Experimental Mechanics

, Volume 28, Issue 4, pp 409–416 | Cite as

Exact interpretation of moiré fringe patterns in digital images

  • C. A. Lee
  • T. G. Richard
  • R. E. Rowlands
Article

Abstract

Geometric moiré enjoys the advantages of simplicity of technique and equipment, and the ability to use white light. However, resolution has been hampered by difficulties in employing more than 40 ℓ per mm. The present paper illustrates the aspects of a digital imaging system relevant to the determination of fractional fringes, and enables reliable analysis from extremely few fringes.

In applying digital imaging to moiré analysis it is imperative that not only the optical characterization but also the features of the image recording system be well understood. Digitization, spatial-averaging operation and the aperture modulation are the most significant features critical to the interpretation of the digital image recorded.

This paper seeks to illustrate the interaction of the moiré technique with the characteristics of a specific image recording system. Examples are presented which experimentally define the nature of moiré fringes recorded with a relatively standard digital imaging system. Further examples are presented which illustrate the influences of the features of this imaging system on the interpretation of the moiré pattern.

Keywords

Mechanical Engineer Fluid Dynamics Digital Imaging Imaging System Significant Feature 

List of Symbols

an, bn

Fourier coefficients of transmittance functions for reference grating and specimen grating, respectively

b,b

width of the opaque bar of Ronchi gratings, undeformed and deformed

F{}

Fourier-transformation operator

G(u)

spectra of transmittance function

I(x)

light intensity at positionx

ID(x)

digitized light intensity

Ī(x)

averaged light intensity

Imax,Imin

local maximum and minimum of intensity profile

I0,I1

average and amplitude of intensity variations

M(u)

frequency-modulation function

N

fringe order

p,p

pitches of Ronchi gratings, underformed and deformed

rect (x, y)

rectangular functions

S(u)

spatial-averaging function

T(x)

transmittance function of overlapped gratings

Tr(x)

transmittance function of reference gratings

Ts(x)

transmittance function of specimen gratings

u(x)

displacement vertical to the reference grating at positionx

u,v

spatial-frequency coordinates

x,y

Cartesian coordinates

convolution operator

δ (x)

dirac delta function

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Copyright information

© Society for Experimental Mechanics, Inc. 1998

Authors and Affiliations

  • C. A. Lee
    • 1
  • T. G. Richard
    • 2
  • R. E. Rowlands
    • 2
  1. 1.Delco Moraine Division of General Motors CorporationDayton
  2. 2.Department of Engineering MechanicsUniversity of WisconsinMadison

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