CN109883353A

CN109883353A - A dynamic three-dimensional measurement method for rigid moving objects

Info

Publication number: CN109883353A
Application number: CN201910121297.XA
Authority: CN
Inventors: 杨延西; 王建华; 张申华; 邓毅; 高异
Original assignee: Xian University of Technology
Current assignee: Jiangsu Gutian Automation Co ltd
Priority date: 2019-02-19
Filing date: 2019-02-19
Publication date: 2019-06-14
Anticipated expiration: 2039-02-19
Also published as: CN109883353B

Abstract

A kind of dynamic 3 D measurement method of rigid motion object, the following steps are included: step 1, the pixel speed that moving object is obtained by the ratio and known transmission line physical speed of physical size in camera fields of view and Pixel Dimensions estimates the pixel-shift between several acquisition stripeds；Step 2, estimate phase offset, generate new projected fringe；Finally, the 12 spoke lines to acquisition carry out pixel-shift；According to four-step phase-shifting algorithm and three frequency heterodyne phase deployment algorithms, actual phase is calculated, is then updated in the phase height relational expression of pre- calibration, rebuilds the three-dimensional appearance of object；The complex process for avoiding transmission line out of service, measurement, transmission line operation, improves measurement efficiency.

Description

A kind of dynamic 3 D measurement method of rigid motion object

Technical field

The invention belongs to optical grating projection three-dimensional measurement technical fields, and in particular to a kind of dynamic 3 D of rigid motion object Measurement method.

Background technique

Test product on automatic production line, shape invariance, position are mobile.Since often shape is more for industrial products Complexity, measurement accuracy is more demanding, and therefore, it is difficult to realize single width striped three-dimensional measurement.And the stationary body three of several fringe projections Tie up that measuring technique is mature, measurement accuracy is high, high reliablity, therefore by the three-dimensional measurement Technique Popularizing of stationary body to rigid motion In the three-dimensional measurement of object, the detection efficiency of product on production line can be greatly improved.

Zhang etc. proposes calibration algorithm, Phase Compensation Algorithm, space phase exhibition on the basis of being based on three step phase shifts Algorithm and GPU parallel processing technique are opened, a set of high speed, high-precision, real-time dynamic 3 D measuring system are constructed, it not only can be into The three-dimensional measurement of row stationary body, and it is able to achieve the measurement of 40 frames/second dynamic 3 D.But above method measuring speed is not high, Only it is able to achieve the three-dimensional measurement of slow dynamics object.Gray code solution phase techniques are extended to the three-dimensional measurement of dynamic object by Liu et al., Realize the measurement of 1000 frames/second high speed dynamic 3 D.But there are deviations in object mass center extraction, and synchronous error is caused to compensate There are deviations, affect the three-dimensional measurement precision of dynamic object.

Summary of the invention

To overcome above-mentioned the deficiencies in the prior art, the object of the present invention is to provide a kind of dynamic 3 Ds of rigid motion object Measurement method avoids transmission line out of service, measurement, passes to realize effective measurement of sports products on automation transmission line The complex process of defeated line operation, improves measurement efficiency.

To achieve the above object, the technical solution adopted by the present invention is that:

A kind of dynamic 3 D measurement method of rigid motion object, comprising the following steps:

Step 1, pass through the ratio and known transmission line physical speed of physical size in camera fields of view and Pixel Dimensions The pixel speed of moving object is obtained, estimates the pixel-shift between several acquisition stripeds, specific practice is:

A scale is placed on the transmission line, records the physical size in camera fields of view along x coordinate, along x in camera fields of view The pixel size of coordinate is known, between available Pixel Dimensions and physical size relationship, k_x=512 (pixels)/118 (mm)≈4.34(pixels/mm)；Pixels indicates pixel；

If the physical speed of transmission line is known, v_m=40 (mm/s), then can get pixel speed is v_p=k × v_m ≈ 174 (pixels/s), three-dimension measuring system synchronized projection and acquisition, the cycle T between consecutive frame is equal and it is known that T= 0.01s, then the pixel-shift P between consecutive frame is also equal, i.e. P=v_p× 0.01 ≈ 1.74 (pixels), when four step phases of use Algorithm and three frequency heterodyne deployment algorithms are moved come pixel-shift when calculating phase information, between the i-th frame image and first frame image It indicates are as follows:

P_i-1=1.74 (i-1), i ∈ [2,12] (1)

The projected fringe of four-step phase-shifting algorithm and three frequency heterodyne deployment algorithms amounts to 12 spoke lines for three frequencies, four phase shifts, when The frequency of projection and acquisition is 100Hz (i.e. T=0.01s), v_mWhen=40 (mm/s), the 2nd~12 spoke line is compared to the 1st spoke The pixel deviations of line are shown in Table 1；

Step 2, estimate phase offset, new projected fringe can be described as:

g_i,j(x, y)=a (x, y)+b (x, y) cos [2 π f_jx+2π(i-1)/N+Δφ_i,j] (2)

In formula, a (x, y) is background light intensity value, and b (x, y) is modulate intensity, and N is total phase shift number, due to selecting four steps Phase shift algorithm, therefore N=4, i indicate i-th phase shift, i ∈ [Isosorbide-5-Nitrae], f_jFor the frequency of projected fringe, due to selecting three frequency heterodynes Phase-unwrapping algorithm, j ∈ [1,3]；Δφ_i,jIndicate phase offset, it can be by pixel deviations P_i-1It calculates；

The key of formula (2) is how according to pixel deviations phase deviation Δ φ to be calculated_i,j, it is clear that Δ φ_1,1=0, I.e. the 1st frame bar print image does not need to deviate, and the 2nd~12 frame bar print image needs to deviate；

Due to project three sets of different frequencies striped, phase deviation calculation formula be it is inconsistent, need to calculate phase The pixel period of three sets of different frequencies of machine acquisition is N_f1,N_f2And N_f3, with N_f1For calculating process, frequency f₁Reference item The wrapped phase of line is calculated by four-step phase-shifting algorithm and is obtained, and the wrapped phase of the 256th row is extracted along x coordinate, obtains having packet Phase hit point is wrapped up in, the pixel number between two adjacent WPJP is N_f1；

N_f1The pseudocode program of calculating, wherein ψ_f1For frequency f₁Reference stripe wrapped phase, ψ_f1(256 :) it is ginseng The 256th row of the wrapped phase of striped is examined, WPJP_cost (j) is the array for storing WPJP, when ψ (256, j) is WPJP, WPJP_cost (j)=1；When ψ (256, j) is not WPJP, institute is can be generated in WPJP_cost (j)=0, function zeros (M, N) M × N matrix that have element all be 0, WPJP_NO are used to store the phase value of WPJP, and WPJP_index (j) exists for storing WPJP Call number in image, i.e. line number and row number, function findindex can find the call number of certain numerical value；

Calculate separately N_f1,N_f2And N_f3, and formula (3) are substituted into, the phase deviation of three sets, 12 spoke lines is obtained, according to formula (3) 11 phase deviations being calculated substitute into formula (2), and the first width does not need to deviate, and generate the new projected fringe of 12 width, remove First width projected fringe, other 11 width projected fringes have made phase offset,

In formula, Δ φ_i,1For frequency f₁The i-th spoke line phase deviation, P_i-1For pixel deviations, N_f1,N_f2And N_f3It is three Cover the pixel period of different frequency；

Finally, camera acquires the modulated striped of 12 amplitude objects, according to the pixel-shift that formula (1) is calculated, to adopting The striped of collection is deviated, as it is assumed that the direction of motion is parallel to the x coordinate of projected fringe, so the striped captured is also along x Coordinate shift does not need to deviate on y-coordinate direction, and it will be following research that object is moved along the x and y coordinates of projected fringe Content,

12 spoke lines of camera acquisition are expressed as g_1,1~g_4,1,g_1,2~g_4,2,g_1,3~g_4,3, this and formula (2) Define it is consistent, with g_4,3Calculating process for, pseudocode program is shown in Table 3, wherein g '_4,3Acquisition striped after indicating offset, Tras indicates transformation matrix, and expression formula is

In formula, P^x _i-1And P^x _i-1For the pixel deviations in the direction x and y；Assuming that the direction of motion is parallel to the x coordinate of projected fringe, So

Striped after the offset of 12 width is expressed as g '_1,1~g '_4,1,g’_1,2~g '_4,2,g’_1,3~g '_4,3, calculated according to four-step phase-shifting Method and three frequency heterodyne phase deployment algorithms calculate actual phase, are then updated in the phase height relational expression of pre- calibration, weight Build the three-dimensional appearance of object.

The measurement of physical size described in step 1, measures it using the T-square of a variety of different accuracies, and guarantees T-square It is vertical with the left or right lateral boundaries of stripe pattern, and the average value repeatedly measured is calculated, as final physical size.

The beneficial effects of the present invention are:

The present invention is the three-dimensional measurement technology for the rigid motion object being unfolded based on phase shift method and three frequency heterodyne phases.This hair It is bright to be based on phase shift method and three frequency heterodyne phase expansion techniques, projected fringe and acquisition striped are handled, the basic principle is that: Firstly, being transported by the ratio and known transmission line physical speed of physical size in camera fields of view and Pixel Dimensions The pixel speed of animal body, so as to estimate the pixel-shift between several acquisition stripeds.Secondly, utilizing the method meter proposed The phase offset between several acquisition stripeds is calculated, to generate the projection item of a set of new, for moving object three-dimensional measurement Line.Finally, deviating according to pixel-shift amount to collected striped, a set of modified stripe pattern is obtained, and calculate phase Position information, to obtain the result close to static three-dimensional measurement accuracy.

Using movement when method of the invention without stopping transmission line, the three-dimensional measurement in product movement may be implemented, Improve measurement efficiency.

Detailed description of the invention

Fig. 1 (a) is the projected fringe figure of the position adjustment of three-dimension measuring system of the present invention.

Fig. 1 (b) is that the direction of motion of the position adjustment of three-dimension measuring system of the present invention is parallel to the x coordinate photograph of projected fringe Piece.

Fig. 1 (c) is that the direction of motion of the position adjustment of three-dimension measuring system of the present invention is not parallel to the x coordinate of projected fringe Photo.

Fig. 2 is the radiometer nomogram of physical size and Pixel Dimensions in viewing field of camera of the present invention.

Fig. 3 (a) is frequency f of the present invention₁Reference stripe wrapped phase.

Fig. 3 (b) is the cross section of certain a line of Fig. 3 (a) of the present invention.

Fig. 4 (a) is the result figure after 12 width acquisition fringes shift of the invention.

Fig. 4 (b) is not using the three-dimensional result figure of moving object on the pipeline of the method for the present invention measurement.

Fig. 4 (c) is not using the two-dimensional result figure of moving object on the pipeline of the method for the present invention measurement.

Fig. 4 (d) is the cross-sectional view of dotted line in Fig. 4 (c).

Fig. 4 (e) is the three-dimensional result figure of moving object on the pipeline using the method for the present invention measurement.

Fig. 4 (f) is the two-dimensional result figure of moving object on the pipeline using the method for the present invention measurement.

Fig. 4 (g) is the cross-sectional view of dotted line in Fig. 4 (f).

Specific embodiment

Invention is further described in detail with reference to the accompanying drawings and examples.

Firstly, the pixel speed of moving object is obtained by the ratio of physical size in camera fields of view and Pixel Dimensions, Estimate the pixel-shift between several acquisition stripeds, specific practice is:

A scale is placed on the transmission line, records the physical size in camera fields of view along x coordinate, as shown in Fig. 2.For The accuracy of the above-mentioned physical size measurement of guarantee, needs to measure it using the T-square of a variety of different accuracies, and guarantee fourth Word ruler is vertical with the left or right lateral boundaries of stripe pattern, and calculates the average value repeatedly measured, as final physical size.By Pixel size in camera fields of view along x coordinate is known, therefore can obtain the pass between Pixel Dimensions and physical size System.For example, in this measuring system, k_x=512 (pixels)/118 (mm) ≈ 4.34 (pixels/mm)；

If the physical speed of transmission line is known, for example v_m=40 (mm/s), then can obtain pixel speed is v_p= k×v_m≈174(pixels/s).Three-dimension measuring system synchronized projection and acquisition, the cycle T between consecutive frame it is equal and it is known that For example T=0.01s, then the pixel-shift P between consecutive frame is also equal, i.e. P=v_p×0.01≈1.74(pixels).Work as use Four-step phase-shifting algorithm and three frequency heterodyne deployment algorithms are come picture when calculating phase information, between the i-th frame image and first frame image Element offset is expressed as:

P_i-1=1.74 (i-1), i ∈ [2,12] (1)

The projected fringe of four-step phase-shifting algorithm and three frequency heterodyne deployment algorithms is three frequencies, the total 12 spoke lines of four phase shifts.When The frequency of projection and acquisition is 100Hz (i.e. T=0.01s), v_mWhen=40 (mm/s), the 2nd~12 spoke line is compared to the 1st spoke The pixel deviations of line see attached list 1；

Secondly, new projected fringe can be described as:

g_i,j(x, y)=a (x, y)+b (x, y) cos [2 π f_jx+2π(i-1)/N+Δφ_i,j] (2)

In formula, a (x, y) is background light intensity value, and b (x, y) is modulate intensity, and N is total phase shift number, due to selecting four steps Phase shift algorithm, therefore N=4.I indicates i-th phase shift, i ∈ [Isosorbide-5-Nitrae], f_jFor the frequency of projected fringe, due to selecting three frequency heterodynes Phase-unwrapping algorithm, j ∈ [1,3], Δ φ_i,jIndicate phase deviation, it can be by pixel deviations P_i-1It calculates；

The key of formula (2) is how according to pixel deviations phase deviation Δ φ to be calculated_i,j, it is clear that Δ φ_1,1=0, That is (i.e. frequency is f to the 1st frame bar print image₁Four width phase shift stripeds in the first width) do not need to deviate, and the 2nd~12 frame bar line Image needs to deviate；

Due to projecting the striped of three sets of different frequencies, phase deviation calculation formula is inconsistent.Firstly, it is necessary to count The pixel period for calculating three sets of different frequencies of camera acquisition is N_f1,N_f2And N_f3.With N_f1For calculating process, frequency f₁Ginseng The wrapped phase for examining striped is calculated by four-step phase-shifting algorithm to be obtained, and as shown in attached drawing 3 (a), is extracted in attached drawing 3 (a) along x coordinate The 256th row wrapped phase, obtain attached drawing 3 (b), there is wrapped phase trip point (WrappedPhase in attached drawing 3 (b) Jump Point, i.e. WPJP), in attached drawing 3 (b), the pixel number between two adjacent WPJP is N_f1。

N_f1The pseudocode program of calculating is as shown in subordinate list 2, wherein ψ_f1For frequency f₁Reference stripe wrapped phase, ψ_f1 (256 :) are the 256th row of the wrapped phase of reference stripe, and WPJP_cost (j) be the array of storage WPJP, when ψ (256, j) When being WPJP, WPJP_cost (j)=1；When ψ (256, j) is not WPJP, WPJP_cost (j)=0, function zeros (M, N) M × N matrix that all elements can be generated all is 0, WPJP_NO are used to store the phase value of WPJP, and WPJP_index (j) is used for WPJP call number (i.e. line number and row number) in the picture is stored, function findindex can find the call number of certain numerical value；

N is calculated separately by subordinate list 2_f1,N_f2And N_f3, and formula (3) are substituted into, obtain the phase deviation of three sets of (12 width) stripeds.It is public 11 phase deviations (the first width does not need to deviate) that formula (3) is calculated substitute into formula (2), to generate the new projection of 12 width Striped.In addition to the first width projected fringe, other 11 width projected fringes have made phase offset,

Finally, carrying out pixel-shift to acquisition striped, 12 new spoke lines are projected, then camera acquires the modulation of 12 amplitude objects Striped afterwards deviates the reference stripe and deforming stripe of acquisition according to the pixel-shift that formula (1) is calculated, by In assuming that the direction of motion is parallel to the x coordinate of projected fringe, so the striped captured is also deviated along x coordinate, in y-coordinate direction On do not need to deviate.It will be following research contents that object is moved along the x and y coordinates of projected fringe；

12 spoke lines of camera acquisition are expressed as g_1,1~g_4,1,g_1,2~g_4,2,g_1,3~g_4,3, this and formula (2) Define it is consistent, with g_4,3Calculating process for, pseudocode program sees attached list 3, wherein g '_4,3Pick-up slip after indicating offset Line, tras indicate transformation matrix, and expression formula is

Striped after the offset of 12 width is expressed as g '_1,1~g '_4,1,g’_1,2~g '_4,2,g’_1,3~g '_4,3.It is calculated according to four-step phase-shifting Method and three frequency heterodyne phase deployment algorithms calculate actual phase, are then updated in the phase height relational expression of pre- calibration, weight Build the three-dimensional appearance of object.

Method of the invention is based on following theory:

1) the position adjustment of measuring system

Firstly, making the direction of motion be parallel to the x coordinate of projected fringe by adjusting three-dimension measuring system.Method particularly includes: There is a white line parallel with x coordinate at projector striped as shown in attached drawing 1 (a), the center of the projected fringe.It is transmitting An identification point is pasted on platform, is moved back and forth workbench and constantly adjustment three-dimension measuring system, is made identification point always in white line, Indicate that working table movement is oriented parallel to the x coordinate of projected fringe.Three movement positions as shown in attached drawing 1 (b).Attached drawing 1 (c) it indicates that the x coordinate of working table movement direction and projected fringe is not parallel, needs to adjust.

2) pixel deviations calculate

A scale is placed on the transmission line, and record the physical size in camera fields of view along x coordinate is as shown in Fig. 2 The accuracy of the above-mentioned physical size measurement of guarantee, needs to measure it using the T-square of a variety of different accuracies, and guarantee fourth Word ruler is vertical with the left or right lateral boundaries of stripe pattern, and calculates the average value repeatedly measured, as final physical size.By Pixel size in camera fields of view along x coordinate is known, therefore can obtain the pass between Pixel Dimensions and physical size System.For example, in this measuring system, k_x=512 (pixels)/118 (mm) ≈ 4.34 (pixels/mm)；

P_i-1=1.74 (i-1), i ∈ [2,12] (1)

The projected fringe of four-step phase-shifting algorithm and three frequency heterodyne deployment algorithms is three frequencies, the total 12 spoke lines of four phase shifts.When The frequency of projection and acquisition is 100Hz (i.e. T=0.01s), v_mWhen=40 (mm/s), the 2nd~12 spoke line is compared to the 1st spoke The pixel deviations of line are shown in Table 1:

3) new projected fringe is generated

New projected fringe can be described as

g_i,j(x, y)=a (x, y)+b (x, y) cos [2 π f_jx+2π(i-1)/N+Δφ_i,j] (2)

In formula, a (x, y) is background light intensity value, and b (x, y) is modulate intensity, and N is total phase shift number, due to selecting four steps Phase shift algorithm, therefore N=4, i indicate i-th phase shift, i ∈ [Isosorbide-5-Nitrae]；f_jFor the frequency of projected fringe, due to selecting three frequency heterodynes Phase-unwrapping algorithm, j ∈ [1,3], Δ φ_i,jIndicate phase deviation, it can be by pixel deviations P_i-1It calculates；

Due to projecting the striped of three sets of different frequencies, phase deviation calculation formula is inconsistent.Firstly, it is necessary to count The pixel period for calculating three sets of different frequencies of camera acquisition is N_f1,N_f2And N_f3.With N_f1For calculating process, frequency f₁Ginseng The wrapped phase for examining striped is calculated by four-step phase-shifting algorithm to be obtained, and as shown in attached drawing 3 (a), is extracted in attached drawing 3 (a) along x coordinate The 256th row wrapped phase, obtain attached drawing 3 (b), there is wrapped phase trip point (WrappedPhase in attached drawing 3 (b) Jump Point, i.e. WPJP).In attached drawing 3 (b), the pixel number between two adjacent WPJP is N_f1；

N is calculated separately by table 2_f1,N_f2And N_f3, and formula (3) are substituted into, obtain the phase deviation of three sets of (12 width) stripeds.Formula (3) 11 phase deviations (the first width does not need to deviate) being calculated substitute into formula (2), to generate the new projection item of 12 width Line.In addition to the first spoke line, other stripeds have made phase offset.

4) offset of camera acquisition striped

12 new spoke lines of projection, then camera acquires 12 spoke print images.The pixel being calculated according to formula (1) is inclined It moves, the reference stripe and deforming stripe of acquisition is deviated.As it is assumed that the direction of motion is parallel to the x coordinate of projected fringe, So the striped captured is also deviated along x coordinate, do not need to deviate on y-coordinate direction.Object along projected fringe x and y Coordinate motion will be following research contents.

12 spoke lines of camera acquisition are expressed as g_1,1~g_4,1,g_1,2~g_4,2,g_1,3~g_4,3, this and formula (2) It defines consistent.With g_4,3Calculating process for, pseudocode program is shown in Table 3, wherein g '_4,3Acquisition striped after indicating offset, Tras indicates transformation matrix, and expression formula is

Striped after 12 width fringes shifts is expressed as g '_1,1~g '_4,1,g’_1,2~g '_4,2,g’_1,3~g '_4,3, according to four step phases Algorithm and three frequency heterodyne phase deployment algorithms are moved, actual phase is calculated.Then it is updated to the phase height relational expression of pre- calibration In, rebuild the three-dimensional appearance of object.

5) it tests

The frequency of three sets of stripeds of researcher's projection is respectively f1=73, f2=64 and f3=56, and N is calculated_f1= 37.4、N_f2=43.4 and N_f3=48.8.4500 projection picture size of DLP LightCraft is necessary for 912 × 1140pixels then generates 12 new width projected fringes and is expressed as

Attached drawing 4 (a)~(g) is the three-dimensional measuring result comparison of moving object on transmission line.Attached drawing 4 (a) is camera acquisition , by offset after 12 width deforming stripes.1st width figure does not deviate, and the offset of the 2nd~12 width figure sees attached list 1.For example, After rounding up, the offset of the 12nd width deforming stripe is 19pixels.In order to realize that high speed projects, using projected fringe two-value Change technology and projector defocus technology.

When attached drawing 4 (b) is shown not using mentioned method, the 3-D view of moving object three-dimensional measurement, attached drawing 4 (c) shows Show when not using proposed method, the two dimension view of moving object three-dimensional measurement.Attached drawing 4 (d) shows in attached drawing 4 (c) 226 rows (cross section of i.e. red dotted line).Attached drawing 4 (e) shows the three-dimensional using proposed method to moving object three-dimensional measurement View, attached drawing 4 (f) show the two dimension view using mentioned method to moving object three-dimensional measurement.Attached drawing 4 (g) shows attached The 226th row (cross section of i.e. red dotted line) in Fig. 4 (f).

The experimental results showed that mentioned method can accurately measure the moving object on transmission line, advantage is as follows:

(1) detection efficiency of product on transmission line is improved.For traditional static three-dimensional measurement method, when measurement, needs Stop the movement of pipeline, the movement of transmission line is further continued for after the completion of three-dimensional measurement.Or testee is carried to three-dimensional inspection Scaffold tower carries transmission back line again after being measured.Mentioned method avoids this problem, greatly improves the detection of pipeline Efficiency.

(2) hardware cost is low.Mentioned method does not need to increase any hardware, therefore has lower hardware cost.

(3) high speed projects.This method is projected using two-value striped, is had high refreshing frequency, is substantially increased Measurement efficiency.

(4) mentioned algorithm is simple, is easy to extend.It extends in the three-dimensional measurement of object moving in two dimensions or rotating object, This will be following main research.

Table 1 is T=0.01s, v_mPixel deviations when=40 (mm/s).

Table 2 is N_f1The pseudocode program of calculating.

Table 3 is that acquisition striped offset calculating is program in machine code.

Table 1

Table 2

Table 3

Claims

1. a dynamic three-dimensional measuring method of rigid moving object, is characterized in that, comprises the following steps:

Step 1: Obtain the pixel speed of the moving object through the ratio of the physical size to the pixel size in the field of view of the camera and the known physical speed of the transmission line, and estimate the pixel offset between multiple acquisition stripes. The specific method is:

A ruler is placed on the transmission line to record the physical size along the x-coordinate in the camera's field of view. The pixel size along the x-coordinate in the camera's field of view is known, and the relationship between the pixel size and the physical size can be obtained, k _x = 512 (pixels )/118(mm)≈4.34(pixels/mm); pixels means pixels;

If the physical speed of the transmission line is known, v _m =40(mm/s), the pixel speed can be obtained as v _p =k× _vm ≈174(pixels/s), the three-dimensional measurement system synchronizes projection and acquisition, phase The period T between adjacent frames is equal and known, T=0.01s, then the pixel offset P between adjacent frames is also equal, that is, P=v _p ×0.01≈1.74(pixels), when the four-step phase shift is used When calculating the phase information using the three-frequency heterodyne expansion algorithm and the three-frequency heterodyne expansion algorithm, the pixel offset between the i-th frame image and the first frame image is expressed as:

P _i-1 = 1.74(i-1), i∈[2,12] (1)

The projected fringes of the four-step phase-shift algorithm and the three-frequency heterodyne expansion algorithm are three-frequency and four-phase-shifted, a total of 12 fringes. When the frequency of projection and acquisition is 100Hz, that is, T=0.01s, v _m =40mm/s, The pixel deviation of the 2nd to 12th stripes compared with the first stripe is shown in Table 1;

Step 2, estimate the phase offset, describe the new projected fringes as:

g _i,j (x,y)=a(x,y)+b(x,y)cos[2πf _j x+2π(i-1)/N+Δφ _i,j ] (2)

In the formula, a(x, y) is the background light intensity value, b(x, y) is the modulation intensity, and N is the total number of phase shifts. Since the four-step phase shift algorithm is selected, N=4, and i represents the i-th Secondary phase shift, i∈[1,4], _fj is the frequency of the projected fringes, j∈[1,3] due to the choice of the three-frequency heterodyne phase unwrapping algorithm; Δφi _,j denotes the phase shift, which can be determined by the pixel Deviation P _i-1 calculation;

The key of formula (2) is to calculate the phase deviation Δφ _i,j according to the pixel deviation. Obviously, Δφ _1,1 = 0, that is, the first frame fringe image does not need to be offset, and the second to 12th frame fringe images need to be offset;

Since three sets of fringes with different frequencies are projected, the calculation formula of phase deviation is inconsistent. It is necessary to calculate the pixel periods of the three sets of different frequencies collected by the camera as N _f1 , N _f2 and N _f3 . Taking the calculation process of N _f1 as an example, the frequency is The wrapping phase of the reference fringe of f ₁ is calculated by a four-step phase shift algorithm, and the wrapping phase of the 256th line is extracted along the x-coordinate to obtain a wrapping phase jump point, and the number of pixels between two adjacent WPJPs is N _f1 ;

Pseudocode program for N _f1 calculation, where ψ _f1 is the wrapped phase of the reference fringe at frequency f ₁ , ψ _f1 (256,:) is line 256 of the wrapped phase of the reference fringe, WPJP_cost(j) is the array storing WPJP, When ψ(256,j) is WPJP, WPJP_cost(j)=1; when ψ(256,j) is not WPJP, WPJP_cost(j)=0, the function zeros(M,N) can generate all elements to be 0 The M×N matrix, WPJP_NO is used to store the phase value of WPJP, WPJP_index(j) is used to store the index number of WPJP in the image, that is, the row number and column number, the function findindex can find the index number of a certain value;

Calculate N _f1 , N _f2 and N _f3 respectively, and substitute them into formula (3) to obtain the phase deviations of three sets and 12 fringes. The 11 phase deviations calculated according to formula (3) are substituted into formula (2), the first No offset is required, 12 new projection fringes are generated. Except for the first projection fringe, the other 11 projection fringes have been phase-shifted.

In the formula, Δφ _i,1 is the phase deviation of the ith fringe of frequency f ₁ , P _i-1 is the pixel deviation, and N _f1 , N _f2 and N _f3 are three sets of pixel periods of different frequencies;

Finally, the camera collects 12 modulated fringes of the object, and offsets the collected fringes according to the pixel offset calculated by formula (1). Since the moving direction is assumed to be parallel to the x-coordinate of the projected fringes, the captured fringes are also Offset along the x coordinate, no offset is required in the y coordinate direction, the motion of the object along the x and y coordinates of the projected fringes will be the content of future research,

The 12 fringes collected by the camera are respectively expressed as g _1,1 ～g _4,1 , g _1,2 ～g _4,2 , g _1,3 ～g _4,3 , which are consistent with the definition of formula (2), Taking the calculation process of g _4,3 as an example, the pseudo-code program is shown in Table 3, where g' _4,3 represents the acquired stripes after offset, tras represents the transformation matrix, and the expression is

In the formula, P ^x _i-1 and P ^x _i-1 are the pixel deviations in the x and y directions; it is assumed that the motion direction is parallel to the x coordinate of the projected fringes, so

After the 12 fringes are shifted, they are expressed as g' _1,1 ～g' _4,1 , g' _1,2 ～g' _4,2 , g' _1,3 ～g' _4,3 , according to the four-step phase shift algorithm And the three-frequency heterodyne phase unwrapping algorithm to calculate the actual phase, and then substitute it into the pre-calibrated phase-height relationship to reconstruct the three-dimensional topography of the object.

2. the dynamic three-dimensional measuring method of a kind of rigid moving object according to claim 1, is characterized in that, the measurement of physical size described in step 1, adopts the T-square of various different precisions to measure it, and guarantees the T-square Perpendicular to the left or right border of the fringe image and calculate the average of the multiple measurements as the final physical size.