DE19716785A1 - Shearing speckle interferometry measuring deformation gradients at free form surfaces - Google Patents

Abstract

The interferometry method and system measures contour inclination, for recording and evaluation and for computing phase distributions from the data obtained. Which allows qualitative and exact quantitative statements regarding the gradients of the contour. Which allow in-plane strains and/or out-of-plane deformations of the under investigation, any curved object surfaces. The coordinate values of the contour inclination are assembled together for the corresp. interference patterns, taking account of the measured deformations. So that they can be evaluated exactly using a computer (s).

Description

State of the art

For the observation of object surfaces for strain measurement using the electronic Speckle Pattern Shearing Interferometry, abbreviated shearography or ESPSI, becomes the Illuminated surface to be examined with coherent light, the reflected light by means of a shearing optics, e.g. B. from a beam splitter and two mirrors Two-beam interferometer exists, imaged in the image plane of an opto-electronic sensor and the measurement result is then evaluated by means of a computer connected to the sensor. When the object is loaded, the position of the light reflecting changes Points not only absolutely, but also relative to each other. This leads to the overlay of the images obtained in the loaded state, the so-called load shearograms the images obtained in the unloaded state, the so-called zero shearograms, or with a correspondingly differently loaded reference state to interference patterns, which, in contrast to holographic deformation measurements, is not a measure of the deformation, but a measure for the gradient or the derivation of the deformation in the shear direction, d. H. in the direction in which the light rays from the shearing element are refracted will. If the object is deformed correctly, the interference patterns obtained are i. a. regularly. If, on the other hand, the object has defects, this will result accordingly different strains that lead to clearly visible irregularities in the interference pattern to lead.

Shearographic processes and the mathematical ones necessary to understand them The basics are generally known to the person skilled in the art (DE 28 06 845 C2, DE 40 36 120 A1, Y. Y. Hung in "Shearography: A Novel and Practical Approach for Nondestructive Inspection", Journal of Nondestructive Evaluation, Vol. 8, No. 2, 1989, p. 55-67 and Y. Y. Hung, A. J. Durelli in "Simultaneous Measurement of Three Displacement Derivatives Using a Multiple Image Shearing Interferometric Camera ", Journal of Strain Analysis, Vol. 14, No. 3, 1979, p. 81-88).

It is already known that in-plane strains are overlaid by an out-of-plane portion are to be made visible (DE 44 46 687 A1 DE 44 46 887 A1 and DE 196 39 213.6; The European Symposium on Optics for Productivity in Manufacturing, Proceedings of the International Society for Optical Engeneering SPIE, June 20-24, 1994, p. 210-221, Frankfurt / Main on the topic "Shearography for direct Measurements of Strains" by W. Steinchen, L. X. Yang, M. Schuth, G. Kupfer; "Strain measurement on the surface of plates and discs by means of the shearography "by W. Steinchen, M. Schuth, L. X. Yang, Journal Strain, p. 105-108 Aug. u. Nov. 1994; p. 139-141, Feb. 1995, p. 25-29 "Strain measurement with digital shearography" by W. Steinchen, G. Kupfer, M. Schuth, L. X. Yang, Technischen Messen, H. 9, 1995, Oberkochen, pp. 337-341).  

It is also known that the inclination of the contour is contained in the shearographic measurement signal is when z. B. the expansion lens of the shearographic measuring device or the illumination source is slightly shifted (see "On the Determination of Slope by Shearography" by C. J. Tay, H. M. Shang, A. N. Poo, M. Luo, Journal Optics and Lasers in Engineering, 1994, pp. 207-217).

Problem definition and solution of the task

Although the shearographic processes of this type because of their simplicity and insensitivity against external influences, e.g. B. mechanical vibrations of the measuring apparatus, large Offer advantages, they also have shortcomings. The main thing is that at Strain measurements on curved surfaces the measurement signal due to the curvature in Comparison to measurement on flat object surfaces is falsified.

Based on this prior art, the invention has for its object to enable the shearographic examination method for measuring strains on arbitrarily curved surfaces with the measurement signal of shearography directly in connection with a one-time contour measurement. In the shearographic measurement signal for the gradient of the deformation, the surface's tendency to contour is included over the entire surface if the optical structure is slightly varied before the measurement and the spatial coordinate values of the contour inclination can be easily and quickly offset against the measured deformations ( Fig. 1). The basic idea of the method is to record the contour tendency as the cause for a systematic deviation of the measurement signal and to derive corresponding compensation measures from this. The basic idea of the method is solved in terms of device technology in that the lines of expansion and inclination occurring in shearography can be measured with one and the same measuring device on flat and arbitrarily curved object surfaces. The characteristic features of claims 1 to 17 serve to solve this problem. The method is subdivided into the measurement of the inclination and the deformation gradients.

I. Measurement of the deformation gradients using shearography

Due to the theoretical basis and the relationship between the interferometric light wave propagation in shearography and the mechanical deformation equations with regard to the relative phase change Δ of the light waves, it is already known that the relative phase change Δ represents the gradient of the deformation.

where u, v, w are the components of the deformation vector, e _x , e _y , e _{z are} the unit vectors in the x, y and z directions and δx, δy are the shear sizes in the x and y directions on the object surface. k _s is the sensitivity vector of the measuring device; it lies in the direction of the bisector of the angle θ between the direction of illumination and observation.

If the direction of illumination is aligned perpendicular to the surface of the object, the direction of the sensitivity vector k _s lies exactly in the z direction, so you get k _s e _x = 0, k _s e _y = 0 and k _s e _z = ↿k _s ↿. From Eqs. (1) and (2) follows:

The Gln. (1) and (2) show that the gradients of deformation with the shearography are direct can be measured, and Eqs. (3) and (4) show that the gradients of the deformation δw / δx or δw / δy can be determined by the illumination perpendicular to the object surface can. The above equations. (3) and (4) can be shaped accordingly, so that with Determination of the strip order N as a result of the change in load a direct evaluation the out-of-plane inclinations becomes possible.

II. Measurement of the contour slope of the object surface by the shearographic structure

Fig. 2 shows this, the ratios of an illuminated by a laser light source object with any curved contour. The laser light source is located at S = (x _s , Y _s , z _s ) and can be shifted by small amounts Dx, Dy, Dz to S '= (x _s + Dx, y _s + Dy, z _s + Dz) . A shear element creates two offset images of the laser light reflected from the object surface on the image plane. Therefore, a point P = (x, y, z) of the object surface at point Q of the image plane interferes with another point of the object surface, which is offset by the corresponding shear amounts δx and δz at the position P '= (x + δx, y , z + δz) is when the x, z-plane, ie in the direction of the curvature of the contour, is sheared.

The optical path length difference dl ₁ between the light beams which run from the light source S or S 'to the image point Q via the object point P is:

where r ² = (xx _s -Dx) ² + (yy _s -Dy) ² + (zz ^s -Dz) ² and R ² = (xx _s ) ² + (yy _s ) ² + (zz _s ) ² . The same applies analogously to the optical path length difference dl ₂ between the light beams which run from the light source S or S 'to the image point Q of the image plane via the point P' of the curved object surface

where t ² = (x + δx-x _s -Dx) ² + (yy _s -Dy) ² + (z + δz-z _s -Dz) ² and T ² = (x + δx-x _s ) ² + ( yy _s ) ² + (z + δz-z _s ) ² . If it is assumed that the amounts of the light source shift Dx, Dy, Dz are small compared to the total light path from the source to the object surface, 2R ≈ r + R can be set. If the shear sizes δx and δz are also assumed to be relatively small compared to the light path from the source to the object, t + T ≈ 2T ≈ 2R applies. This assumption creates the prerequisite for the application of the binomial theorem, according to which the light path difference ΔΦ increases

results. The fraction counter can now be multiplied out. It remains as a difference

If the light source is only moved in the z-direction, Dx = 0. If you resolve to δz / δx and at the same time select the point S = (x _s , y _s , z _s ) as the coordinate origin, you get for the Contour slope with x, y, z as coordinates of the respective point of the curved surface:

Eq. (9a) shows the general solution for the change in the optical path length ΔΦ that of the displacement of the light source is caused. The path length change corresponds to ΔΦ the relative phase change that occurs in photographic shearography with the stripe order n due to the contour slope and the wavelength λ of the laser according to ΔΦ = [(2n + 1) λ] / 2 with ± n = 0, 1, 2, 3,. . . for the dark interference fringes. By however, phase shift shearography can determine the relative phase change and thus the tilt the contour not only for whole numbers, but also for decimals in each pixel point be determined. The values correspond to the gray values of the digitization hardware. According to Eq. (9a) represents the interference fringe pattern that emerges from the shearograms before and after the displacement of the light source, thus lines of constant displacement gradients, d. H. represents the 1st derivative of the contour or the lines of constant contour inclination.

The relationships derived here, Eq. (5) - (9a) for measuring the contour inclination can in principle also be transmitted by shifting the image plane in the z-axis in connection with the shearing unit. The geometric relationships illustrated FIG. 3.

In order to avoid decorrelation of the pixels, only a shift in the z direction should be provided, if possible. It is also possible to shift the light source and the receiving optics simultaneously by the same or different amounts. . After the geometric relationships of Figure 4, for which the same shift direction and the same amount Dz be adopted, there is the phase difference ΔΦ = (dl _s2 + dl _q2) - (dl _s1 + dl _q1), where dl _s1 = rs- Rs, dl _s2 = ts-Ts, dl _q1 = rq-Rq and dl _q2 = rq-Tq. If it is assumed that the light source and the receiving optics are located close to each other, it can be further simplified to ΔΦ = 2 (dl ₂ - dl ₁ ). This gives the same amount of phase difference with half the shift Dz compared to Eq. (9a) or the inclination according to:

III. Elimination of the deviation in the in-plane strain or the out-of-plane deformation gradient by knowing the measured contour slope distribution

The relationships described above for measuring the gradients δw / δx or δw / δy according to Eq. (3) and (4) are for applications in quality assurance for visualization of strain concentrations e.g. B. sufficient in the case of material defects. For a strain analysis, however, the knowledge of the in-plane components δu / δx and δv / δy or δu / δy and δv / δx necessary. These parts are in the measurement signal of the shearography according to the Gln. (1) and (2) contain when the sensitivity vector is not in the z-direction as described above but there is side lighting or observation.

Are by sequential illumination under two mutually equal lighting angles + θ _xz and -θ _xz . Generating 4 phase distributions in x, z-plane using a two-beam illumination method with vertical observation, namely 2 phase distributions before (state 1) and after the deformation (state 2), the relative results for both states result from the subtraction of the corresponding measured phase distributions Phase changes

Δ _{+ θxz} = ϕ (+ θ _xz ) ₂ - ϕ (+ θ _xz ) ₁ (10)

Δ _-θxz = ϕ (-θ _xz ) ₂ - ϕ (-θ _xz ) ₁ . (11)

The lighting angles + θ _yz and -θ _yz result in an analogous _manner . in the y, z-plane the corresponding relative phase changes and.

For shearography on flat components, the digital addition of the corresponding lateral phase distributions for both states results in the pure out-of-plane deformation gradients δw / δx or δw / δy corresponding to the respective illumination angle θ of the respective illumination level x, z or y, z:

Δ _A = Δ _{+ θ} + Δ _-θ , (12)

Subtraction, on the other hand, creates the pure in-plane gradients δu / δx or δv / δy

Δ _s = Δ _{+ θ} - Δ _-θ (13)

The combination of the x, z and y, z illumination planes and the x and y shear directions result in 2 pure and 2 mixed in-plane components, whereby the superposition of half the mixed relative phase changes would result in the glide (γ _xy = γ _yx ). The components for the flat part of the distortion tensor and 2 additional out-of-plane terms are thus determined.

The digital subtraction or addition of the phase distributions is based on the equality of the two sensitivity vectors lying between the direction of illumination and the observation their size and reciprocal direction. The symmetry is approximate, if the dimensions of the object surface are relatively small compared to the distance from the Illumination source to the surface of the object. The direction of the sensitivity vector is now determined by the optical structure and is therefore independent of the shape and inclination  of the object. The subtraction or addition of the phase distributions is therefore also in permitted on concave or convex curved object surfaces. Result it However, there are deviations with regard to the actual strains on the measuring surface:

The first deviation is that the measured components δw / δx or δw / δy and δu / δx and δv / δy or δu / δy and δv / δx are parallel or perpendicular to the optical axis, regardless of the surface inclination. The prerequisite of the previous technology, in which it is assumed that the surface of the object is flat and perpendicular to the optical axis (z), is therefore no longer met if the measuring surface is inclined. The second deviation results from the projection of the true shear distance of the component surface into the image plane as a function of the contour inclination of the object. The true shear distance, which plays a decisive role in the quantitative evaluation of the shea program, can thus be expressed as a function of the contour inclination ΔΦ and a reference shear distance δx _ref . Obviously, the shear distance on a plane perpendicular to the optical axis (z) should be assumed for this.

Seen from the image plane, the reference shear distance δx _{ref is} set, the depth dz is not recognized. The true shear distance is the projection of the reference shear amount and is therefore, according to FIG. 5, δx = δx _ref / cos (α) = δx _ref / cos [arctan (δz / δx)] for the x, z plane and correspondingly δy = δy _ref / cos (β) = cos [arctan (δz / δy)] in the y, z plane ( Fig. 5).

With the true shear distance and -θ _xz = + θ _xz we get the equations. (10) u. (11):

By subtracting Eq. (15) from Eq. (14) according to Eq. (13) results

After dissolving Eq. (16) according to δu / δx and analogously for δv / δy from Δ _Sy one obtains

By adding the Eqs. (14) and (15) according to Eq. (12) results

Resolution of Eq. (18) according to δw / δx and analogously for δw / δy from Δ _Ay

The Gln. (16) and (18) represent the respective proportions in a direction parallel or perpendicular to the optical axis, taking into account the respective true Sher distance in the corresponding direction and depending on the contour inclination ( FIG. 6). The measured components δw / δx or δw / δy and correspondingly δu / δx and δv / δy or δu / δy and δv / δx must now be "aligned" by a transformation according to the contour inclination. The general rule for the transformation of the x, z-plane is x = x 'cos (α) - z' sin (α) or z = x 'sin (α) + z' cos (α) and accordingly for the y, z plane y = y 'cos (β) - z' sin (β) or z = y 'sin (β) + z' cos (β).

For δu / δx this transformation gives:

In Eq. (20) contains the constant sizes of the measuring device (factor F _Ax or F _Bx ). It can therefore be simplified for the expansion δu _a / δx _a :

For the elongation δv / δy there is analogous to the Gln. (20) and (21) with the inclination β:

The transformation of δw / δx gives:

With the constant sizes of the measuring device (factor F _Ax or F _Bx ) it can be simplified:

For δw / δy we get analogous to Eq. (23) with the inclination β = arctan (δz / δy):

The deformation gradients δw _α / δx _a and δw _β / δy _β are now aligned perpendicular to x _α and y _β , however δw _α / δx _α is still at an angle (90 ° -β) in the y, z- Directed plane and corresponding to δw _β / δy _β at the angle (90 ° -α) in the x, z plane ( Fig. 6). However, in order to maintain the out-of-plane components in the normal direction, a further transformation would have to take place.

However, on the surface of components i. a. a biaxial or flat stress state, since there is usually no load in the direction of the surface normal. For an analysis of the flat stress state, the two components δu _α / δx _α and δv _β / δy _{β are} in the equations. (21) and (22) of interest. They represent in-plane strains. The transformed deformation gradients δw _β / δy _β and δw _α / δx _α are initially of less importance. With the in-plane strains on the surface obtained here, however, the stresses of the biaxial stress state cannot simply be determined. One reason is that this is only possible with knowledge of two strains if they are in the main directions of stretching. I. a. the main directions of stretching are unknown and pointing in a different direction at every point, especially on a freeform surface. This means that for each point z. B. in the case of the use of strain gauges (DMS) a further third stretch in a further direction z. B. must be determined at 45 ° or alternatively z. B. is measured in three directions at 60 ° (DMS rosette). The advantage of shearography and especially of the measuring device compared to the strain gauge method is that not only the strains, but also analogously to Eqs. (20) to (23) the individual terms of the glides δu _α / δy _α and δv _β / δx _β can be measured by assigning the shear distance to the illumination plane rotated by 90 ° and can be transformed according to the strains. From the relationships of the general triaxial stress state, taking into account σ _zz = τ _xz = τ _yz = 0, the normal stresses and shear stresses are obtained from Hock's expanded law on the basis of a Cartesian coordinate system:

σ _x = [E / (lv ² )] (ε _xx + νε _yy )
σ _y = [E / (lv ² )] (ε _y + νε _x )
τ _xy = Gγ _xy = G (δu _α / δy _α + δv _β / δx _β ) (26)

The practical implementation of the optical structure is part of the following section.

IV. Implementation of technical equipment

From the equations developed under I and III, the optical elements for a Derive the implementation of the measuring device and outline the basic structure. For one complete determination of the contour inclinations tan (α) = δz / δx or tan (β) = δz / δy without change the shear device are two interferometer arrangements or two shear devices  and two CCD cameras for the x (Eq. (16)) and y direction (Eq. (18)) are required. Also for the determination of the biaxial voltage state is only two interferometers Arrangements or 2 CCD cameras necessary. The contour slope is due to the shift one or more lighting sources or the receiving device can be measured (Eq. (5) to (9)). To realize the lighting angle + θ or -θ for the determination of the relative Phase changes in three directions are 2.2. B. in the form of Laser diodes of the same wavelength and their control z. B. required via closures (Eqs. (10) and (11)). These four lighting sources can also be changed by appropriate Beam splitters, deflecting mirrors, closures and be replaced by a single laser light source.

The invention is described below in connection with the accompanying drawing of exemplary embodiments explained in more detail. Show it:

Fig. 1 shows schematically an apparatus for detecting out-of-plane tilts and in plane-strain on any curved object surfaces,

Fig. 2 illuminated object surface with arbitrarily curved contour,

Fig. 3 displacement of the image plane in z-direction for the shearing device,

Fig. 4 Schematic representation of the alternative determination of the contour slope,

Fig. 5 contour inclination of the object surface,

X Fig. 6 Transformation of the global coordinate system of the object surface y in the coordinate system x _{β, β} y,

. Fig. 7 contour slope of a hemisphere with application of the device according to Figure 1 after moving the laser light source 1 or 15 from S to S '(left to right: phase image with Verscherung in the y direction, demodulation of the phase image and inclination along the demodulated image line)

Fig. 8 shows a first embodiment of the device according to the invention with four light beams,

Fig. 9 shows a second embodiment of the device according to the invention with three light beams and a displaceable structural unit formed from two shearing mirrors and

FIGS. 10 and 11 each have a third and fourth embodiment of the device according to the invention with two shearing units.

The device according to FIG. 1 is used in a manner known per se to determine the derivatives of in-plane deformations and to determine the out-of-plane terms. For this purpose, the device has coherent light-emitting light sources 1 and 15 , preferably lasers, a holder (not shown in more detail) for an object 2 to be examined, a shearing arrangement 3 , e.g. B. a two-beam interferometer with a beam splitter 7 and two mirrors 4 and 5 , and an image plane 6 in which an image sensor, for. B. a photographic film, an optoelectronic image recorder based on CCD or any other recording medium for recording and storage of a photographic image is arranged. In the exemplary embodiment, an optoelectronic sensor 6 a is provided. The image of the object surface registered by the optoelectronic sensor 6 a is stored as a basic interferogram in an object 2 in the undeformed state in a frame grabber (image memory) 8 . The image of the load interferogram recorded by the optoelectronic sensor 6 a when the object 2 is in the deformed state is subtracted or added therefrom. The result of the subtraction or addition is shown on the screen 10 of a computer. Storage, subtraction or addition and display take place pixel by pixel for each point of object 2 . The image of the deformed object state 2 is subtracted or added from the image stored in the image memory and displayed on the screen 10 .

The known method of shearography is that the object 2 or its surface to be examined is first illuminated or irradiated with coherent light in the unloaded state and the light diffusely reflected by this surface is imaged in the image plane 6 . A shearing unit in the form of the mirror 5 causes part of the light coming from any point P of the object surface to be collected in a point Q and the remaining part of the light coming from point P 'in a point Q' of the image plane 6 . the distance between the points Q and Q 'is usually referred to as the shear distance in the image plane. The direction of displacement of the two points Q and Q ', i.e. H. the shear direction depends on the location, d. H. from the tilting of the shearing mirror 5 including the mirror holder. The object surface is displaced in the y direction as a result of tilting the mirror 5 about the axis of a Cartesian coordinate system, which is indicated schematically in FIG. 1, and analogously, the object surface is observed in the x direction as a result of tilting the mirror 5 about the y axis . The x, y plane of the coordinate system lies at a point on the surface of the object 2 to be considered. The shear distance can be adjusted by the size of the respective tilt angle of the plane mirror 5 . The mirror 4 can optionally also be used as the shearing unit.

For arranging the object surface by an adjustable size and direction Tilting angles are preferably provided adjustable micrometers, so that shear direction and shear distance can be adjusted.

For the zero shea program, defined phase-shifted images are registered by means of a piezo crystal attached to the mirror 4 , which is controlled via a D / A converter 9 connected to the computer 10 . The phase is determined from this for each pixel. This process is then repeated for the deformed object state. This enables computer-aided evaluation of the strains from shearograms.

The amounts for the quantities δw / δx and δw / δy can be obtained when using a light source whose axis forms the smallest possible angle θ _xz with the z axis or the optical axis and lies in the x, z plane or forms the smallest possible angle θ _yz and lies in the y, z plane.

For in-plane illumination and in-plane observation with the apparatus according to FIG. 1, the prerequisite must at least be met that the angles θ _xz and θ _yz must be non-zero, which can be done with the device according to FIG. 1 by appropriate pivoting light sources 1 and 15 are easy to implement. Under this condition, the interference pattern obtained with the otherwise identical device, depending on the corresponding tilting of a shearing unit, e.g. B. the mirror 5 of the shearing arrangement 3 , a measure of δu / δx and δu / δy if the beam axis and the z-axis lie in the x, z-plane or a measure of the values δv / δx and δv / δy if the beam axis and the z axis lie in the y, z plane. It is assumed in Fig. 1 that for measuring or visualizing the derivatives of the in-plane deformations z. B. by means of the force ± F _x an expansion (or compression) of the object 2 in the x direction is brought about. Alternatively, it would be possible to bring about an expansion (or compression) in the y direction or any other direction within the x, y plane with a force ± F _y .

Methods and devices of the type described are basically known to the person skilled in the art (e.g. DE 44 14 287 A1 and additional application for P 44 46 887.3) and therefore need not to be explained in more detail. The patent application P 44 46 887.3 aims at out-of-plane Eliminate parts of shearographic in-plane strain measurement completely separate both parts so that an exact in-plane strain measurement is possible. With this patent application is said in the patent application P 44 46 887.3 plus the additional application for the first time on curved object surfaces, including those in shearographic Inclined contour inclination applied.

In the device according to FIG. 1, it is assumed that the object 2 is preferably mirror-symmetrically illuminated from two directions with two illuminating beams 11 and 12 and that a shutter 13 or 14 is arranged in each of these beams. This makes it possible in a simple manner to illuminate the object surface by opening or closing the shutters 13, 14 from different sides in the basic or loading state and then to record 3 phase-shifted shea programs with the two-beam interferometer arrangement. The sheagrams are subjected to various arithmetic operations in order to separate the in-plane and out-of-plane components from each other by means of computational methods. In addition, by varying the lighting devices and the shear directions, the gradients of the in-plane deformations in different directions can be formed and represented numerically.

In the device according to FIG. 1, for the sake of simplicity, the two illuminating beams 11 and 12 are generated by two different light sources 1 and 15 , in particular lasers. With regard to coherence and the same wavelength, however, the generation of both beams 11 , 12 is preferably carried out using the same light source 1 , for example by B. an additional beam splitter forming the beam 12 is introduced into the illuminating beam 11 . Alternatively, a single light source can be swiveled or redirected according to the specified positions.

As shown in FIG. 1, the two illuminating beams 11 and 12 lie opposite one another on both sides of the x, z plane, the relevant angles being denoted by + θ _xz and -θ _xz . The two-beam interferometer arrangement 3 is oriented in such a way that it receives the light of both beams 11 and 12 reflected by the object 2 . The displacement and phase shift also take place in a known manner in this embodiment. First, the shutter 14 is closed and the shutter 13 is opened and the object 2 is illuminated with the beam 11 in the basic state under the illumination angle + θ _xz . The speckle interference image that generates this first illumination is from the computer 10 by means of the image sensor 6 a, z. B. a CCD camera stored. The intensity distributions are measured as usual from a number of shearograms which are phase-shifted by a predetermined angle using the known phase shifting technique, and the phase values ϕ (+ θ _xz ) ₁ are calculated for each point of the speckle interference field. Then the shutter 13 is closed and the shutter 14 is opened. The object is thus illuminated by the further illuminating beam 12 at the illuminating angle -θ _xz and, analogously, the phase distribution θ (+ θ _xz ) ₁ of the speckle interference field generated by the illuminating beam 12 is determined in the computer 10 .

After the object 2 is loaded, the speckle interference field changes accordingly. Again, the phase distribution ϕ (+ θ _xz ) ₂ for the illuminating beam 11 at the angle + θ _xz with the shutter 14 closed and with the shutter 13 open and the phase distribution ϕ (-θ _xz ) ₂ for the illuminating beam 12 at the angle - θ _{xz determined} with the closure 14 open and with the closure 13 closed and determined from the measured intensity distributions of the phase-shifted shea programs.

By digital subtraction of the phase distributions in the unloaded or loaded state of the object 2 by means of the computer 10 , the relative phase change _values Δ _{+ θxz} for the illuminating beam 11 can be determined at the angle + θ _{xz of} the light source 1 . Similar to Δ _{+ θ} , the relative phase change _values Δ _-θxz for the illuminating beam 12 at the angle -θ _{xz of} the light source 15 according to Eq. (10), (11) and (13) can be calculated. The digital subtraction of the phase distributions in the unloaded or loaded state of the object 2 in the case of revision in the yz plane and phase shift is carried out analogously.

By digitally adding the phase distributions in the unloaded or loaded state of the object 2 by means of the computer 10 , the relative phase change values Δ _{+ θ} for the illuminating beam 11 can be determined at the angle + θ _{xz of} the light source 1 . Similar to Δ _{+ θ,} the relative phase change values Δ _-θ can be used for the illumination beam 12 at the angle -θ _xz the light source 15 by Gln. (10) - (12) can be calculated.

From this procedure it follows that the terms δw / δx and δw / δy in Eq. (13) not occur more and therefore only in it the characteristic of in-plane deformations Sizes are included. On the other hand, this procedure gives the terms δw / δx and δw / δy using Eq. (14) and therefore exclusively for the out-of-plane inclinations characteristic quantities for their determination (patent application DE 196 39 213.6).

The digital subtraction or addition of the phase distributions is based on the equality of the 2 sensitivity vectors in size between the direction of illumination and observation and mutual direction, which applies to flat objects without restriction. For concave or convexly curved object surfaces, this fact only applies to a limited extent. B. at a circular recess transverse to the direction of loading of a tension rod only for the Notch reason, because here the out-of-plane tendency of the deformation has no projection, however  not for the side parts of it.

FIG. 7 shows the strip image of the contour inclination for a sphere by means of the device according to FIG. 1. If the image of the surface of the test object of any desired shape is recorded in the electronic memory - also called zero shea program - and with the video clock of the subsequent images of the curved images acquired as a result of the change in light path length If the surface is referred to as a contour heagram in the image memory (frame grabber) 8 , a stripe pattern is formed which is visible on the monitor 10 and shows the lines of constant contour inclination. By rotating the illuminating beams 11 and 12 in pairs from the x, z to the y, z plane, the respective contour inclination is recorded by means of a CCD camera.

As already described above for the measuring device for recording the shea programs, the illuminating beams 11 and 12 for recording the shea programs are generated by two different light sources 1 and 15 , in particular lasers; a light source with a beam splitter for 11 and 12 or a light source pivoted into corresponding positions can also serve this purpose. Therefore, the 2-dimensional in-plane deformation gradient field can be measured simultaneously by the pair of illuminating beams 11 and 12 in the xz and in the yz and the out-of-plane inclination in the z-direction plane.

In the procedure explained above with reference to the device according to FIG. 1, the opening and closing times of the closures 13 and 14 can be controlled so quickly that their half, single or double frequency coincides with the excitation frequency of an object excited to vibrate, whereby the plane strains can be recorded with the optoelectronic sensor 6 a. For this purpose, the closures 13 and 14 are to be replaced by acousto-optical or electro-optical modulators in the same place in the beam path 11 and 12 . The rapid control of the opening and closing times of the closures 13 and 14 leads to real-time registration of pure in-plane expansions and out-of-plane inclinations on curved object surfaces.

Fig. 8 on the caps 18 and 19 shows a first embodiment of the device according to the invention with four light beams, the light beams 16 and 17 for mutual illumination of arbitrarily curved surface in the y, z plane (+ θ _yz or -θ _yz control . Fig. 9 shows a second embodiment of the device according to the invention with three light beams and a movable, formed by two mirrors shearing assembly and FIG. 10 and 11 each have a third and fourth embodiment of the device according to the invention with two shearing units.

Claims (18)

1. Method and device for shearographically determining derivatives of the in-plane and out-of-plane deformations of an arbitrarily curved surface of an object ( 2 ) in at least one selected direction, characterized in that with knowledge of the local inclinations of the examined object, which is obtained by a shearographic measurement, the systematic deviations of the in-plane and out-of-plane deformation gradients of the shearographic measurement technology, which are due to the inclination of the contour, are taken into account and transformed into the tangential and normal direction with respect to the respective local object surface inclination , wherein the measurement of the deformation gradients and the contour inclinations is realized by means of a measuring setup by irradiating the object surface with coherent light from a light source ( 1 and 15 ), the light diffusely reflected by this by means of an interferometer arrangement ( 3 ) and an op optical axis (z) having an optical system in an image plane ( 6 ) and at least one zero shea program and one load shea program are recorded from the object surface, the arbitrarily curved one being used to determine pure in-plane expansions or out-of-plane inclinations Object surface from different directions (+ θ _xz '-θ _xz or + θ _yz ' -θ _yz ) is sequentially irradiated, the irradiation from two directions (+ θ _xy '-θ _xy ) preferably mirror-symmetrically to a common, the first plane (xz) enclosing the optical axis (z) takes place while the radiation from the third (or fourth) direction (+ θ _xz (or -θ _yz )) preferably takes place in a second plane (yz) lying perpendicular to the first plane, including the optical axis (z), and the pure in-plane or out-of-plane Shares are determined by combining the sheagrams thus obtained and by irradiating the object surface with coherent light from a light source ( 1 and 15 ) before and / or after the exposure, the light diffusely reflected by the latter by means of an interferometer arrangement ( 3 ) by an optical one Optical system having axis (z) is imaged in an image plane ( 6 ), whereby to determine the inclination of the contour, at least one of the following measures produces a change in the light path lengths from the illumination source to the image plane, which reflects the inclination of the contour, wherein the set superimposition of the pixels is preferably in the plane of the illumination directions + θ _xz , and -θ _xz or + θ _yz and -θ _yz . 2. The method according to claim 1, characterized in that the irradiation takes place from four directions, the irradiation from the third and fourth directions (+ θ _yz and -θ _yz ) takes place in the second plane (y, z). 3. The method according to claim 1 or 2, characterized in that the angles at which the irradiations take place from three directions are preferably the same, and that the angles (± θ _xz or ± θ _yz ) at which the irradiations from four Directions take place in each plane (x, z or y, z) are preferably identical to one another. 4. The method according to the above claims, characterized in that the combination of Shearograms are done by subtracting or adding relative phase changes. 5. The method according to any one of claims 1 to 4, characterized in that the irradiation of the arbitrarily curved object surface takes place from the three or four different directions with the required phase shifts, for each direction in the reference or in the unloaded and in the loaded state Images of the object ( 2 ) obtained are stored digitally and the relative phase changes derived therefrom are added or subtracted. 6. Device for shearographically determining derivatives of the deformations on an arbitrarily curved surface of an object ( 2 ) in selected shear directions, comprising: Coherent light-generating means ( 1 and 15 ) for irradiating the object surface from different directions (+ θ _xz '-θ _xz or + θ _yz '-θ _yz ), an image plane ( 6 ), an optical system having an optical axis (z) and at least one interferometer arrangement ( 3 ) for imaging the arbitrarily curved object surface in the image plane ( 6 ) and means to determine pure in-plane strains and / or out-of-plane inclinations, according to patent (patent application P 44 46 887.3), characterized in that the means for irradiating the object ( 2 ) from at least three directions (+ θ _xz '- θ _xz '+ θ _yz ) are set up, the radiation from two directions (+ θ _xz ' -θ _xz .) preferably mirror-symmetrically to a common one which includes the optical axis (z) Most plane (x, z) takes place, while the radiation from the other directions (+ θ _yz '-θ _yz .) takes place in a second plane (y, z) which is perpendicular to the first plane and includes the optical axis (z). 7. The device according to claim 6, characterized in that the means have three or four light sources ( 1 e, 1 f, 1 g or 1 a, 1 b, 1 c, 1 d), two of which for irradiating the object ( 2 ) in the first plane (x, z) and the others for irradiating the object ( 2 ) in the second plane (y, z). 8. The device according to claim 7, characterized in that the interferometer arrangement ( 3 ) has two shearing elements ( 5 a, 5 b) which can be displaced parallel to the optical axis (z) and are arranged for perpendicularization in directions perpendicular to one another. 9. The device according to claim 7, characterized in that the interferometer arrangement ( 3 ) two shearing units ( 5 a or 5 c, 7 a, 4 and 5 b or 5 d, 7 b, 4 ), 1 beam splitter - Element ( 7 ), 2 phase shifting devices ( 4 ) and 2 cameras ( 6 a, 6 b). 10. The device according to claim 9, characterized in that the shearing units are assigned a common phase shift element ( 4 ). 11. The device according to claim 7, characterized in that the interferometer arrangement ( 3 b, 3 c) a beam splitter ( 7 ) which divides the light beams ( 29 ) coming from the object ( 2 ) into two light beams ( 30, 31 ), and each one of these two light bundles (30, 31) associated with shearing units (3 b, 3 c) has. 12. Device according to one of claims 9 to 11, characterized in that each interferometer unit is each connected to a separate means ( 6 a, 6 b) for determining the strains and the contour slope. 13. The device and method according to the above claims, characterized in that by means of the device for measuring the derivatives of the deformations a change in the light wavelengths from the illumination source to the image plane can be generated by either the expansion optics including or only the light source and the actuators for steering the Light is shifted in a known direction (preferably in the optical axis (z)) by a known amount or by the interferometer arrangement ( 3 ) together with the image plane ( 6 ) in the optical axis (z) is shifted by a known amount or by combining these two options. 14. Device and method according to the above claims, characterized in that the gradients of the contour or inclinations to be measured by the device of claim 13 are preferably determined in the direction which corresponds to the measured in-plane deformation gradients by the set superimposition of the Pixels by means of the interferometer arrangement ( 3 ) are preferably in the plane of the illumination or tightening planes of the above-mentioned directions + θ _xz and -θ _xz or + θ _yz and -θ _yz . 15. The device and method according to the above claims, characterized in that the measurement of the gradient of the contour or inclinations in the individual, different directions simultaneously with a single change in the light path lengths from the illumination source to the image plane (preferably according to the method of claim 13) the use of two interferometer units ( 3 a, 3 b according to claims 8, 9 and / or 11) with different superimposition of the pixels can take place. 16. The device and method according to the above claims, characterized in that the Measurement of the gradient of the contour by varying the light wavelength or the laser light frequency gives the information about the contour. 17. The device and method according to the above claims, characterized in that by superimposing the object with a likewise illuminated with coherent light and preferably diffusely reflecting reference surface in an image plane ( 6 ), the differences in the deformation with respect to this reference surface are represented by the overlay by a corresponding size of the direction of shear is realized by the / the mirrors (5) in the interferometer arrangement (3) and wherein the reference surface is preferably planar and remains unchanged between the recordings before and after the load of the object under investigation and is not to be subjected to a load change , so that the contour or deformation of the object is determined from these differences according to the method and can be processed by further means ( 6, 8, 10 ) with numerical methods (e.g. differentiation, integration). 18. Device and method according to the above claims, characterized in that the frequencies of the sequential illumination times of the object (z. B. realized by the opening and / or closing times of the closures ( 13 ) and ( 14 )) with the nth Part or multiple of the excitation frequency of the object excited to oscillate can match.