Applications of The Moiré Optical Technique in ......A square grid is glued or drawn on the object surface meanwhile a Ronchi grid is placed between the square grid and the camera

EFITA/WCCA 2005 25-28 July 2005, Vila Real, Portugal

2005 EFITA/WCCA JOINT CONGRESS ON IT IN AGRICULTURE

Applications of The Moiré Optical Technique in Agricultural Engineering Problems.

Inacio Maria Dal Fabbro *, Silvestre Rodrigues **, Roberto Alves Braga Jr ***

* [email protected] - Professor,Faculty of Agricultural Engineering, UNICAMP, Campinas, SP, Brazil

**PhD candidate, ,Faculty of Agricultural Engineering, UNICAMP, Campinas, SP, Brazil

***Professor, Departament of Engineerin, Federal University of Lavras, Lavrtas, MG, Brazil

Abstract

The name moiré has its origin in the French language, referring to wave like pattern. When screens of same mesh density are superposed, fringes are generated which move when its relative positions are displaced (Sciammarella, 1982). Lord Rayleigh, 1874 (Oster et al, 1964) proposed the application of a moiré technique in testing diffraction grids. Mulot (1925) applied that technique in studying deformations of mica layers. Later on, Tollenar (1945) reported that moiré fringes can be used to magnify displacements, being also suitable as a photoelastic method. Recent reports present comprehensive classifications of the methods termed as moiré. Albiero et al (2003) reported the preceding research work, in which a divergent light beam, a less precise angle and distance data measurement and a slightly discontinuous sinusoidal grid have been employed, generating noise and image distortion. By improving the geometrical measurements, a highly continuous sinusoidal grid as well as a collimated light beam and a higher resolution CCD camera, the superposition of image discontinuities during the unwrapping procedure of the Phase Shifting method, as well as noise occurrence were satisfactorily avoided, improving the image processing.

I. Introduction. The name moiré has its origin in the French language, referring to wave like pattern. The phenomenon is generated when screens of certain mesh density are superposed, producing wave like patterns or fringes, which move when its relative positions are displaced (Sciammarella, 1982). The literature discloses the name of Lord Rayleigh ,1874 (Oster et al, 1964) which proposed the application of a moiré technique in testing diffraction grids. Mulot (1925) employed this technique in studying deformations of mica layers. Later on, Tollenar (1945) found that moiré fringes serve to magnify displacements, being suitable to photoelastic analysis. Recent reports present comprehensive classifications of the methods termed as moiré.

A very popular greed, named Ronchi grid, consists of parallel and equidistant dark stripes alternated by clear and transparent ones, as shown by Figure ....(A). The line located at the center of a clear or dark strip is called greed line and the distance between two consecutive lines is named period (p) and its inverse frequency (f), generally expressed in number of lines per millimeter. Any small change on the angle between greed lines will generate significative displacement on the fringes. This can be understood as a magnification effect on the displacement. Nishijima (1964) and Oster et al. (1964) present the following geometrical interpretation applied to moiré fringes. Considering two grids of equidistant lines, being greed R1 which keeps its stripes parallel to the y axis holding a period called p1 superposed on a R2 grid with a period named p2 different of p1 , being θ the angle between them. A third grid called moiré fringes will be observed as shown on the Figure 2.2. A close examination of this figure will lead to

θ

θϕ

cos2

sensen21

22

21

2

pppp

p

−+= (1)

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And

θcos2 21

22

21

21

pppp

ppp m−+

= (2)

in case of identical grids, i.e., equal spacing (a = b) the above equation will be reduced to:

( )2sen2 θap m = (3)

These fringes exhibit a sinusoidal appearance as it is seen on Figure 2. Observed light intensity is

the average intensity of the light transmitted through the grids 1 and 2 and the maximum intensity is observed at the center of the clear stripes and zero intensity value at the center of the dark stripes. The use of sinusoidal grids as shown on Figure 4. are associated to the geometry survey of non continuous surfaces. Concentric circles, ellipses or even uniformly sprayed points, as many other arrangements as well any surface exhibiting periodical configuration as brick wall, eye retina, TV definition lines, the grains of photographic films or laser speckle grains are able to generate the moiré phenomena. Figure 5 shows (A) a Ronchi grid, (B) a reticular grid and (C) a circular grid.

Figure 1 . Moiré fringes generation by superposition of two grids. Cloud (1988)

Figure 2. Moiré fringes generated by light transmission through two superposed parallel grids. Cloud (1988)

Figure 3 . Moiré fringes generated by the superposition of two parallel line grids.

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Figure 4 . Sinusoidal grids π/2 radian out of phase from each other (Albiero, 2003).

(A) Ronchi grid (B) reticular grid and (C) circular grid

Figure 5. Types of Grids ( Post, 1994; Malacara, 1992 ).

II. Methodology. The following moiré methods are considered fundamental methods, from which variations and

combination of methods are proposed. Shadow moiré method. This method consists in painting the object with white opaque painting to increase the contrast with

the grid dark lines. A Ronchi grid is then placed between the object and a white light source and a camera, resulting in a triangular disposition as shown on Figure .6 Fringes are generated between the real and projected grids.

Grid

Camera

Light SourceSpecimen

Grid

Figure 6. Shadow moiré setup (Post, 1994).

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Relative displacement method. A square grid is glued or drawn on the object surface meanwhile a Ronchi grid is placed between

the square grid and the camera Object, camera and light source form a triangular geometry as shown on Figure.7 Fringes are then generated in U (x) as well as V (y) principle directions.

Light Source

Camera

Specimen

Specimen Grid

Reference Grid

Specimen Grid

Figure 7. Relative displacement moiré setup.

Fringes conduction method.

In this case the specimen is axially loaded and deformed, inducing to a displacement of the grid

through the object surface. This procedure will provide a larger number of points containing information on surface topography or displacement to obtain relative displacement maps. Figure 8 exhibits the setup for this method.

Light Source

Camera

SpecimenLoad

LoadSpecimen Grid

Figure 8. Fringes conduction setup moiré method.

Fringes shift method.

In this case the reference grid moves either in a perpendicular direction of the grid lines or in the

axis normal to the reference grid surface or both, which also generates a fringe movement. Such a procedure will generate an increasing number of points with the desired information. Figure 9 exhibits the setup for this method.

Light Source

Camera

Specimen

Reference Grid

Reference Grid

Figure 9. Setup for the fringes shift method.

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Projection moiré method.

This method employs the projection of a grid onto the object surface by means of a slide projector

or multimedia projector. One or two projecting system setup can be used as shown on Figure 10 and Figure 11 In the second case three-dimensional information can be obtained.

Projector

Camera

Specimen Projector

Camera

Specimen

Projector

Figure 10. Projection moiré setup with one

projector. Figure 11. Projection moiré setup with two

projector.

Phase shifiting projection method.

In this method 3 or four out of phase sinusoidal grids are projected onto the object surface. An

adequate image processing will yield a topographic image of the object. Figure 12 shows the setup for this method.

Camera

ProjectorSpecimen

Sinusoidal Wave

Figure 12 Setup for the phase shifting projection method.

Virtual grids moiré method.

In this technique two out of phase coherent and collimated light beams are projected onto the

object surface generating a grid as well as the moiré patterns. Figure .13 exhibits the setup for this method.

Laser

Laser

Camera

Specimen

Virtual Grid

Figure 13. Setup for the virtual grids moiré method.

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Microscopic moiré with immersion interferometer method. Light speed exhibits constant value in the vacuum which diminishes as soon as it reaches a

refracting media because its frequency does not depends on the medium characteristics. This way, wavelength should decrease, increasing the projected grid frequency which increases the sensitivity in data adquisition. Resolution frequently reaches the error level of 0.08 micro meter. Figure 14 exhibits the setup for this method.

Imersion fluid

Mirror

Microscope

Laser Beam

Prism

Imersion Interferometer

Specimen

Virtual Grid

Figure 14. Setup microscopic moiré with immersion interferometer method.

II Results.

Several trials have been carried out with the objective of testing moiré techniques and selecting

methods as well as different setups, involving common agricultural subjects and needs. The following figures illustrates obtained final results.

Figure 15 . Three dimensional plant image

generated from a projection moiré technique by means of a sinusoidal grid. (Albiero et al, 2004).

Figure 16. Fringes generated on a tomato fruit through the shadow .moiré technique using a Ronchi grid. (Lopes et al, 2004).

Figure 17. Fringes generated on a wood

specimen under compression through the..moiré technique using a cartesian grid. (Albiero et al, 2004).

Figure 18. Fringes generated on a soil specimen under compression through the ..moiré technique using a cartesian grid. (Albiero et al, 2004).

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Figure 19 . Fringes generated on a egg

throughthe .moiré technique using a cartesian grid. (Shitakubo et al, 2004).

Figure 20. Three dimensional femoral bone image generated from projection moiré technique by means of sinusoidal grid (Piedade et al, 2004).

Figure 21. Fringes generated on a fish model

by means of a ....... moiré technique and processed by the Corel Photo Paint 10 software using cartesian grid.

Figure 22. Directional gradient map of an orange under diametrical compression of 7% , generated from a moiré technique using .grid.

Figure 23. Moiré fringes generated on a rotating rubber disk by means of a .moiré technique using a cartesian grid. (Mazzeti et al, 2004).

Figure 24. Isostrain contour lines on a bamboo internode, axialy loaded, generated from a moiré tecnique by means of a cartezian grid . ( Beraldo, Dal Fabbro, Albiero, Rodrigues, 2004).

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Figure 25. Front view of a loaded wooden

connection with fringes generated by the moiré process using reticular grid

Figure 26. .Pear fruit digital model generated by the phase shift shadow moiré using Ronchi grid.

Conclusions. Based on what it has been exposed before, it can be concluded that moiré techniques are of very

simple application and very useful in assisting the solutions of several agricultural engineering problems.

References. Mazzeti, V.; Dal Fabbro, I.M.; Braumbeck, O.. Application of a Moiré Technique in the Stress Distribution Mapping of Circular Rotors. Ciência e Tecnologia, pg 31-34, volume 10, year VII, Campinas, SP, Brazil, june, 2004. Vieira M. A. P. ; Dal Fabbro, I.M.; Gazzola, J. ; Rodrigues, S.; Albiero, D.; Lino, A.C.L. ; Moiré Assisted Three Dimensional Shape Survey of Symmetric Bodies. International Congress of Agricultural Engineering. Leuven, Belgium. CDRom. 12-16/09/04. Lopes, T.O.P. ; Shitakubo, F.; Dal Fabbro, I.M.. Three Dimensional Shape Survey of Fresh Tomatoes. International Congress of Agricultural Engineering. Leuven, Belgium. CDRom. 12-16/09/04. Piedade, S.R,; Dal Fabbro, I.M.; Albiero, D.; Rodrigues, S.; Maciel, A.J.S. Topographic Anatomy of the Human Knee (Distal Femoral Bone Model) Assisted by a Moiré Technique. International Congress of Agricultural Engineering. Antwerpen, Belgium. CD Rom. 12-16/09/04. Albiero, D.; Dal Fabbro, I.M.; Vieira, M.A.P,; Atarassi, R.; Rodrigues, S.; Lino, A.C.L. Moiré Interferometry Applied to Plant Architectural Studies II. International Congress of Agricultural Engineering. Leuven, Belgium. CD Rom. 12-16/09/04. Albiero, D.; Dal Fabbro, I.M.; Maciel, A. J. S.; Lanças, K. P.; Rodrigues, S. Lino, A.C.L.. Moiré Albiero, D.; Beraldo, A.L.; Dal Fabbro, I.M.; Rodrigues, S. Wood Characterization Based on a Moiré Technique. International Congress of Agricultural Engineering. Leuven, Belgium. CDRom. 12-16/09/04. Dias, F. S., Dal Fabbro, I.M. ; Shitakubo, F.; Albiero, D. A Moiré Supported Mechanical Behavior Study of Packed Nearly Spherical Fruits. International Congress of Agricultural Engineering. Leuven, Belgium. CD Rom. 12-16/09/04. Técnica de Moiré aplicada al análisis de tensiones en compresión en el Bambú Guadua. Simposio Internacional Guadua 2004. Pereira, Colombia. CDRom. 27 /09 - 02/10 /04. Beraldo, A. L. ; Dal Fabbro, I. M.; Albiero, D. ; S. Rodrigues. ffonso, E. A. ; Dal Fabbro, I. M.; Demarzo, M. A. Application of a Moiré Technique in Studying Wooden Structural Connections. International Congress - Information Technology in Agriculture, Food and Environment. ITAFE 03. Izmir, Turkey. CD Rom07-10 /10 /03. Vieira, M.A. P. ;Dal Fabbro, I. M.; Laurenti, R. Application of a Moiré Interferometric Technique in a Simple Structural Member Vibration Analysis. International Congress - Information Technology in Agriculture, Food and Environment. ITAFE 03. Izmir, Turkey. CDRom. 07-10 /10 /03. Affonso, E. A.; Dal Fabbro, I. M. ; Demarzo, M. A. Application of a Moiré Technique in Studying Wooden Structural Connections. International Congress - Information Technology in Agriculture, Food and Environment. ITAFE 03. Izmir, Turkey. CDRom. 07-10 /10 /03. Lino, A. C. L. ; Dal Fabbro; I. M. Shape survey of plant organs through moiré technique. International Congress of Agricultural Engineering. Budapest. CDRom. 30/06 - 04/07/2002.

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