Microscopic three-dimensional topometry with ferroelectric liquid-crystal-on-silicon displays

When three dimensional measurements are conducted with fringe projection, the quality of the grating used for the generation of the fringes is important. It has a direct influence on the achievable depth resolution in a given measurement setup. In the past, Ronchi grating or gratings written in nematic liquid-crystal displays or in digital micromirror devices have been used. We report on the application of a reflective ferroelectric liquid-crystal-on-silicon display as the fringe-generating element in a setup based on a stereo microscope. With this device the depth resolution of measurements by use of phase-shifting algorithms can be significantly improved compared with the application of a Ronchi grating or a nematic liquid-crystal display.     

Application of generalized grating imaging to pattern projection in three-dimensional profilometry

The theory of generalized grating imaging for a one-dimensional grating is applied to a pattern projection system in pattern projection profilometry. Contrast of the projected grating image is calculated under various conditions. The results help to determine the conditions suitable for obtaining high contrast grating images in a large space. Although the gratings required for the profilometry are hexagonal, the theory for two-dimensional gratings is prohibitively complex. Therefore, the projection system was designed using the one-dimensional theory. The projection system using two-dimensional hexagonal gratings was constructed and experiments were done with it. The result agrees approximately with the theoretical calculations for one-dimensional gratings. This suggests that the one-dimensional theory may be used for estimating the approximated behavior for hexagonal gratings for use in pattern projection profilometry. Some discussions are given for the application of the projection system for profiling the mannequin or human body.     

虚拟光栅变频投影三维测量技术的研究

虚拟光栅变频投影三维测量技术采用多光束干涉条纹形成虚拟余弦光栅,将虚拟余弦光栅投影到被测物体上得到被物体形貌调制的变形虚拟光栅。通过调整多光束干涉的楔角改变虚拟光栅频率,将两幅不同频率的变形虚拟光栅经过光学接收系统成像在CCD像机上,对CCD像机记录的变频变形光栅图像进行综合处理从而获取被测物体的三位形貌。本文给出了这种测量技术的原理,实验结果表明,采用变频虚拟光栅投影三维形貌测量技术可以有效地解决三维测量中被测物体高度变化率过大引起相位展开困难的问题。     

Spatially resolved phase imaging of a programmable liquid-crystal grating

Phase imaging is used to compare near-field measurements with the corresponding far-field intensity distribution. A liquid-crystal device serves as a phase object that can be programmed as a variable grating. Real-time phase visualization then provides an avenue for direct optimization of complex phase gratings.     

Optical frequency-domain imaging microprofilometry with a frequency-tunable liquid-crystal Fabry-Perot etalon device

An optical frequency-domain interference microscope with a liquid-crystal Fabry-Perot interferometer as an optical frequency-scan device was developed for microscopic three-dimensional shape measurements. The proposed system can perform absolute measurement of the discontinuous surface profile of a microscopic object without use of mechanically moving components such as a piezoelectric transducer or a grating spectrometer. Experimental results are presented that demonstrate the validity of the principle.     

Miniaturized three-dimensional endoscopic imaging system based on active stereovision

A miniaturized three-dimensional endoscopic imaging system is presented. The system consists of two imaging in channels that can be used to obtain an image from an object of interest and to project as tructured light onto the imaged object to measure the surface topology. The structured light was generated with a collimated monochromatic light source and a holographic binary phase grating. The imaging and projection channels were calibrated by use of a modified pinhole camera. The surface profile was extracted by use of triangulation between the projected feature points and the two channel ofthe endoscope. The imaging system was evaluated in three-dimensional measurements of several objects with known geometries. The results show that surface profiles of the objects with different surfaces and dimensions can be obtained at high accuracy. The in vivo measurements at tissue sites of human skin and an oral cavity demonstrated the potential of the technique for clinical applications.     

基于相位测量轮廓术的复合光栅优化设计

基于复合光栅的相位测量轮廓术在物体三维信息重建中是一种非接触、实时的测量方法.通过对这种光栅的形成机理分析,发现当复合光栅中的空间调制光栅的频率一定时,其中相移光栅周期与三维重构精度有关,并且存在一个重构均方差最小值的相移光栅周期,其大小与被测物体的形貌有关.因此,可通过优化复合光栅结构的方法来提高测量精度.利用数字投影仪将连续改变相移光栅周期得到的复合光栅投影到物体,获取变形光栅图像来重建物体的三维信息,从周期数与均方差关系曲线中找到对应的复合光栅的最优化参数,以实现复合光栅最优化设计.通过数字模拟和实验都证实采用优化设计的复合光栅来提高物体的测量精度是有效的.     

Two-wavelength phase-shifting interferometry with a superimposed grating displayed on an electrically addressed spatial light modulator

A two-wavelength moire phase-shifting interferometer that uses a superimposed grating has been developed. The optical phase shifts for the two wavelengths are given by digital phase shifts of a superimposed grating displayed on a liquid-crystal spatial light modulator. A phase shift of the moire fringe is achieved by equal phase shifts with opposite signs in the two gratings. A moire phase-shifting interferometer with no moving parts and no requirement for calibration of the value of the phase shifts was obtained. Our experimental result shows measurements of the profile of a step object with a 2.65-microm synthetic wavelength.     

Electro-optical investigations of holographic-polymer-dispersed ferroelectric liquid crystals

Uniform alignment of ferroelectric liquid-crystal domains encapsulated by a polymer binder was established through a holographic exposure process. The refractive index modulation in these thin films is modeled as a phase grating that can be electrically addressed to erase the optical diffractive properties. A phenomenological model is developed to take into account a distribution of domain sizes and an effective field that stabilizes the ferroelectric liquid-crystal domains. A diffraction model successfully predicts changes in normalized intensities for first-order diffraction with applied field. These gratings demonstrate microsecond-scale response and relaxation times for various grating pitch sizes between approximately 3 and approximately 12 microm.     

Nematic liquid-crystal polarization gratings by modification of surface alignment

The stylus of an atomic force microscope is used to scribe preferred directions for liquid-crystal alignment on a polyimide-coated substrate. The opposing substrate that comprises the liquid-crystal cell is rubbed unidirectionally, resulting in a twisted nematic structure associated with each micrometer-sized pixel. The polarization of light entering from the uniformly rubbed substrate rotates with the nematic director by a different amount in each pixel, and each of the two emerging polarization eigenmodes interferes separately. Two examples are discussed: a square grating that allows only odd-order diffraction peaks and a grating that combines rotation with optical retardation to simulate a blazed grating for circularly polarized light. The gratings can be electrically switched if used with semitransparent electrodes.     

Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting

The use of an optical fringe projection method with two-step phase shifting for three-dimensional (3-D) shape measurement of small objects is described. In this method, sinusoidal linear fringes are projected onto an object's surface by a programmable liquid-crystal display (LCD) projector and a long-working-distance microscope (LWDM). The image of the fringe pattern is captured by another LWDM and a CCD camera and processed by a phase-shifting technique. Usually a minimum of three phase-shifted fringe patterns is necessary for extraction of the object shape. In this method, a new algorithm based on a two-step phase-shifting technique produces the 3-D object shape. Unlike in the conventional method, phase unwrapping is performed directly by use of an arccosine function without the need for a wrapped phase map. Hence, shape measurement can be speeded up greatly with this approach. A small coin is evaluated to demonstrate the validity of the proposed measurement method, and the experimental results are compared with those of the four-step phase-shifting method and the conventional mechanical stylus method.     

Area modulation grating for sinusoidal structure illumination on phase-measuring profilometry

Sinusoidal structured illumination is used widely in three-dimensional (3-D) sensing and machine vision. Phase algorithms, for example, in phase-measuring profilometry, are inherently free of errors only with perfect sinusoidal fringe projection. But it is difficult to produce a perfect sinusoidal grating. We propose a new concept, area modulation, to improve the sinusoidality of structured illumination. A binary-coded picture is made up of many micrometer units. An aperture is open in every micrometer unit, and its area is determined by the value of the sinusoidal function. When such a grating is projected onto an object surface, the image of the grating becomes sinusoidal because of the convolution function of an optical system. We have designed and manufactured an area modulation grating for sinusoidal structure illumination using a large-scale integration technique. The area modulation grating has been used in the high-precision phase-measuring profilometry system, and the phase errors caused by the area modulation grating are reduced to 0.1%. The grating guaranteed the entire measuring accuracy to a 1% equivalent wavelength. The experimental results proved that area modulation grating would be of significant help in improving the phase-measurement accuracy of the 3-D sensing system.     

Imaging with a rectangular phase grating applied to displacement metrology

We achieved displacement metrology with a high-amplitude signal by using a rectangular phase grating as the pupil in a grating imaging system. The imaging phenomenon with a pupil transmission grating that has a bilevel profile with a 50% duty ratio is discussed on the basis of the optical transfer function. By optimizing the imaging condition, we obtained high-contrast images with high light power under a magnified or demagnified imaging system. The amplitude of the signal in the displacement measurement was four times higher than that of the conventional grating imaging system with amplitude gratings.     

Calculation of the efficiency of polarization-insensitive surface-stabilized ferroelectric liquid-crystal diffraction gratings

A rigorous analysis is presented of the diffraction efficiency of a polarization-insensitive surface-stabilized ferroelectric liquid-crystal (SSFLC) phase grating, taking full account of the internal structure of the ferroelectric liquid-crystal layer. When no field is applied, the twisted director profile in the relaxed state gives an optimum diffraction efficiency for a device thickness between the half-wave-plate and the full-wave-plate conditions. The influence of the magnitude of the spontaneous polarization and applied ac fields are investigated, and it is shown that the diffraction efficiency of a binary SSFLC phase grating can be strongly enhanced with the technique of ac stabilization.     

In situ optical control and stabilization of the curing process of holographic gratings with a nematic film-polymer-slice sequence structure

We report on the realization of what we believe to be a new holographic setup for the fabrication of polymer liquid-crystal polymer-slice diffraction gratings, which utilizes an optical-feedback-driven nanopositioning technique. We have increased the stability of the interference pattern by means of a simple piezomirror used in a feedback configuration to keep constant the phase of the interferometer. The feedback system is driven by a proportional, integral, derivative control software, and the stability degree is controlled by the reference signal coming from a standard test grating. A preliminary experimental characterization indicates that good control and stabilization of parasitic fluctuations of the interference pattern are obtained.     

Acoustic grating fringe projector for high-speed and high-precision three-dimensional shape measurements

A new acoustic grating fringe projector (AGFP) was developed for high-speed and high-precision 3D measurement. A new acoustic grating fringe projection theory is also proposed to describe the optical system. The AGFP instrument can adjust the spatial phase and period of fringes with unprecedented speed and accuracy. Using rf power proportional-integral-derivative (PID) control and CCD synchronous control, we obtain fringes with fine sinusoidal characteristics and realize high-speed acquisition of image data. Using the device, we obtained a precise phase map for a 3D profile. In addition, the AGFP can work in running fringe mode, which could be applied in other measurement fields.     

Polarizationally Non-sensitive Pseudo-holographic Computer Reconstruction of Random Rough Surface

Abstract

The function, describing a profile of a random rough surface (RRS) is expanded in a Fourier series, i.e. the surface is considered as a composition of sinusoidal gratings. The total diffracted optical field from this RRS is a sum of the fields due to all harmonic gratings, since Kirchhoff's condition for ‘locally flat surface’ is realized for each harmonic grating at a given light wavelength and at an appropriate choice of the basic grating period. The registered s and p components of the diffracted (+1 diffraction orders of each harmonic gratings), incident and mixed optic fields are separated with an optical analyser. These fields are experimentally measured and from these values the phase and the amplitude of each grating are determined. The profile of the surface is reconstructed for s and p polarization of the light scattered field, when the electric vector of the incident light concludes an arbitrary angle with the incidence plane. The mean roughness is determined in both cases. It is shown, that both reconstructions of the profile and the determination of the mean roughness are not dependent on the polarization of the incident light. The separation of the s and p components is of great importance at the two-dimensional reconstruction, when independent of incident light polarization (s or p), the scattered optical field is always depolarized. In this case the profile of the two-dimensional surface can be easily reconstructed with s or p component of the mixing and diffracted fields.     

Time multiplexing superresolution based on interference grating projection

In a previous work done by the authors, it was shown that the superresolution concept based on two moving gratings could be effected by a physical grating attached to the object and a virtual grating. This concept was shown to be very efficient and exhibited features that are helpful in removing some artifacts caused when coherent illumination is used. Furthermore, it simplifies the optical and mechanical modules of the super-resolving system by removing the need for mechanical movement of one grating. However, the system still required the need for moving the first (encoding) grating attached to the input. In this study the encoding grating is replaced by use of a projected grating. This approach simplifies the need for attaching the grating to the input object and thus new applications, such as remote sensing can be considered. The theoretical concept is demonstrated and experimental results are shown.     

Microshape and rough-surface analysis by fringe projection

A fringe-projection system for microscopic applications, fringe-projecting microscopy, is developed and analyzed. Projection of the grating and imaging of the fringe system, modulated by the surface, are accomplished by the same high-aperture objective. The spectrum of the grating is spatially filtered and projected into the aperture with a lateral shift, which leads to a telecentric projection under oblique incidence and telecentric imaging. Topographies of specularly as well as diffusely reflecting surfaces can be obtained. The measurement of highly rough surfaces is described together with preprocessing steps. The resulting intensity distribution of the fringes is analyzed. Formulas for vertical and lateral resolution, measuring range, and dynamic range, based on noise considerations, are presented and verified by topographies of technical surfaces.