Determination of small angular displacement by moiré fringes of matched radial–parallel gratings

Abstract

We investigate the properties of the moiré fringes of matched radial-parallel (MRP) gratings that are useful for the fine visual indication of angular displacements. Moiré patterns formed by overlapping two different MRP gratings of angular pitches, P(theta) and P(theta)? (<P(theta)), can provide a simple fringe-counting method for determining both the angle and the direction of the relative angular displacement of the gratings within the accuracy of (P(theta)?/M(theta)), where M(theta) is the angular magnification for radial vernier fringes.

A moiré method of visualizing electromagnetic force lines

“…On the other hand, we can also get the following relation from solving Eq. (12) and putting f m ðx; yÞ ¼ C 0 :…”

“…In the past years the moire´fringes formed by overlapping simple structures such as line, radial, and circular gratings have been widely examined [4][5][6][7][8]. Also, complicated types of gratings such as Fresnel zones, skewed radial lines, spiral lines, matched radial-parallel lines and elongated circles have been studied for specific applications in moire´metrology [9][10][11][12][13][14]. If any two gratings are superimposed onto each other, optical moire´s readily appear even under the illumination of a white light source.…”

Program for Enlightened and Productive Creativity Illustrated With a Moiré Patterns Lesson

“…These overlapped patterns are called moiré patterns. We have widely used these moiré patterns for measurement of rigid body translation and angular displacement (Kim et al, 1997;Song et al, 1998), surface contour generation , analysis of the three-dimensional moiré fringes (Yuk & Chang, 2001), refractive-index measurement (Nishijima & Oster, 1964), and computational imaging and vision (Amidror, 2000) in physics and technology. It consists of a new pattern of alternating dark and bright areas, which is clearly observed at the superposition (Amidror, 2000;Patorski & Kujawinska, 1993).…”

“…Theocaris (1969) said that these moiré patterns are a kind of intensity interference that can be acquired using incoherent light sources. There are various types of gratings such as parallel lines (Yuk & Chang, 2001;, criss-crossed (Yuk, Ryu, & Kim, 1995), circular (Song, Lee, Jo, Chang, & Yuk, 1998), radial, spiral (Yuk & Chang, 2001), elongated circular (Song et al, 1998), and matched radial parallel (Kim et al, 1997). According to the study by Takasaki (1970), there are shadow moiré and projection moiré techniques.…”

High accuracy zoom magnification measurement

“…The zoom magnification is mainly obtained from the distance measurement of two line edges. The measurement accuracy, therefore, is limited by the quality and position accuracy of the lines and the measurement accuracy of the line edges.A barcode [2][3][4] combined with image processing technology [5][6][7][8][9][10][11][12] has been widely used in measurement such as digital-level instrument for land survey, angular encoder and absolute linear encoder [13][14][15] . In this paper a barcode is applied to zoom magnification measurement for the first time.…”