CN104111039A - Calibrating method for randomly placing fringe projection three-dimensional measuring system - Google Patents

Abstract

The invention provides a calibrating method for randomly placing a fringe projection three-dimensional measuring system. The calibrating method comprises the following steps of: 1, designing a calibrating plate, wherein the calibrating plate is a chessboard pattern with equal intervals; 2, placing the calibrating plate into a measuring system view field for CCD (Charge Coupled Device) camera calibration; 3, placing the chessboard pattern on any different positions in a measurement field, projecting a phase shifting sine fringe pattern to the surface of the chessboard pattern on each placement position, and then collecting images and calculating the distribution phi of an unwrapped phase of each pixel point positioned on the surface of the chessboard pattern and the distance h from the unwrapped phase to a reference surface; 4 establishing three polynomials to express the relationship between the unwrapped phase phi and a height h, between the height h and a horizontal coordinate X and between the height h and a horizontal coordinate Y; 5 converting the horizontal coordinates (X, Y) which are from the unwrapped phase to actual height data and correspond to the height data by utilizing calibrated polynomial coefficient to complete the calibration of the three-dimensional measuring system.

Description

For putting arbitrarily the scaling method of fringe projection three-dimension measuring system

Technical field

The present invention relates to the scaling method of the optical three-dimensional measurement system based on fringe projection, be specially and adopt fringe projection commercial measurement body surface phase place, set up the relation of launching between phase place and height and height and horizontal ordinate, for the technical field of object dimensional surface shape measurement.

Background technology

Along with the fast development in the fields such as precision optical machinery processing, automobile making, precision optics processing, semicon industry, exact instrument manufacture, Design of Dies, reverse-engineering, people wish accurately to measure precision parts, workpiece object day by day urgently, traditional 2-D data measuring equipment can not meet the production requirement of modernization increasingly, robotization, and three-dimensional measurement technology is arisen at the historic moment.But high accuracy three-dimensional measuring technique be unable to do without system calibrating technology.

The internal and external parameter of current existing three-dimensional measuring systems calibration method or dependence calibration for cameras unit and projecting cell, calculate the relative position of the two and the geometric parameter of whole measuring system, replace manual measurement, this kind of method execution difficulty and the parameter degree of accuracy obtaining are not high yet, thereby finally cannot obtain high accuracy three-dimensional data; Or the three-dimensional parameter that relies on accurate standard component carries out matching, set up the relation of phase place and height, this kind method manufacturer's standard part is very difficult and cost is expensive; Or rely on accurately mobile and positioning and demarcating plate, set up the relation of phase place and height, simultaneously high to measuring system structural requirement, must ensure that camera optical axis is vertical with reference surface, thus nominal time length and be confined to complete in laboratory environment.And the three-dimensional information of pixel and altitude information formation, the true three-dimension information that cannot provide horizontal ordinate and altitude information to form all can only be provided above-mentioned three class scaling methods.In applicant's range of search, the typical scaling method of three-dimension measuring system can be seen following pertinent literature information:

" demarcation of 3-d shape measurement system " (Calibration of a three-dimensional shape measurement system that 1.Q.Y.Hu etc. deliver, Opt.Eng.42.487-493 (2003)), propose one projector has been equivalent to CCD camera, demarcated the internal and external parameter of CCD camera and projector simultaneously.But due to the image of CCD camera and digital projector lens distortion, this procedure is complicated and cannot provide system external parameter accurately, thereby the three dimension system precision of demarcating is not high.

" for the least square scaling method of fringe projection technology of profiling " (Least-squares calibration method for fringe projection profilometry that 2.H.W.Guo etc. deliver, Opt.Eng.44,033603 (2005)), study and utilized accurate mobile horizontal shift platform movement High Accuracy Flat to obtain nominal data, then data are carried out to least square fitting, obtain phase height relation.The accurate application restric-tion that moves horizontally platform this kind of method can only in laboratory, complete, be not suitable for practical application.

3.Z.H.Zhang Deng " a kind of simply, flexibly the phase calculation scaling method based on the 3-D imaging system " (Simple delivering, flexible calibration of phase calculation-based three-dimensional imaging system, Opt.Lett.36,1257-1259 (2011)), studied a kind of simple calibrating method that utilizes chessboard grid and demarcate blank, scaling board can at random, at random be placed on any position in visual field.But this method requires camera optical axis vertical with reference surface, has in actual applications limitation.

" a kind of flexible calibration technology based on fringe projection technology of profiling 3-D imaging system " (Flexible calibration technique for fringe-projection-based three-dimensional imaging that 4.Minh Vo etc. delivers, Opt.Lett.35,3192-3194 (2010)), study a kind of three-dimensional scaling method for any system architecture.The method requires low to the structure setting of measuring system, but also can only provide phase height data relationship, can not provide the scaling method of horizontal ordinate.

Can be seen and be had calibration technique or process complexity, be difficult to realize by above-mentioned document, or equipment cost costliness, the practicality of not having, or system structure design be required harsh, or to provide be that three-dimensional data is comprehensive not.Therefore, the full coordinate of fringe projection three-dimension measuring system is demarcated, and particularly demarcation in actual applications, is a difficult problem for a not yet fine solution.

Summary of the invention

For the deficiencies in the prior art, the technical matters that quasi-solution of the present invention is determined is, provide a kind of for putting arbitrarily the scaling method of fringe projection three-dimension measuring system, this demarcation is based on fringe projection technology and CCD camera calibration technology, can determine fast, accurately, simply the full coordinate relation between phase place and height, height and horizontal ordinate, particularly be applicable to the actual demarcation of engineering and use, and with low cost.

The present invention to achieve these goals, by the following technical solutions:

For putting arbitrarily a scaling method for fringe projection three-dimension measuring system, the method comprises:

Step 1, design are demarcated dull and stereotyped, and scaling board is equidistant alternate chessboard grid, and has diffuse reflection surface;

Step 2, place described scaling board in any diverse location of measurement field, gather the scaling board image of each placement location, then to several phase shift sine streaks figure of scaling board surface projection of each placement location, and gather several sine streak images of the scaling board reflection of each placement location, wherein scaling board image is for the inner parameter matrix A of calibration for cameras and the external parameter matrix [R of this position, T], sine streak image is used to phase shift algorithm and phase-unwrapping algorithm and solves the expansion PHASE DISTRIBUTION Φ of this placement location;

Step 3, the volume coordinate (X of each pixel (m, n) in camera coordinates system that calculates the some correspondence on the scaling board of position according to the inside and outside portion parameter matrix obtaining in step 2 _c, Y _c, Z _c);

Step 4, in the diverse location described in step 2, choose arbitrarily a position as with reference to plane, and according to the volume coordinate (X of this position obtaining in step 3 _c, Y _c, Z _c) matching three dimensions plane equation;

Step 5, obtain the volume coordinate of other position scaling boards according to step 3, utilize point to calculate the height value h of each point to reference surface to the space length formula of plane, and the horizontal ordinate (X, Y) of the vertical point of the vertical line equation computer memory point that utilizes space plane in reference planes;

Step 6, set up a polynomial expression, for expressing phase place Φ and the relation between h highly launched:

$h(m,n)=\frac{1+a_1(m+n)\·\mathrm{\Φ}(m,n)}{a_2(m,n)+a_3(m,n)\·\mathrm{\Φ}(m,n)}$

In formula, h (m, n) is the height that different spaces that pixel (m, n) is corresponding is put reference planes, the expansion PHASE DISTRIBUTION that Φ (m, n) is this pixel, a ₁(m, n), a ₂(m, n), a ₃(m, n) is multinomial coefficient to be solved, and launches gained height value h in phase place and step 5 utilize least square method to solve multinomial coefficient according to step 2 gained;

Step 7, set up a polynomial expression respectively, for expressing the relation between height h (m, n) and horizontal ordinate X, Y:

$\left\{\begin{array}{c}X=\underset{k=0}{\overset{M}{\mathrm{\Σ}}}{b}_k(m.n)\·h^k(m,n)\\ Y=\underset{k=0}{\overset{M}{\mathrm{\Σ}}}{c}_k(m,n)\·h^k(m,n)\end{array}\right.$

In formula, (X, Y) is intersection point horizontal ordinate, and M is the maximal value of polynomial expression level time k, and is positive integer, b _k(m, n), c _k(m, n) is multinomial coefficient to be solved, and utilizes least square method to solve multinomial coefficient according to gained height value h in step 5 and horizontal ordinate (X, Y).

Step 8, utilize the multinomial coefficient of step 6 and step 7 gained, conversion launches phase place to actual three-dimensional data, completes the demarcation of three-dimension measuring system.

In technique scheme, the scaling board in described step 1 is equidistant alternate square chessboard grid, and has diffuse reflection surface.

In technique scheme, camera calibration in step 2, obtains inner parameter matrix A and external parameter matrix [R, T], and detailed process is as follows:

1), first scaling board is placed on to the multiple optional positions in viewing field of camera, and gathers the image of each position; 2), by the coordinate X of the angle point of each position scaling board medium square _w, Y _wwith corresponding pixel coordinate (m, n) substitution internal and external parameter compute matrix, calculate the external parameter matrix [R, T] of inner parameter matrix A and each position;

$\left[\begin{array}{c}m\\ n\\ 1\end{array}\right]=A\×\left[\begin{array}{c}{X}_C\\ Y_C\\ Z_C\end{array}\right]=A\×[R,T]=A\×\left[\begin{array}{ccc}{R}_{11}& R_{12}& T_1\\ R_{21}& R_{22}& T_2\\ R_{31}& R_{32}& T_3\end{array}\right]\×\left[\begin{array}{c}{X}_W\\ Y_W\\ 1\end{array}\right]$

(X in formula _c, Y _c, Z _c) be the volume coordinate in camera coordinate system, s is scale factor, m, n is pixel coordinate, R11, R12, R21, R22, R31, R32 is the element of R in external parameter matrix, T1, T2, T3 are the element of T in external parameter matrix.

In technique scheme, in step 3, calculate the volume coordinate (X of each pixel (m, n) in camera coordinates system _c, Y _c, Z _c), detailed process is as follows:

1), first define matrix G, as follows

$G=\left[\begin{array}{ccc}{g}_1& g_2& g_3\\ g_4& g_5& g_6\\ g_7& g_8& g_9\end{array}\right]={[R,T]}^{-1}\×A^{-1}={\left[\begin{array}{ccc}{R}_{11}& R_{12}& T_1\\ R_{21}& R_{22}& T_2\\ R_{31}& R_{32}& T_3\end{array}\right]}^{-1}\×A^{-1},$

2), by matrix below pixel (m, n) substitution, obtain volume coordinate (X _c, Y _c, Z _c).

$\left[\begin{array}{c}{X}_C\\ Y_C\\ Z_C\end{array}\right]=\frac{1}{{\mathrm{mg}}_7+{\mathrm{ng}}_8+g_9}\×A^{-1}\×\left[\begin{array}{c}m\\ n\\ 1\end{array}\right]$

In technique scheme, in described step 4, adopt the three dimensions plane equation of least square fitting reference planes: $a{X}_C^r+{\mathrm{bY}}_C^r+Z_C^r+c=0.$

Wherein for the volume coordinate of each point in reference planes in camera coordinate system, (a, b, c) is the equation coefficient for the treatment of matching, and (a, b, 1) also claims the normal vector of reference surface.

In technique scheme, the bar graph gathering in described step 2 can be expressed as:

I(X,Y)＝A(X,Y)+B(X,Y)cos[Φ(X,Y)]

Wherein I (X, Y) light distribution of expression collected by camera, A (X, Y) be background light intensity, B (X, Y) is that degree of modulation distributes, Φ (X, Y) be and the PHASE DISTRIBUTION of body surface height correlation, (X, Y) is the two-dimentional horizontal ordinate of deforming stripe image.

The present invention possesses following beneficial effect:

What the present invention was the most outstanding is propose first a kind of for putting arbitrarily the scaling method of fringe projection three-dimension measuring system.The method has advantages of simply, flexible, cost is low, can accurately provide the relation between PHASE DISTRIBUTION and object height data and altitude information and horizontal ordinate (X, Y) simultaneously.Disclosed by the invention for putting arbitrarily the scaling method experiments of measuring of fringe projection three-dimension measuring system, success, obtained efficiently and accurately the three-dimensional data information of object, the method has the advantages such as easy to operate, low cost, spirit and property are strong with respect to additive method.

Brief description of the drawings

Fig. 1 is that system arranges any fringe projection three-dimension measuring system figure;

Fig. 2 is that this measuring system is demarcated gridiron pattern pattern used;

Fig. 3 is the bar graph on the scaling board of digital camera record;

Fig. 4 is the deforming stripe figure of the face mask surface of digital camera record;

Fig. 5 is the expansion PHASE DISTRIBUTION of the face mask that demodulates;

Fig. 6 is the horizontal 2-D data figure of face mask;

Fig. 7 is the three-dimensional data figure of face mask;

Fig. 8 is the measurement result to 4mm position;

Fig. 9 is the measurement result to 16mm position;

Figure 10 is workflow diagram.

Embodiment

The invention discloses a kind of for putting arbitrarily the scaling method of fringe projection three-dimension measuring system, the method by fringe projection technology of profiling (FPP) and in conjunction with CCD camera calibration technology for fringe projection 3 d shape measure.Below in conjunction with the drawings and specific embodiments, working of an invention scheme is illustrated.

Step 1: experimental measurement system is set: system mainly comprises camera, projector, scaling board, object under test, control computer and support.The distribution of projector, camera, scaling board is random, and relative position is any, as shown in Figure 1.Adjustment System makes digital camera can photograph the candy strip on scaling board and object under test surface.

Step 2: scaling board is positioned over to the optional position in measuring system visual field.In each position, produce and project the sinusoidal phase shift candy strip of several standards by computer control projector, digital camera is taken the bar graph by demarcating surface reflection.Fig. 2 and Fig. 3 have shown the scaling board and the bar graph that in the method, use.

Step 3: to the bar graph of each position acquisition, the continuous phase that utilizes phase shift algorithm and space phase method of deploying to demodulate this scaling board surface, position distributes.The full coordinate that completes measuring system according to camera calibration technology and volume coordinate, distance relation is demarcated, and solves multinomial coefficient a ₁(m, n), a ₂(m, n), a ₃(m, n) and b _k(m, n), c _kthe value of (m, n), creates the coefficient storage unit of corresponding each location of pixels, sets up the phase height of each pixel position, highly-horizontal ordinate relation, completion system staking-out work in pixel index mode.

Step 4: produced and projected the sinusoidal phase shift candy strip of several standards by computer control projector, digital camera is taken by the deforming stripe figure of determinand surface reflection.Utilize phase shift algorithm and space phase method of deploying to demodulate the continuous phase distributed intelligence on determinand surface.

Step 5: the phase height relation providing according to full coordinate scaling method obtains object under test surface elevation information, then provide height-horizontal ordinate relation according to full coordinate scaling method and obtain the horizontal ordinate that each pixel is corresponding.Finally complete the measurement of three-dimensional data.Fig. 5 is the expansion PHASE DISTRIBUTION demodulating, and this phase place and object height information are closely related.Fig. 6 represents that Fig. 7 represents the object Shape ' after reconstruction according to the three-dimensional data of demarcating gained phase height relation and height-horizontal ordinate relation and obtain body surface.Can find out from Fig. 6, Fig. 7, Fig. 8, Fig. 9, a kind of full coordinate scaling method for any fringe projection three-dimension measuring system that this patent proposes has higher accuracy and validity, and simple to operate.

Embodiment 1

For a full coordinate scaling method for any fringe projection three-dimension measuring system, it is characterized in that comprising following step:

A., experimental measurement system is set: system mainly comprises camera, projector, scaling board, object under test, control computer and support.The distribution of projector, camera, scaling board is random, and relative position is any.Adjustment System makes digital camera can photograph the candy strip on scaling board and object under test surface.

B. scaling board is positioned over to the multiple optional positions (in this example, scaling board being positioned over arbitrarily to 20 diverse location places) in measuring system visual field.In each position, produce and project the sinusoidal phase shift candy strip of 10 width standards by computer control projector, digital camera is taken the bar graph by demarcating surface reflection, as shown in Figure 3.This example adopts the white equidistant alternate square grid of 18 × 27 indigo plants, and the length of side of grid is 10mm, as shown in Figure 2.In this example, CCD camera is Prosilica GT1660C, and camera uses the tight shot (Computar M5018-MP2) of 50mm.

C. the bar graph to each position acquisition, utilizes 10 step phase shift algorithm and space phase method of deploying to demodulate the continuous phase distributed intelligence on this scaling board surface, position.The full coordinate that completes measuring system according to camera calibration technology and volume coordinate, distance relation is demarcated, and solves multinomial coefficient a ₁(m, n), a ₂(m, n), a ₃(m, n) and b _k(m, n), c _kthe value of (m, n), creates the coefficient storage unit of corresponding each location of pixels, sets up the phase height of each pixel position, highly-horizontal ordinate relation, completion system staking-out work in pixel index mode.

D. produced and projected the sinusoidal phase shift candy strip of 10 width standards by computer control projector, digital camera is taken by the deforming stripe figure of determinand surface reflection.In this example, adopt face mask as object under test, as shown in Figure 4.The deforming stripe light intensity gathering can be expressed as:

I(X,Y)＝A(X,Y)+B(X,Y)cos[Φ(X,Y)]

Wherein I (X, Y) light distribution of expression collected by camera, A (X, Y) be background light intensity, B (X, Y) is that degree of modulation distributes, Φ (X, Y) be and the PHASE DISTRIBUTION of body surface height correlation, (X, Y) is the two-dimentional horizontal ordinate of deforming stripe image.

E. the stripe pattern to gained, utilizes 10 step phase shift algorithm and space phase method of deploying to demodulate the continuous phase distributed intelligence Φ (X, Y) on determinand surface, as shown in Figure 5.

F. obtain, after continuous Φ (X, Y), utilizing the phase height relation of the demarcation in step C, can obtain the three-dimensional altitude information on object under test (face mask) surface.Step C solves coefficient a ₁(m, n), a ₂(m, n), a ₃after (m, n), phase place height relationships is as follows:

$h(m,n)=\frac{1+a_1(m+n)\·\mathrm{\Φ}(m,n)}{a_2(m,n)+a_3(m,n)\·\mathrm{\Φ}(m,n)}$

Here Φ (m, n)=Φ (X, Y), because in measuring system, the corresponding different lateral coordinates of each pixel.

G. calculating after altitude information h (m, n), utilizing height-horizontal ordinate relation of demarcating in step C, can obtain the horizontal 2-D data of object under test (face mask), as shown in Figure 6.Step C solves coefficient b _k(m, n), c _k(m, n) is rear, highly-horizontal ordinate relation is as follows:

$\left\{\begin{array}{c}X=\underset{k=0}{\overset{M}{\mathrm{\Σ}}}{b}_k(m.n)\·h^k(m,n)\\ Y=\underset{k=0}{\overset{M}{\mathrm{\Σ}}}{c}_k(m,n)\·h^k(m,n)\end{array}\right.$

Here M is the maximal value of polynomial expression level time k, and we allow M=3.

The horizontal ordinate (X, Y) of the relevant position that the altitude information h (m, n) that H. comprehensive step F obtains and step G obtain, completes the three-dimensional measurement to object under test (face mask), as shown in Figure 7.

Embodiment 2

For the phase height relation of checking the inventive method demarcation and accuracy and the validity of height-horizontal ordinate relation, in measurement field, relative reference face position, accurately positioning and demarcating plate is in 4mm and two positions of 16mm.Its measurement result as shown in Figure 8 and Figure 9.Measurement result is got to average, be respectively 4.053mm and 16.057mm, its corresponding standard deviation is 0.028 and 0.033.To the measurement of horizontal ordinate, we adopt the spacing of grid angle point on scaling board as assessment.At 4mm place, the average of directions X is 9.968mm, and the average of Y-direction is 9.977mm, and its corresponding standard deviation is 0.062 and 0.075.At 16mm place, the average of directions X is 10.061mm, and the average of Y-direction is 10.070mm, and its corresponding standard deviation is 0.064 and 0.073.

To sum up, the present invention has higher degree of accuracy and validity, the visible last process flow diagram of its staking-out work process.

Claims (5)

1. for putting arbitrarily a scaling method for fringe projection three-dimension measuring system, the method comprises:

Step 1, design are demarcated dull and stereotyped, and scaling board is equidistant alternate chessboard grid, and has diffuse reflection surface;

Step 2, place described scaling board in any diverse location of measurement field, gather the scaling board image of each placement location, then to several phase shift sine streaks figure of scaling board surface projection of each placement location, and gather several sine streak images of the scaling board reflection of each placement location, wherein scaling board image is for the inner parameter matrix A of calibration for cameras and the external parameter matrix [R of this position, T], sine streak image is used to phase shift algorithm and phase-unwrapping algorithm and solves the expansion PHASE DISTRIBUTION Φ of this placement location;

Step 3, the volume coordinate (X of each pixel (m, n) in camera coordinates system that calculates the some correspondence on the scaling board of position according to the inside and outside portion parameter matrix obtaining in step 2 _c, Y _c, Z _c);

Step 4, in the diverse location described in step 2, choose arbitrarily a position as with reference to plane, and according to the volume coordinate (X of this position obtaining in step 3 _c, Y _c, Z _c) matching three dimensions plane equation;

Step 5, obtain the volume coordinate of other position scaling boards according to step 3, utilize point to calculate the height value h of each point to reference surface to the space length formula of plane, and the horizontal ordinate (X, Y) of the vertical point of the vertical line equation computer memory point that utilizes space plane in reference planes;

Step 6, set up a polynomial expression, for expressing phase place Φ and the relation between h highly launched:

$h(m,n)=\frac{1+a_1(m+n)\·\mathrm{\Φ}(m,n)}{a_2(m,n)+a_3(m,n)\·\mathrm{\Φ}(m,n)}$

In formula, h (m, n) is the height that different spaces that pixel (m, n) is corresponding is put reference planes, the expansion PHASE DISTRIBUTION that Φ (m, n) is this pixel, a ₁(m, n), a ₂(m, n), a ₃(m, n) is multinomial coefficient to be solved, and launches gained height value h in phase place and step 5 utilize least square method to solve multinomial coefficient according to step 2 gained;

Step 7, set up a polynomial expression respectively, for expressing the relation between height h (m, n) and horizontal ordinate X, Y:

$\left\{\begin{array}{c}X=\underset{k=0}{\overset{M}{\mathrm{\Σ}}}{b}_k(m.n)\·h^k(m,n)\\ Y=\underset{k=0}{\overset{M}{\mathrm{\Σ}}}{c}_k(m,n)\·h^k(m,n)\end{array}\right.$

In formula, (X, Y) is intersection point horizontal ordinate, and M is the maximal value of polynomial expression level time k, and is positive integer, b _k(m, n), c _k(m, n) is multinomial coefficient to be solved, and utilizes least square method to solve multinomial coefficient according to gained height value h in step 5 and horizontal ordinate (X, Y).

Step 8, utilize the multinomial coefficient of step 6 and step 7 gained, conversion launches phase place to actual three-dimensional data, completes the demarcation of three-dimension measuring system.

2. according to claim 1 a kind of for putting arbitrarily the scaling method of fringe projection three-dimension measuring system, it is characterized in that: the scaling board in described step 1 is equidistant alternate square chessboard grid, and has diffuse reflection surface.

3. according to claim 1 a kind of for putting arbitrarily the scaling method of fringe projection three-dimension measuring system, it is characterized in that: camera calibration in step 2, obtain inner parameter matrix A and external parameter matrix [R, T], detailed process is as follows:

1), first scaling board is placed on to the multiple optional positions in viewing field of camera, and gathers the image of each position; 2), by the coordinate X of the angle point of each position scaling board medium square _w, Y _wwith corresponding pixel coordinate (m, n) substitution internal and external parameter compute matrix, calculate the external parameter matrix [R, T] of inner parameter matrix A and each position;

$\left[\begin{array}{c}m\\ n\\ 1\end{array}\right]=A\×\left[\begin{array}{c}{X}_C\\ Y_C\\ Z_C\end{array}\right]=A\×[R,T]=A\×\left[\begin{array}{ccc}{R}_{11}& R_{12}& T_1\\ R_{21}& R_{22}& T_2\\ R_{31}& R_{32}& T_3\end{array}\right]\×\left[\begin{array}{c}{X}_W\\ Y_W\\ 1\end{array}\right]$

(X in formula _c, Y _c, Z _c) be the volume coordinate in camera coordinate system, s is scale factor, m, n is pixel coordinate, R11, R12, R21, R22, R31, R32 is the element of R in external parameter matrix, T1, T2, T3 are the element of T in external parameter matrix.

4. according to claim 1 a kind of for putting arbitrarily the scaling method of fringe projection three-dimension measuring system, it is characterized in that: in step 3, calculate the volume coordinate (X of each pixel (m, n) in camera coordinates system _c, Y _c, Z _c), detailed process is as follows:

1), first define matrix G, as follows

$G=\left[\begin{array}{ccc}{g}_1& g_2& g_3\\ g_4& g_5& g_6\\ g_7& g_8& g_9\end{array}\right]={[R,T]}^{-1}\×A^{-1}={\left[\begin{array}{ccc}{R}_{11}& R_{12}& T_1\\ R_{21}& R_{22}& T_2\\ R_{31}& R_{32}& T_3\end{array}\right]}^{-1}\×A^{-1},$

2), by matrix below pixel (m, n) substitution, obtain volume coordinate (X _c, Y _c, Z _c).

$\left[\begin{array}{c}{X}_C\\ Y_C\\ Z_C\end{array}\right]=\frac{1}{{\mathrm{mg}}_7+{\mathrm{ng}}_8+g_9}\×A^{-1}\×\left[\begin{array}{c}m\\ n\\ 1\end{array}\right]$

5. according to claim 1 a kind of for putting arbitrarily the scaling method of fringe projection three-dimension measuring system, it is characterized in that: the three dimensions plane equation that adopts least square fitting reference planes in described step 4: $a{X}_C^r+{\mathrm{bY}}_C^r+Z_C^r+c=0.$

Wherein for the volume coordinate of each point in reference planes in camera coordinate system, (a, b, c) is the equation coefficient for the treatment of matching, and (a, b, 1) also claims the normal vector of reference surface.