringe and regions for which there is no air density variation in a dynamic flow. Experimental proof of concept is demonstrated with a supersonic jet when the injection pressure varies.     

Elimination of zero-order diffraction in digital off-axis holography

A simple experimental method of eliminating zero-order diffraction in the reconstructed image of off-axis digital holography is presented. Holographic diffraction grating acting as a beam splitter, an off-axis holography system is formed. The holograms of object with different recording parameters are obtained by adjusting the reflecting mirror in the recording optical system to vary the incidence orientation of the object beam in CCD to introduce a phase shift. The zero-order image can be eliminated by numerically processing the holograms of object with different recording parameters. The theoretical analyses have been done in detail and the experimental results are also given. The zero-order image eliminated, the area of reconstructed image increases remarkably, the image quality can then be significantly improved and the better resolution obtained. The experimental results show that the method presented in this paper is feasible, simple in optical system and easy in operation and data processing.     

Digital holography at millimetre wavelengths

In this paper, we describe a method for wavefront reconstruction at millimetre wavelengths using off-axis holography, a frequently used image recording technique at visible wavelengths first demonstrated in the 1960’s. Millimetre radiation has been highlighted recently in the imaging of non-conducting materials and objects, which often show significant transparency at these long wavelengths, even though opaque at visible and infrared wavelengths. Holography provides a method for recording a lens-less image of an object thus reducing loss of spatial frequency information, which is important for obtaining maximum resolution at long wavelengths. An experimental arrangement based on a simple form of Fresnel off-axis holography is described, with the object illumination and reference beams derived using two radiating horn antennas fed by a single coherent source (a Gunn diode oscillator operating at 100 GHz – wavelength 3 mm) via a 3 dB cross-guide coupler. The process is discussed in the context of imaging and in the validation of millimetre wave radiation sources (horns). We show that the entire fields from these and other components can be analysed using computational optics with data derived from a single measurement obtained using inexpensive equipment.     

Simulation of simultaneous measurement for red blood cell thickness and refractive index

Red blood cell (RBC) parameters are of great importance for diagnostic purposes. Using the simulation method, the variations of both the thickness and the refractive index of a RBC were investigated in a dual-medium quantitative measurement (DMQ), which is realized via phase-shifting digital holography with two types of cell media. Results show that both the calculated thickness and the calculated refractive index agree well with the original ones with an average relative deviation of 2.13% and of 0.12% in valid regions, respectively. The simulation for RBC will provide some guidance for experimental parameter setting and data processing in DMQ.     

数字全息变焦系统的研究及应用

从4f系统及照像机变焦镜头的设计思想出发,提出并设计了一个由三面透镜组成的数字全息变焦系统.该系统具有4f系统的性能,且可以方便地改变横向放大率,适应实际检测物体尺寸及形状的变化.用几何光学表述了变焦系统的工作原理,基于矩阵光学理论介绍了变焦系统的设计方法,利用衍射的角谱理论对像空间波面重构计算方法进行了介绍.并且,给出了实验证明及应用实例.     

Surface Shape Measurement by Phase-Shifting Digital Holography

Surface contouring by phase-shifting digital holography is proposed that provides surface height from a change of reconstructed phase due to tilting of the object illumination. After phase-unwrapping it directly delivers surface shape. Its sensitivity depends on the tilting angle as well as on the initial incident angle. Although the sensitivity is the same as in the conventional fringe projection, a simpler setup is used without imaging lens and measurement depth is increased due to numerical focusing. We also performed noise suppression by employing nonlinear image-data compression technique that considers amplitude values and attained standard height deviation less than 30 #x03BC;m from a flat surface.     

Four-pulse interferometric recordings of transient events by pulsed TV holography

With traditional double-pulsed holographic interferometry or pulsed TV holography, the experiment usually has to be repeated to allow the recording of a time sequence of interferograms of the event. With the proposed technique a sequence of four interferograms of a solitary transient event is measured. A twin oscillator, injection-seeded, pulsed Nd:YAG laser is incorporated into a pulsed TV holography set-up. With orthogonal polarisation and double pulsing of each of the two channels of the laser, four pulses are recorded on two separate CCD-frames. Four interferograms of a laser-impacted plate obtained from the same experiment, show how the bending waves develop and propagate in the plate.     

Lensless digital holography with short-coherence light source for three-dimensional surface contouring of reflecting micro-object

In this paper, a new lensless digital holography system with short-coherence light source is reported for recording three-dimensional surface contouring of reflecting micro-objects. In the experiment, each of the layers on the inwall of a conical pore is respectively recorded by changing the path length of the object beam, instead of changing that of the reference beam, which can reduce the recording complexity and errors. In addition, the least-square-polynomial-fitting is used for the first time to carry out three-dimensional reconstruction with a series of two dimensional intensity images of a micro-object, which can be used not only to reduce obviously the complication of the three-dimensional reconstruction, but also to carry out three-dimensional reconstruction of a micro-object with strong laser speckle noise, of which the phase images can not be obtained from the conventional phase unwrapping process.     

High-resolution digital transmission microscopy—a Fourier holography approach

A spherical reference field is used to construct a digital holographic system with a demonstrated resolution up to 228 line pairs per mm. The reference field originates from a GRIN lens placed 1 mm from the illuminated object. This allows the use of a standard sensor to record the hologram with the required numerical aperture. The image is determined by evaluation of the Rayleigh–Sommerfeld diffraction integral that relates the object field in the image plane to the object field in the sensor plane. Experimental results are given for two charge coupled device sensors and one complementary metal-oxide-semiconductor active pixel sensor.     

Possibility to break through limitation of measurement range in dual-wavelength digital holography

By using the beat frequency technique, the dual-wavelength digital holography(DWDH) can greatly increase the measurement range of the system. However, the beat frequency technique has a limitation in measurement range. The measurement range is not larger than a synthetic wavelength. Here, to break through this limitation, we propose a novel DWDH method based on the constrained underdetermined equations, which consists of three parts:(i) prove that the constrained underdetermined equation has a unique integer solution,(ii) design an algorithm to search for the unique integer solution,(iii) introduce a third wavelength into the DWDH system, and design a corresponding algorithm to enhance the anti-noise performance of DWDH. As far as we know, it is the first time that we have discovered that the problem of DWDH can belong in a problem of contained underdetermined equations, and it is also the first time that we have given the mathematical proof for breaking through the limitation of the measurement range. A series of results is shown to test the theory and the corresponding algorithms. More importantly, since the principle of proposed DWDH is based on basic mathematical principles, it can be further extended to various fields, such as dual-wavelength microwave imaging and dual-wavelength coherent diffraction imaging.     

Use of digital color holography for crack investigation in electronic components

This paper presents the experimental optical analysis of the crack inside an electronic component. The optical setup is used to carry out multidimensional deformation measurements using digital color holography and the spatial multiplexing of holograms. Since the Fresnel transform method depends on wavelength, a wavelength-dependent-zero-padding algorithm is described and results in a rigorous sizing of each reconstructed monochrome image. The criterion to optimize the parameters is presented and is based on minimizing the widening of the impulse response of the full recording/reconstruction process. The application of the proposed method is illustrated through the analysis of the mechanical deformation of the electronic component, and offers keys to understand its failure mode in industrial conditions.     

微型光学元件的透过波面畸变的数字化检测

介绍了由浙江大学研制的CQG II型车间数字干涉仪检测 φ3 6mm× 0 5mm平行平面玻璃的透过波面畸变的情况。最近研制出的干涉仪测量的最大口径为 φ60mm ,采用移相式条纹扫描数字化处理 ,基于WINDOWS操作系统实现实时检测 ,以优于λ/ 30的精度计算出被检件的波面误差。工厂生产检测表明 :在上述仪器上增加一个 4倍口径的放大系统 ,可以使通光口径 φ3 1mm的工件达到 42 0 0个采样点 ,仪器的透射测量标准干涉腔误差PV≤ 0 0 2 8λ ,仪器隔日多次测量重复性PV≤ 0 0 3λ。该仪器已经正常投入使用 ,生产的用于光学信息产品的微型光学件已为日本先锋公司 (PIONEER)复检通过 ,成为工厂批量生产过程质量控制 (QC)的重要手段。     

Non-coherent noise reduction in digital holography based on root mean square technique

In this paper, the root mean square (rms) technique is applied in order to reduce the non-coherent noise in phase-contrast image. The proposed technique is applied to a sample of 200 μm step height nominally. The recorded off-axis interferograms generated from two different wavelengths are processed to obtain an object wave (amplitude and phase) for each wavelength separately. The independent phase maps are subtracted and a phase map for the beat-wavelength is obtained and converted to height map. The rms values of 10 pixels profiles from the obtained height map are calculated automatically to show the three-dimensional (3D) profile. The experimental results show that the non-coherent noise is reduced by the order of 90% when the rms technique is applied and the uncertainty in measurement has been found to be of the order of 1.5 μm. The proposed technique can provide a simple and real solution for measuring 3D objects having high abrupt height difference.     

采用短相干光数字全息术实现反射型微小物体的三维形貌测量

针对反射型微小物体，设计了一种可在三维形貌测量中实现微小物体分层记录的短相干光源无透镜傅里叶变换数字全息记录系统，并利用该系统对锥形微孔壁实现了分层记录.该系统可通过调节待测物体的位置，改变全息记录中的物光光程，从而获得重构三维物体所需要的一系列子全息图.该系统具有光路简洁，系统的附加误差小的特点.实验测量的轴向误差约为3.5%，横向误差约为2.6%.此外，在三维重构的过程中，为避免因散斑噪声较大而无法利用位相信息进行三维重构的情况，采用了最小二乘多项式拟合方法，将微小物体的一系列再现强度图像进行三维重构.由于避免了复杂的相位展开，所以不但运算简单，而且具有较强的抗散斑噪声能力.     

Green's formulation for robust phase unwrapping in digital holography

We present, for the first time to the best of our knowledge, a phase unwrapping method based on an algorithm which makes use of Green's first identity. This method aims at recovering the correct phase information encoded in a fringe pattern after digital holography (DH) numerical processing. DH provides a quantitative measurement of the three-dimensional surface profile of objects. The information about the profile can be obtained in principle from the phase-map. However, the measured phase-map provides the actual phase values wrapped mod.2π so that an unwrapping process is required in order to reconstruct the object profile.     

Surface contouring by phase-shifting real-time holography using photorefractive sillenite crystals

This work proposes to obtain surface contouring by phase-shifting real-time holography using photorefractive sillenite crystals which provides the surface contouring from a change in phase of wavefront of the object illumination beam. The real-time holography using the photorefractive Bi₁₂SiO₂₀ crystal and the four-frame phase-shifting technique was used to obtain the phase map, this map was filtered by an anisotropic sin/cos filter and the unwrapping process used was the cellular-automata technique. We obtained experimental results of the surfaces of the large objects with real discontinuities, and these results agree with the dimensions of the object.     

Surface contouring by phase-shifting digital holography

Surface contouring by phase-shifting digital holography is proposed that provides surface height from a change of reconstructed object phases due to the tilt of object illumination. Surface height from a reference plane is directly obtained from the phase change. Its sensitivity depends on the tilt angle as well as on the initial incident angle. By proper selection of the angles we can derive surface height without phase unwrapping. The sensitivity can be enhanced by increasing the tilt angle. Then we need phase unwrapping that is sensitive to noise due to laser speckles in the reconstructed images. This noise could be suppressed by selecting phase values at points of the maximum product of amplitudes before and after the illumination change in the course of data reduction from 1024×1024 to 512×512 and by selecting paths for phase unwrapping by looking for the intensity maximum. The observed height resolution is 20 μm. Effects of numerical focusing have also been investigated. The present method has the same sensitivity as the fringe projection method, but it has larger measurement depth and is also applicable to the deformation measurement with the same arrangement.     

基于相位分析的时间平均数字全息测振研究

传统的时间平均全息术通过对再现像光强分布的测量来实现振幅分布的检测,由于噪音影响往往得不到满意的结果.第一类零阶贝塞尔函数相位只有0和π两个取值,所以利用再现光场的相位可以确定振幅分布.理论分析发现,以往的讨论忽略了照明光之间位移引起的相位变化,研究通过叠加一个相位因子对此进行了修正,并利用贝塞尔函数平方的相位特点提出了消除该相位因子的办法.实验结果表明,该相位因子确实存在并影响测量,用本文所提出的方法可以很好地消除该相位因子的影响,使利用时间平均数字全息再现光场的相位检测振动物体的振幅分布变得方便和准确.