CN106247952B - A kind of speckle pattern photography in-plane displacement quantity algorithm based on Fourier transformation phase - Google Patents
A kind of speckle pattern photography in-plane displacement quantity algorithm based on Fourier transformation phase Download PDFInfo
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- CN106247952B CN106247952B CN201610780416.9A CN201610780416A CN106247952B CN 106247952 B CN106247952 B CN 106247952B CN 201610780416 A CN201610780416 A CN 201610780416A CN 106247952 B CN106247952 B CN 106247952B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
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Abstract
The present invention discloses a kind of speckle pattern photography in-plane displacement quantity algorithm based on Fourier transformation phase, before ohject displacement, digital speckle figure afterwards carries out Fourier transformation respectively, and their Fourier transformation is divided by obtain a two-dimensional complex number, then the phase angle of the two-dimensional complex number is calculated, by the way that equivalent Mechanical Study On Young Interference figure can be obtained as cos operation to the phase angle, Fourier transformation is made to Mechanical Study On Young Interference figure, by searching for the coordinate of Fourier transformation power spectrum maximum value in addition to zero-frequency, the size of available in-plane displacement amount, according to the positive and negative direction of displacement that may determine that object of phase angle gradient, the derivative algorithm of the algorithm can also realize the displacement calculation of sub-pix；The present invention overcomes the shortcomings that traditional algorithm complex steps, operand be big, inconvenient operation, and speckle field minimum movement amount especially that can be detected is greater than the average diameter equal to speckle particle, can not achieve sub-pix detection, and can not determine ohject displacement direction.
Description
Technical field
The present invention relates to a kind of algorithm with digital speckle photographic measurement object in-plane displacement amount size, specifically one
Speckle pattern photography in-plane displacement quantity algorithm of the kind based on Fourier transformation phase, belongs to field of optical detection.
Background technique
Using the in-plane displacement amount of the available object of digital speckle, as a kind of means of optical measurement, because it has
The advantages that non-contact and highly sensitive, is widely used in various fields, but traditional Processing Algorithm is to displacement
Forward and backward digital speckle figure carries out the addition of pixel in airspace or subtracts each other to obtain synthesis speckle pattern, then by synthesis speckle pattern
Make Fourier transformation, then to obtained image（The power spectrum of Fourier transformation）Make filtering and eliminating noise, image enhancement, binaryzation and
Stripe thinning finally carries out fringe spacing and extracts to obtain amount of movement, and traditional algorithm directly uses intensity signal（Fu Li
The power spectrum of leaf transformation）, the speckle field minimum movement amount that may only detect requires to be greater than（At least equal to）Speckle particle is averaged
Diameter can not realize that sub-pix detects, and can not determine speckle displacement direction.
Summary of the invention
The purpose of the present invention is overcoming existing traditional algorithm, a kind of speckle based on Fourier transformation phase is provided
Photograph in-plane displacement quantity algorithm, carries out according to the following steps：
（1）Record two width digital speckle images of the mobile front and back of objectf 1(x,y) andf 2(x,y), and Fourier is carried out respectively
Transformation, obtains respective Fourier transformation frequency spectrumF 1(u,v)、F 2(u,v)；
（2）WithF 1(u,v) divided byF 2(u,v), it is denoted asU(u,v),U(u,v) it is a two-dimensional complex number, and calculateU(u,v)
Phase angleφ(u,v)；
（3）To phase angleφ(u,v) make cos operation, equivalent Young's interfenrece fringes is obtained, is denoted asI(u,v), i.e.,：I(u,v)=cos[φ(u,v)]；
（4）It willI(u,v) Fourier transformation is carried out, it obtainsI(u,v) Fourier transformation frequency spectrumFI(ζ,η), measurementFI(ζ,η) position coordinates of maximum value other than zero-frequency, the size of object plane intrinsic displacement is obtained multiplied by pel spacing.
The algorithm is applied to sub-pix speckle pattern photography in-plane displacement quantity algorithm, and specific step is as follows：
（1）Record two width digital speckle images of the mobile front and back of objectf 1(x,y) andf 2(x,y), and Fourier is carried out respectively
Transformation, obtains respective Fourier transformation frequency spectrumF 1(u,v)、F 2(u,v)；
（2）WithF 1(u,v) divided byF 2(u,v), it is denoted asU(u,v), it calculatesU(u,v)nPower is denoted asU n (u,v),nTo appoint
Meaning positive integer, i.e.,：U n (u,v)=U(u,v)×U(u,v)×……×U(u,v), then calculateU n (u,v) phase angleφ n (u,v)；
（3）To phase angleφ n (u,v) make cos operation, equivalent Young's interfenrece fringes is obtained, is denoted asI n (u,v), i.e.,：I n
(u,v)=cos[φ n (u,v)]；
（4）It willI n (u,v) Fourier transformation is carried out, it obtainsI n (u,v) Fourier transformation frequency spectrumFI n (ζ,η), measurementFI n
(ζ,η) position coordinates of maximum value other than zero-frequency, divided byn, the displacement moved in object plane is obtained multiplied by pel spacing.
The present invention is by calculating step（2）The phase angleφGradientWithPositive and negative judge speckle
Moving direction, i.e., according to the positive and negative of gradient it may determine that speckle is mobile to the forward direction or negative sense of reference axis.
It is described abovexWithyThe horizontal and vertical coordinate of speckle pattern is respectively indicated,uWithvRespectively indicate speckle pattern Fourier change
Rear horizontal and vertical frequency is changed,ζWithηRespectively indicate the horizontal and vertical coordinate of equivalent Young's interfenrece fringes frequency spectrum.
Beneficial effects of the present invention：
（1）Minimum detectable speckle amount of movement of the present invention is less than speckle size, unrelated with speckle size, is able to achieve sub-pix
Detection, and energy accurate judgement speckle displacement direction, thus judgment object in-plane displacement direction.
（2）Inventive algorithm is simple, is easy to implement.
Detailed description of the invention
Fig. 1 is schematic diagram of calculation flow of the present invention；
Fig. 2 is that the embodiment of the present invention 1 acquires digital speckle figure（Laser speckle）Index path；
Fig. 3 is the digital speckle figure that the embodiment of the present invention 1 recordsf 1(x,y)（Part, 200 × 200 pixels）；
Fig. 4 is the phase diagram of the embodiment of the present invention 1φ(u,v)（Part, 400 × 400 pixels）；
Fig. 5 is the equivalent Young's interfenrece fringes figure of the embodiment of the present invention 1I(ζ,η)（Part, 400 × 400 pixels）；
Fig. 6 is the spectrogram of 1 Young's interfenrece fringes of the embodiment of the present inventionFI(ζ,η)（Part, 400 × 400 pixels）；
Fig. 7 is 1 phase of the embodiment of the present inventionφHatching line（400 rows of part）；
Fig. 8 is the embodiment of the present invention 1FI(ζ,η) andFI 5(ζ,η) hatching line（200 rows of part）；
Fig. 9 is that the embodiment of the present invention 2 acquires digital speckle figure（White light speckle）Index path；
Figure 10 is the white light digital speckle figure that the embodiment of the present invention 2 recordsf 1(x,y)；
Figure 11 is the white light digital speckle figure that the embodiment of the present invention 2 recordsf 2(x,y)；
Figure 12 is the Displacements Distribution figure that the embodiment of the present invention 2 is calculated；
Figure 13 is the effect that the Displacements Distribution that the embodiment of the present invention 2 is calculated is added on white light digital speckle figure；
Figure 14 is the partial enlarged view for the Displacements Distribution that the embodiment of the present invention 2 obtains（White wire frame portion in corresponding diagram 13
Point）；
In figure：1- laser, 2- computer, 3- beam splitter, 4- loose impediment sand paper, 5-CMOS video camera, 6- mikey
The inferior interferometer of that, the feeler lever of 7- assistor, 8- stress object sponge, 9- digital camera.
Specific embodiment
With reference to the accompanying drawing and embodiment, the invention will be further described, but the contents of the present invention be not limited to it is described
Range, narration content is not existing conventional techniques in detail.
Embodiment 1
Speckle pattern photography in-plane displacement quantity algorithm described in the present embodiment based on Fourier transformation phase, for calculating sand paper
In-plane displacement, optical path and related experiment equipment such as Fig. 2, laser 1（YAG laser, wavelengthλ=533nm）The laser beam of sending is logical
It crosses beam splitter 3 to shine directly on sand paper 4, reflected light is reflected into cmos camera 5 by beam splitter 3（Resolution ratio be 1744 ×
1308 pixels, pixel spacing are 3.2 μm of 3.2 μ m）Upper formation speckle, light intensity, which is converted to electric signal and passes in computer 2, to be saved
Get off, obtain digital speckle figure, due to sand paper and Michelson's interferometer 6（Illumination light is He-Ne laser, wavelengthλ 0=633nm）
It is connected, so the in-plane displacement amount of sand paper 4 can be measured accurately, cmos camera 5 can be replaced with CCD camera, shown in Fig. 1
Algorithm flow chart, carry out according to the following steps：
（1）The digital speckle figure before width sand paper movement is first recorded using above-mentioned experimental provisionf 1(x,y), it, can be with such as Fig. 3
See, since laser beam is without spreading direct irradiation sand paper, the size of speckle particle is very big, has been far longer than cmos camera
5 single pixel dimension, for convenience of observing, Fig. 3 gives the part of speckle pattern（200 × 200 pixels）, then rotate Michael
The ratchet of inferior interferometer 6 drives sand paper 4 mobile, the digital speckle figure after record is mobilef 2(x,y), it is calculated in computer 2f 1
(x,y) andf 2(x,y) Fourier transformation, respectively obtain Fourier transformation frequency spectrumF 1(u,v) andF 2(u,v), whereinxWithyRespectively
Indicate the horizontal and vertical coordinate of speckle pattern,uWithvHorizontal and vertical frequency after speckle pattern Fourier transformation is respectively indicated, under
Together；
（2）It willF 1(u,v) withF 2(u,v) be divided by obtainU(u,v),U(u,v) it is a two-dimensional complex number, and calculateU(u,v)
Phase angleφ(u,v), as shown in Figure 4（Part, 400 × 400 pixels）；
（3）To phase angleφ(u,v) cos operation is taken, obtain equivalent Young's interfenrece fringesI(u,v), i.e.,：I(u,v)=cos
[φ(u,v)], as shown in Figure 5（Part, 400 × 400 pixels）, it can be seen that the contrast of striped is fine；
（4）It is right againI(u,v) make Fourier transformation, it obtainsI(u,v) Fourier transformation frequency spectrumFI(ζ,η), whereinζWithη
The horizontal and vertical coordinate of equivalent Young's interfenrece fringes frequency spectrum is respectively indicated, similarly hereinafter, as shown in Figure 6（What is provided is with zero-frequency
Centered on part, 400 × 400 pixels）, give hereFI(ζ,η) hatching line（Part, 200 rows）, as a result such as Fig. 8 solid line institute
Show, the white dashed line in hatching line position such as Fig. 6, measurementFI(ζ,η) position coordinates of maximum value other than zero-frequency, sand paper can be obtained
Displacement in face, in conjunction with diagram, it can be seen thatFI(ζ,η) coordinate of maximum value is 11 in addition to zero-frequency, obtained speckle displacement
Amount is 11 pixels, i.e. displacement in sand paper face is 11 × 3.2 μm=35.2 μm.
It is calculated according to sub-pix speckle pattern photography in-plane displacement amount is generated, specific step is as follows：
（1）Record two width digital pictures of the mobile front and back of objectf 1(x,y) andf 2(x,y), and Fourier's change is carried out respectively
It changes, obtains respective Fourier transformation frequency spectrumF 1(u,v)、F 2(u,v), whereinxWithyRespectively indicate the horizontal and vertical of speckle pattern
Coordinate,uWithvRespectively indicate horizontal and vertical frequency after speckle pattern Fourier transformation；
（2）WithF 1(u,v) divided byF 2(u,v), it is denoted asU(u,v), it calculatesU(u,v) 5 power, obtain a two-dimensional complex number,
It is denoted asU 5 (u,v), i.e.,：U 5(u,v)=U(u,v)×U(u,v)×U(u,v)×U(u,v)×U(u,v), then calculateU 5(u,v)
Phase angleφ 5(u,v)；
（3）To phase angleφ 5(u,v) obtained as cos operationI 5(u,v), equivalent Young's interfenrece fringes is obtained, i.e.,：I 5 (u,v)=cos[φ 5 (u,v)]；
（4）It is right againI 5(u,v) as Fourier transformation obtain Fourier transformation frequency spectrumFI 5(ζ,η), whereinζWithηIt respectively indicates
The horizontal and vertical coordinate of equivalent Young's interfenrece fringes frequency spectrum, measurementFI 5(ζ,η) position coordinates of maximum value other than zero-frequency,
Here it givesFI 5(ζ,η) hatching line（Part, 200 rows）, white as a result as shown in Fig. 8 dotted line, in hatching line position such as Fig. 6
Dotted line, then divided by 5, the in-plane displacement amount for generating the sand paper of sub-pix speckle can be obtained, in conjunction with diagram,FI 5(ζ,η) maximum
Coordinate be 54, divided by 5 be 10.8, obtained speckle displacement amount be 10.8 pixels, i.e., the displacement in sand paper face be 10.8 ×
3.2μm=34.56μm。
The mobile actual displacement of the sand paper of Michelson's interferometer record is 34.50 μm, is coincide with the above calculated result, and
The same digital speckle result obtained with sub-pix calculation method of desiring to make money or profit is more accurate.
In order to judge the direction of displacement of speckle pattern, phase angle is calculatedφGradientWith, according to gradient just,
It bears it may determine that speckle is, for convenience of observing, to give phase angle here to the movement of the forward direction or negative sense of reference axisφ's
Hatching line（Part, 400 rows）, as shown in fig. 7, the black dotted lines in corresponding position such as Fig. 4,>0,>0, so
Direction of displacement edge is calculatedxWithyAxis is positive, matches with the moving direction of sand paper in experiment.
Embodiment 2
Speckle pattern photography in-plane displacement quantity algorithm described in the present embodiment based on Fourier transformation phase, for measure object by
In-plane displacement after power（Deformation）, optical path and related experiment equipment such as Fig. 9, assistor feeler lever 7 connect with stress object sponge 8
It touches, white speckle is sprayed on sponge 8, change the size of power on assistor, deformation occurs for stress object, and deformation process is digital
Camera 9 is recorded, and white light digital speckle figure is obtained, and two width speckle patterns is inputted in computer, by algorithm process of the invention
The in-plane displacement of each point on available sponge carries out according to the following steps to obtain deformation situation：
（1）The digital speckle figure under a width Afterburning condition 1 is first recorded using above-mentioned experimental provisionf 1(x,y), such as Figure 10 institute
Show, then increases the power on assistor, record the digital speckle figure under Afterburning condition 2f 2(x,y), as shown in figure 11, calculating
It will in machinef 1(x,y) andf 2(x,y) be all divided intoMA zonule（M=18×18）, calculate in a computerMIn a zonule respectively
It is correspondingf 1(x,y) andf 2(x,y) Fourier transformation, respectively obtainMCorresponding Fourier transformation frequency spectrum in a zonuleF 1(u,v) andF 2(u,v)；
（2）The method that sub-pixel speckle displacement amount is calculated described in embodiment 1, the step corresponded to according to it（2）To step
Suddenly（4）, whereinN takes 5,Calculate separately correspondenceMIn-plane displacement amount and direction in a zonule；
（3）The displacement of each zonule is drawn out with small arrow, arrow length and direction correspond to amount of displacement and side
To such as Figure 12；
（4）The displacement diagram marked with small arrow is superimposed with deformable object speckle pattern, convenient for observing the stress and deformation of each point
Situation, as shown in figure 13, Figure 14 are the partial enlarged view of the corresponding Displacements Distribution of white frame portion in Figure 13.
The experimental results showed that can quickly calculate object with method of the invention（Sponge）The deformation of each point after stress（Displacement
Amount）Size and direction coincide with actual conditions.
Claims (3)
1. a kind of speckle pattern photography in-plane displacement quantity algorithm based on Fourier transformation phase, which is characterized in that according to the following steps into
Row：
（1）Record two width digital speckle images of the mobile front and back of objectf 1(x,y) andf 2(x,y), Fourier transformation is carried out respectively,
Obtain respective Fourier transformation frequency spectrumF 1(u,v)、F 2(u,v)；
（2）WithF 1(u,v) divided byF 2(u,v), it is denoted asU(u,v), and calculateU(u,v) phase angleφ(u,v)；
（3）To phase angleφ(u,v) make cos operation, equivalent Young's interfenrece fringes is obtained, is denoted asI(u,v), i.e.,：I(u,v)=
cos[φ(u,v)]；
（4）It willI(u,v) Fourier transformation is carried out, it obtainsI(u,v) Fourier transformation frequency spectrumFI(ζ,η), measurementFI(ζ,η) zero
The position coordinates of maximum value other than frequency obtain the size of in-plane displacement multiplied by pel spacing；
WhereinxWithyThe horizontal and vertical coordinate of speckle pattern is respectively indicated,uWithvIt respectively indicates after speckle pattern Fourier transformation laterally
With longitudinal frequency,ζWithηRespectively indicate the horizontal and vertical coordinate of equivalent Young's interfenrece fringes frequency spectrum.
2. algorithm described in claim 1 is applied to sub-pix speckle pattern photography in-plane displacement quantity algorithm, which is characterized in that specific steps
It is as follows：
（1）Record two width digital speckle images of the mobile front and back of objectf 1(x,y) andf 2(x,y), and Fourier's change is carried out respectively
It changes, obtains respective Fourier transformation frequency spectrumF 1(u,v)、F 2(u,v)；
（2）WithF 1(u,v) divided byF 2(u,v), it is denoted asU(u,v), it calculatesU(u,v)nPower is denoted asU n (u,v),nFor arbitrarily just
Integer, i.e.,：U n (u,v)=U(u,v)×U(u,v)×……×U(u,v), then calculateU n (u,v) phase angleφ n (u,v)；
（3）To phase angleφ n (u,v) make cos operation, equivalent Young's interfenrece fringes is obtained, is denoted asI n (u,v), i.e.,：I n (u,v)=
cos[φ n (u,v)]；
（4）It willI n (u,v) Fourier transformation is carried out, it obtainsI n (u,v) Fourier transformation frequency spectrumFI n (ζ,η), measurementFI n (ζ,η)
The position coordinates of maximum value other than zero-frequency, divided byn, the displacement moved in object plane is obtained multiplied by pel spacing；
WhereinxWithyThe horizontal and vertical coordinate of speckle pattern is respectively indicated,uWithvIt respectively indicates after speckle pattern Fourier transformation laterally
With longitudinal frequency,ζWithηRespectively indicate the horizontal and vertical coordinate of equivalent Young's interfenrece fringes frequency spectrum.
3. algorithm according to claim 1, which is characterized in that by calculating step（2）The phase angleφGradient
WithThe positive and negative moving direction to judge speckle.
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| CN1844844A (en) * | 2006-05-17 | 2006-10-11 | 中国科学院上海光学精密机械研究所 | Device and method for measuring micro displacement by femtosecond laser speckle correlation method |
| CN102135413A (en) * | 2010-12-14 | 2011-07-27 | 河南科技大学 | Phase vortex based digital speckle correlation measurement method |
| CN102353332A (en) * | 2011-06-28 | 2012-02-15 | 山东大学 | Electronic speckle-interference digital-compensating method and system thereof |
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| JP3955899B2 (en) * | 2002-09-20 | 2007-08-08 | 国立大学法人埼玉大学 | Deformation measurement method and apparatus using electronic speckle interferometry |
| US7359065B2 (en) * | 2005-07-14 | 2008-04-15 | Coherix, Inc. | Method of combining holograms |
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| CN1844844A (en) * | 2006-05-17 | 2006-10-11 | 中国科学院上海光学精密机械研究所 | Device and method for measuring micro displacement by femtosecond laser speckle correlation method |
| CN102135413A (en) * | 2010-12-14 | 2011-07-27 | 河南科技大学 | Phase vortex based digital speckle correlation measurement method |
| CN102353332A (en) * | 2011-06-28 | 2012-02-15 | 山东大学 | Electronic speckle-interference digital-compensating method and system thereof |
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