CN114608480A - Phase-height relation calibration method based on phase-shifting fringe projection - Google Patents
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
- G01B11/25—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures by projecting a pattern, e.g. one or more lines, moiré fringes on the object
- G01B11/2504—Calibration devices
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
- G01B11/06—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material
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- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
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Abstract
The invention discloses a phase-height relation calibration method based on phase-shifting fringe projection, which comprises the following steps: determining a calibration body and a reference plane; assembling a projector and a CCD camera to form a measuring head, and fixedly placing the measuring head relative to a reference plane; respectively calculating a phase shift fringe pattern of the reference plane and a phase shift fringe pattern of the calibration body by using a three-step phase shift method; subtracting the phase calculated by the phase shift fringe pattern of the reference plane and the phase shift fringe pattern of the calibration body to obtain the phase change of the standard body relative to the reference plane; and (3) taking any two lines of data in the phase change, and calculating a phase-height relation coefficient according to the surface height of the calibration body corresponding to the two lines of data. The invention can obtain the phase-height relation coefficient in the whole measuring range only by one measuring and calculating process, and has the characteristics of rapidness and easy use.
Description
Technical Field
The invention relates to the technical field of three-dimensional measurement system calibration, in particular to a phase-height relation calibration method based on phase-shifting fringe projection.
Background
Optical three-dimensional shape measurement systems also have great potential for product inspection because they capture shape data from surfaces in the form of point clouds. So that the non-contact inspection of the finished products has succeeded in different fields, such as the automotive industry, semiconductor inspection, food and pharmaceutical manufacturing, etc. The optical three-dimensional shape measurement system may also allow the manufacturer to check, one by one, whether the goods (silicon wafers, semiconductor chips or the surface of a painted vehicle) are defective, with the aim of controlling the parameters of the industrial process once the defect is found. The flexibility, reliability, higher operating speed, consistency and objectivity of the techniques make them more competitive with conventional measurement systems.
Calibration is a fundamental requirement of vision-based measurement systems measurement procedures, as it evaluates the vision system parameters necessary to infer three-dimensional information from two-dimensional images obtained by a camera. Calibration has been the subject of a great deal of research work due to its effect on the overall accuracy of the final measurements, as well as the fact that many acquisition tasks must be performed on site, and often in a limited time.
The existing calibration method often needs to be changed by adjusting the relative position of the camera and the projector to adapt the camera and the projector to the measured surface, but after each position and optical configuration change, the system needs to be recalibrated, and the operation is complicated. A calibration plane parallel to the reference plane needs to be moved several times within the measurement range so that it has different distances from the reference plane; or at least two parallel positions and one inclined plate are required within the maximum measurement range. Therefore, the measurement and calculation processes need to be repeated for many times to obtain the phase-height relation coefficient in the whole measurement range.
Therefore, it is an urgent need to solve the above-mentioned problems by those skilled in the art to provide a phase-height calibration method that is fast, easy to use, and capable of simplifying the measurement calculation process.
Disclosure of Invention
In view of this, the invention provides a phase-height relationship calibration method based on phase-shifting fringe projection, which can obtain a phase-height relationship coefficient in the whole measurement range only through one measurement and calculation process, and has the characteristics of rapidness and easy use.
In order to achieve the purpose, the invention adopts the following technical scheme:
a phase-height relation calibration method based on phase-shifting fringe projection comprises the following steps:
determining a calibration body and a reference plane;
assembling a projector and a CCD camera to form a measuring head, and fixedly placing the measuring head relative to the reference plane;
projecting a group of sine function fringe patterns to the reference plane by using the projector, recording the fringe patterns on the reference plane by using the CCD camera, and calculating the phase shift fringe pattern phi of the reference plane by using a three-step phase shift methodR(x,y)；
Placing the calibration body on the reference plane, projecting a group of sine function fringe patterns on the calibration body by using the projector, recording the fringe patterns on the calibration body by using the CCD camera, and calculating the phase shift fringe patterns phi of the calibration body by using a three-step phase shift methodO(x,y)；
Will phiO(x, y) and phiR(x, y) subtracting to obtain the phase change p (x, y) of the standard body relative to the reference plane;
and any two lines of data are taken in the phase change p (x, y), and a phase-height relation coefficient is calculated according to the surface height of the calibration body corresponding to the two lines of data.
Further, in the phase-height relationship calibration method based on phase shift fringe projection, the calibration body has an inclined surface, the height of the inclined surface covers the whole measurement height, and the width is greater than or equal to the maximum measurement width.
Further, in the phase-height relationship calibration method based on phase shift fringe projection, the calibration body is in the shape of an inclined plane or a roof ridge surface.
Further, in the phase-height relationship calibration method based on phase shift fringe projection, when the calibration body is in the shape of a roof ridge surface, the roof ridge line is adjusted to be parallel to the optical center connecting line of the projector and the CCD camera after the calibration body is placed on the reference plane.
Further, in the phase-height relationship calibration method based on phase shift fringe projection, each row of pixels in the phase change p (x, y) has the same height corresponding to the point on the surface of the calibration body.
Furthermore, in the phase-height relationship calibration method based on phase shift fringe projection, the phase shift fringe pattern phi of the reference planeR(x, y) and phase-shift fringe pattern phi of the calibration bodyOThe calculation method of (x, y) is the same, and comprises the following steps:
recording three fringe patterns by using a three-step phase shift method;
calculating the wrapping phase of the reference plane or the calibration body based on the three fringe images;
and adding or subtracting a multiple of 2 pi on the wrapping phase, and eliminating a discontinuous point of the arctan function at the position of 2 pi to obtain a phase shift fringe image of the reference plane or the calibration body.
Further, in the phase-height relationship calibration method based on phase-shifting fringe projection, the calculation formula of the phase-height relationship coefficient is as follows:
wherein p (x, i) and p (x, j) respectively represent that two rows of data positioned on the surface of the calibration body are arbitrarily taken from p (x, y), i row and j row; h (i), h (j) indicate the height of the corresponding calibration body surface in the ith and jth rows of p (x, y), respectively.
According to the technical scheme, compared with the prior art, the phase-height relation calibration method based on the phase shift fringe projection is disclosed, the phase-height relation coefficients a (x, y) and b (x, y) in the whole measurement range can be obtained only through one measurement and calculation process by utilizing the calibration body which can cover the whole measurement height along the y direction, the whole measurement process is fast, accurate and easy to use, and the requirement that the measurement equipment moves to different positions and covers the whole scene or the whole workpiece can be met.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the prior art descriptions will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a flow chart of a phase-height relationship calibration method based on phase-shifting fringe projection according to the present invention;
FIG. 2 is a geometric diagram of the phase shift p versus the height h provided by the present invention;
FIG. 3(a) is a front view of an optical schematic diagram of a phase-height relationship calibration method based on phase-shifting fringe projection according to the present invention;
FIG. 3(b) is a right view of the optical principle of the phase-height relationship calibration method based on phase-shifting fringe projection according to the present invention;
FIGS. 4(a) -4(b) are schematic structural views of a calibration body provided by the present invention;
FIG. 5 is a phase shifted fringe pattern of a reference plane provided by the present invention;
FIG. 6 is a phase shift fringe pattern of a calibration body provided by the present invention;
FIG. 7(a) is a phase distribution diagram of the surface of a calibration body provided by the present invention;
FIG. 7(b) is a schematic diagram illustrating the variation of the phase at different heights on the surface of the quasimon body along the X direction;
FIG. 8 is a schematic diagram of phase-height relationship coefficients provided by the present invention;
FIG. 9 is a graph of phase-shifted fringes of a proof body provided by the present invention;
FIG. 10 is a phase diagram of a validation organism provided by the present invention;
fig. 11 is a measurement result of the verifier provided by the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
As shown in fig. 1, fig. 3(a), and fig. 3(b), an embodiment of the present invention discloses a phase-height relationship calibration method based on phase-shifting fringe projection, including:
s1, determining a calibration body and a reference plane;
s2, assembling the projector and the CCD camera to form a measuring head, and fixedly placing the measuring head relative to a reference plane;
s3, projecting a set of sine function fringe patterns to the reference plane by using a projector, recording the fringe patterns on the reference plane by using a CCD camera, and calculating the phase shift fringe patterns phi of the reference plane by using a three-step phase shift methodR(x,y)；
S4, placing the calibration body on the reference plane, projecting a set of sine function fringe patterns to the calibration body by using a projector, recording the fringe patterns on the calibration body by using a CCD camera, and calculating the phase shift fringe pattern phi of the calibration body by using a three-step phase shift methodO(x,y)；
S5, will phiO(x, y) and phiRSubtracting (x, y) to obtain the phase change p (x, y) of the standard body relative to the reference plane;
s6, any two lines of data are taken in the phase change p (x, y), and the phase-height relation coefficient is calculated according to the surface height of the calibration body corresponding to the two lines of data.
The phase shift versus height relationship is further explained below in conjunction with fig. 2.
In fig. 2, Dc is the image plane of the CCD camera, and Prj is the object plane of the projector; i1, I2 are principal points of the projector and the CCD camera, respectively; and alpha is the included angle of the optical axes of the projector and the CCD camera. The projected fringe direction is parallel to the Y-axis.
Original geometric relationship:
a. d is a point on the P1 plane of height h. It coincides with the point C on the reference plane Pref on the image plane of the camera Dc, and the coordinates of the point C are set to (X, 0).
b. I1, I2 are the optical centers (principal points) of the projection and camera, respectively, with coordinates I1(Xp, Zp), I2(0, Zc), respectively, and the camera optical axis is perpendicular to the reference plane.
c. The X' axis is perpendicular to the projection optical axis. Thus, the phase shift produced by point D relative to point C is proportional to the length of C 'A', denoted as p.
From the geometrical relationship in fig. 2, one can derive:
p＝Lp(tan(α-β1)-tan(α-β2)) (1)；
wherein:
tan(β1)＝((Xp-X))/Zp (2)；
tan(β2)＝(Xp-Xd)/(Zp-h)
tan(β2)＝(ZcXp-(Zc-h)X)/Zc(Zp-h) (3)
the following formulas (2), (3) and (4) can be obtained:
the relation of phase variation with height can be obtained by bringing formulas (5) and (6) into formula (1):
or height versus phase change:
equations (7), (8) ignore a coefficient associated with the projected fringe.
As can be seen from the above equation:
(1) after the phase distribution caused by the height modulation of the measured object is obtained through calculation, the height distribution of the object is related to configuration parameters of a measuring system, such as Zc, Zp, Xp and Lp; wherein (Xp, Zp) is the coordinates of the optical center of the projector; zc is the z-coordinate of the optical center of the CCD camera (i.e. the perpendicular distance of the optical center of the camera to the reference plane); lp is the distance from the optical center of the projector to point O (the origin of the reference plane coordinate system).
(2) Given the phase, the measured point height is also related to the X coordinate of the measured point, and not to the Y coordinate of the measured point.
The formula (8) can be rewritten as follows:
thus, by appropriate calibration methods, the coefficients a (x), b (x) for a given measurement system are determined to obtain a phase-height correspondence for each spatial point within the measurement volume of the system.
Based on this, it can be seen that the phase-height coefficients a (x, y), b (x, y) are independent of y, and that a calibration body can be used which can cover the entire measurement height in the y direction. The coefficients a (x, y) and b (x, y) in the whole measuring range can be obtained only by one measuring and calculating process.
Specifically, the calibration device of the embodiment of the invention comprises a reference plane and a calibration body, wherein the width W of the calibration body is more than or equal to the designed maximum measurement width and the height hmaxShould be close to the designed maximum measurement height. The direction of the inclined plane of the calibration body is consistent with the direction of the projection stripe; the bevel angle α is not particularly required. As shown in FIGS. 4(a) -4(b), the shape of the calibration bodyWhich may be a bevel or roof-ridge shape, the upper surface of the calibration body may be sprayed with a regular pattern to determine the height of the upper surface of the calibration body for each pixel in the two-dimensional image.
In one embodiment, in S3, when the phase calculation is performed on the reference plane, the reference plane is calculated by using a three-step phase shift method.
A three step phase shifted sine function fringe pattern of the reference plane is taken as shown in fig. 5. .
For the three-step phase shift method, taking the reference plane as an example, the recorded fringe pattern can be represented as:
IR1(x,y)＝I0(x,y)+Imod(x,y)cos[φR(x,y)-2π/3] (10)；
IR2(x,y)＝I0(x,y)+Imod(x,y)cos[φR(x,y)] (11)；
IR3(x,y)＝I0(x,y)+Imod(x,y)cos[φR(x,y)+2π/3] (12)。
wherein, I0(x, y) is the direct current component (background), Imod(x, y) is the modulation signal amplitude, phiR(x, y) is the phase of the reference plane and 2 π/3 is the phase shift angle. The wrapped phase of the reference plane can be calculated according to the following equation:
the phase is folded between 0 and 2 pi due to the arctan operation and is all called the "wrapped phase". Phi'RAdding or subtracting the multiple of 2 pi on the (x, y) value to eliminate the discontinuous point of the arctan function at 2 pi, which is called phase unwrapping, and obtaining the phase-shift fringe pattern phi of the reference planeR(x,y)。
In S4, taking a roof-shaped calibration body as an example, when the calibration body is in the shape of a roof, the roof line is adjusted to be parallel to the optical center connecting line of the projector and the CCD camera after the calibration body is placed on the reference plane. Then repeating the three-step phase shift method in S3, and calculating the phase shift fringe pattern phi of the calibration bodyO(x,y)，As shown in fig. 6.
In S5, phi isRThe (x, y) and (x, y) are subtracted to obtain the phase change p (x, y) of the standard body with respect to the reference plane, as shown in fig. 7(a) -7 (b).
In S6, since the calibration body is a standard body with known geometric parameters, the height of the point on the surface of the calibration body corresponding to any one pixel in the phase shift fringe pattern of the calibration body can be easily determined. In the present invention, the standard body has the same height relative to the point on the surface of the calibration body corresponding to each row of pixels in the phase change p (x, y) of the reference plane. According to the height phase relation equation (14):
arbitrarily taking two lines of data (i line and j line, for example) p (x, i), p (x, j) in the phase calculation result; and obtaining their corresponding alignment body surface heights h (i), h (j); the height phase relation coefficients a (x), b (x) can be calculated by the following equations.
The coefficients a (x), b (x) calculated from the calibration body are shown in FIG. 8. The final objective of the present invention is to obtain the coefficients a (x), b (x) (actually a (x, y), b (x, y) quickly, since equation (8) illustrates that the phase-height relationship is independent of the y coordinate on the image plane, the phase-height relationship is determined over the entire measurement range of a (x), b (x). Therefore, after the phase distribution is calculated, the height distribution can be directly obtained from equation (14). Thereby avoiding the need to accurately determine system parameters such as Zc, Zp, Xp, Lp, etc. and calculate the height distribution using equation (8). The structural parameters Zc, Zp, Xp and Lp of the measuring system can be changed conveniently to adapt to different measuring environments.
To verify the effectiveness of the calibration method of the present invention, a square prism with a flat top height of 140 mm was measured, the three-step phase shift of which is shown in fig. 9 as a fringe pattern, the phase distribution of which is shown in fig. 10 as a distribution pattern, and the final measurement results obtained by using the phase-height relationship coefficient and equation (14) are shown in fig. 11.
Therefore, the phase-height relation coefficients a (x), b (x) and obtained by the method can accurately reflect the phase-height relation and obtain accurate measurement results.
In the present specification, the embodiments are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed in the embodiment corresponds to the method disclosed in the embodiment, so that the description is simple, and the relevant points can be referred to the description of the method part.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (7)
1. A phase-height relation calibration method based on phase-shifting fringe projection is characterized by comprising the following steps:
determining a calibration body and a reference plane;
assembling a projector and a CCD camera to form a measuring head, and fixedly placing the measuring head relative to the reference plane;
projecting a group of sine function fringe patterns to the reference plane by using the projector, recording the fringe patterns on the reference plane by using the CCD camera, and calculating the phase shift fringe pattern phi of the reference plane by using a three-step phase shift methodR(x，y)；
Placing the calibration body on the reference plane, projecting a group of sine function fringe patterns on the calibration body by using the projector, recording the fringe patterns on the calibration body by using the CCD camera, and calculating the phase shift fringe patterns phi of the calibration body by using a three-step phase shift methodO(x，y)；
Will phiO(x, y) and phiR(x, y) subtracting to obtain the phase change p (x, y) of the standard body relative to the reference plane;
and any two lines of data are taken in the phase change p (x, y), and a phase-height relation coefficient is calculated according to the surface height of the calibration body corresponding to the two lines of data.
2. The phase-height relationship calibration method based on phase-shifting fringe projection as claimed in claim 1, wherein the calibration body has an inclined surface, and the height of the inclined surface covers the whole measurement height, and the width is greater than or equal to the maximum measurement width.
3. The phase-height relationship calibration method based on phase-shifting fringe projection as claimed in claim 2, wherein the calibration body is in the shape of an inclined plane or a roof-ridge plane.
4. The phase-height relationship calibration method based on phase-shifting fringe projection as claimed in claim 3, wherein when the calibration body is in the shape of a roof ridge surface, the roof ridge line is adjusted to be parallel to the optical center connecting line of the projector and the CCD camera after the calibration body is placed on the reference plane.
5. The phase-height relationship calibration method based on phase-shifting fringe projection as claimed in claim 1, wherein each row of pixels in phase variation p (x, y) has the same height corresponding to the point on the surface of the calibration body.
6. A method according to claim 1, based on phase-shifted fringe projectionThe phase-height relation calibration method is characterized in that the phase shift fringe pattern phi of the reference planeR(x, y) and phase-shift fringe pattern phi of the calibration bodyOThe calculation method of (x, y) is the same, and comprises the following steps:
recording three fringe patterns by using a three-step phase shift method;
calculating the wrapping phase of the reference plane or the calibration body based on the three fringe images;
and adding or subtracting a multiple of 2 pi on the wrapping phase, and eliminating a discontinuous point of the arctan function at the position of 2 pi to obtain a phase shift fringe image of the reference plane or the calibration body.
7. The phase-height relationship calibration method based on phase-shifting fringe projection as claimed in claim 1, wherein the phase-height relationship coefficient is calculated by the following formula:
wherein p (x, i) and p (x, j) respectively represent that two rows of data positioned on the surface of the calibration body are arbitrarily taken from p (x, y), i row and j row; h (i), h (j) indicate the height of the corresponding calibration body surface in the ith and jth rows of p (x, y), respectively.
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