CN111174730B - A Fast Phase Unwrapping Method Based on Phase Encoding - Google Patents

A Fast Phase Unwrapping Method Based on Phase Encoding Download PDF

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CN111174730B
CN111174730B CN202010013707.1A CN202010013707A CN111174730B CN 111174730 B CN111174730 B CN 111174730B CN 202010013707 A CN202010013707 A CN 202010013707A CN 111174730 B CN111174730 B CN 111174730B
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CN111174730A (en
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伏燕军
张鹏飞
韩勇华
桂建楠
江光裕
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Nanchang Hangkong University
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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
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Abstract

本发明公开了一种基于相位编码的快速相位解包裹方法，由相移法基本原理、相位编码方法基本原理和相位解包裹原理三大关键部分组成。具体步骤包括：首先利用计算机生成两幅正弦条纹、两幅相位编码条纹图和一幅空白图；其次利用一张空白图生成额外的两幅正弦条纹图和两幅相位编码条纹图；然后利用四幅正弦条纹图求解出包裹相位，利用四幅相位编码条纹图求解出条纹级次，继而得到物体的绝对相位；最后利用相位‑高度转换公式得到物体真实的三维信息。本方法只需五幅图就能实现物体的三维重建，提高了测量速度，在快速测量领域具有潜在的应用前景和实用价值。

Figure 202010013707

The invention discloses a fast phase unwrapping method based on phase coding, which consists of three key parts: the basic principle of the phase shift method, the basic principle of the phase coding method and the phase unwrapping principle. The specific steps include: first, use a computer to generate two sinusoidal fringes, two phase-encoding fringe images, and a blank image; secondly, use a blank image to generate two additional sinusoidal fringe images and two phase-encoding fringe images; then use four The wrapping phase is solved by the sinusoidal fringe pattern, the fringe order is solved by using the four phase-encoding fringe patterns, and then the absolute phase of the object is obtained; finally, the real three-dimensional information of the object is obtained by using the phase-height conversion formula. The method can realize the three-dimensional reconstruction of the object with only five images, improves the measurement speed, and has potential application prospect and practical value in the field of rapid measurement.

Figure 202010013707

Description

Rapid phase unwrapping method based on phase encoding
Technical Field
The invention relates to an optical three-dimensional measurement method, belongs to the technical field of photoelectric detection, and particularly relates to a rapid phase unwrapping method based on phase encoding.
Background
With the rapid development of modern industry and information technology, the requirements for the speed and precision of three-dimensional measurement of objects are higher and higher. Among a plurality of methods for acquiring three-dimensional information of an object, an optical three-dimensional measurement technology widely relates to various subjects such as optical imaging, computer technology, photoelectron information, image processing and the like, has the characteristic of integrating the advantages of other measurement methods, and gradually becomes a trend in the field of three-dimensional topography measurement. The optical three-dimensional measurement technology actually reconstructs a surface shape of a three-dimensional object by using a two-dimensional projection image, namely, information is acquired from the two-dimensional projection image, and then the geometric dimension of the object in a three-dimensional space is obtained by processing digital information. Among them, the three-dimensional measurement method based on the grating fringe projection is one of popular measurement methods in the optical three-dimensional measurement method, and has irreplaceable superiority for obtaining three-dimensional surface information, and in recent years, remarkable progress has been made in practical and commercial applications.
Through the current research situation and development trend analysis research at home and abroad, the traditional three-dimensional measurement technology is developed more mature, but is mostly static measurement. In recent years, high-speed, real-time and high-precision three-dimensional measurement is widely applied to the aspects of industrial on-line detection, virtual reality, medical diagnosis, object deformation analysis and the like, and along with the improvement of the performances of acquisition equipment, projection equipment and a high-speed processor, a high-speed, real-time and high-resolution three-dimensional measurement method is gradually becoming an important direction for the development of an optical three-dimensional measurement technology. Therefore, how to solve the absolute phase of the object to be measured by using less projection fringe frame number becomes a breakthrough. In the traditional measuring method, more than or equal to six fringe images are usually needed to realize the measurement of the absolute phase, so that the time consumption is long, and the measuring speed is directly influenced.
Compared with the traditional phase coding method, the rapid phase unwrapping method based on the phase coding has higher measurement precision and speed, and has potential application prospect and practical value in the field of rapid measurement.
Disclosure of Invention
The invention aims to provide a quick phase unwrapping method based on phase encoding, which only needs to project two frames of sinusoidal phase shift fringe patterns, two frames of phase encoding fringe patterns and one frame of blank patterns, has short time consumption, can effectively improve the measuring speed, and has potential application prospect and practical value in the field of quick measurement.
In order to achieve the purpose, the invention adopts the following technical scheme: a fast phase unwrapping method based on phase encoding, the method comprising the steps of:
generating two sinusoidal stripe graphs, two phase coding stripe graphs and a blank graph by using a computer, and shooting five graphs projected to an object to be measured by using a camera;
generating two additional sine stripe graphs and two phase coding stripe graphs by using the blank graph;
obtaining the wrapping phase of the object by using the four sinusoidal fringe patterns, obtaining the fringe order of the object by using the four phase coding fringe patterns, and further obtaining the absolute phase of the object to be measured through calculation;
and step four, obtaining real three-dimensional information of the object to be measured by using a phase-height conversion formula through the obtained absolute phase.
Preferably, the two sinusoidal fringe graphs generated by the computer in the first step are represented by I1(x,y)、I2(x, y), two phase encoded fringe patterns generated are shown as I3(x,y)、I4(x, y) and phase shifts of 0 and pi/2, respectively, and a blank graph represented by I5(x, y), the optical expressions of the five figures are respectively:
Figure BDA0002358073250000021
Figure BDA0002358073250000022
Figure BDA0002358073250000023
Figure BDA0002358073250000024
I5(x,y)＝2A(x,y) (5)
where A (x, y) is background light intensity, B (x, y) is modulation intensity, T is fringe period number, I5(x, y) is twice the dc component of the blank.
Preferably, the specific implementation method of the second step is as follows: two additional sinusoidal fringe patterns I generated by equation (6)6(x,y)、I7(x, y) and two phase encoded fringe patterns I8(x,y)、I9(x, y) whose optical expressions are:
Ii(x,y)＝I5(x,y)-Ij(x,y)；j＝1,2,3,4 (6)
Figure BDA0002358073250000031
Figure BDA0002358073250000032
Figure BDA0002358073250000033
Figure BDA0002358073250000034
preferably, the acquisition method of the wrapped phase, the fringe order and the absolute phase in the third step is as follows:
two sine fringe patterns I shot by a camera are solved by using a formula (11)1(x,y)、I2(x, y) and two additionally generated sinusoidal fringe patterns I6(x,y)、I7Wrapped phase contained in (x, y):
Figure BDA0002358073250000035
code phase
Figure BDA0002358073250000036
Expressed by equation (12):
Figure BDA0002358073250000037
where x is the pixel point of the projector in the horizontal direction, p is the fringe spacing or the number of pixels per fringe period, floor [ x ] is the rounding function, and mod (x, y) is the remainder function.
Embedding the code phase into the sinusoidal fringe pattern to obtain a phase code fringe pattern, and obtaining the step phase by using the formula (13):
Figure BDA0002358073250000038
from the step phase, the fringe order k (x, y) is determined using equation (14):
Figure BDA0002358073250000041
where fix x is a function rounded to 0.
After the fringe order is obtained, the final absolute phase is obtained using equation (15):
Figure BDA0002358073250000042
preferably, the specific implementation method of the step four is as follows: and performing phase-height conversion through the obtained absolute phase, and obtaining the real height information of the object to be measured by using a formula (16):
Figure BDA0002358073250000043
wherein f is0The method is characterized in that the method is a method for measuring the sine stripe frequency on a reference plane, delta phi is the absolute phase difference of corresponding points of the surface of an object to be measured and the reference plane, d is the distance between a projector and a camera, and L is the distance between the projector and the camera and the reference plane.
The invention has the advantages that:
(1) compared with the traditional phase encoding method: the traditional phase coding method can reconstruct the three-dimensional appearance of an object by using at least six images, the method can achieve the effect of 8 images in the traditional method by only five images, and the measuring speed is higher than that of the traditional method;
(2) the code word is determined by using the phase instead of the strength, so that the code word is insensitive to the surface contrast, the ambient light and the camera noise and has stronger robustness;
(3) because the projection stripe number is small, the measurement speed is high, and the method has potential application prospect and practical value in the rapid and real-time three-dimensional measurement of the dynamic object.
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FIG. 1 is a schematic view of a measurement system for three-dimensional measurements according to an embodiment of the present invention;
FIG. 2 is a graph of two sinusoidal fringe patterns, two phase-encoded fringe patterns and a blank pattern generated in the embodiment of the present invention, in which (a) is a sinusoidal fringe pattern I1(x, y), (b) are sine stripe patterns I2(x, y), (c) are blank I5(x, y), (d) are phase-encoded fringe patterns I6(x, y), (e) are phase-encoded fringe patterns I7(x,y)；
FIG. 3 is a diagram of a row of wrapping phases and fringe orders of an object under test according to an embodiment of the present invention;
fig. 4 is an absolute phase diagram of an object to be measured according to an embodiment of the present invention.
Detailed Description
It is easily understood that various embodiments of the present invention can be conceived by those skilled in the art according to the technical solution of the present invention without changing the essential spirit of the present invention. Therefore, the following detailed description and the accompanying drawings are merely illustrative of the technical aspects of the present invention, and should not be construed as all of the present invention or as limitations or limitations on the technical aspects of the present invention. The present invention will be described in further detail with reference to the following description of the drawings, which are not intended to limit the present invention, and all similar structures and similar variations using the present invention shall fall within the scope of the present invention.
An optical three-dimensional measurement system based on a phase encoding fast phase unwrapping method is shown in fig. 1 and comprises a DLP projector 1, a CCD camera 2, a computer 3, a measurement support 4, a reference plane 5 and an object to be measured 6. The DLP projector 1 and the CCD camera 2 are placed on a measuring bracket 4; the DLP projector 1 and the CCD camera 2 are respectively connected with the computer 3 through data lines; the object 6 to be measured is placed on the reference plane 5; the computer 3 comprises an image acquisition card, projection software and measurement software. The DLP projector 1 focuses and projects stripes with characteristic information onto the surface of an object to be measured 6, the CCD camera 2 collects the stripe information, the characteristic information is extracted after the processing of the computer 3, and three-dimensional reconstruction is carried out according to a specific algorithm.
The invention relates to a fast phase unwrapping method based on phase encoding, which comprises the following steps:
the method comprises the following steps: two sinusoidal fringe patterns I generated by computer 31(x,y)、I2(x, y), two phase encoded fringe patterns I3(x,y)、I4The (x, y) phase shifts are respectively 0 and pi/2, and a blank diagram I5(x, y), the optical expressions of the five figures are respectively:
Figure BDA0002358073250000051
Figure BDA0002358073250000052
Figure BDA0002358073250000061
Figure BDA0002358073250000062
I5(x,y)＝2A(x,y) (5)
where A (x, y) is background light intensity, B (x, y) is modulation intensity, T is fringe period number, I5(x, y) is twice the dc component of the blank.
Step two: two additional sinusoidal fringe patterns I generated by equation (6)6(x,y)、I7(x, y) and two phase encoded fringe patterns I8(x,y)、I9The (x, y) optical expressions are:
Ii(x,y)＝I5(x,y)-Ij(x,y)；j＝1,2,3,4 (6)
Figure BDA0002358073250000063
Figure BDA0002358073250000064
Figure BDA0002358073250000065
Figure BDA0002358073250000066
step three: the acquisition method of wrapped phase, fringe order and absolute phase is as follows:
the wrapping phases contained in the two sinusoidal fringe patterns shot by the CCD camera 2 and the two additionally generated sinusoidal fringe patterns are solved by using the formula (11):
Figure BDA0002358073250000067
code phase
Figure BDA0002358073250000068
Expressed by equation (12):
Figure BDA0002358073250000069
wherein x is a pixel point in the horizontal direction of the DLP projector 1, p is a fringe spacing or a pixel number of each fringe period, floor [ x ] is a rounding function, and mod (x, y) is a remainder function.
Embedding the code phase into the sinusoidal fringe pattern to obtain a phase code fringe pattern, and obtaining the step phase by using the formula (13):
Figure BDA0002358073250000071
from the step phase, the fringe order k (x, y) is determined using equation (14):
Figure BDA0002358073250000072
where fix x is a function rounded to 0.
After the fringe order is obtained, the final absolute phase is obtained by equation (15).
Figure BDA0002358073250000073
Step four: three-dimensional reconstruction, phase-height conversion: obtaining the real height information of the object 6 to be measured by using the formula (16):
Figure BDA0002358073250000074
wherein f is0Is the frequency of the sine stripe on the reference plane 5, and delta phi is the absolute phase difference of the surface of the object to be measured 6 and the corresponding point of the reference plane 5. d is the distance between the DLP projector 1 and the CCD camera 2, and L is the distance between the DLP projector 1 and the CCD camera 2 to the reference plane 5.
Without being limited thereto, any changes or substitutions that are not thought of through the inventive work should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope defined by the claims.

Claims (2)

1.一种基于相位编码的快速相位解包裹方法，其特征在于，包括以下步骤：1. a fast phase unwrapping method based on phase encoding, is characterized in that, comprises the following steps: 步骤一、利用计算机生成的两幅正弦条纹图表示为I1(x,y)、I2(x,y)，生成的两幅相位编码条纹图表示为I3(x,y)、I4(x,y)且其相移分别为0、π/2，生成的一幅空白图表示为I5(x,y)，其五幅图的光学表达式分别为：Step 1. The two sine fringe patterns generated by the computer are represented as I 1 (x,y), I 2 (x, y), and the generated two phase-encoding fringe patterns are represented as I 3 (x,y), I 4 (x, y) and its phase shifts are 0 and π/2, respectively, a blank image is generated and expressed as I 5 (x, y), and the optical expressions of the five images are:
Figure FDA0003012037930000011
Figure FDA0003012037930000011
Figure FDA0003012037930000012
Figure FDA0003012037930000012
Figure FDA0003012037930000013
Figure FDA0003012037930000013
Figure FDA0003012037930000014
Figure FDA0003012037930000014
 I5(x,y)＝2A(x,y) (5)I 5 (x,y)=2A(x,y) (5) 其中A(x,y)为背景光强，B(x,y)为调制强度，T为条纹周期数，I5(x,y)为空白图直流分量的两倍，where A(x, y) is the background light intensity, B(x, y) is the modulation intensity, T is the number of fringe periods, and I 5 (x, y) is twice the DC component of the blank image, 步骤二、利用公式(6)生成的额外两幅正弦条纹图I6(x,y)、I7(x,y)和两幅相位编码条纹图I8(x,y)、I9(x,y)，其光学表达式分别为：Step 2. Use the additional two sinusoidal fringe patterns I 6 (x, y), I 7 (x, y) and two phase-encoding fringe patterns I 8 (x, y) and I 9 (x) generated by formula (6) , y), and their optical expressions are: Ii(x,y)＝I5(x,y)-Ij(x,y)；j＝1,2,3,4 (6)I i (x,y)=I 5 (x,y)-I j (x,y); j=1,2,3,4 (6)
Figure FDA0003012037930000015
Figure FDA0003012037930000015
Figure FDA0003012037930000016
Figure FDA0003012037930000016
Figure FDA0003012037930000017
Figure FDA0003012037930000017
Figure FDA0003012037930000018
Figure FDA0003012037930000018
 步骤三、利用四幅正弦条纹图得到待测物体的包裹相位，利用四幅相位编码条纹图得到待测物体的条纹级次，通过计算进而求得待测物体的绝对相位，方法如下所示：Step 3: Obtain the wrapping phase of the object to be measured by using the four sinusoidal fringe patterns, obtain the fringe order of the object to be measured by using the four phase-encoding fringe patterns, and then obtain the absolute phase of the object to be measured by calculation. The method is as follows:
Figure FDA0003012037930000019
表示包裹相位，利用公式(11)求解出相机拍摄的两幅正弦条纹图I1(x,y)、I2(x,y)和额外生成的两幅正弦条纹图I6(x,y)、I7(x,y)所包含的包裹相位：
Figure FDA0003012037930000019
Represents the wrapping phase, and uses formula (11) to solve the two sine fringe images I 1 (x, y), I 2 (x, y) captured by the camera and the additionally generated two sine fringe images I 6 (x, y) , the wrapped phase contained in I 7 (x,y):
Figure FDA0003012037930000021
Figure FDA0003012037930000021
Figure FDA0003012037930000022
表示编码相位，用公式(12)表示：
Figure FDA0003012037930000022
represents the encoding phase, expressed by formula (12):
Figure FDA0003012037930000023
Figure FDA0003012037930000023
 其中x为投影仪水平方向的像素点，p为条纹间距或每个条纹周期的像素数，floor[x]为取整函数，mod(x,y)为取余函数；Where x is the pixel point in the horizontal direction of the projector, p is the stripe spacing or the number of pixels per stripe period, floor[x] is the rounding function, and mod(x,y) is the remainder function; 将编码相位嵌入正弦条纹图得到相位编码条纹图，再利用公式(13)得到阶梯相位：Embed the encoded phase into the sinusoidal fringe pattern to obtain the phase encoded fringe pattern, and then use the formula (13) to obtain the stepped phase:
Figure FDA0003012037930000024
Figure FDA0003012037930000024
 根据阶梯相位，利用公式(14)求得条纹级次k(x,y)：According to the step phase, the fringe order k(x, y) is obtained by formula (14):
Figure FDA0003012037930000025
Figure FDA0003012037930000025
 其中fix[x]为向0取整函数；where fix[x] is the rounding function to 0; 得到条纹级次后，利用公式(15)求得最终的绝对相位φ(x,y)，After obtaining the fringe order, use formula (15) to obtain the final absolute phase φ(x, y),
Figure FDA0003012037930000026
Figure FDA0003012037930000026
 2.根据权利要求1所述的一种基于相位编码的快速相位解包裹方法，其特征在于，通过获得的所述绝对相位，进行相位-高度转换，利用公式(16)得到待测物体真实的高度信息：2. a kind of fast phase unwrapping method based on phase encoding according to claim 1, is characterized in that, by the described absolute phase obtained, carry out phase-height conversion, utilize formula (16) to obtain the true value of object to be measured. Altitude information:
Figure FDA0003012037930000027
Figure FDA0003012037930000027
 其中f0为参考平面上的正弦条纹频率，Δφ为待测物体表面和参考平面对应点的绝对相位差，d为投影仪和摄像机之间的距离，L为投影仪和摄像机到参考平面的距离。where f 0 is the frequency of the sinusoidal fringes on the reference plane, Δφ is the absolute phase difference between the surface of the object to be measured and the corresponding point on the reference plane, d is the distance between the projector and the camera, and L is the distance between the projector and the camera to the reference plane .
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