CN106017357A - Defocused projection three-dimensional measuring method based on colorful triangular wave fringes - Google Patents

Abstract

The invention discloses a defocused projection three-dimensional measuring method based on colorful triangular wave fringes. The method includes four key parts including the colorful triangular wave fringe encoding principle, a defocused projection system, the principle of eliminating color crosstalk between channels and the three-dimensional measuring principle. The method has the advantages that compared with a traditional fringe projection method needing to project three frames of fringes (phase shift of each frame is 120 degrees), only one frame of colorful triangular wave fringes needs to be projected in the method, and three-dimensional measuring speed is greatly increased; the triangular wave fringes are subjected to slight defocused projection, and ideal sine fringes can be obtained on a reference plane; the colorful triangular wave fringe defocusing method is adopted, so high-order harmonics can be filtered out, the gamma effect can be reduced, and accordingly measuring precision is further improved. The method has potential application prospects and practical value in quick and real-time three-dimensional measuring of dynamic objects.

Description

Three-dimensional measurement method based on color triangular wave fringe defocus projection

technical field

The invention relates to a three-dimensional measurement method, in particular to a three-dimensional measurement method based on defocused projection of colored triangular wave fringes.

Background technique

Fringe projection profilometry is of great significance in 3D measurement due to the advantages of non-contact, full-field measurement, fast measurement speed, high precision and easy information processing. The three-dimensional measurement system is shown in Figure 1, including a projector 1, a color CCD camera 2, a workstation 3, a measurement bracket 4, a reference plane 5, and an object to be measured 6; the projector 1 and the color CCD camera 2 are placed on the measurement bracket 4 and They are respectively connected to the workstation 3 through data lines; the workstation 3 includes an image acquisition card, projection software, and measurement software. The projector 1 properly defocuss the fringes with characteristic information into sinusoidal fringes and projects them onto the reference plane 5 , the fringe information is collected by the color CCD camera 2 , and the reference phase is obtained after processing by the workstation 3 . Then put the object 6 to be measured at the same position, get the corresponding deformed fringe image through the workstation 3, calculate the phase, and subtract the reference phase to get the phase change caused by the surface shape of the object to be measured, so that according to the phase and the surface topography of the object 3D reconstruction of the corresponding relationship. The optical axis of the DLP projector 1 and the optical axis of the color CCD camera 2 intersect at point O. The projector 1 and the color CCD camera 2 are at the same height, the distance between them is d, and the distance between them and the reference plane is l ₀ . The height calculation formula of the measured object 6 is:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&phi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&pi;f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&phi;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

where _f0 is the sinusoidal fringe frequency on the reference plane, and Δφ is the continuous phase difference between the object surface image and the corresponding point of the reference plane image.

Through the analysis and research of domestic and foreign research status and development trends, in recent years, high-speed, real-time, high-precision 3D measurement has been widely used in medical diagnosis, product online detection, face and fingerprint recognition, etc. At home and abroad, a series of researches have been done on the theory and application of rapid three-dimensional measurement of object surface topography. Usually, the three-dimensional measurement methods for dynamic scenes include Fourier transform profilometry and color coding methods. Using Fourier transform profilometry based on fringe projection can realize three-dimensional surface shape measurement in dynamic process. Capturing facial expressions of characters can be realized by using the color coding method. The advantage of the above two methods is that the number of fringes that need to be projected is small during measurement, which greatly improves the measurement speed. The traditional three-dimensional measurement method needs to project at least three frames of fringe images, which takes a long time and directly affects the measurement speed. This single-channel measurement technology can no longer meet the current development trend of measuring the three-dimensional shape of objects with faster speed and higher precision. . The present invention proposes a three-dimensional measurement method based on defocused projection of colored triangular wave fringes. This method only needs to project one frame of colored triangular wave fringes, which takes less time, thereby increasing the measurement speed, and is suitable for fast and real-time three-dimensional measurement. At the same time, the triangular wave fringe defocus projection method is adopted to reduce the influence of gamma effect and improve the measurement accuracy. In addition, the present invention can reduce the crosstalk between the channels by adding an algorithm, and compensate the intensity imbalance of the channels, thereby correcting the error of the truncated phase and further improving the measurement accuracy.

In many industrial automation inspections, it is necessary to measure and obtain the three-dimensional information data of the object. Therefore, the realization of high-speed and high-precision three-dimensional measurement methods for the surface topography of objects has attracted more and more attention from researchers. Since color images have richer information and better recognition features than grayscale images, the number of projection frames can be reduced. Therefore, using the color information of color fringes to perform fast, real-time, and high-precision 3D measurement has become a new method. . The three-dimensional measurement method based on the defocused projection of colored triangular wave fringes proposed by the present invention will play an important role in high-speed and high-precision three-dimensional measurement.

Contents of the invention

The invention proposes a three-dimensional measurement method based on the defocused projection of colored triangular wave fringes. Compared with the traditional three-dimensional measurement method of sinusoidal fringe projection, the method reduces the gamma effect and improves the measurement accuracy and speed.

The three-dimensional measurement method based on the defocused projection of colored triangular wave fringes proposed by the present invention is characterized in that: the coding principle of colored triangular wave fringes, a defocused projection system, the principle of eliminating color crosstalk between channels, and the principle of three-dimensional measurement;

The coding principle of the colored triangular wave stripes is to obtain the colored triangular wave stripes by embedding the same frequency and the phases of the triangular wave stripes of -120°, 0°, and 120° in the three channels of RGB, respectively, and then synthesizing them;

The out-of-focus projection system performs Fourier analysis on triangular wave fringes:

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; A</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; A</span>}}{{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In the above formula, A is the amplitude value, k is the harmonic order, and w ₀ is the fundamental frequency. It can be seen that the triangular wave fringe contains a number of high-order harmonics. By defocusing it moderately, the high-order harmonics can be filtered out to obtain standard sine fringes;

According to the three-dimensional measurement principle, the three-color sinusoidal fringes of red, green, and blue separated from the colored triangular wave fringes after eliminating crosstalk are used to obtain the truncated phase value by using a three-step phase shift method:

$\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}\frac{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Then use the mass-guided method to unwrap the phase to obtain continuous phase values, and then use the phase-height formula (3) to obtain the height information of each point on the surface of the object.

The advantages of the present invention are: (1) compared with the traditional sinusoidal fringe projection method: the traditional method needs to project three frames of sinusoidal fringes respectively (each frame is phase-shifted by 120°); Three-dimensional measurement can be realized by projecting onto the surface of the object, which can better meet the real-time requirements; (2) The triangular wave fringes are defocused and projected, and the sinusoidal fringes are obtained on the reference plane. The degree of focus is shallower, and ideal sinusoidal fringes can be obtained only in a slightly defocused state; (3) The defocused projection method of colored triangular wave fringes is adopted, which can filter out high-order harmonics, high-frequency noise and overcome the projector's The non-linear Gamma effect greatly improves the accuracy of 3D measurement. This method has high practical value in high-speed and high-precision 3D measurement.

Description of drawings

Fig. 1 is a schematic diagram of the three-dimensional measurement system of the present invention.

Fig. 2 is the triangular wave fringe pattern 1 of the three-step phase shift of the present invention.

Fig. 3 is the triangular wave fringe diagram II of the three-step phase shift of the present invention.

Fig. 4 is the third triangular wave fringe diagram of the three-step phase shift of the present invention.

Fig. 5 is a color triangular wave fringe intensity diagram after synthesis of red, green and blue three channels of the present invention.

Fig. 6 is a colored triangular wave fringe diagram of the present invention.

Fig. 7 is a triangular wave fringe spectrum diagram of the present invention.

Fig. 8 is a sinusoidal fringe diagram obtained after the triangular wave fringes are defocused according to the present invention.

In the figure, 1 is a projector, 2, a color CCD camera, 3, a workstation, 4, a measuring support, 5, a reference plane, and 6, an object to be measured.

detailed description

The implementation of the present invention will be described in further detail below in conjunction with the accompanying drawings, but this embodiment is not intended to limit the present invention, and all similar structures and similar changes of the present invention should be included in the protection scope of the present invention.

The present invention works and implements in this way, based on the three-dimensional measurement method of defocus projection of colored triangular wave stripes, it is characterized in that: four key points are the coding principle of colored triangular wave stripes, the defocus projection system, the principle of eliminating color crosstalk between channels, and the principle of three-dimensional measurement Partial composition.

1. Traditional color sine stripes

The traditional color sinusoidal fringe is obtained by using three-step phase shift method to obtain the phase value of the sinusoidal fringes of the three channels of red (Red), green (Green), and blue (Blue), and the phase value between each two of the three colored lights The difference is 120°, and the light intensity of red, green, and blue colors in each pixel (x, y) is as follows:

I _R (x,y)=I'(x,y)+I"(x,y)cos[φ(x,y)-2π/3] (5)

I _G (x,y)=I'(x,y)+I"(x,y)cos[φ(x,y)] (6)

I _B (x,y)=I'(x,y)+I"(x,y)cos[φ(x,y)+2π/3] (7)

I _R (x, y), I _G (x, y), and I _B (x, y) are the light intensity values on the red, green, and blue color channels, respectively. I'(x,y) is the background intensity, I"(x,y) is the modulation intensity, and φ(x,y) is the phase distribution.

2. Color triangular wave stripe coding principle

Traditional RGB color coding stripes adopt a sinusoidal pattern, and there are nonlinear Gamma effects and high-order harmonics of the projector, which directly affect the measurement accuracy. So it is usually used in the measurement of low precision requirements. For this reason, the present invention proposes to solve the above problems based on the defocused projection method of colored triangular wave stripes, that is, to code the triangular wave stripes of the red, green, and blue channels in the RGB image, and the phases are separated by 120° successively, as shown in Fig. 2, Fig. 3 and As shown in Figure 4; through synthesis, the colored triangular wave stripes are obtained, as shown in Figure 5 and Figure 6.

3. Defocused projection of colored triangular wave stripes

By performing a Fourier analysis of the triangular wave fringes:

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; A</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; A</span>}}{{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

The Fourier spectrum is expressed as formula (9):

X(f _t )＝Csinc(ft _t /2f ₀ )comb(ft _t /f ₀ ) (9)

In formula (9), c is a constant, and f ₀ is the fundamental frequency of triangular wave stripes.

The projection optical transfer function is as follows (10):

H(f _t )＝J ₁ (2πf _t r ₀ )/πf _t r ₀ (10)

Among them, J ₁ is the first-order Bessel function, and r ₀ is the radius of the discrete circle formed by defocusing.

When f _t =kf ₀ , where k is a natural number, the OTF of the out-of-focus system can be rewritten as:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

In formula (11), b is a defocus parameter,

The optical defocusing system is used as a Gaussian low-pass filter to filter out the high-frequency components of the triangular wave stripes (as shown in Figure 7). In addition, as the degree of defocus deepens, the radius r ₀ of the circle of confusion will increase, followed by the increase of b, which means that the standard The sinusoidal stripes (as shown in Figure 8).

Therefore, by properly defocusing the colored triangular wave stripes, good colored sinusoidal stripes can be obtained.

4. The principle of eliminating color crosstalk between color sinusoidal stripe channels

Use the color triangular wave stripes in (2) to eliminate the crosstalk of each channel through the compensation formula, and then correct the intensity of each channel.

Five, three-dimensional measurement principle

Color triangular wave fringes after eliminating crosstalk According to the method in (3), the separated colored sinusoidal fringes of red, green and blue are obtained. The truncated phase value is obtained by the three-step phase shift method:

$\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}\frac{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Then use the mass-guided method to unwrap the phase to obtain its continuous phase value, and then use the phase-height formula (3) to obtain the height of the object.

Claims (1)

1. Based on the three-dimensional measurement method of defocused projection of colored triangular wave stripes, it is characterized by four key parts: the coding principle of colored triangular wave stripes, the defocused projection system, the principle of eliminating color crosstalk between channels, and the principle of three-dimensional measurement; The coding principle of the colored triangular wave stripes is to obtain the colored triangular wave stripes by embedding the same frequency and the phases of the triangular wave stripes of -120°, 0°, and 120° in the three channels of RGB, respectively, and then synthesizing them; The out-of-focus projection system performs Fourier analysis on triangular wave fringes: $\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; A</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; A</span>}}{{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; 5</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; 5</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ It can be seen that the triangular wave stripes contain high-order harmonics, and the high-order harmonics can be filtered out by properly defocusing it to obtain standard sinusoidal stripes; The three-dimensional measurement principle is to obtain the separated color sinusoidal fringes of red, green, and blue from the color triangular wave fringes after eliminating crosstalk according to the method in the defocus projection system, and use the three-step phase shift method to obtain the truncated phase value : $\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}\frac{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ Then use the mass-guided method to unwrap the phase to obtain continuous phase values, so as to use the phase-height formula: $\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&phi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&pi;f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; \&phi;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$ Obtain the height information of each point on the surface of the object.