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» Moire pattern. Moire fringe method and its application to determine stresses and strains Structure formation or thin structure

Moire pattern. Moire fringe method and its application to determine stresses and strains Structure formation or thin structure

The specialists of the Neman company have perfectly mastered the technology of applying polymer powder coating to both ready doors, and on non-standard designs. For this you have everything you need - knowledge, experience, strength and desire. Polymer painting is a waste-free and clean technology that allows you to obtain high-quality decorative, protective and decorative coatings.

Note that the appearance is formed from polymer powders applied to the painted part of the product fabric. Next, the product is heated and held at a certain temperature for several minutes. The low polymerization temperature makes it possible to paint glass and metal using this technology. In the last decade, this technology has gained great popularity and is gradually replacing traditional methods of applying paint and varnish coatings.

One of the finishing options offered by the Neman company is Moire. What is this coating? This is the finish front door, offering a special powder coating structure. So, upon completion of the work there will be a special pattern on the canvas. Speaking figuratively, moire can be compared to the effect that gives sandpaper. The main advantages of this type are: practicality, aesthetics and versatility. Typically, such products are used in cases where it is necessary to obtain the maximum practicality possible. It is also effectively used to hide defects in the outer part of a metal door.

What benefits does a consumer receive when choosing moire coloring?

  • High resistance to aggressive environments (alkalies, acids, organic solvents);
  • Resistance to mechanical stress;
  • Increased adhesion. IN in this case adhesion of paint particles to the surface being treated is 500 kg/nm;
  • High anti-corrosion resistance;
  • Environmental friendliness. The paint does not contain organic solvents or other types of volatile substances.

The main point of the painting method is to spray on previously cleaned metal coating powder paint. You need to know what paint particles get electrostatic charge, which allows the particle to stick to an object that has the opposite charge. Particles that have not had time to settle are captured in the spray chamber and can be used again. After this, the product is placed in a polymerization chamber for subsequent baking of the paint at a temperature level ranging from 180 to 200 degrees Celsius. Thus, a reliable, high-quality and safe decorative and protective design for humans is created on the canvas. Metal doors with Moire painting can be used not only for installation in apartments, cottages, but also in industrial facilities.

The production of “moire”, hammer, crackling, and “antique” coatings is based on the ability of certain paint and varnish materials during film formation, form beautiful patterns in the form of wrinkles, embossing or tears. Such coatings based on liquid paints have long been used in mechanical engineering, instrument making, the electrical industry and other industries. IN Lately similar coatings are obtained using appropriate powder paints. Hammer coatings are especially popular, as they have a smooth surface that does not become dusty and weakly retains radioactive contamination.

Moire coatings (Fig. 11.5, A) obtained by using powder epoxy paint P-EP-135 different colors. Similar

Paints are produced by many domestic and foreign enterprises. The corresponding wrinkled pattern is formed due to the presence of a special additive in the paint, which provides different speed curing of the film former along the thickness of the coating. Paints are applied to the surface using electrostatic spraying; coatings (thickness 80-120 microns) are cured at 180 °C for 15 minutes.

Moiré coatings can also be obtained using liquid paints(MA-224 paint on compacted (polymerized) tung or oitis oil). The coating technology in this case is much more complicated. Paints are applied to a pre-primed surface, usually in two layers with an interval of 5-10 minutes. The formation of the coating is carried out in two stages: at the first stage, the pattern is revealed, at the second it is fixed. Identification of the pattern is carried out at 80±5 °C for 25-40 minutes, the fixing operation is carried out at 100-170 °C depending on the type of paint and its color.

Hammer coatings (Fig. 11.5, B) in appearance they resemble characteristic patterns, obtained by minting metal. This effect is achieved by introducing into liquid enamels non-floating (low-grease) aluminum powder and pattern formers, which are organosilicon compounds - silicone oils, SKT rubber, Vaseline KV-EM-1. The latter, by changing the surface tension of the film former, contribute to its “contraction” (collection into drops) on the surface of the substrate and powder particles. In this case, violation of the continuity of the coating is not allowed.

To obtain hammer coatings, the industry produces melamine alkyd (ML-165 and ML-165M), nitrate cellulose (NTs-221), alkyd styrene (MS-160) and other enamels. Along with aluminum powder, they contain small amounts of covering mineral or organic pigments that give the coating a corresponding color tint. Enamels are usually applied by spraying (1-2 layers) onto a previously prepared and primed surface. Before use, a pattern former is introduced into them in the form of a 10% solution in xylene at the rate of 1-10 g per 1 kg of enamel. A drawing (pattern) is formed immediately after applying enamel to the surface. It is fixed (coatings are cured) in the case of ML-165 and ML-165M enamels at 120 °C for 1 hour, NTs-221 - at room temperature for 24 hours.

Powder paints (P-EP-258 and others) have also been developed to form hammer coatings. When using them, pattern formation occurs at the moment of coating formation due to surface effects in the film. They also contain aluminum powder. Depending on the type of color pigment, they form coatings of different colors and shades.

Hammer coatings made from liquid paints are used for finishing metal and wooden products: devices, movie cameras, sewing machines, cases for devices, etc. Powder paint coatings have the same purpose, but they are suitable for painting only heat-resistant substrates.

Cracked coatings (Fig. 11.5, IN) imitate the pattern of crocodile skin. To obtain them, both liquid and powder paints are used. As liquid formulations Nitrate cellulose paints are used, which are highly filled systems that are diluted with highly volatile solvents, such as acetone. Cracking is caused by the low cohesive strength of the resulting films and large internal stresses that arise during the rapid volatilization of solvents.

Paints are applied over a background layer of cellulose nitrate enamels, the color of which is usually chosen to contrast with the color of the cracking paint. In thick layers the paint cracks with large tears, in thin layers it cracks with small ones. Cracking occurs immediately after applying paint to the surface. After drying from solvents, the coating can be covered with a layer of varnish or enamel.

Recently, these paints have practically lost their importance for environmental reasons and fire hazard. This niche has been firmly occupied by powder paints that are more convenient to use. They are obtained by introducing aluminum powder and special structuring additives into thermosetting powder compositions, which, by stretching the powder particles in the surface layer, imitate the state of a cracked film. Unlike liquid paints, powder paints practically do not create a surface relief (it remains smooth), which contributes to the non-contamination of coatings. The size of the pattern depends on the viscosity of the melt.

Cracked coatings have a purely decorative purpose. Sometimes they are used to finish dashboards, cladding slabs and panels indoors.

Textured coatings (Fig. 11.6) create the effect of a surface with a large “shagreen”, similar to coatings made from paints and varnishes with poor spreading. The most widely used coatings are textured coatings based on thermosetting powder paints. Regulation of film texture is achieved purely by prescription - by introducing additives that change

Rice. 11.7. Antique colored coatings:

A- with aluminum powder; B- with bronze; IN- with zinc powder

Viscosity of melts (aerosil, thermoplastic polymers, etc.). Coatings can be different color, containing reflective pigments and not containing them. An example of compositions of this type are epoxy-polyester paints P-EP-259-T-1 and P-EP - 259-T-2, produced by OJSC NPF "Pigment". The macrorelief of the coatings formed from them makes it possible to hide defects in the surface of metals - casting, stamping, small irregularities with a film thickness of 80-100 microns.

"Antiques" (Fig. 11.7). The term “antique” appeared in coating technology with the development of a large number of powder paints containing flaked reflective pigments and fillers - powders made of aluminum, bronze, copper, zinc and other metals, as well as mica, pearlescent pigments, etc. Variation possibilities decorative effect Such coatings are practically unlimited. They are determined not only by the type of reflective component, but also by its dispersion, the method of introduction into the composition, the nature and amount of color pigments, and the presence or absence of structuring agents.

There are basically two methods of introducing flake pigments into powder compositions: before extrusion and after extrusion. In the first case, powder particles are chaotically distributed in the melt of the film former and, due to its high viscosity, lose the ability to float when producing coatings. A high reflective effect is achieved only in the second case, when the powder composition, after extrusion and grinding, is mechanically mixed with powder. Particularly attractive for obtaining compositions is the bonding process (mixing under moderate heat), in which powder particles are firmly attached to film-forming particles. This eliminates the separation of powder compositions when applied in an electric field. Any thermosetting film formers are suitable for producing antique-type coatings. The powder paint manufacturer Ekolon (St. Petersburg) has achieved particularly great success in developing formulations for such compositions.

Among other decorative coatings special attention deserve paint coatings called "chameleon". Their main feature is the change in color when viewed from different angles. Powder varnishes for chameleon-type coatings are produced on the basis of light-resistant polyester film formers with the use of special pigments, which are SiO2 compounds WITH microlayers TiO2, Fe2O3 and 2Yu2. Such pigments are offered by the company "Megsk".

moire, the name of the fabric) is a pattern that appears when two periodic mesh patterns are superimposed. The phenomenon is due to the fact that the repeating elements of the two patterns follow with slightly different frequencies and either overlap each other or form gaps.

A moire pattern is observed when superimposed on each other. various parts tulle curtains.

The concept of "moiré" comes from fabric moire, in the finishing of which this phenomenon was used.

Moiré pattern occurs when digitally photographing and scanning reticles and other periodic images if their period is close to the distance between the photosensitive elements of the equipment. This fact is used in one of the mechanisms for protecting banknotes from counterfeiting: a wave-like pattern is applied to the banknotes, which, when scanned, can become covered with a very noticeable pattern that distinguishes the counterfeit from the original.

Digital image processing

The appearance of moire during scanning

In everyday life, moire often appears when scanning printed images. This occurs because the scanner re-rasterizes an image that already has the original raster in it. It can be more simply imagined this way: if you take a tracing paper with one ornament and put it on a tracing paper with the same ornament, but depicted from a different angle, then the resulting ornament will differ from both the first and the second. If you put them so that they coincide, then the first ornament will coincide with the second.

The round “rosettes” at the intersection of two rectangles result in image distortion, which is visible in the first picture.

The appearance of moire during the screening process

Moire can also occur due to incorrect installation angles between the lines of primary colors when screening. Both are, in fact, the interference of two sets of raster lines. There are several types of moire rosettes, by the appearance of which you can often find out the cause of moire.

Scanning, in fact, is the modulation of signals in the scanner grid nodes by the brightness of the typographic raster nodes. IN general view the result is a product of two modulated sinusoids (gratings) with different periods of spatial oscillations. One harmonic may have a longer period, equal to the sum periods of both gratings, which causes moire. The second always has a period equal to the modulus of the difference between the grating periods and disappears because it cannot be implemented at a given scanning resolution.

Paints that affect moire

When printing with any set of inks, the most intense (dark) ink, which has a value of 30 to 70% over a large area, can produce moire. That is, if in a CMYK photograph the black channel does not dominate (<10-15 %) то вероятность возникновения различимого глазом муара минимальна. Таким образом можно почти не обращать внимание на жёлтый канал CMYK фотографии. Угол поворота растра между самыми проблемными каналами должен быть как можно ближе к 45°.

When printing “solid” (that is, with >95% coverage), the concept of “raster inclination angle” practically disappears (even if we're talking about about photography).

see also

  • Wave interference - a moiré pattern creates a superposition of waves of different lengths or directions.
  • Vernier - the overlapping of scales with different pitches generates a moiré pattern of parallel lines ( English).

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An excerpt characterizing the Moiré pattern

“Third, I said, third,” the prince shouted briefly, pushing away the letter, and, leaning his elbows on the table, pulled up a notebook with geometry drawings.
“Well, madam,” the old man began, bending close to his daughter over the notebook and placing one hand on the back of the chair on which the princess was sitting, so that the princess felt surrounded on all sides by that tobacco and senile pungent smell of her father, which she had known for so long. . - Well, madam, these triangles are similar; would you like to see, angle abc...
The princess looked fearfully at her father’s sparkling eyes close to her; red spots shimmered across her face, and it was clear that she did not understand anything and was so afraid that fear would prevent her from understanding all her father’s further interpretations, no matter how clear they were. Whether the teacher was to blame or the student was to blame, the same thing was repeated every day: the princess’s eyes grew dim, she saw nothing, did not hear anything, she only felt close to her. dry face strict father, felt his breath and smell and only thought about how she could quickly leave the office and understand the problem in her own open space.
The old man lost his temper: he pushed the chair he was sitting on with a loud noise, made an effort to not get excited, and almost every time he got excited, cursed, and sometimes threw his notebook.
The princess made a mistake in her answer.
- Well, why not be a fool! - the prince shouted, pushing away the notebook and quickly turning away, but immediately stood up, walked around, touched the princess’s hair with his hands and sat down again.
He moved closer and continued his interpretation.
“It’s impossible, princess, it’s impossible,” he said when the princess, having taken and closed the notebook with the assigned lessons, was already preparing to leave, “mathematics is a great thing, my madam.” And I don’t want you to be like our stupid ladies. Will endure and fall in love. “He patted her cheek with his hand. - The nonsense will jump out of your head.
She wanted to go out, he stopped her with a gesture and took out a new uncut book from the high table.
- Here’s another Key of the Sacrament your Eloise sends you. Religious. And I don’t interfere with anyone’s faith... I looked through it. Take it. Well, go, go!
He patted her on the shoulder and locked the door behind her.
Princess Marya returned to her room with a sad, frightened expression that rarely left her and made her ugly, sickly face even more ugly, sat down at her desk, lined with miniature portraits and littered with notebooks and books. The princess was as disorderly as her father was decent. She put down her geometry notebook and impatiently opened the letter. The letter was from the princess’s closest friend since childhood; this friend was the same Julie Karagina who was at the Rostovs’ name day:
Julie wrote:
"Chere et excellente amie, quelle chose terrible et effrayante que l"absence! J"ai beau me dire que la moitie de mon existence et de mon bonheur est en vous, que malgre la distance qui nous separe, nos coeurs sont unis par des liens indissolubles; le mien se revolte contre la destinee, et je ne puis, malgre les plaisirs et les distractions qui m"entourent, vaincre une certaine tristesse cachee que je ressens au fond du coeur depuis notre separation. Pourquoi ne sommes nous pas reunies, comme cet ete dans votre grand cabinet sur le canape bleu, le canape a confidences? Pourquoi ne puis je, comme il y a trois mois, puiser de nouvelles forces morales dans votre regard si doux, si calme et si penetrant, regard que j"aimais tant et que “je crois voir devant moi, quand je vous ecris.”
[Dear and priceless friend, what a terrible and terrible thing is separation! No matter how much I tell myself that half of my existence and my happiness lies in you, that, despite the distance that separates us, our hearts are united by inextricable bonds, my heart rebels against fate, and, despite the pleasures and distractions that surround me, I I cannot suppress some hidden sadness that I have been experiencing in the depths of my heart since our separation. Why aren’t we together, like last summer, in your big office, on the blue sofa, on the sofa of “confessions”? Why can’t I, like three months ago, draw new moral strength from your gaze, meek, calm and penetrating, which I loved so much and which I see before me at the moment I write to you?]
Having read up to this point, Princess Marya sighed and looked back at the dressing table, which stood to her right. The mirror reflected an ugly, weak body and a thin face. The eyes, always sad, now looked at themselves in the mirror especially hopelessly. “She flatters me,” thought the princess, turned away and continued reading. Julie, however, did not flatter her friend: indeed, the princess’s eyes, large, deep and radiant (as if rays of warm light sometimes came out of them in sheaves), were so beautiful that very often, despite the ugliness of her whole face, these eyes became more attractive than beauty. But the princess had never seen a good expression in her eyes, the expression they took on in those moments when she was not thinking about herself. Like all people, her face took on a tense, unnatural, bad expression as soon as she looked in the mirror. She continued reading: 211

When two systems of contrasting stripes are superimposed, a pattern appears formed by their thickening in places where the stripes of one system fall into the spaces between the stripes of the other system. The occurrence of such patterns is called moire effect.

The simplest moiré pattern occurs when two systems of equidistant parallel stripes (lines) intersect at a slight angle. A small change in the angle of rotation of one of the systems leads to significant changes in the distance between the elements of the moire pattern.

A moire pattern is also formed when two non-intersecting systems of equidistant parallel lines are superimposed, when the step size of one of the systems is slightly different from the other. Moreover, the smaller the difference in pitch, the greater the distance between the moire fringes. This makes it possible to obtain a colossal increase (millions of times) in the difference in the width of the spaces between the lines. In other words, the moire effect makes it possible to visually detect, without the use of optical systems, minute deviations in almost identical periodic structures. Currently, the moiré method is widely used to control the accuracy of dividing devices for the manufacture of diffraction gratings.

Moiré appears in an electron micrograph of two crystals superimposed so that their atomic lattices are almost identical. Any defect that disrupts the regularity of the crystal structure is clearly visible in the moiré pattern. The magnification is such that it allows one to see displacements of atoms, the magnitude of which is less than the diameter of the atom itself.

If two lattices of equidistant parallel straight lines, slightly different in step size, are moved one relative to the other in a direction perpendicular to the lines, then the stripes of the moiré pattern will move at a speed much greater than the relative speed of movement of the lattices themselves. In this case, the direction of their movement coincides with the direction of the relative displacement of the lattice with a smaller step. Thus, a small movement of one of the gratings results in a large movement of the moiré fringes, which is easy to detect and measure.

Application example:

A method for determining deformations from a pattern of moire fringes, characterized in that, in order to increase the accuracy of measuring deformations, the ratio of the speeds of mutual movement of the deformed and reference meshes and the speed of movement of the moire fringe is determined, and the magnitude of the deformations is judged by the value of this ratio.

The described manifestation of the moire effect has long been used in all measuring instruments with nondus, such as a micrometer or caliper.

The moiré effect can be used to visualize minute changes in the refractive index of transparent media by placing them between gratings. For example, you can visually study the dynamics of the dissolution of two substances.

The same principle allows for express analysis of the quality of optical parts. The lenses are placed between the gratings; the presence of a convex lens increases the elements of the moire pattern, while a concave lens decreases them. In this case, both lenses rotate the pattern in opposite directions at an angle proportional to the focal length. In places where the structure or shape of the lenses is inhomogeneous, the pattern lines are distorted.

Another example of optical control:

An interference method for measuring the wedge shape of optical transparent plates, which consists in focusing a beam of light from a laser using a lens into the plane of a hole in the screen, behind which a controlled plate is installed, differing in that, in order to increase the accuracy and productivity of measurements, from the controlled plate with its In a fixed position, a transparent copy of the interference rings is obtained, the plate is rotated in its plane by 180, the interference pattern is superimposed on the copy, and the wedge shape of the platinum is measured using the width of the moiré fringes formed from the overlap.

A variety of moiré patterns can be created by combining lattices formed by a wide variety of lines, such as concentric circles, spiraling wavy or radially radiating lines from a point, and even families of evenly spaced dots. In this way, it is possible to simulate many complex physical phenomena, such as the interaction of electrostatic fields, wave interference, and others. Some problems of architectural acoustics are solved using similar methods.

In Japan, it has been proposed to use the moire effect to compile topographic maps of objects. The object is photographed through a grid of thin threads, casting a clear shadow on it. The shadow is deformed in accordance with the relief of the object and when it interacts with the real lattice, a moiré pattern appears, superimposed on the image of the object. In the photograph, the distance between the moire lines corresponds to the depth of the relief. This method is very effective, for example, in studying the deformation of rapidly rotating parts, in analyzing the flow of a surface layer of liquid around bodies in medical anatomical studies.

The versatility of the moire method, the ease of converting various quantities with its help, close to IFR, high resolution - all this suggests that inventors will turn to the moire effect more than once in their practice.

When two or more grids (rasters) consisting of lines, dots or other geometric elements are superimposed, a picture appears consisting of alternating dark and light stripes. This phenomenon is called moire effect. A moiré pattern occurs if these two rasters are rotated relative to each other by any amount or have a slight difference in pitch (the distance between adjacent light or dark stripes of the same name).
What explains the phenomenon of moire? The human eye has limited resolution. A system of alternating dark and light stripes, the distance between which is visible at a viewing angle of less than 1A, is perceived by the eye as a solid gray field. When two systems of lines are superimposed, the intensity of light across the surface of the image changes, and this change in intensity is perceived as a moiré pattern.
The center of the light moire stripe coincides with point A, where the light lines of both rasters are combined. The center of the dark moiré stripe coincides with point B, where the dark line of one raster overlaps the light line of another raster.


Thus, the moire effect is an optical phenomenon that occurs when fine meshes are superimposed. The wavelength of the light does not matter in this effect, which is why the moiré effect is sometimes called mechanical interference. by analogy with ordinary light interference.
Interference is the addition of two periodic phenomena, which results in a third phenomenon with a larger period.
Moire stripes have the property of increasing movement.
Moiré stripe pitch


where a0, a1 are the pitch of the original and distorted rasters; φ - angle of rotation between raster lines.
From the analysis of the above equation it follows that small values ​​of the difference between the steps and the angle of rotation correspond to a large step size of the moiré fringes, that is, small deformations that cause raster distortion correspond to large parameters of the moiré pattern.
Let us determine the value of the relative degree of deformation εat φ = 0, if the step of the original raster a0 and the step of the moiré stripe n are known.

Where


The moire effect was discovered by Lord Rellay in 1874, but only in the second half of the 20th century, when it became possible to obtain sufficiently small and accurate rasters (up to 100 lines per 1 mm), this method began to be widely used in research practice.
The moire effect when studying the stress-strain state (SSS) of a metal is used in two directions:
- to study the stress-strain state by directly applying a raster to the surface of the model under study;
- to study the deflections of plates and shells by projecting rasters on them.

Study of stress-strain state when directly applying a raster to the metal surface


The raster is applied to the surface under study by scratching, etching or photo printing. The sample is then subjected to deformation, during which the raster is also deformed. Then the reference raster (the same as it was before the deformation) is superimposed on the deformed raster. As a result of their interference, a moiré pattern is obtained.
Moire stripes in this case are lines of equal movements of metal particles. That is, all particles lying on the moire stripe received the same movements equal to the pitch of the original raster. Therefore, by selecting the initial raster with the required pitch, it is possible to obtain data on metal deformation with the required degree of accuracy.


Since the moiré pattern carries information about the movement of metal particles only in the direction perpendicular to the raster lines, to obtain data on deformation in the plane under study it is necessary to apply another raster with the pin direction perpendicular to the first raster. Usually if VAT is investigated; in any cross-sectional plane of the sample, then a raster with a longitudinal lineature is applied to one half of the sample, and a cross-section to the other half; if the model under study has an axis of symmetry, then rasters with mutual perpendicular arrangement lines.
Denoting the displacement in the direction of the x1 axis through U, and in the direction of the x2 axis through V, the deformations can be written:

Taking into account that the moire stripe is a line of equal movements, knowing its order and price, the movements at the points of interest can be determined as follows:


where n,m is the serial number of the moire stripe; a0 - step of the original raster.
To determine the sign of deformation (compression or tension), one of the properties of moiré fringes is used, namely, the original raster superimposed on the deformed surface under study begins to rotate. If the moire stripes turn (shift) to the side, opposite direction rotation of the undeformed raster, then the sample was subjected to compressive deformation (the deformation has a negative sign); if the direction of rotation of the raster coincides with the direction of displacement of the moire fringes, tensile deformation occurs.

When determining the deformation at points that do not lie on the moire fringes, the interpolation method is used with the assumption that the movement of line to line occurs according to a linear law. In this case, the movement at point B


Using the found components of the deformation tensor at a point, the intensity of the deformation can be calculated


Knowing the relationship between the intensity of deformation (εi) and the intensity of stress (σi), the value of σi is determined. Then the components of the stress tensor are found.


When solving the problem for a plane stress state, these dependencies have the form:

As a result of processing the moiré pattern of displacements, it is possible to obtain fields of partial derivatives of lines of equal deformations, deformation rates, etc.
Thus, depending on the research task, a moiré pattern can provide large and varied information.

VAT research thin-walled structures, plates and shells


When studying the bends of shells, two research methods are used using the moire stripe method:
- using reflection of the designed raster (bending study on mirror models);
- using a shadow image of the designed raster (on surfaces that do not have a mirror surface). The essence of the first method of obtaining moiré patterns is that a mirror plate 2 is installed in front of the screen 3, on which the raster is depicted, and through a hole in the screen, the camera 1 records the image of the raster on the surface of the undeformed plate.
Then the model is loaded and the raster image is photographed again, but on the surface of the deformed model.


The angles of inclination of the curved surface of the deformed model dφ/dx in this case cause a shift in the lines of the reflected
raster images at an angle of 2dφ/dx. Overlays of the reflected raster before and after loading form a picture of moiré fringes, which are level lines constant angles rotation of the normal to the surface under study. Knowing the curvature of the surface through the angles of inclination of the normal, we can
Obtaining a mirror moiré pattern, calculate the stresses acting in the plate.
The disadvantages of this method include:
- the need for double photography of the reflected raster, since it is impossible to visually capture the moiré pattern;
- special preparation of the mirror surface of the object under study.
A moiré pattern, which characterizes the amount of surface deflection, can be obtained in another way - using a shadow image of the projected raster.
To obtain a shadow moiré pattern, a translucent raster 1 (made on glass or made of stretched threads) is placed at a fairly close distance above the model 2 under study. With oblique lighting (light source 3) in a direction perpendicular to its lines, a shadow image of the raster is formed on the surface of the model . By observing the raster and its shadow in a direction perpendicular to the raster plane (or at some angle β to it), one can see the pattern of moiré fringes as a result of the interference of the original and shadow rasters. This picture can be photographed and observed visually.
Deflection value for moiré stripe points


where m is the serial number of the moire stripe; a is the pitch of the original raster; α, β-angles (see figure).
Thus, in this case, the moiré stripe is the geometric locus of points of the same distance from the plane of the original raster to the surface under study.


Advantages moire method:
- research on real materials;
- high degree of accuracy in determining deformations;
- the method allows you to obtain an integral picture of the deformable state throughout the entire volume under study;
- the ability to study deformations regardless of their physical nature under static and dynamic loading.
The disadvantages of this method include the following:
- impossibility of studying large plastic deformations (more than 50%) and small elastic deformations (less than 1%);
- difficulty in obtaining small rasters (less than 20 lines per 1 mm).

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