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Showing papers on "Moiré pattern published in 2002"


Journal ArticleDOI
TL;DR: In this paper, an x-ray interferometer was developed that uses two transmission phase gratings to analyze wave front distortions in the hard X-ray range, which was used for differential phase contrast imaging of low absorbingbing test objects.
Abstract: An x-ray interferometer has been developed that uses two transmission phase gratings to analyze wave front distortions in the hard x-ray range. The interferometer is insensitive to mechanical drift and vibrations, and it is tunable over a wide range of photon energies. This setup was used for differential phase contrast imaging of low-absorbing test objects. We obtained micrographs with moire fringes of good visibility, which revealed the local phase shift gradient caused by the objects. A comparison with numerically simulated images indicates that quantitative analysis of unknown phase objects is possible.

620 citations


Journal ArticleDOI
TL;DR: An optical technique based on the shadow moire method which allows the measurement and digitization of three-dimensional surfaces and was applied to obtain external surfaces of sheet metal stamped parts, showing the effectiveness of this technique.
Abstract: In this paper we present an optical technique based on the shadow moire method which allows the measurement and digitization of three-dimensional surfaces. The technique was tested through experimental work and the results were compared with those obtained by a coordinate measuring machine. Moving from the conventional shadow moire method, new features were implemented enabling us to overcome the main shortcomings of the conventional moire method. These include the need to assign the fringe order, the incapability of discerning concavity or convexity, the poor resolution and the complexity in the signal processing. All these problems have been solved by adding an element to generate a carrier fringe pattern to the equipment of the conventional shadow moire technique and processing the obtained signal using the Fourier transform method. The proposed technique was applied to obtain external surfaces of sheet metal stamped parts. The experimental results show the effectiveness of this technique.

39 citations


Proceedings ArticleDOI
04 Jan 2002
TL;DR: It is found that spectral domain manipulation gives the best results in the detection of moire patterns, which may appear during film-to-video transfer using Telecine devices.
Abstract: In this paper we focus on the detection of moire patterns, which may appear during film-to-video transfer using Telecine devices. A model of moire distortion is created and studied. A new suppression algorithm using the spectral model is presented and applied for real video sequences. The non-linear filter is based on analysis of the magnitude of the Fourier spectrum of the image. As an alternative, an algorithm using parametric identification of the moire patterns is investigated. It is found that spectral domain manipulation gives the best results.

38 citations


Patent
Viktors Berstis1
21 Mar 2002
TL;DR: In this article, a two-dimensional array of non-uniformly spaced pixels having a plurality of overlaid pixel sets for avoiding moire patterns in digital images by avoiding producing an inherent "frequency" or pattern that may interfere with details or harmonics present in the image source, thereby eliminating the occurrence of moire pattern and the need for application of image processing to remove Moire patterns.
Abstract: A two-dimensional array of non-uniformly spaced pixels having a plurality of overlaid pixel sets for avoiding moire patterns in digital images by avoiding producing an inherent “frequency” or pattern that may interfere with details or harmonics present in the image source, thereby eliminating the occurrence of moire patterns and the need for application of image processing to remove Moire patterns. A first set of pixels, (imaging sensors or display elements) are arranged along a two axes according to a non-uniform predictable process. The first set pixels spacing inherently produces non-uniformly spaced and sized “gaps”, in which additional sets of pixels potentially having a different characteristics from the first set, may be placed, thereby yielding an array comprised of multiple overlaid arrangements of non-uniformly spaced pixels. As such, images samples from or displayed on the additional sets of pixel sensors also avoid production of Moire patterns.

36 citations


Journal ArticleDOI
Moon-sik Jeong1, Seung-Woo Kim1
TL;DR: In this article, a high-speed moire method of color grating projection is presented, which performs phase-shifting 3D contouring with only a single operation of fringe capturing.
Abstract: We present a high-speed moire method of color grating projection, which performs phase-shifting 3-D contouring with only a single operation of fringe capturing. Three red, green, and blue pairs of projection and viewinggratings are fabricated on a single glass plate with predetermined lateral offsets. The glass plate is translated along with the color gratings during measurement at a fast speed, so that a color CCD camera simultaneously monitors three separate patterns of moire fringes with 2π/3 phase offset. This time-integral fringe capturing enables us to obtain high-quality moire fringes with the line images of the original viewing gratings inherently removed, which leads to better measurement accuracy with less computational burden of fringe processing.

28 citations


Journal ArticleDOI
TL;DR: This work deals with the less-studied case of images formed at finite distances from the gratings, using an extended monochromatic light source.
Abstract: 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 moire 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.

24 citations


Journal ArticleDOI
TL;DR: In this article, a digital collimation technique based on the self-imaging phenomenon is proposed, where a moire pattern is observed by viewing the Fresnel image of an original selfimaged grating through a second grating.

13 citations


Patent
11 Jun 2002
TL;DR: In this article, the dot cells of color images of C, M, K are set under the condition of a non-rational tangent, and a halftone image is generated using dot cells thus produced.
Abstract: Dot cells are made up of halftone threshold data of color images of C, M, Y, K. At least the dot cells of color images of C, M, K are set under the condition of a non-rational tangent. Halftone screen periods and screen angles of said three color images of C, M, K are set such that a period and an angle of a primary moire pattern produced when two of the three color images of C, M, K are superposed are substantially equal to a halftone screen period and a screen angle of the remaining one of the three color images of C, M, K. A halftone image is generated using dot cells thus produced.

13 citations


Journal ArticleDOI
TL;DR: This work describes a novel approach of strain segmentation for the moire pattern using a multichannel Gabor filter that allows for user-specific segmentation, which is essentially in engineering design and analysis.
Abstract: Moire interferometry is a powerful technique for high sensitivity in-plane deformation contouring. However, from an engineering viewpoint, the derivatives of displacement, i.e., strain, are the desired parameter. Thus there is a need to differentiate the displacement field. Optical and digital methods have been proposed for this differentiation. Optical methods provide contours that still need to be quantified, while digital methods suffer from drawbacks inherent in the digital differentiation process. We describe a novel approach of strain segmentation for the moire pattern using a multichannel Gabor filter. Appropriate filter design allows for user-specific segmentation, which is essentially in engineering design and analysis.

12 citations


Journal ArticleDOI
TL;DR: In this paper, an application of shear plate interferometry combined with moire readout to monitor/measure out-of-plane vibrations is presented, where Moire fringes are produced between the fringe pattern from the Shear plate and interferometric grating recorded by photographing the interference pattern generated from the shear plates.

10 citations


Proceedings ArticleDOI
29 May 2002
TL;DR: This paper proposes a phase- shifting scanning moire method using a DMD, which can obtain an image of equal-height contours within a frame time and develops a D MD reflection-type CCD camera called as 'DMD camera'.
Abstract: Grating projection methods have been often used for non- contacting shape measurement An image of equal-height contours of an object can be obtained in real-time using moire topography We have developed the phase-shifting scanning moire method for real-time shape measurement with high resolution But there is a problem that the measuring error becomes larger when the object is moving speedily because several images are captured while shifting the grating phase In this paper, we propose a phase- shifting scanning moire method using a DMD, which can obtain an image of equal-height contours within a frame time The direction of a ray reflected at each mirror of a DMD can be selected quickly For this purpose, we developed a DMD reflection-type CCD camera called as 'DMD camera' The camera works as a camera whose each pixel has a shutter The structure and an experimental result to confirm the algorithm to obtain a contour image using het DMD camera are shown

Journal ArticleDOI
01 May 2002
TL;DR: In this article, a light guide with prismatic grooves and micro scatterers on the surface was designed and prototyped, and the new pattern of the micro scaterers effectively prevents moire patterns, and improves the luminance homogeneity.
Abstract: the notion of discrepancy, we developed a new technique for generating uniformly distributed dot patterns. We designed and prototyped a light guide having prismatic grooves and micro scatterers on the surface. We experimentally confirmed that the new pattern of the micro scatterers effectively prevents moire patterns, and improves the luminance homogeneity.

Patent
22 Mar 2002
TL;DR: In this paper, a lattice pattern-projecting-based 3D shape measuring method was proposed to measure the shape of a hard object and a soft object by projecting moire fringes obtained by overlaying two lattices one on top of the other.
Abstract: PROBLEM TO BE SOLVED: To provide a three-dimensional shape measuring method and device capable of improving a lattice-pattern-projecting-type three-dimensional shape measuring method and measuring not only the three-dimensional shape of a hard object but also that of a soft object such as a living body by projecting moire fringes obtained by overlaying two lattices one on top of the other and obtaining a projection pattern with high sinusoidal properties SOLUTION: The plurality of lattices GA and GB are overlaid one on top of the other at appropriate distances from an object to be measured A to make the relative angle θ between the lattices variable, and the lattices are arranged in such a way as to be simultaneously or relatively moved The relative angle and relative distance between the lattices are adjusted according to the three- dimensional shape of the object to be measured A A light source C is applied from behind the lattices GA and GB to project moire fringes by each lattice to the surface of the object to be measured via a projecting lens The image of a fringe pattern formed on the surface of the object is picked up to obtain image pickup data, and arithmetic processing is performed on the image pickup data to obtain the three-dimensional shape of the object

Patent
Ryuuji Sakita1
08 Mar 2002
TL;DR: In this article, a method and an apparatus for surface configuration measurement of the present invention use stereoscopic lattice type of moire optics as testing optics, which accurately shifts moire fringes of particular fringe order by a preselected phase without any shift error.
Abstract: A method and an apparatus for surface configuration measurement of the present invention use stereoscopic lattice type of moire optics as testing optics. The moire optics accurately shifts moire fringes of particular fringe order by a preselected phase without any shift error. A line sensor camera, which is a specific form of a camera, limits a measurement range to the vicinity of the particular fringe order. The camera outputs at least three moire image data shifted in phase. A phase shifting method can therefore be easily applied to the stereoscopic lattice type of moire optics without giving any consideration to the accurate phase shift of the entire fringe orders. The apparatus can measure the surface configuration of a work with high accuracy.

Patent
27 Mar 2002
TL;DR: In this paper, a surface shape measurement apparatus for measuring a shape of an object to be examined by a simple mechanism for rotating a reference grid is presented, which consists of a stage on which the object is rested, a reference Grid disposed in parallel to the stage, illumination means for illuminating the reference Grid and projecting an grid pattern onto the object surface, photographing means for photographing the grid pattern projected onto the surface through the reference grid and obtaining an image of moire fringes, rotation means for rotating the reference grids about an axis normal to a grid surface of the grid
Abstract: A surface shape measurement apparatus for measuring a shape of an object to be examined by a simple mechanism for rotating a reference grid. The apparatus comprises a stage on which the object is rested, a reference grid disposed in parallel to the stage, illumination means for illuminating the reference grid and projecting an grid pattern onto the object surface, photographing means for photographing the grid pattern projected onto the object surface through the reference grid and obtaining an image of moire fringes, rotation means for rotating the reference grid about an axis normal to a grid surface of the grid plate, and analysis means for analyzing the shape of the object surface based on information about a rotation angle of the reference grid and intensity of the moire fringes.

Journal ArticleDOI
TL;DR: An alternative object positioning technique based on digital moire, which applies the concept of measuring a global maximum contrast to each image, which allows to obtain both the best contrast and the adequate rotation.

Journal ArticleDOI
TL;DR: In this article, a novel fringe processing method is proposed to obtain the curvature fringes by a quasi-real-time technique incorporating the developed opto-digital system, and the proposed moire reconstruction scheme is employed to extract the curvatures information from the carrier slope fringes.

Book ChapterDOI
01 Jan 2002
TL;DR: The topic of moire pattern synthesis deals with creating images that, when superimposed, will reveal certain desired moire patterns.
Abstract: Moire phenomena occur when two or more images are nonlinearly combined to create a new “superposition image”. Moire patterns are patterns that don’t exist in any of the original images but appear in the superposition image for example as the result of a multiplicative superposition rule. The topic of moire pattern synthesis deals with creating images that, when superimposed, will reveal certain desired moire patterns.

Patent
01 Apr 2002
TL;DR: In this article, a device for inspecting parts is provided to improve the device using Moire interference pattern, where a projection grid glass generates image of projection grid with light from a lighting device and a relay lense images the Moire pattern.
Abstract: PURPOSE: A device for inspecting parts is provided to improve the device using Moire interference pattern. CONSTITUTION: A device includes a projection grid glass(43); a lense(34); a grid lense(42); a relay lense(39); a charge coupled device(CCD) camera(30); a beam splitter(41); and a signal processing part. The projection grid glass generates image of projection grid with light from a lighting device(32). The lense forms the image of projection grid pattern on a surface of an electronic part(46') by projecting the image of projection grid pattern on the surface of the electronic part and images the image of projection grid pattern reflected from the surface of the electronic part. The image forming grid is interfered with the image of projection grid pattern passing the lense to form Moire pattern. The relay lense images the Moire pattern. The CCD camera take a picture of the Moire pattern. The beam splitter reflects image of pattern formed by the projection grid to the lense and passes image of projection grid pattern reflected from the surface of the electronic part. The signal processing part processes the Moire pattern detected by the CCD camera to form a three-dimensional image.

Patent
18 Sep 2002
TL;DR: In this article, the phase shift method was applied to a stereoscopic lattice type moire optical system without any shift errors by a desired shift, and a line sensor camera was used for an image pickup camera for limiting the measurement range close to a specific order of fringes.
Abstract: PROBLEM TO BE SOLVED: To easily apply the phase shift method to a stereoscopic lattice type moire method without any difficulty. SOLUTION: The stereoscopic lattice type moire optical system is used as an inspection optical system, a moire fringe having a specific order of fringes is accurately shifted without any shift errors by a desired shift, and at the same time a line sensor camera is used for example for an image pickup camera for limiting the measurement range close to a specific order of fringes for obtaining image data of at least three moire fringes that are phase-shifted, thus eliminating the need for considering the accurate phase shift of the total order of fringes, easily applying the phase shift method to the stereoscopic lattice type moire method without any difficulty, and accurately measuring the surface shape of an object to be measured.

Patent
16 Dec 2002
TL;DR: In this paper, the problem of providing an image processing apparatus and an image recording apparatus capable of obtaining high-definition copying result was solved. But the problem was not addressed in this paper.
Abstract: PROBLEM TO BE SOLVED: To provide an image processing apparatus and an image recording apparatus capable of obtaining high-definition copying result. SOLUTION: Input image data obtained by reading an image from an original by an image input section 12 are subjected to color conversion from RGB to YMCK by an image processing section 14, the color-converted data are dithered and formed into dots for each color to be supplied to a printing section 16. In this case, a dot recognizing section 24 obtains the number of lines of dots and angles of an image represented by the input image data i.e. an input image, thereby obtaining the feature of dot periodic patterns on the input image. A halftone generating section 26 generates a halftone screen having a pattern being the same as the number of lines and the angles which are obtained i.e. the dot pattern, and the generated halftone screen is used for dithering of the input image in a halftone processing section 22. As described above, by matching the pattern of the halftone screen with the dot pattern, interference between the both can be eliminated, and the generation of moire at the time of performing printing processing in the printing section 16 can be eliminated. COPYRIGHT: (C)2004,JPO&NCIPI

Journal Article
TL;DR: Moire fringe scanning method of digital ring gratings is proposed instead of generating ring Moire fringe by superposition of real circular grating and non-fractive beam, the author photographed the beam images into computer, and then superposed them with a digital circle grating, whose center position is close to the measured images.
Abstract: Moire fringe scanning method of digital ring gratings is proposed Instead of generating ring Moire fringe by superposition of real circular grating and nondiffractive beam, the author photographed the beam images into computer,and then superposed them with a digital circular grating, whose center position is close to the measured images Changing the phase of digital grating can realize Moire fringe scanning The global center of beam pattern can be calculated by multi_frame scanning images Because the total data of pattern are used in calculation, the determination of center of the ring pattern with noise is realized with subelement sensitivity Statistical analysis shows that this method features good anti_interference ability The application of this method in the measurement of space straightness error is also introduced

Proceedings ArticleDOI
15 Feb 2002
TL;DR: In this article, a hybrid grating which consists of a conventional binary grating and a liquid crystal (LC) binary gating is proposed to overcome the non-sinusoidal transmittance of the grating.
Abstract: This paper describes a structured lighting method for the measurement of surface profiles of mat objects. In this kind of profilometry, a grating with binary transmittance distribution has been utilized. In these cases such a problem is known that an error is caused due to the non- sinusoidal transmittance of the grating. Another practical difficulty is in mechanical shifting of the grating. Here we propose to use a hybrid grating which consists of a conventional binary grating and a liquid crystal (LC) binary grating. Moire pattern produced by superposing these two binary gratings is available to overcome these problems. When two binary gratings are overlapped, the resultant moire pattern becomes closely sinusoidal in intensity distribution. And, when the LC grating pattern is moved, the projected pattern can be shifted arbitrarily in phase. Surface profiles of some samples are measured to show validity of hybrid grating projection and utility of the prototype system.

Proceedings ArticleDOI
23 Jul 2002
TL;DR: In this article, the projection moire topography is used for the measurement of three-dimensional shapes of objects, which is referred to as the topography, and the measurement is illustrated on the example of measuring pump blade.
Abstract: The article is dealing with the measurement of three-dimensional shapes of objects. Such measurement is called the topography. The one of moire methods — the projection moire topography —is used. For improvement of measurement quality some methods are introduced. At first it is the washing-up method which deletes the linear background. At second the fringe-shifting method is described used for increasing of data quantity. And finally the optical/digital fringe multiplication is mentioned as a method for increasing the accuracy ofmeasurement. The topography is illustrated on the example ofmeasurement ofpump blade including its theory, experimental set-up and results.

Proceedings ArticleDOI
10 Dec 2002
TL;DR: An adaptive method for smoothing the moire patterns in image space is proposed in this paper, which uses moire strength information that is determined off-line by analyzing interference between different color halftone patterns.
Abstract: The color inverse halftoning technique was developed for the use of scanned color halftone images in digital applications, which is basically a smoothing method of halftone patterns. Smoothing of the moire phenomenon in color halftoning unfortunately leads to excessive blurring of the boundaries because moire patterns form very low-frequency peaks in the spectral domain. An adaptive method for smoothing the moire patterns in image space is proposed in this paper, which uses moire strength information that is determined off-line by analyzing interference between different color halftone patterns. The information is stored in tables and is looked up directly with color values of each pixel, so the proposed method works very fast. Through several experiments, we found that our experimental method smoothed moire patterns well without blurring the boundaries much.

Patent
27 Dec 2002
TL;DR: In this paper, a halftone dot area mask was created to suppress generation of moire for performing high quality reduction ratio conversion on image data including an image expressed by halFTone dots in digital image processing.
Abstract: PROBLEM TO BE SOLVED: To suppress generation of moire for performing high quality reduction ratio conversion on image data including an image expressed by halftone dots in digital image processing. SOLUTION: A halftone dot area recognition means 11 detects the halftone dots by a pixel assembly unit from the image data to recognize the halftone dot area with the halftone dots. A halftone dot area mask creation means 12 creates a mask pattern from a distance between the halftone dots. A halftone dot area separation means 13 separates the halftone dot area from other non-halftone dot areas in the mask pattern. A halftone dot area reduction ratio conversion means 14 converts the respective halftone dots in the halftone dot area so that they give an approximately linear symmetric shape by adding/removing pixels. A non-halftone dot area reduction ratio conversion means 15 converts the non-halftone dot area by another technique. A halftone dot area/non-halftone dot area synthesis means 16 synthesizes the converted halftone dot area and non-halftone dot area. COPYRIGHT: (C)2004,JPO&NCIPI

Journal ArticleDOI
TL;DR: In this paper, the intensity of the fringes is related to the depth information of a body and the order of fringes are determined by means of an intensity analysis of the moire pattern, the depth regions are divided into several depth regions, and the phase analysis is carried out to compute the depth value.
Abstract: In the conventional moire topography, equicontour patterns can be obtained from one image. Since the problem of determination of the number of fringes remains, unique depth distance cannot be measured and hence automatic measurement is difficult. In the present research, the intensity-modulated projection light and a transmission coefficient-modulated observation grating are used to generate an intensity-modulated moire in which the intensity of the fringes is related to the depth information of a body. Next, by means of an intensity analysis of the moire pattern, the order of the fringes is determined and the moire pattern is divided into several depth regions. Finally, in each depth region the phase analysis is carried out to compute the depth value. Based on this research, a simple apparatus is used for resolving the problem described above and automation of moire three-dimensional measurement is realized. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 85(1): 71–80, 2002

Journal ArticleDOI
Jun Mochizuki1, Toshio Asano1
TL;DR: The authors quantify the display acquisition image, then clarify how to find the acquisition moire from the dimensions of the display system and acquisition target using computations, and formulate a method for determining a pixel shift which inverts the moire phase in a pixel-shifted image.
Abstract: Creating valid digital images for display surfaces is vital for the quantification of display quality (defects, spots) for display devices. However, when imaging a spatially discrete display surface using individual acquisition elements, an acquisition moire appears in the acquisition image. In this paper the authors quantify the display acquisition image, then clarify how to find the acquisition moire from the dimensions of the display system and acquisition target using computations. Based on these results, the authors formulate a method for determining a pixel shift which inverts the moire phase in a pixel-shifted image. They then propose a method to compute the average in pixel units of gradations between a reference image and a pixel-shifted image given by a reference image and a pixel-shifted image created using the above method. Finally, they verify the effects of reducing the acquisition moire using simulations. © 2001 Scripta Technica, Syst Comp Jpn, 33(1): 27–37, 2002

01 Jan 2002
TL;DR: A method for combining two dispersed-dot halftoning masks for two colors that generalizes the traditional angular displacement used with clustered- dot halftone screens is investigated.
Abstract: We investigate a method for combining two dispersed-dot halftoning masks for two colors that generalizes the traditional angular displacement used with clustered-dot halftone screens. Our masks were two variations of the Linear Pixel Shuffling algebraic mask algorithm involving numbers arising from two different third order, Fibonacci-like recurrences, As an alternative to screen rotation, these masks were repositioned by flipping and rotating, and all pairwise positional combinations of the transposed, inverted masks were used two at a time to generate cyan and magenta images, each at nominal dot fractions of 0.25. The resulting blue images were evaluated for color uniformity and moire using visual evaluations, Fourier analysis, and a color micro-variation analysis. This presentation will describe the analytical techniques used to evaluate color uniformity and moire. 1. Background: Dispersed Dot Halftoning Masks The halftone mask method to convert a gray-scale image, I, to a bi-level image, B, employs a mask, M, as follows. Given a gray-scale image, I, of dimension H x W, we can use a mask M, of the same dimensions to convert I to a similar looking bi-level image B by the following rule: 1, if I ≥ M pq pq Bpq =  0, if I pq < Mpq (1) In this form, we assume that the values of the image and of the mask are in the same range, typically 0–255 or 0.0–1.0. M can be constructed many ways. Roberts’s methods simply uses pseudorandom numbers (white noise) and produces barely acceptable, mottled, bi-level images. B. Bayer introduced a method of constructing M in terms of 3 replicated sub-windows or tiles. R. Ulichney presents a 4 wide variety of methods for constructing such tiles. We previously presented methods for creating masks 1,2 based on third-order linear recurrences, which we briefly review here. Two useful recurrences are the sequences referred to as G and T given by G 0 = 0, G1 = G2 = 1 (2) G = Gn-1 + Gn-3 for n > 2 (3) n T 0 = 0, T1 = T2 = 1 (4) T = Tn-1 + Tn-2 + Tn-3 for n > 2 (5) n T is known as the Tribonacci sequence, a generalization of the Fibonacci sequence. Let A = Sn, B = Sn+1, C = Sn+2 (6) where {Sn} is either of our sequences. Define a mask, M by the rule Mpq = (pA + qB)%C (7) 0 9 5 1 10 6 2 11 7 3 12 8 4 6 2 11 7 3 12 8 4 0 9 5 1 10 12 8 4 0 9 5 1 10 6 2 11 7 3 5 1 10 6 2 11 7 3 12 8 4 0 9 11 7 3 12 8 4 0 9 5 1 10 6 2 4 0 9 5 1 10 6 2 11 7 3 12 8 10 6 2 11 7 3 12 8 4 0 9 5 1 3 12 8 4 0 9 5 1 10 6 2 11 7 9 5 1 10 6 2 11 7 3 12 8 4 0 2 11 7 3 12 8 4 0 9 5 1 10 6 8 4 0 9 5 1 10 6 2 11 7 3 12 1 10 6 2 11 7 3 12 8 4 0 9 5 7 3 12 8 4 0 9 5 1 10 6 2 11 Figure 1. A tile of an algebraic mask for halftone mask with parameters A = 6, B = 9, C = 13. This defines a mask with valued periodic in p and q with period C in both cases—that is a C x C tile—with the values {0, 1, ...,C 1} each appearing C times in the tile. The latter observation is a consequence of gcd (Sn, Sn+1, Sn+2) =1 (8)

01 Jan 2002
TL;DR: In this article, a method of spatial straightness measurement by means of non diffracting beam and moire fringe is proposed, where a ring grating is mounted on the moving object.
Abstract: A method of spatial straightness measurement by means of non diffracting beam and moire fringe is proposed. The non diffracting beam is used as a straightness datum. A ring grating is illuminated by this beam. Because the cross section pattern of the non diffracting beam is also a set of ring fringes, a ring moire fringe on the grating surface will be generated. The grating is mounted on the moving object. If the movement track of the grating depart from the center line of the non diffracting beam, the position of the moire ring will also depart. The quantity of the moire ring departure is many times greater than that of the grating. Therefore an amplified two dimensional straightness signal is generated. Image processing techniques are used to calculate the center of the moire ring. Theoretical analyses and experiment results show that the proposed straightness measurement method has the advantages of high sensitivity and resistance of laser beam drift.