CN107036555A - A kind of cross-axis optical grating projection measurement analogue system and its implementation - Google Patents
A kind of cross-axis optical grating projection measurement analogue system and its implementation Download PDFInfo
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Abstract
The invention discloses a kind of cross-axis optical grating projection measurement analogue system, (so-called cross-axis is that the mutual alignment of projector's optical axis and camera optical axis in the system is to intersect, overcome the shortcoming that two optical axises must intersect at a point in existing analogue system), using windows systems as development platform, pass through inverse Ray-tracing Method, with computer programming language, by writing optical grating projection module, simulation testee and bench top module, image capture module, realizing, there is high-precision optical grating projection to measure analogue system.The analogue system does not need projector's optical axis and camera optical axis to intersect at a point, and can realize the emulation of cross light shaft type optical grating projection measuring system.The system can simulate the object position that shadow region occurs in measurement process, and the differentiation of the differentiation and workbench top shadow region to body surface top shadow region applies different method of discrimination, the precision and distinguishing speed of shadow region differentiation are improved.
Description
Technical Field
The invention relates to a projection measurement simulation system of a crossed optical axis grating and an implementation method thereof, in particular to a structured light projection simulation system for simulating a grating modulation process in reality by using a computer, and belongs to the field of structured light measurement.
Background
With the rapid development of scientific technology and the continuous improvement of social productivity, the requirements of various fields on the measurement technology are continuously improved, and particularly the requirements on the measurement mode, the measurement efficiency and the measurement precision of the measurement technology are more strict. As well as computational techniques. The optical measurement technology and the digital image processing technology are rapidly developed, and the three-dimensional shape measurement method is infinite. Structured light measurement techniques stand out from a large number of measurement methods by virtue of their non-contact and high accuracy.
The traditional contact type three-dimensional measurement technology needs to contact a measured object through a mechanical probe, and accurate coordinate information of the surface of the object is obtained through a point. The contact type three-dimensional measurement technology has many advantages such as high measurement precision and no requirement on the color of a measured object, but also has the great defects such as long time consumption in the measurement process and contact deformation of the surface of the object caused by a mechanical probe in the process of contacting with the object. More importantly, the surface shape of some objects is too complex to reach by a mechanical probe, and the contact type three-dimensional measurement technology for the objects cannot measure the objects.
The optical measurement technology is a non-contact three-dimensional measurement technology, and can make up for the defects of the contact three-dimensional measurement technology. The grating projection measurement technology is an effective optical three-dimensional measurement technology, and the grating is projected on the surface of an object, the grating is modulated on the surface of the object to cause deformation, then an image collector is used for capturing the deformed grating stripes, and finally the surface information of the object can be obtained through demodulation. The technology has a large amount of information, high efficiency and high accuracy, is concerned about and has wide market prospect.
In order to obtain the surface topography information of the three-dimensional object by using a Fringe Projection System (FPS), a design scheme is preferably verified by simulation before the experiment. The simulation can avoid the trouble of building the FPS platform, and the simulation is faster and more flexible, and can be conveniently used by other people. FPS theoretical verification needs to establish a high-precision grating projection system, an image collector, an experimental equipment calibration device and the like. It is therefore necessary to develop an FPS simulation system as an alternative. Compared with an FPS platform, the FPS simulation system has the advantages of high speed, economy, higher flexibility and precision, and can provide great convenience for setting system parameters and analyzing errors.
Optical simulation systems based on fringe projection technology have been proposed by many researchers. The simulation algorithms used in most documents mainly use ray tracing techniques. At present, the ray tracing method is widely applied to the field of optical simulation, but the ray tracing method has many problems: firstly, due to the problem of Boolean union, three-dimensional information is reduced by one dimension, so that two problems are caused, the operation of a three-dimensional object is normalized, and the finite precision of machine operation brings errors in line-plane intersection point calculation. Introducing simple near-regularization rules may ignore some small errors, but may produce some side effects. Secondly, due to the limitation of floating point operation, many common intersection point solving algorithms have some obvious numerical problems. Especially, the ray passes through the free-form surface, and different situations are discussed through a complex algorithm.
The method is of great significance for researching the modulation process of the grating fringe on the surface of an object, researching the influence of system parameters on measurement, evaluating the quality of an algorithm and determining a reasonable technical scheme and a system structure. However, the existing simulation methods for the grating projection simulation system are based on the fact that two optical axes intersect at a point, and if the method is still used for simulation of the grating projection measurement system with intersecting optical axes, the simulated result image can generate serious shape distortion.
Disclosure of Invention
The invention aims to solve the technical problem of providing a cross optical axis grating projection measurement simulation system and an implementation method thereof, which are used for solving the problem of the shape distortion of a result image in the conventional grating projection simulation system.
The technical scheme adopted by the invention is as follows: a simulation system for projection measurement of crossed optical axis grating,
the windows system is used as a development platform, a grating projection module projector, a simulated Object-Object and a workbench module-plane R are compiled by a back light tracing method and a computer programming language1R2R3R4And an image acquisition module-Camera, implementing a simulation model with a raster projection measurement system, wherein the optical axes of the simulated projector and Camera do not have an intersection point,
the grating projection module is used for simulating a projector to generate a grating stripe image, and setting a grating modulation frequency and an initial phase so as to project the grating stripe image to the surface of a measured object;
the measured object and workbench module is used for simulating an object to be measured and an experiment table where the object is located;
the image acquisition module is used for acquiring modulated grating stripes by the analog camera, the grating stripes can be modulated by the surface of the object after the analog grating is projected onto the surface of the object, so that deformation is generated, and the image of the deformed grating stripes is acquired by the analog industrial camera.
An implementation method of a cross optical axis grating projection measurement simulation system comprises the following specific steps:
step1, calculating the coordinates of a point D corresponding to the point E in the CCD array, wherein: point E is the center of CCD pixel, point D is the extension line of line segment EC and reference plane R1R2R3R4The intersection point of (a);
step2, calculating the coordinates of the intersection point A of the straight line CD and the surface of the object;
step3, transforming the coordinates of the points A and D obtained from the world coordinate system into the projector coordinate system to obtain the coordinates of the points A 'and D' in the projector coordinate system;
step4, calculating the x 'coordinate of the intersection point B' of the straight line PA 'and the projector reference plane and the x' coordinate of the intersection point W 'of the straight line PD' and the projector reference plane according to the calculated point coordinates A 'and D';
step5, calculating the intensity values of the pixels corresponding to the points A and D on the CCD array according to the x ' coordinates of B ' and W ' in Step 4;
step6, judging the area where the shadow appears on the surface of the object by using a vector method;
step7, judging plane R by using intersection point number method1R2R3R4Upper shaded areas.
In the Step1, a similar triangle principle is used for calculation, which is specifically as follows:
the E point is CCD picture element, the length and width of each picture element are respectively Sx，SyTo show that the row and column of point E on CCD array are respectively represented by i, j, the extended line of the connecting line EC of the image element E and the optical center intersects with the surface of the object at point A, and the extended line intersects with the plane R1R2R3R4Intersecting with the D point, obtaining the coordinates of the D point by formulas (1) and (2) according to the similar triangle principle,
where i denotes the pixel in the ith row, f denotes the camera focal length, and l denotes the camera center to the reference plane R1R2R3R4The distance of (c).
The coordinate calculation of the intersection point a of the straight line CD and the object surface in Step2 is calculated by using a variable Step size iterative method, which specifically comprises the following steps:
since point a is on the straight line CD, we can derive equations (3), (4), (5) according to the principle of similar triangles,
zA＝f(xA,yA)(5)
directly calculating coordinates of an intersection point A in a three-dimensional space by adopting an iterative method, wherein the point A is the intersection point of a straight line CD and the surface of an object, and a point Q (x) is assumed to be arranged on the straight line of the CDq，yq，zq) The auxiliary line GH passing through the Q point is perpendicular to the reference plane, and H is a straight line GH and the reference planeThe intersection point G is the intersection point of the straight line GH and the object surface1＝QH，h2Long term GQ, term h1，h2Can be respectively calculated by formula (6) and formula (7),
h2＝f(xq,yq) (7)
wherein, z ═ f (x, y) is a function expression of a curved surface,
and (3) taking the point D as an initial iteration point, setting the initial step length s as 1, performing iteration search in the direction of the point C, and obtaining the following results after each iteration is performed:
is the abscissa and ordinate of the Q point obtained after n +1 iterations, k represents the ratio of the ordinate and the abscissa of the Q point, k is j/i, where i, j represent the abscissa and the ordinate of the E point pixel,
determining iteration stop point, defining three variables d1、d2、kdLet h be calculated for the first time1、h2Difference d of1＝h1-h2H is calculated after the Q point iteration1、h2Difference d of2＝h1-h2Let kd＝d1·d2The process will repeat d once again for each iteration step1、d2Is assigned once, h when the Q point is on the DA line segment1＞h2(QH > GH) having h1-h2Less than 0; when the Q point is on the AC line segment h1＞h2Has the following advantages1-h2Is greater than 0; if k isdThe sign of (a) is changed in the nth iteration, which indicates that the Q point is on the DA line segment in the nth-1 iteration and the Q point is on the AC line segment in the nth-1 iteration, namely, the Q point is already iterated to the vicinity of the A point, the value of the step length s is reduced after the Q point exceeds the A point, the iteration is carried out in the opposite direction, so that s is equal to-s/2, and then the iteration is carried out for multiple times by using the method until | s | is less than 0.001, and the iteration is stopped.
In Step4, the x 'coordinate of the intersection point B' of the straight line PA 'and the projector reference plane and the x' coordinate of the intersection point W 'of the straight line PD' and the projector reference plane are calculated from the obtained coordinates of the points a 'and D', as follows:
points A ', B ', D ' and W ' respectively correspond to A, B, D, W points in a world coordinate system, and the point B ' is a straight line PA and a plane R when observed in a projector coordinate system5R6R7R8The straight line B ' F ' is perpendicular to the y ' axis; point W 'is a straight line PD' and a plane R5R6R7R8The intersection point of the straight line W 'G' is vertical to the y 'axis, the formulas (10) and (11) can be obtained according to the similar triangle principle, then the x' coordinates of the points B 'and W' can be obtained,
in the Step5, the intensity values of the pixels corresponding to the points a and D on the CCD array are calculated according to the x ' coordinates of the points B ' and W ' in Step4, which is specifically as follows:
the grating pitch projected on the plane x 'O' y 'is λ, and the initial phase of the O' point is 0, then the grating phases at the B 'point and the W' point can be calculated by the equations (12) and (13), respectively:
wherein, B' F ═ xB'，W'G'＝xW',
If the line ED has an intersection with the object surface, the point E (i, j) on the CCD array represents the intensity image of the grating fringe modulated by the object surface, the intensity of the point E and the reference plane R5R6R7R8The intensity of the point B' above corresponds to the intensity value calculated according to equation (14), and if there is no intersection between the line ED and the object surface, the point E (i, j) on the CCD array represents the grating fringe intensity image on the reference plane, the intensity of the point E and the reference plane R5R6R7R8The intensity of the point W' above corresponds to its intensity value, which can be calculated according to equation (15),
where a represents the background light intensity and b represents the maximum intensity of the projection grating.
Step7, judging the area where the shadow appears on the reference plane by using an intersection number method, which is specifically as follows:
for the point D on the plane, the camera can see the point D, but the light of the projector can not be illuminated, so the intensity of the point A seen by the camera is the black background light, the interpolation method is applied to the situation, the iterative search is carried out from the point D to the point P, a plurality of intersection points are judged between the straight line PD and the object surface, if the intersection points between the straight line PD and the object surface are more than 1, the point D can be judged to be blocked by the object, the light intensity is equal to the background light intensity, and the method for judging the number of the intersection points is as follows:
h is a point on the straight line PD, let MH be H1，MN＝h2The size of which can be calculated by equation (16),
taking the point D as an initial iteration point, performing iterative calculation in the direction of P, setting the iteration step length as s to be 1, performing iterative search by using a formula (17),
wherein, is the abscissa and ordinate of the Q point obtained after n +1 iterations,
four variables d are defined1、d2、kdN, let h be calculated for the first time1、h2Difference d of1＝h1-h2H is calculated after the Q point iteration1、h2Difference d of2＝h1-h2Let kd＝d1·d2The process will repeat d once again for each iteration step1、d2Assigning once, making n equal to 0, if kdIf n is less than 0, executing n-n +1, and according to the method, sequentially carrying out iterative calculation from the D point to the P point until the P point stops the iteration, and if the final obtained result is that the value of n is the intersection pointIf n is more than or equal to 1, the straight line PD is determined to have an intersection point, so that the point D can be judged to be in a shadow area, and the background light intensity can be used for assigning a value to the point E corresponding to the point D on the CCD array.
The invention has the beneficial effects that:
1. convenient to use
In order to obtain the surface topography information of the three-dimensional object by using a fringe grating projection system (FPS), a design scheme is preferably verified by simulation before the experiment. The simulation can avoid the trouble of building the FPS platform, and the simulation is faster and more flexible, and can be conveniently used by other people. FPS theoretical verification needs to establish a high-precision grating projection system, an image collector, an experimental equipment calibration device and the like. Compared with an FPS platform, the FPS simulation system has the advantages of high speed, economy, higher flexibility and precision, and can provide great convenience for setting system parameters and analyzing errors.
2. Cross optical axis type grating projection measurement simulation
The cross optical axis is the mutual position of the optical axis of the projector and the optical axis of the camera in the system is crossed, and the defect that the two optical axes must be crossed at one point in the existing simulation system is overcome. The existing simulation methods for grating projection simulation systems are based on the fact that two optical axes intersect at a point, and if the method is still used for simulation of a grating projection measurement system with intersecting optical axes, a simulated result image can generate serious shape distortion. The method solves the problem of image shape distortion of the result of the conventional grating projection simulation system.
Drawings
FIG. 1 is a schematic diagram of the system of the present invention;
FIG. 2 is a two-dimensional schematic diagram of iterative calculation of point A (intersection of a straight line and a curved surface);
FIG. 3A is a flow chart of the point algorithm;
FIG. 4 is a three-dimensional schematic diagram of coordinates of each point in a projector coordinate system;
FIG. 5 is a plane R1R2R3R4A two-dimensional schematic diagram of an upper shadow area distinguishing method;
FIG. 6 is a flow chart of an implementation method of the grating projection simulation system with crossed optical axes in the present invention.
Detailed Description
The invention is further elucidated below with reference to an embodiment and a drawing, without the inventive content being limited to the described scope.
Example (b): referring to fig. 1-6, a simulation system for cross-axis grating projection measurement adopts a 64-bit win7 operating system, an intel (r) core (tm) i5-2410M CPU @2.30 processor, a 4GB memory, and selects C + + builder6.0 as development software. By a back light tracing method and C + + language, a simulation model with a grating projection measurement system is realized by compiling a grating projection module-projector, a simulation measured object, a workbench module and an image acquisition module-camera (wherein a point C is the optical center of a camera); where the optical axes of the simulated projector and camera need not have an intersection. In the embodiment, the parameters of the simulation system are selected as follows: the CCD pixel is 800x600, the camera focal length f is 1.5mm, and the pixel size sx＝0.0032mm，sy0.0032mm, camera from reference plane R1R2R3R4Distance l is 100mm, projector is from reference plane R5R6R7R8Distance l' of 150mm, projector mounting position: xp-150 mm, yp-0 mm, zp-100 mm.
A projection measurement simulation system of crossed optical axis grating comprises the following specific steps:
step1, calculating the coordinates of a point D corresponding to a point E in the CCD array, wherein the point E is the center of a CCD pixel, and the point D is the extension line of a line segment EC and a reference plane R1R2R3R4The intersection point of (a);
step2, calculating the coordinates of the intersection point A of the straight line CD and the surface of the object;
step3, transforming the coordinates of the points A and D obtained from the world coordinate system into the projector coordinate system to obtain the coordinates of the points A 'and D' in the projector coordinate system;
step4, calculating the x 'coordinate of the intersection point B' of the straight line PA 'and the projector reference plane and the x' coordinate of the intersection point W 'of the straight line PD' and the projector reference plane according to the calculated point coordinates A 'and D';
step5, calculating the intensity values of the pixels corresponding to the points A and D on the CCD array according to the x ' coordinates of B ' and W ' in Step 4;
step6, judging the area where the shadow appears on the surface of the object by using a vector method;
step7, judging the area where the shadow appears on the reference plane by using an intersection point number method;
further, the Step1 is to calculate by using the principle of similar triangle, which is as follows: in FIG. 1, the point E is a CCD pixel, and the length and width of each pixel are respectively Sx，SyTo show that the row and column of point E on CCD array are respectively represented by i, j, the extended line of the connecting line EC of the image element E and the optical center intersects with the surface of the object at point A, and the extended line intersects with the plane R1R2R3R4Intersecting with the D point, obtaining the coordinates of the D point by formulas (1) and (2) according to the similar triangle principle,
where i denotes the pixel in the ith row, f denotes the camera focal length, and l denotes the camera center to the reference plane R1R2R3R4The distance of (c).
Further, the coordinate calculation of the intersection point a of the straight line CD and the object surface in Step2 is calculated by using a variable Step size iterative method, which is specifically as follows: as shown in fig. 1, since point a is on the straight line CD, we can derive equations (3), (4), (5) according to the principle of similar triangles.
zA＝f(xA,yA)(5)
Since the coordinates of the intersection point a cannot be directly calculated in the three-dimensional space by using the above formula, an iterative method is adopted for numerical calculation. As shown in FIG. 2, point A is the intersection of line ED and the surface of the object, assuming that there is a point Q (x) on the CD lineq，yq，zq) The Q-point-crossing auxiliary line GH is perpendicular to the reference plane, H is the intersection point of the straight line GH and the reference plane, G is the intersection point of the straight line GH and the object surface, and H is the order of the intersection point of the straight line GH and the object surface1＝QH，h2Long term GQ, term h1，h2Can be respectively calculated by formula (6) and formula (7),
h2＝f(xq,yq) (7)
and (3) taking the point D as an initial iteration point, setting the initial step length s as 1, performing iteration search in the direction of the point C, and obtaining the following results after each iteration is performed:
is the abscissa and ordinate of the Q point obtained after n +1 iterations, k represents the ratio of the ordinate and the abscissa of the Q point, k is j/i, where i, j represent the abscissa and the ordinate of the E point pixel,
determining iteration stop point, defining three variables d1、d2、kdLet h be calculated for the first time1、h2Difference d of1＝h1-h2H is calculated after the Q point iteration1、h2Difference d of2＝h1-h2Let kd＝d1·d2The process will repeat d once again for each iteration step1、d2And the value is assigned once. H when Q point is on DA line segment1＞h2(QH > GH) having h1-h2Less than 0; when the Q point is on the AC line segment h1＞h2Has the following advantages1-h2Is greater than 0; if k isdThe sign of (a) changes at the nth iteration, which indicates that the point Q is on the DA line segment at the nth-1 iteration and the point Q is on the AC line segment at the nth-1 iteration, i.e., indicates that the point Q has iterated to the vicinity of the point a. And after the point Q exceeds the point A, the value of the step length s is reduced, the iteration is carried out in the opposite direction, s is made to be-s/2, then the iteration is carried out for multiple times by using the method until | s | is less than 0.001, and the iteration is stopped, so that the obtained point Q is the intersection point A. The flow chart of the A-point algorithm is shown in FIG. 3.
Further, in Step4, the straight line PA ' and the D ' are calculated from the obtained point coordinates a ' and DThe x ' coordinate of the intersection point B ' of the projector reference plane and the x ' coordinate of the intersection point W ' of the straight line PD ' and the projector reference plane are as follows: as shown in FIG. 4(A ', B ', D ', W ' correspond to A, B, D, W in the world coordinate system, respectively), when viewed in the projector coordinate system, point B ' is a straight line PA and a plane R5R6R7R8The straight line B ' F ' is perpendicular to the y ' axis; point W 'is a straight line PD' and a plane R5R6R7R8The straight line W ' G ' is perpendicular to the y ' axis. Equations (10) and (11) can be obtained according to the principle of similar triangles, and then the x ' coordinates of the points B ' and W ' can be obtained.
Further, in Step5, the intensity values of the pixels corresponding to the points a and D on the CCD array are calculated according to the x ' coordinates of B ' and W ' in Step4, which is specifically as follows: the grating pitch projected on the plane x 'O' y 'is λ, and the initial phase of the O' point is 0, then the grating phases at the B 'point and the W' point can be calculated by the equations (12) and (13), respectively:
wherein, B' F ═ xB'，W'G'＝xW'，
If the line ED has an intersection with the object surface, the point E (i, j) on the CCD array represents the intensity image of the grating fringe modulated by the object surface, the intensity of the point E and the reference plane R5R6R7R8The intensity of the point B' corresponds to its intensity value, which can be calculated according to equation (14). If there is no intersection between the line ED and the object surface, the E (i, j) point on the CCD array represents the grating fringe intensity image on the reference plane, the E point intensity and the reference plane R5R6R7R8The intensity of the point W' above corresponds to its intensity value, which can be calculated according to equation (15).
Where a represents the background light intensity and b represents the maximum intensity of the projection grating.
Further, in Step7, the area where the shadow appears on the reference plane is determined by using an intersection number method, which is specifically as follows:
as shown in fig. 5, the D point on the table plane is visible to the D point camera, but the projector light is not illuminated, so the intensity of the a point seen by the camera is black background light. For the situation, the patent uses an interpolation method to judge the shadow area, starts from point D, carries on iterative search to point P, judges there are several intersection points between straight line PD and object surface, if the intersection point of straight line PD and object surface is more than 1, then can judge that point D is blocked by the object certainly, its light intensity is equal to the background light intensity, the method to judge the number of the intersection points is as follows:
as shown in FIG. 5, H is a point on the straight line PD, let MH be H1，MN＝h2The size can be calculated by equation (16).
And (5) taking the point D as an initial iteration point, performing iterative calculation in the direction of P, setting the iteration step length to be s equal to 1, and performing iterative search by using a formula (17).
Wherein, are the abscissa and ordinate of the Q point obtained after n +1 iterations.
Four variables d are defined1、d2、kdN, let h be calculated for the first time1、h2Difference d of1＝h1-h2H is calculated after the Q point iteration1、h2Difference d of2＝h1-h2Let kd＝d1·d2The process will repeat d once again for each iteration step1、d2Assigning once, making n equal to 0, if kdIf n is less than 0, executing n to n +1, and sequentially carrying out iterative calculation from the point D to the point P according to the method until the point P stops iterative calculation, if the final obtained result is that the value of n is the number of intersection points, if n is more than or equal to 1, the straight line PD can be obtained to have intersection points, so that the point D can be judged to be in a shadow area, and at the moment, the point E corresponding to the point D on the CCD array can be assigned by using the background light intensity. The flow of the implementation method of the system is shown in fig. 6.
The present invention is described in terms of embodiments, and various modifications and equivalent substitutions may be made thereto without departing from the scope of the invention, so that the invention is not limited to the embodiments disclosed, and any simple modifications of the embodiments within the technical scope of the present invention as apparent to those skilled in the art may be made within the technical scope of the present invention.
Claims (7)
1. The utility model provides a crossing optical axis grating projection measurement simulation system which characterized in that:
the windows system is used as a development platform, a grating projection module projector, a simulated Object-Object and a workbench module-plane R are compiled by a back light tracing method and a computer programming language1R2R3R4And an image acquisition module-Camera, implementing a simulation model with a raster projection measurement system, wherein the optical axes of the simulated projector and Camera do not have an intersection point,
the grating projection module is used for simulating a projector to generate a grating stripe image, and setting a grating modulation frequency and an initial phase so as to project the grating stripe image to the surface of a measured object;
the measured object and workbench module is used for simulating an object to be measured and an experiment table where the object is located;
the image acquisition module is used for acquiring modulated grating stripes by the analog camera, the grating stripes can be modulated by the surface of the object after the analog grating is projected onto the surface of the object, so that deformation is generated, and the image of the deformed grating stripes is acquired by the analog industrial camera.
2. A realization method of a cross optical axis grating projection measurement simulation system is characterized in that: the method comprises the following specific steps:
step1, calculating the coordinates of a point D corresponding to the point E in the CCD array, wherein: point E is the center of CCD pixel, point D is the extension line of line segment EC and reference plane R1R2R3R4The intersection point of (a);
step2, calculating the coordinates of the intersection point A of the straight line CD and the surface of the object;
step3, transforming the coordinates of the points A and D obtained from the world coordinate system into the projector coordinate system to obtain the coordinates of the points A 'and D' in the projector coordinate system;
step4, calculating the x 'coordinate of the intersection point B' of the straight line PA 'and the projector reference plane and the x' coordinate of the intersection point W 'of the straight line PD' and the projector reference plane according to the calculated point coordinates A 'and D';
step5, calculating the intensity values of the pixels corresponding to the points A and D on the CCD array according to the x ' coordinates of B ' and W ' in Step 4;
step6, judging the area where the shadow appears on the surface of the object by using a vector method;
step7, judging plane R by using intersection point number method1R2R3R4Upper shaded areas.
3. The method for implementing the cross optical axis grating projection measurement simulation system according to claim 2, wherein: in the Step1, a similar triangle principle is used for calculation, which is specifically as follows:
the E point is CCD picture element, the length and width of each picture element are respectively Sx，SyTo show that the row and column of point E on CCD array are respectively represented by i, j, the extended line of the connecting line EC of the image element E and the optical center intersects with the surface of the object at point A, and the extended line intersects with the plane R1R2R3R4Intersecting with the D point, obtaining the coordinates of the D point by formulas (1) and (2) according to the similar triangle principle,
where i denotes the pixel in the ith row, f denotes the camera focal length, and l denotes the camera center to the reference plane R1R2R3R4The distance of (c).
4. The method of claim 3, wherein the simulation system comprises: the coordinate calculation of the intersection point a of the straight line CD and the object surface in Step2 is calculated by using a variable Step size iterative method, which specifically comprises the following steps:
since point a is on the straight line CD, we can derive equations (3), (4), (5) according to the principle of similar triangles,
zA＝f(xA,yA) (5)
directly calculating the intersection point A in the three-dimensional space by adopting an iteration methodIn the notation, point A is the intersection of the line CD and the surface of the object, assuming that there is a point Q (x) on the CD lineq，yq，zq) The Q-point-crossing auxiliary line GH is perpendicular to the reference plane, H is the intersection point of the straight line GH and the reference plane, G is the intersection point of the straight line GH and the object surface, and H is the order of the intersection point of the straight line GH and the object surface1＝QH，h2Long term GQ, term h1，h2Can be respectively calculated by formula (6) and formula (7),
h2＝f(xq,yq) (7)
wherein, z ═ f (x, y) is a function expression of a curved surface,
and (3) taking the point D as an initial iteration point, setting the initial step length s as 1, performing iteration search in the direction of the point C, and obtaining the following results after each iteration is performed:
is the abscissa and ordinate of the Q point obtained after n +1 iterations, k represents the ratio of the ordinate and the abscissa of the Q point, k is j/i, where i, j represent the abscissa and the ordinate of the E point pixel,
determining iteration stop point, defining three variables d1、d2、kdLet h be calculated for the first time1、h2Difference d of1＝h1-h2H is calculated after the Q point iteration1、h2Difference d of2＝h1-h2Let kd＝d1·d2The process will repeat d once again for each iteration step1、d2Assignment of valueOnce, h when the point Q is on the DA line segment1＞h2(QH > GH) having h1-h2Less than 0; when the Q point is on the AC line segment h1＞h2Has the following advantages1-h2Is greater than 0; if k isdThe sign of (a) is changed in the nth iteration, which indicates that the Q point is on the DA line segment in the nth-1 iteration and the Q point is on the AC line segment in the nth-1 iteration, namely, the Q point is already iterated to the vicinity of the A point, the value of the step length s is reduced after the Q point exceeds the A point, the iteration is carried out in the opposite direction, so that s is equal to-s/2, and then the iteration is carried out for multiple times by using the method until | s | is less than 0.001, and the iteration is stopped.
5. The method of claim 4, wherein the simulation system comprises: in Step4, the x 'coordinate of the intersection point B' of the straight line PA 'and the projector reference plane and the x' coordinate of the intersection point W 'of the straight line PD' and the projector reference plane are calculated from the obtained coordinates of the points a 'and D', as follows:
points A ', B ', D ' and W ' respectively correspond to A, B, D, W points in a world coordinate system, and the point B ' is a straight line PA and a plane R when observed in a projector coordinate system5R6R7R8The straight line B ' F ' is perpendicular to the y ' axis; point W 'is a straight line PD' and a plane R5R6R7R8The intersection point of the straight line W 'G' is vertical to the y 'axis, the formulas (10) and (11) can be obtained according to the similar triangle principle, then the x' coordinates of the points B 'and W' can be obtained,
6. the method of claim 5, wherein the simulation system comprises: in the Step5, the intensity values of the pixels corresponding to the points a and D on the CCD array are calculated according to the x ' coordinates of the points B ' and W ' in Step4, which is specifically as follows:
the grating pitch projected on the plane x 'O' y 'is λ, and the initial phase of the O' point is 0, then the grating phases at the B 'point and the W' point can be calculated by the equations (12) and (13), respectively:
wherein, B' F ═ xB'，W'G'＝xW',
If the line ED has an intersection with the object surface, the point E (i, j) on the CCD array represents the intensity image of the grating fringe modulated by the object surface, the intensity of the point E and the reference plane R5R6R7R8The intensity of the point B' above corresponds to the intensity value calculated according to equation (14), and if there is no intersection between the line ED and the object surface, the point E (i, j) on the CCD array represents the grating fringe intensity image on the reference plane, the intensity of the point E and the reference plane R5R6R7R8The intensity of the point W' above corresponds to its intensity value, which can be calculated according to equation (15),
where a represents the background light intensity and b represents the maximum intensity of the projection grating.
7. The method of claim 6, wherein the simulation system comprises: step7, judging the area where the shadow appears on the reference plane by using an intersection number method, which is specifically as follows:
for the point D on the plane, the camera can see the point D, but the light of the projector can not be illuminated, so the intensity of the point A seen by the camera is the black background light, the interpolation method is applied to the situation, the iterative search is carried out from the point D to the point P, a plurality of intersection points are judged between the straight line PD and the object surface, if the intersection points between the straight line PD and the object surface are more than 1, the point D can be judged to be blocked by the object, the light intensity is equal to the background light intensity, and the method for judging the number of the intersection points is as follows:
h is a point on the straight line PD, let MH be H1，MN＝h2The size of which can be calculated by equation (16),
taking the point D as an initial iteration point, performing iterative calculation in the direction of P, setting the iteration step length as s to be 1, performing iterative search by using a formula (17),
wherein, is the abscissa and ordinate of the Q point obtained after n +1 iterations,
four variables d are defined1、d2、kdN, let h be calculated for the first time1、h2Difference d of1＝h1-h2H is calculated after the Q point iteration1、h2Difference d of2＝h1-h2Let kd＝d1·d2The process will repeat d once again for each iteration step1、d2Assigning once, making n equal to 0, if kdIf n is less than 0, executing n to n +1, and sequentially carrying out iterative calculation from the point D to the point P according to the method until the point P stops the iteration, if the final obtained result is that the value of n is the number of intersection points, if n is more than or equal to 1, the straight line PD can be obtained to have intersection points, so that the point D can be judged to be in a shadow area, and at the moment, the point E corresponding to the point D on the CCD array can be assigned by using the background light intensity.
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