The influence of unresolved speckles on the pixelwise modulation in phase shifting techniques has been investigated in recent publications by several authors. It has been shown that the number of points with sufficient modulation does not automatically decrease when unresolved speckles are used. However, the effect of unresolved speckles on the resulting phase map has not been examined. In this paper it is investigated how the averaging of speckles over the area of a pixel affects the validity of the phase resulting from phase shifting techniques. Special attention is given to the effect of unresolved speckles on phase singularities, since interferometric measurements with fully resolved speckles result in a phase map which contains a large number of phase singularities. Phase singularities are points where no phase value is defined, so that the appearance of singularities decreases the lateral resolution of the measurement. Additionally these points and their direct neighbourhood are a source of trouble for unwrapping algorithms. It is investigated how a slightly averaging of speckles alters the appearance of these problematic regions.
Recent advances in laser technology, optical sensing, and computer processing of data, have lead to the development of advanced quantitative optical metrology techniques for high accuracy measurements of absolute shapes and deformations of objects. These techniques provide noninvasive, remote, and full field of view information about the objects of interest. The information obtained relates to changes in shape and/or size of the objects, characterizes anomalies, and provides tools to enhance fabrication processes. Factors that influence selection and applicability of an optical technique include the required sensitivity, accuracy, and precision that are necessary for a particular application. In this paper, sensitivity, accuracy, and precision characteristics in quantitative optical metrology techniques, and specifically in optoelectronic holography (OEH) based on CMOS cameras, are discussed. Sensitivity, accuracy, and precision are investigated with the aid of National Institute of Standards and Technology (NIST) traceable gauges, demonstrating the applicability of CMOS cameras in quantitative optical metrology techniques. It is shown that the advanced nature of CMOS technology can be applied to challenging engineering applications, including the study of rapidly evolving phenomena occurring in MEMS and micromechatronics.
In this paper we describe a highly miniaturized sensor head based on digital holography for endoscopic measurements. The system was developed to measure the shape and the 3D-deformation of objects which are located at places that cannot be accessed by common measurement systems. Therefore, a miniaturized optical sensor including a complete digital-holographic interferometer with a CCD-camera is placed at the end of a flexible endoscope. The diameter of the head is less than 10 mm. The system enables interferometric measurements with a speed of three reconstructions per second and it can be used outside of the laboratory in a usual environment. Shape measurements are performed with two wavelength contouring, while the deformation is measured with digital holographic interferometry. To obtain full 3D-data in displacement measurements the object can be illuminated sequentially from three different illumination directions. To increase the lateral resolution temporal phase shifting is used.
Digital holography provides the direct access to the interference phase. This basic quantity of interferometry can be used for the measurement of 3D-coordinates and 3D-displacement fields of objects subjected to a certain kind of load. For the inspection of objects which cannot be accessed directly such as hidden surfaces inside a cavity endoscopic systems are applied. In this paper a miniaturized sensor is described that can be fixed at the distal end of a flexible endoscope. The sensor head integrates all components of a holographic interferometer including the CCD-camera as well as the beam splitting and guiding components for three illumination directions using glass fibers. An optimized design of the interferometer setup makes it possible to measure the 3D components of the measurement quantity with high accuracy. After a short introduction to the principles of digital holography and 3d-displacement measurement the basics of perturbation theory are presented. This theory is applied for the design of the interferometer and finally some consequences with respect to the statistical error analysis are discussed.
Phase measurements require the measurement of interferogram intensities. In this paper it is investigated how the validity of the evaluated phase is affected by the averaging of the interferogram intensities across the pixels of a CCD-array. In our previous works it has been shown numerically that the validity of the phase values depends on the topology of the speckle field. Here, it is examined analytically how the topology influences the phase evaluation with respect to averaging. One result is that in certain cases the absolute value of the phase gradient can be determined solely from the intensity of the speckle field, without any reference beam. Based on this result the phase error at intensity maxima, saddle points and for stationary points of the phase is examined.
Applications for coherent optical metrology usually use lasers as light sources, because of the excellent spatial and temporal coherence of the emitted light. By comparison, the demands of speckle shearography concerning the coherence of the light source are low. This enables certain white-light sources like mercury arc lamps to be an option. But using such a light source leads to new problems. Both the spatial and the temporal coherence are low. Due to the fact that multiple wavelengths are involved, dispersion effects become an issue and must be considered. Therefore, in this paper the multiband speckle shearography using a mercury arc lamp is investigated. Especially the problems arising from the light source are regarded. Finally, some experimental investigations of an object under load are presented.
This paper presents an endoscopic digital holographic interferometry system which is based on phase-shifting in-line digital holography. The system is able to measure both the shape and deformation of an object with the advantages of digital holography, such as real-time processing of the hologram. Two theoretical problems are briefly described: phase-shifting in- line holography and hologram data re-sampling for 2-wavelength contouring. In addition, initial experimental results of the deformation of a metal piece and surface 3D-shape measurement of a bottle cap are given.
The quality of interferometric measurement methods, such as fault detection by shearography, is highly influenced by the intensity distribution of the illuminating light. Usually it is intended to obtain a homogeneous object illumination while common laser light sources provide a Gaussian intensity distribution. In this paper it is investigated how the intensity distribution of the detected light is influenced by the polarization states of the incident and the scattered light. In literature usually the Stratton-Chu equation is used to describe depolarization effects. However, this equation is valid only in the Fraunhofer region, which is unsuitable for most interferometric measurements. For this reason a still unpublished general expression for the amplitude of the electromagnetic field close to the scattering surface is derived. Based on this novel formula the correlation between the intensity distribution and the polarization state of the scattered light is investigated analytically, numerically and experimentally. In the numerical part the integral formula is used to generate the light field scattered by a metal plate. As input data for the simulation the measured surface structure of a real metal plate is used. Additionally, the theoretical results are compared to measured intensity distributions for several combinations of input and output polarization states.
It is known, that phase dislocations in objective speckle fields can be found at regions where the intensity of the wave-field disappears. In interferograms, created by object I've speckle fields, those dislocations usually form dipoles. They arise when the position of the dislocations changes between two object state. In this paper it is shown, that phase dislocations in interferograms from subjective speckle fields also form dipoles. They produce a noise- amplitude on the corresponding phase-map, which makes unwrapping more difficult. The mean width and the number of theses dipoles are investigated in dependence of the correlation and the density of the corresponding subjective speckle field. All these results have been obtained experimentally and have been additionally proofed by means of simulations. Because dipoles on the phase map appear at regions, where the corresponding intensity disappears, a modified line-scan-algorithm is proposed which only takes the bright areas into consideration.
Singularities in speckle fields are single points where the phase value is not defined. Consequently phase singularities decrease the resolution of interferometric measurement methods such as ESPI or HI. In this paper the behavior of phase singularities in the image plane is investigated for the case that the illuminated object is displaced along the optical axis. The investigations have been performed by means of simulations and measurements. Both, the model used to simulate subjective speckle fields and the experimental setup to measure the phase changes in the image plane are described. To observe the appearance and the disappearance of singularities, the object displacement was divided into a series of smaller displacement steps. The lateral speckle phase in the image plane was generated numerically for each displacement step. This way the transformation of the whole phase field could be visualized and the path of the singularities could be traced. The results obtained from these simulations are verified experimentally: For each displacement step the speckle phase was measured interferometrically along a column of a CCD-sensor. The behavior of the measured speckle phase is compared to the numerical results. Based on these results the consequences for interferometric out-of-plane displacement measurements are discussed.
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