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Digital Halftoning
Published in Edward R. Dougherty, Digital Image Processing Methods, 2020
Paul G. Roetling, Robert P. Loce
Spatial resolution and aliasing are two key considerations of digital image processes. People often refer to spatial resolution as the highest frequency that may be reproduced. To be more precise, we should separate resolution and addressability. Resolution is the highest spatial frequency that can be seen, and half the addressability frequency is the highest the system may represent. Aliasing, or moire, refers to spurious low-frequency components introduced by the digital imaging process. These fundamental sampled system issues are often best understood from a frequency-domain perspective. Such is the case in ordered- dither halftoning. The Fourier transform of the halftone image can be expressed in series form, where one term is the Fourier transform of the original image. Resolution, information density, and aliasing can be understood by examining the other terms of the series. These terms depend on the halftone-dot fill order. Due to nonlinearity of the process, the analysis is quite lengthy and complicated. Here we present only a qualitative description of the results. The reader is directed to the references for a detailed mathematical analysis [2,3,42,71].
Performance Assessment of Small Animal Imaging Systems and Common Standards
Published in George C. Kagadis, Nancy L. Ford, Dimitrios N. Karnabatidis, George K. Loudos, Handbook of Small Animal Imaging, 2018
Aliasing usually appears as a Moire interference pattern superimposed on the image. Aliasing means that the imaging system has undersampled the object and the image representation is not accurate as a result, with higher frequency signals being presented as low-frequency signals. All frequencies above the Nyquist frequency, defined as half the sampling frequency, will be aliased resulting in reduced fine detail in the image. Unfortunately, aliasing is unlikely to be completely eliminated in any digital imaging application; however, increasing the sampling frequency can reduce the effects of aliasing. For spatially aliased images, the solution is to increase the number of pixels in the image that represent the object. In addition, using a field of view that is smaller than the object can cause aliasing, so increasing the size of the field of view may also improve the images. For images that are obtained from a series of projections at different angles around the subject, such as CT, SPECT, and PET, increasing the number of angles used to obtain the data can reduce angular aliasing. Finally, for studies that are monitoring dynamic processes, temporal aliasing can occur. Reducing the temporal aliasing will require faster electronics to obtain each image faster, thereby increasing the sampling frequency.
Nondestructive Evaluation (NDE) of Materials and Structures from Production to Retirement
Published in Yoseph Bar-Cohen, Advances in Manufacturing and Processing of Materials and Structures, 2018
Moire interferometry is used to measure tiny deformations of solid bodies, caused by mechanical forces, temperature changes, or other environmental changes. Displacement, rotation, curvature, and strain of a body are the key parameters that are typically evaluated. With the aid of some special patterns, known as the moire patterns, the effects of the distortions of the body are magnified to provide a visual picture (Sharpe, 2008). In moire interferometry, the visual patterns are produced by the superposition of two regular motifs that geometrically interfere. Regular motifs can be a set of equispaced parallel lines, rectangular arrays of dots, concentric circles, or equispaced radial lines. One needs to understand the basic theory of geometric moire to measure displacements and strains from the moire patterns formed by the moire interferometry. The theory of geometric moire is described in a simple manner in the following section.
The off-axis moiré effect in double-layered cylinder
Published in Journal of Modern Optics, 2023
The moiré effect is an optical effect, ‘a well-known phenomenon which occurs when repetitive structures (such as screens, grids or gratings) are superposed or viewed against each other. It consists of a new pattern of alternating dark and bright areas which is clearly observed at the superposition, although it does not appear in any of the original structures’ [1]. In other words, the moiré effect is the effect of the formation of patterns of a longer period caused by the point-by-point interaction between similar periodic structures of shorter periods, accompanied by the averaging (or another low-pass filter) in the neighbourhood of the corresponding points.
Measurement of microscopic strain distributions of CFRP laminates with fiber discontinuities by sampling moiré method
Published in Advanced Composite Materials, 2022
M. J. Mohammad Fikry, Qinghua Wang, Masaru Irita, Shien Ri, Nobuyuki Toyama, Vladimir Vinogradov, Shinji Ogihara
In recent years, the moiré technique has attracted considerable attention and has been applied to the deformation measurement of various materials. Ever since the moiré technique was first reported in 1948 [31], various moiré methods have been successively developed for in-plane and out-of-plane deformation measurements [18,32–37]. A study by Yoneyama et al. [32] applied the Virtual Fields Method in combination with moiré interferometry to identify the through-thickness material properties of CFRP. Although moiré interferometry has very high sensitivity and works well in micron/nano-scale deformation measurement, the light path is complicated, and high-level operation experience is necessary [34]. In recent years, apart from the traditional moiré methods (moiré interferometry, geometric moiré, the digital moiré method, etc.), a sampling moiré method [34] has been proposed and developed for micron/nano-scale deformation measurement [33,35]. The displacement can be accurately measured from a single-shot grid image using a spatial phase-shifting technique. Wang et al. (2019) showed some applications of the sampling moiré method in the microscopic strain measurement of CFRP laminates [36], where the interlaminar shear behavior of an angle-ply-laminated CFRP specimen was investigated. In this study, a recently developed sampling moiré method based on previous developments by Wang et al. [18,33,35] and Ri et al. [34] was applied to measure the existing strain around the resin pocket due to fiber discontinuity in unidirectional (UD) CFRP laminates. This was done to investigate the deformation behavior that caused the damage due to fiber discontinuity in these laminates. A UD laminate, with its simpler damage behavior compared to other laminate configurations, was used to acquire a deeper understanding based on previous efforts on material characterization [10–13].