CN1284648A - Method for measuring derivative field - Google Patents

Abstract

A method for measuring derivative field is a method using image processing. Firstly, a double-beam interference measuring light path is adopted to take an interference image before and after a measured object is deformed, and the two interference images are subtracted to obtain an out-of-plane deformation fringe field. And measuring the actual deformation of the measured object by the out-of-plane deformation fringe field, and obtaining out-of-plane deformation according to the mathematical expression of the fringe field. And obtaining the derivative field of the deformation of the measured object according to the Laplace factor of the fringe field and the absolute value of the actual brightness derivative of the fringe field. Derivative fields of different directions and different precisions can be obtained.

Description

The measuring method of derivative field

The present invention is a kind of derivative field measuring method based on image processing techniques.

Derivative field measuring technique and characteristics thereof in the technology formerly:

The displacement of object or the derivative field of deflection are the important parameters of weighing deformation of body and internal stress distribution situation, often need in producing and testing mechanical component or building model are carried out the derivative field measurement check of deflection, to analyze its internal stress distribution situation, estimate the quality of its structure or performance.So the derivative field measurement is one of detection means of using always.The measurement of derivative field realizes by the shear interference method in the flash ranging technology.The light path that is adopted shown in Fig. 1 among Fig. 1-1, the center vertical line O on testee 1 surface ₂O ₂Optical axis O perpendicular to light source 6 ₁O ₁, a semi-transparent semi-reflecting lens 2 and above-mentioned center vertical line O ₂O ₂With optical axis O ₁O ₁Angle at 45.Be equipped with between semi-transparent semi-reflecting lens 2 and imaging lens 3 and split shape shear mirror 5, the video camera 4 behind the imaging lens 3 is connected on the computing machine 8.Split shape shear mirror 5 with common interferometry its outstanding feature of comparing for before the imaging lens 3 of video camera 4, placing one.The structure of shear mirror 5 is shown in Fig. 1-2, splitting the angle is β, its effect is that making through its first half light generation angle is the deflection of θ, the size at θ angle is determined by the angle β between 5 liang of minute surfaces of shear mirror, after testee 1 is sheared imaging system through such one, system as the plane on will obtain two identical pictures, stagger each other between two pictures one very little of d, the size and Orientation of d is determined by the placement direction of angle beta and shear mirror 5.With this system testee 1 is taken a picture before testee 1 deforms He after deforming, comparison film is handled then, just can obtain representing the photo measure bar graph of testee 1 distortion derivative.

Referring to technology formerly:

[1] Cheng Chuanfu, Jiang Jinhu, Shen Yongzhao, the white light speckle shear interference metering art of light source coding, optics journal, 1990,10. (10): 938～943.

[2] Wang Kaifu, Shen Yongzhao, rotation aperture axicon lens cutting speckle photographic process, optics journal, 1993,13 (3): 287～288

[3] Gu Jie, polarization shear camera and directly measure curvature and turn round rate, Chinese laser, 1990,17 (5) 296～300)

The deficiency of this measuring method is obvious: at first because when measuring, to a concrete shear mirror 5 and Saying that its shearing displacement and shear direction fix, also can only be the measurement of deciding direction and deciding precision so measure. As Fruit is expected the derivative field of different directions and different accuracy, must change repeatedly shear mirror, to same testee Carry out repeatedly duplicate measurements, but this duplicate measurements have destructive or unrepeatable testee at some But be unallowed in the measurement, multi-direction measurement this moment often is difficult to realize. The second, in the measurement of reality, remove Need to measure outside the derivative field, generally also need to measure the derivative of other form such as twisting coefficient, although this can pass through Design various special shear mirrors and realize, but increased experimental cost, increase simultaneously the complexity of processing means, And effect is unsatisfactory. The 3rd, the side that utilizes shear interference with upper derivate for second order and the second order of deflection Method can not be measured.

The objective of the invention is to measure the problem that derivative field exists by shear interference in the technology for overcoming formerly, because shear mirror is the basis of realizing shear interference, it also is the various circumscribed basic place in the derivative field measuring method of technology formerly, the present invention proposes directly to extract derivative field information with image process method from general measurement bar graph for this reason, avoid using shear mirror, can obtain the all-order derivative field of the testee distortion of different directions different accuracy simultaneously with a width of cloth common survey bar graph, thereby solve the variety of issue that exists in the above-mentioned shear interference measurement fully.

Measuring method of the present invention is to replace shear interference method in the above-mentioned technology formerly with image process method, and concrete steps are:

1. adopt the double beam interference measuring light path, as shown in Figure 2, the central point of adjusting video camera overlaps the focal length of also adjusting camera lens exactly with testee centre of surface vertical line makes the shooting function carry out clear shooting to testee.

2. use above-mentioned measuring light road, before the testee distortion, take first width of cloth interference image.

3. use above-mentioned measuring light road, take second width of cloth interference image in testee distortion back.

4. above-mentioned two width of cloth interference images are subtracted each other, obtain the surface deformation fringe field, as shown in Figure 3, the mathematical notation formula of fringe field is:

I (x, y)=a (x, y)+b (x, y) (1+cos (I (x in φ (x, y)) (1) (1) formula, y) represent in the fringe field at point (x, y) locate the intrinsic brilliance of striped, (x y) represents this point (x to a, y) background luminance of striped, (x y) represents this point (x, fringe contrast y) to b, φ (x, y) represent testee at this point (x, surface deformation y), surface deformation φ (x, y) and by the testee that records in the above-mentioned surface deformation fringe field this practical distortion amount h (x, y) and the pass of light wavelength lambda be: $\mathrm{\φ}(x,y)=2\mathrm{\π}\frac{h(x,y)}{\mathrm{\λ}}$ 5. (1) formula substitution as a result following (2) formula is tried to achieve the derivative field of the testee distortion on the different directions $\cos \left(k{\mathrm{\φ}}_{\mathrm{\α}}(x,y)\right)=\cos [k(t{g}^{-1}(-\frac{\left|I^{\′}(x+\cos \mathrm{\α},y+\sin \mathrm{\α})\right|}{L\left(I\right(x+\cos \mathrm{\α},y+\sin \mathrm{\α}))})-t{g}^{-1}(-\frac{\left|I^{\′}(x,y)\right|}{L\left(I\right(x,y\left)\right)}))]---\left(2\right)$ (2) in the formula, K is an integer factor, φ _α(x y) is the surface deformation derivative on the α in any direction of testee. $L\left(I\right(x,y\left)\right)=\frac{{\∂}^{2}I(x,y)}{\∂x^2}+\frac{{\∂}^{2}I(x,y)}{\∂y^2}$ Laplce's factor for fringe field. $\left|I^{\′}\right(x,y\left)\right|=\left|\frac{\∂I(x,y)}{\∂x}\right|+\left|\frac{\∂I(x,y)}{\∂y}\right|=2b(x,y)\left|\sin \left(\mathrm{\φ}(x,y)\right)\right|$ (x y) locates striped intrinsic brilliance I (x, derivative absolute value y) at point for fringe field.

The concrete formation of the measurement light path that 1. above-mentioned measuring process is adopted is: the centre of surface vertical line O of testee 1 ₂O ₂Optical axis O with light source 6 ₁O ₁Putting the minute surface of a semi-transparent semi-reflecting lens 2 and testee 1 centre of surface vertical line O mutual vertically ₂O ₂With light source 6 optical axis O ₁O ₁All putting to angle at 45, imaging lens (3) and ccd video camera (4) are positioned at the center vertical line O of testee 1 ₂O ₂On, light source 6 emitted light beams are mapped to the optical axis O of a reflecting surface perpendicular to light source 6 after seeing through semi-transparent semi-reflecting lens 2 ₁O ₁On the plane mirror of placing 7, the output of ccd video camera 4 is connected on the computing machine 8.

Above-mentioned (1) formula is resulting to be that (x, bar graph y) are that (x, bar graph y) are concrete processing procedures to φ below and our purpose will obtain its derivative for φ about testee.

(ⅰ) the Laplce's factor with Laplace transform removal bias light fringe field is: $L\left(I\right(x,y\left)\right)=\frac{{\∂}^{2}I(x,y)}{\∂x^2}+\frac{{\∂}^{2}I(x,y)}{\∂y^2}$ (1) formula substitution (3) formula is got:

Universal law a (x according to fringe field, y), φ (x, y) under general situation, it can be treated contrast b (x when differentiating as constant, y) generally comprise noise contributions, cannot directly handle, but earlier image be carried out filtering, after noise is removed substantially as tempolabile function, (x y) still can be regarded as tempolabile function to b.(3 ') formula under above-mentioned condition can abbreviation be:

L (I (x, y))=-2b (x, y) cos (φ (x, y)) (4) (ⅱ) sine streak field calculates (1) formula is differentiated, and adopt and above ask identical being similar to of Laplace's operation: $\left|I^{\′}\right(x,y\left)\right|=\left|\frac{\∂I(x,y)}{\∂x}\right|+\left|\frac{\∂I(x,y)}{\∂y}\right|=2b(x,y)\left|\sin \left(\mathrm{\φ}(x,y)\right)\right|---\left(5\right)$ (ⅲ) derivative field calculating (5) gets divided by (4) formula: $\mathrm{\β}(x,y)=\frac{\left|I^{\′}(x,y)\right|}{L\left(I(x,y)\right)}=-\frac{\left|\sin \left(\mathrm{\φ}(x,y)\right)\right|}{\cos \mathrm{\φ}(x,y)}---\left(6\right)$ The order: φ (x, y)=2n π+ψ (x, y), wherein-π≤ψ (x, y)≤π then (6) formula turn to: $\mathrm{\β}(x,y)=\frac{\left|I^{\′}(x,y)\right|}{L\left(I\right(x,y\left)\right)}=-\frac{\sin \left(\right|\mathrm{\ψ}(x,y)\left|\right)}{\cos \[\mathrm{\ψ}(x,y)\]}=-\frac{\sin \left(\right|\mathrm{\ψ}(x,y)\left|\right)}{\cos \left(\right|\mathrm{\ψ}(x,y)|}=-\mathrm{tg}\left|\mathrm{\ψ}(x,y)\right|---\left(7\right)$ The tangent of negating again after (7) formula taken advantage of-1 gets: $\mathrm{\θ}(x,y)=t{g}^{-1}(-\mathrm{\β}(x,y))=t{g}^{-1}\left(\mathrm{tg}\right(\left|\mathrm{\ψ}(x,y)\right|\left)\right)=\left|\mathrm{\ψ}(x,y)\right|---\left(8\right)$

Because φ (x, y)=2n π+ψ (x, y), so the derivative on any direction α of position phase (α for the angle of X-axis) is: φ _α(x, y)=φ (x+cos α, y+sin α)-φ (x, y)=2n1 π+ψ (x+cos α, y+sin α)-2n0 π-ψ (x, y) (9)

An integer factor k is multiply by at (9) formula two ends simultaneously, gets surplus profound function call again:

cos(kφ _α(x，y))=cos[k(ψ(x+1，y)-ψ(x，y))] (10)

What (10) formula obtained is exactly that (fringe density can be regulated with k for x, derivative fringe field y) about measured information φ.Because (x y) represents adjacent position phase at 2 with ψ (x+cos α, y+sin α), so remove ψ (x to ψ, y) outside the point of ≈ 0, its two symbol is identical, cos (| ψ (x+cos α, y+sin α)-ψ (x, y) |)=cos ((| ψ (x+cos α, y+sin α) |-| ψ (x, y) |).So (10) formula can turn to: $\cos \left(k{\mathrm{\φ}}_{\mathrm{\α}}(x,y)\right)=\cos \left[k\left(\right|\mathrm{\ψ}(x+\sin \mathrm{\α},y+\cos \mathrm{\α})|-|\mathrm{\ψ}(x,y)\left|\right)\right]---\left(11\right)$ With (6), (8) two formula substitution (11) formulas both can obtain complete ask φ (x, y) at the formula of α directional derivative field: $\cos \left(k{\mathrm{\φ}}_{\mathrm{\α}}(x,y)\right)=\cos \[k\left(t{g}^{-1}\right(-\frac{\left|I^{\′}(x+\cos \mathrm{\α},y+\sin \mathrm{\α})\right|}{L\left(I(x+\cos \mathrm{\α},y+\sin \mathrm{\α})\right)})-t{g}^{-1}(-\frac{\left|I^{\′}(x,y)\right|}{L\left(I(x,y)\right)}))\]---\left(12\right)$

So sum up the above process, if according to (3) and (5) formula calculate L[I (x, y)] and I ' (x, the derivative field on any direction α that y) substitution (12) formula can obtain being out of shape about testee.Obtain the derivative field of testee distortion easily according to same reason at other any direction

The advantage of measuring method of the present invention:

1. because the present invention adopts image process method, the light path of measuring is the double beam interference measuring light path, so from measuring on the light path as can be seen, compare method of the present invention with shear interference method in the technology formerly and saved shear mirror, the measuring light rood has reduced the measurement cost simultaneously to simplifying.

2. because method of the present invention is not used shear mirror, so its measuring accuracy regulated at will does not as required resemble the restriction that measuring accuracy formerly the shear interference of technology is measured is subjected to shear mirror.

3. from above-mentioned measuring process as can be seen, method of the present invention does not have the directivity restriction, can obtain the derivative of any direction according to actual needs, and these characteristics are very superior.

4. method of the present invention can be measured and shear second order and the above derivative field of second order that measuring method can not be measured.

Description of drawings:

Fig. 1 is that the shear interference of technology is formerly measured light path.

Wherein: Fig. 1-1 is actual measurement light path synoptic diagram.

Fig. 1-2 is the enlarged diagram of the shear mirror 5 among Fig. 1-1.

Fig. 2 is a double beam interference measuring light path synoptic diagram of the present invention.

The surface deformation stripe pattern of Fig. 3 testee that to be the present invention arrive with the measuring light rood shown in 2 figure.

Fig. 4 is a testee of the present invention distortion derivative field under three different measuring precision in vertical direction.

Wherein: Fig. 4-the 1st, integer factor K equal the distortion derivative field on 1 o'clock the vertical direction.

Fig. 4-the 2nd, integer factor K equal the distortion derivative field on 2 o'clock the vertical direction.

Fig. 4-the 3rd, integer factor K equal the distortion derivative field on 4 o'clock the vertical direction.

The distortion derivative field that Fig. 5 is a testee 1 of the present invention under three different measuring precision on the 45 direction.

Wherein: Fig. 5-the 1st, integer factor K equal 1 o'clock distortion derivative field on the 45 direction.

Fig. 5-the 2nd, integer factor K equal 2 o'clock distortion derivative fields on the 45 direction.

Fig. 5-the 3rd, integer factor K equal 4 o'clock distortion derivative fields on the 45 direction.

Embodiment

For setting forth the operability of method of the present invention, provide a concrete practical measuring examples here.Measure light path (imaging lens 3 is that TP-505D, image plate model are CA5300 for sea-gull three adjustable camera lenss, ccd video camera 4 models) as shown in Figure 2, the circular uniformly distributed load test specimen of testee 1 selection standard, material for test is the thick organic glass of 3mm, and diameter is 100mm.Utilize measurement light path shown in Figure 2, by above-mentioned steps 1., 2., 3., 4. obtain original about the surface deformation stripe pattern of testee under load as shown in Figure 3,5. after handling with above-mentioned steps again, once can obtain 6 derivative field bar graphs of along continuous straight runs and miter angle direction different accuracy, as Fig. 4, shown in Figure 5, wherein each width of cloth derivative field bar graph all is to draw according to the distortion derivative value of resulting 512 * 512 points of step.If the shear interference method with technology is formerly measured, reach so so that effect needs duplicate measurements 6 times, gather 12 width of cloth original photo at least, relatively its superiority-inferiority of workload of the two is conspicuous.Because what present embodiment adopted is standard specimen, so from the direct correctness of its result as can be seen of resulting result.

Claims (2)

1. the measuring method of a derivative field is at first measured the interference image on testee surface, it is characterized in that adopting image process method, and concrete step is:

1. adopt the double beam interference measuring light path, the central point of adjustment video camera and testee centre of surface vertical line coincide and adjust lens focus exactly;

2. use above-mentioned measurement light path, before the testee distortion, take first width of cloth interference image;

3. use above-mentioned measurement light path, take second width of cloth interference image in testee distortion back;

4. above-mentioned two width of cloth interference images are subtracted each other, obtain the surface deformation fringe field, the mathematical notation formula of fringe field is:

I (x, y)=and a (x, y)+b (x, y) (1+cos (φ (x, y)) I (x in the formula of (1) (1), y) be that (x y) locates the intrinsic brilliance of striped, a (x at point in the fringe field, y) be this point (x, y) background luminance of striped, (x y) is this point (x to b, the contrast of striped y), (x is that testee is at this point (x, surface deformation y) y) to φ, surface deformation φ (x, y) with by the testee that records in the above-mentioned surface deformation fringe field this point (x, practical distortion amount h y) (x y) and with the pass of light wavelength lambda is: $\mathrm{\φ}(x,y)=2\mathrm{\π}\frac{h(x,y)}{\mathrm{\λ}}$ 5. with substitution as a result (2) formula of above-mentioned (1) formula, try to achieve the derivative field of the testee distortion on the different directions: $\cos \left(k{\mathrm{\φ}}_{\mathrm{\α}}(x,y)\right)=\cos \[k({\mathrm{tg}}^{-1}(-\frac{|I\′(x+\cos \mathrm{\α},y+\sin \mathrm{\α})|}{L\left(I(x+\cos \mathrm{\α},y+\sin \mathrm{\α})\right)})-{\mathrm{tg}}^{-1}(-\frac{|I\′(x,y)|}{L\left(I(x,y)\right)}))\]---\left(2\right)\]$ (2) in the formula, K is an integer factor, φ _α(x y) is the surface deformation derivative on the α in any direction of testee, $L\left(I(x,y)\right)=\frac{{\∂}^{2}I(x,y)}{\∂x^2}+\frac{{\∂}^{2}I(x,y)}{\∂y^2}$ Be Laplce's factor of fringe field,

| I ' (x, y) |=2b (x, y) | sin (φ (x, y) | (x y) locates striped intrinsic brilliance I (x, derivative absolute value y) at this point for fringe field.

2. the measuring method of derivative field according to claim 1 is characterized in that the measurement light path that is adopted is the double beam interference measuring light path, and its concrete formation is the centre of surface vertical line (O of testee (1) ₂O ₂) and the optical axis (O of light source (6) ₁O ₁) putting the minute surface of a semi-transparent semi-reflecting lens (2) and testee (1) centre of surface vertical line (O mutual vertically ₂O ₂) and light source (6) optical axis (O ₁O ₁) all putting to angle at 45, the central point of imaging lens (3) and ccd video camera (4) is positioned at the center vertical line (O of testee (1) ₂O ₂) on, light source (6) emitted light beams is mapped to a reflecting surface perpendicular to light source optical axis (O after seeing through semi-transparent semi-reflecting lens (2) ₁O ₁) on the plane mirror (7) put, the output of ccd video camera (4) is connected on the computing machine (8).

The central point of camera (4) is positioned at the center vertical line (O of testee (1) ₂O ₂) on, light source (6) emitted light beams is mapped to a reflecting surface perpendicular to light source optical axis (O after seeing through semi-transparent semi-reflecting lens (2) ₁O ₁) on the plane mirror (7) put, the output of ccd video camera (4) is connected on the computing machine (8).

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