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.     

Talbot effect of a grating with different kinds of flaws

The Talbot effect of a grating with different kinds of flaws is analyzed with the finite-difference time-domain (FDTD) method. The FDTD method can show the exact near-field distribution of different flaws in a high-density grating, which is impossible to obtain with the conventional Fourier transform method. The numerical results indicate that if a grating is perfect, its Talbot imaging should also be perfect; if the grating is distorted, its Talbot imaging will also be distorted. Furthermore, we evaluate high-density gratings by detecting the near-field distribution with the scanning near-field optical microscopy technique. Experimental results are also given.     

Experimental measurements of generalized grating images

The term generalized grating imaging is used to describe the process of image formation of a grating using only another grating as imaging system. The moiré and the Lau effects could be regarded as particular cases of such a process. Here we deal with the less-studied case of images formed at finite distances from the gratings, using an extended monochromatic light source. Some experimental results are shown for the images obtained in this last case, and they are compared with theoretical predictions.     

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.     

Influence of unparallel grating planes in talbot interferometry with cross gratings of different spatial frequencies in two directions

The effects of an arbitrary small inclination between two cross gratings on the moiré fringes in Talbot interferometry are discussed when the frequencies of the grating differ in two perpendicular directions. We show that the small angles, alpha and beta, by which the beam-splitter cross grating is rotated around the two axes parallel to the two perpendicular line directions of the cross grating, have a greater influence on the moiré fringes with cross gratings than that with one-dimensional gratings. A simple and practical detection method for the angles between the two unparallel grating planes in Talbot interferometry is also proposed. The theoretical analyses are proved by experimental results.     

Talbot array illuminator for single-shot measurements of laser-induced-damage thresholds of thin-film coatings

A highly efficient Talbot array illuminator for single-shot, laser-induced-damage test measurements of optical thin-film coatings is proposed. With a periodic binary phase grating, a laser beam is transformed into an ensemble of Gaussian-like spots, which are known as the Fresnel image of the grating. For this purpose hexagonal phase gratings were fabricated and analyzed. With a peak fluence distribution of ~1 order of magnitude, the damage threshold of thin films can be deduced by use of the data from only a single shot.     

Generalized Curvilinear Diffraction Gratings: III . Euclidian diffraction gratings

This paper is the third in a series of papers on the diffraction and imaging properties of generalized curvilinear diffraction gratings. Here we study classes of plane uncrossed diffraction gratings which have the common property that their Fourier transform patterns consist of sharp-line caustics. These types of generalized gratings are referred to as ‘Euclidian diffraction gratings’, because the condition for the formation of line caustics is equivalent to the global vanishing of the gaussian curvature of the grating line pattern function. The analysis is applied to the laser material processing system discussed in our last paper [1].     

Perturbed Talbot patterns for the measurement of low particle concentrations in fluids

Behind periodic amplitude or phase objects, the object transmittance is repeated at the so-called Talbot distances. In these planes perpendicular to the propagation direction, Talbot self-images are formed. In the case of plane wave illumination, the distances between the self-images are equally spaced. A periodic pattern called optical carpet or Talbot carpet is formed along the propagation direction. We show theoretically how the presence of spherical particles (10 to 100 μm in diameter) behind gratings of 20 and 50 μm period affects the formation of Talbot carpets and Talbot self-images at 633 nm illumination wavelength. The scattering of the particles is modeled by the Fresnel diffraction of its geometrical shadow. We analytically calculate the interference of the diffraction orders of rectangular and sinusoidal amplitude gratings disturbed by the presence of particles. To verify our model, we present measurements of Talbot carpets perturbed with both opaque disks and transparent spheres, and discuss the effects for various size parameters. We present an approach to simulate the movement of particles within the Talbot pattern in real time. We simulate and measure axial and lateral particle movements within a probe volume and evaluate the effect on the signal formation in a Talbot interferometric setup. We evaluate the best system parameters in terms of grating period and particle-detector-distance for a prospective measuring setup to determine characteristics of flowing suspensions, such as particle volume concentration or particle size distribution.     

Self-imaging of gratings with rough strips

We analyze the self-imaging process produced by a transmission grating whose strips present two different roughness levels. This kind of grating periodically modulates the transmitted light owing only to the different microtopographic properties of the strips. In spite of the fact that the grating is not purely periodic, it produces a kind of self-image at Talbot distances. These self-images gradually appear as light propagates, but they are not present just after the grating, as occurs in amplitude or phase gratings. There exists a distance from the grating, which depends on the stochastic properties of roughness, from which the contrast of the self-images becomes stable. Important cases are analyzed in detail, such as low- and high-roughness limits. We assume for the calculations that the grating can be used in a mobile system. Simulations using the Rayleigh-Sommerfeld regime have been performed, which confirm the validity of the theoretical approach proposed in this work.     

Analytic phase-factor equations for Talbot array illuminations

Under specific circumstances the fractional Talbot effect can be described by simplified equations. We have obtained simplified analytic phase-factor equations to describe the relation between the pure-phase factors and their fractional Talbot distances behind a binary amplitude grating with an opening ratio of (1/M). We explain how these simple equations are obtained from the regularly rearranged neighboring phase differences. We point out that any intensity distribution with an irreducible opening ratio (M(N)/M) (M(N) < M, where M(N) and M are positive integers) generated by such an amplitude grating can be described by similar phase-factor equations. It is interesting to note that an amplitude grating with additional arbitrary phase modulation can also generate pure-phase distributions at the fractional Talbot distance. We have applied these analytic phase-factor equations to neighboring (0, pi) phase-modulated amplitude gratings and have analytically derived a new set of simple phase-factor equations for Talbot array illumination in this case. Experimental verification of our theoretical results is given.     

Variations of the growth of harmonic reflections in fiber Bragg gratings fabricated using phase masks

The growth of reflectance peaks from optical fiber Bragg gratings has been studied to determine the relative importance of grating features when writing with the phase-mask technique. Measurements of spectra for two different fiber types using two distinct phase masks allowed the contribution from grating features of half the phase-mask periodicity and of the phase-mask periodicity at the Bragg wavelength to be determined. The dominance of the latter periodicity was ascribed to either the small fiber core diameter that limited the extent of the Talbot diffraction pattern, or the enhanced ±2 diffraction orders of a custom-made phase mask used.     

3-D Contouring of Diffuse Objects by Talbot-projected Fringes

Abstract

Talbot fringe projection, a moiré technique, is applied to three-dimensional contouring of diffuse targets for absolute shape measurement. The basic system relies on depth coding the test target surface by projecting the Talbot image of a linear grating. A second grating, similar to that used for the Talbot image, is employed to obtain the moiré fringes. These fringes represent surface contours of equal depth. Using a phase measurement technique and digital image processing algorithms, the surface shape information is obtained from the contour maps. Experimental results, merits and limitations of the system are discussed.     

Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry

We assesses the efficiency of x-ray Talbot interferometry (XTI), a technique based on the Talbot effect for measuring a wavefront gradient, in terms of how quickly it can capture a high-quality phase image with a large signal-to-noise ratio for a given incident photon number. Photon statistics cause errors in the phase of the moiré fringes and impose a detection limit on the wavefront gradient. The relation between the incident photon number and the detection limit is determined, and a figure of merit of XTI for a monochromatic cone beam is then defined. The dependence of the figure of merit on optical system parameters, such as grating pitch and position, is then discussed. The effects of varying the pattern height and linewidth of the second grating are shown for rectangular and trapezoidal teeth. Finally, we show how to design a practical cone-beam Talbot interferometer for certain boundary conditions.     

Invariant grating pseudoimaging using polychromatic light and a finite extension source

The Talbot effect is a well studied phenomenon by which grating pseudoimages appear at certain periodic distances when monochromatic light is used. Recently, numerical simulations have shown a new phenomenon; when a polychromatic light beam is used in a double grating system, the intensity of the pseudoimages presents a transverse-profile that remains unaffected over a wide range of propagation distances. This effect can be used to increase the tolerances of gratings based optical devices, such as displacement measurement systems, interferometers, and spectrometers. The pseudoimages formation with a polychromatic and finite extension light source is analytically and experimentally demonstrated. Relatively simple analytical expressions for the intensity and the contrast allow us to predict when pseudoimages present a constant contrast and when they disappear. Furthermore, we experimentally obtain the pseudoimages using the proposed configuration, corroborating the theoretical predictions.     

基于双频光栅的微分干涉相衬方法

针对传统微分干涉相衬技术对双折射性物体成像会有伪像的问题,用双频闪耀光栅取代传统微分干涉相衬的分光元件诺曼斯基棱镜,设计了一种微分干涉相衬方法.对双频闪耀光栅设计,模拟入射平面波通过它之后的光强分布,结果表明它能产生两束剪切角很小的光.用双频光栅微分干涉相衬方法对纯相位样品模拟成像,仿真结果和物体的相位轮廓一致.分析了...     

Surface profiling of a transparent object by use of phase-shifting Talbot interferometry

Talbot interferometry is used to study the surface profile of a transparent object. Periodic patterns are produced by illuminating a grating with a collimated laser beam. The object is placed on the self-image plane of the grating. The deformed grating image, which interferes with another grating, results in the Talbot interferometric fringes. The fringe pattern is recorded on a CCD camera for subsequent analysis, and the phase variation is achieved by a linear translation stage. In this application two specimens are tested to demonstrate the validity of the method; one is a transparent object with a spherical shape with a height of less than 350 microm, and the other is a transparent object with an uneven surface of 50-microm average height. The experimental results are compared with the test results obtained with the mechanical stylus method.     

Polarization-dependent Talbot effect

The term "polarization-dependent Talbot effect" means that the Talbot self-imaging intensity of a high-density grating is different for TE and TM polarization modes. Numerical simulations with the finite-difference time-domain method show that the polarization dependence of the Talbot images is obvious for gratings with period d between 2 lambda and 3 lambda. Such a polarization-dependent difference for TE and TM polarization of a high-density grating of 630 lines/mm (corresponding to d/lambda=2.5) is verified through experiments with the scanning near-field optical microscopy technique, in which a He-Ne laser is used as its polarization is changed from the TE mode to the TM mode. The polarization-dependent Talbot effect should help us to understand more clearly the diffraction behavior of a high-density grating in nano-optics and contribute to wide application of the Talbot effect.     

Extension du Concept D'espaces de Fourier à la Spectroscopie

This paper is the second in a series [1] of papers on the diffraction and imaging properties of generalized curvilinear diffraction gratings. In this article, a set of generalized ray equations is derived and applied to the calculation of the caustic properties of generalized gratings. No restriction is placed on the form of the ruling pattern or on the shape of the grating surface. For generalized uncrossed and off-axis plane gratings, the ruling pattern may be regarded as a contour map of some abstract surface. In this case, it is shown that the far-field caustic properties of the grating are determined by the regions of vanishing gaussian curvature on the abstract surface. As an application of the theory, a new method for laser material processing is discussed.     

On coherence in neutron imaging

The variety of imaging signals in neutron radiography and tomography became quite large compared to the pure absorption and scattering contrast in neutron radiographies and topographies in the early sixties or seventies of the last century. The diversity of absorption based techniques for neutron radiography and tomography is comparable to coherence based imaging techniques such as phase contrast, differential phase contrast, dark field imaging, diffraction enhanced contrast, refraction contrast, ultra small angle scattering contrast, grating interferometry and crystal interferometry, also the spin of the neutron was successfully used for imaging [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11] and [12]. We show which effects (total reflection, diffraction, refraction) contribute to e.g. a step boundary or a phase boundary. Taking this simple object, one can learn to understand the imaging procedure and what is displayed in a radiograph.     

Full field of view super-resolution imaging based on two static gratings and white light illumination

The usage of two static gratings for obtaining super-resolved imaging dates back to the work by Bachl and Lukosz in 1967. However, in their approach a severe reduction in the field of view was the necessary condition for improving the resolution. We present an approach based on two static gratings without sacrificing the field of view. The key idea for not paying with the field of view is to use white light illumination to average the ghost images obtained outside the region of interest since the positions of those images are wavelength dependent. Moreover, large magnification is achieved by using a commercial microscope objective instead of a test system with a unity magnification as presented in previous works. Because of the large magnification, the second grating has a low spatial period. This allows us to create an intermediate image and use a second imaging lens with low resolution capability while still obtaining an imaging quality as good as that provided by the first imaging lens. This is an important improvement in comparison with the original super-resolving method with two fixed gratings.