CN114492082B

CN114492082B - Grating phase extraction method of grating projection imaging system

Info

Publication number: CN114492082B
Application number: CN202210230582.7A
Authority: CN
Inventors: 杨建柏; 周国辉; 许智梁; 赵妍; 陈佳昕
Original assignee: Harbin Normal University
Current assignee: Harbin Normal University
Priority date: 2021-12-20
Filing date: 2022-03-10
Publication date: 2022-10-04
Anticipated expiration: 2042-03-10
Also published as: CN114492082A

Abstract

The grating phase extraction method of the grating projection imaging system solves the problem of how to overcome the nonlinear error and the intensity noise of the grating phase in the prior art, and belongs to the technical field of digital grating projection three-dimensional measurement. The invention includes: step one, forming a matrix X by expanding acquired N index grating images through a neighborhood; step two, constructing a covariance matrix C according to the matrix X:

and diagonalizing the covariance matrix C to obtain a diagonal matrix D as: d = ACA ^T (ii) a Wherein, the first and the second end of the pipe are connected with each other,

after removing background item for exponential raster image, A is orthogonal transformation matrix, D is N row H X W column, [ 2 ]] ^T Representing a transpose; step three, acquiring a principal component matrix:

the principal components of the first two maximum eigenvalues in the P are respectively I _c And I _s According to I _c And I _s The phase of the index grating is obtained as follows:

where (i, j) is the camera pixel coordinate. The invention overcomes the nonlinear phase error and the intensity noise simply and effectively.

Description

Grating phase extraction method of grating projection imaging system

Technical Field

The invention relates to an error compensation method for reconstructing index grating phase by a neighborhood extension PCA method, belonging to the technical field of digital grating projection three-dimensional measurement.

Background

In a digital grating projection three-dimensional measurement system, a high-quality grating image is a precondition for obtaining a high-precision measurement result, and there are many error sources influencing the quality of the grating image, such as nonlinear errors of a camera and a projector, intensity noise when the grating image is acquired, an out-of-focus error of a lens, errors caused by movement, and the like. Among the main error sources, intensity noise and camera and projector non-linearity errors in acquiring an image are among the most important error sources.

In practical measurement systems, the nonlinear effects of the camera and projector can cause phase reconstruction errors. Most industrial cameras have good linearity and are therefore negligible, and if commercial digital projectors are used, this source of error is often referred to as the projector's nonlinear gamma effect. The projector non-linear gamma effect is a non-linear response to the gray values of the projector input, which is intentionally incorporated into off-the-shelf digital projectors as a visual enhancement of the non-linear sensitivity of human vision to intensity. The non-linear mapping of the projector input to the acquired image intensity can result in distortion of the grating image, resulting in large errors in the reconstructed phase. The intensity of the grating image at each point of the measured object is collected by a camera, and is inevitably influenced by intensity noise. The intensity noise sources include ambient light, illumination noise of the projector, flicker of the camera and the projector, noise of the camera, quantization errors of the projector and the camera, and the like. When the collected grating image is interfered by intensity noise, the phase reconstructed by the standard phase shift formula deviates from an ideal value, so that phase reconstruction errors are caused.

When a projection device such as a commercial projector is used for projection display, the performance parameters of the projection device are designed to mainly comply with the visual effect of a user. Due to the non-linear perception characteristic of human vision, the display device often needs to perform non-linear transformation on the gray-scale value of the original image during image reconstruction, and the gray-scale value of the image before and after the transformation generally has a corresponding relation of a power exponential function, which is the non-linear gamma effect of the projector.

Thus, in the case of a commercial projector, a grating acquisition model of a grating projection imaging system may be used as shown in FIG. 1; phase measurement errors caused by the nonlinear effect of a digital projector seriously affect the three-dimensional measurement precision, so that various phase error compensation methods are generated, and can be mainly summarized as follows: passive phase error compensation, active phase error compensation, inverse compensation, defocused projection, etc. These phase error compensation methods are often complex and require significant computational resources or additional overhead to implement.

Disclosure of Invention

The invention provides a grating phase extraction method of a grating projection imaging system, aiming at solving the problems of the existing method that the nonlinear error of the grating phase and the intensity noise are overcome.

The invention discloses a method for extracting a grating phase of a grating projection imaging system, which comprises the following steps:

step one, forming a matrix X by N acquired index grating images;

step two, constructing a covariance matrix C according to the matrix X:

and diagonalizing the covariance matrix C to obtain a diagonal matrix D as follows:

D＝ACA ^T

wherein the content of the first and second substances,

after removing background item for exponential grating image, A is orthogonal transformation matrix, D is N row H x W column, [ 2 ]] ^T Representing a transpose;

step three, acquiring a principal component matrix:

where (i, j) is the camera pixel coordinate.

Preferably, the first step includes:

connecting each pixel of the N exponential grating images to form a one-dimensional column vector

Connecting the processed vectors in series, and forming a matrix X by an N-dimensional data matrix:

X＝[I _1,i,j ,I _2,i,j ,…,I _N,i,j ] ^T wherein I _n,i,j Representing the intensity of light at pixel position i, j in the nth index raster image, N =1,2 \8230;

selecting a neighborhood M range taking coordinates i, j as a center, adding neighborhood M range information into a data matrix in a column vector form, wherein the data matrix is changed into:

the matrix X is an MN-dimensional matrix.

Preferably, when M is 5,

preferably, when M is 9,

the invention has the beneficial effects that: (1) The invention does not need to use additional auxiliary conditions of constructing a phase compensation model, calibrating a gamma value, fitting a response curve and the like, and simply and effectively overcomes the nonlinear phase error; (2) The method has universality, is not only suitable for three-step or four-step phase shift algorithm, but also is suitable for phase shift algorithm with more than four steps in principle; (3) The method for expanding the spatial information of the data matrix is simple, has universality and can be applied to other PCA-based methods.

Simulation and experiment results show that the method basically eliminates non-linear errors, has an effect obviously better than that of a phase shift method and an original PCA method under the condition of noise, and improves the phase extraction precision. Although the time is increased, the overall efficiency is not affected and is within an acceptable range.

Drawings

FIG. 1 is a schematic diagram of a grating collection principle of the grating projection of the present invention;

FIG. 2 is a computer generated graph of various gratings, (a) sinusoidal, (b) exponential, (c) nonlinear sinusoidal, (d) nonlinear exponential;

FIG. 3 is a cross-sectional view of various gratings with pixel values on the abscissa and intensity values on the ordinate;

FIG. 4 is a diagram of neighborhood selection, where (a) is a 5 neighborhood and (b) is a 9 neighborhood;

FIG. 5 is a graph showing the wrapped phase and cross-section of a grating, (a) a graph showing the wrapped phase and cross-section of a conventional sinusoidal grating, (b) a graph showing the wrapped phase and cross-section of an exponential grating phase shift method, and (c) a graph showing the wrapped phase and cross-section of an exponential grating PCA method; the abscissa is the pixel value and the ordinate is the phase value

FIG. 6 is a diagram of the absolute phase obtained by solving a conventional sinusoidal grating; the x and y coordinates are pixel values, and the z coordinate is an absolute phase value;

FIG. 7 is a diagram of absolute phase obtained by solving an exponential grating; the x and y coordinates are pixel values, and the z coordinate is an absolute phase value;

FIG. 8 is a cross-sectional contrast diagram of absolute phase for two grating modes; the abscissa is a pixel value, and the ordinate is an absolute phase value; FIG. 9 is a graph of phase error contrast for two grating modes; the abscissa is the pixel value and the ordinate is the phase error value;

fig. 10 is an exponential raster pattern at different σ, (a) σ =0.07, (b) σ =0.1; σ =0.07 for (c), (0.1 for (d);

fig. 11 is a phase error diagram obtained by each method when σ =0.1, (a) a phase error diagram obtained by a phase shift method, (b) a phase error diagram obtained by a PCA method, (c) a phase error diagram obtained by a PCA-5 method, and (d) a phase error diagram obtained by a PCA-9 method; the x and y coordinates are pixel values, and the z coordinate is a phase error value;

FIG. 12 is a diagram of a conventional grating collected;

figure 13 is a collected index grating.

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 derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

It should be noted that the embodiments and features of the embodiments of the present invention may be combined with each other without conflict.

The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.

In a raster projection system, a conventional sequence of phase-shifting fringes is generated by a cosine function. The input sinusoidal fringe pattern for a projector is generated by a computer and its intensity can be expressed as:

I _n (x ^p ,y ^p )＝I _b (x ^p ,y ^p )+I _m (x ^p ,y ^p )cos[φ(x ^p ,y ^p )+δ _n ] (1)

wherein (x) ^p ,y ^p ) As projector pixel coordinates, I _b (x ^p ,y ^p ) In order to be the background intensity,I _m (x ^p ,y ^p ) For modulating the intensity, phi (x) ^p ,y ^p ) For the desired phase, delta _i Where = 2N/N represents the initial phase of the first image in the raster sequence, N =0,1 \ 8230n, N being the image number, N being the number of images in the raster sequence, and because of the nonlinear gal effect of the projector, the output intensity of the raster image can be expressed as:

I _n (x ^p ,y ^p )＝{I _b (x ^p ,y ^p )+I _m (x ^p ,y ^p )cos[φ(x ^p ,y ^p )+δ _n ]} ^γ (2)

where γ is the projector system gamma value, and after the projector projects a grating image onto the object surface, the reflected grating image is captured by the camera. Assuming that the camera responds linearly to the light intensity and ignores the ambient light, the light intensity of the captured distorted grating pattern can be expressed as:

I _n (i,j)＝{I _b (i,j)+I _m (i,j)cos[φ(i,j)+δ _n ]} ^γ (3)

wherein (I, j) is the camera pixel coordinate, I _b (i,j)，I _m (i, j), phi (i, j) are respectively background intensity, modulation intensity, phase to be solved, and wrapping phase can be solved by using a phase shift method:

in order to overcome the non-linear gamma effect in the traditional fringe projection method, babaei et al propose a new grating projection method, which represents a grating map as an exponential function and proposes a mathematical model of phase reconstruction unrelated to gamma. The intensity of the index raster image can be expressed as:

let I _i Satisfy the requirements of

The background intensity and modulation intensity should satisfy the following equations:

assuming that the camera responds linearly to the light intensity and ignores the ambient light, the light intensity of the captured distorted grating pattern can be expressed as:

the logarithm is taken at the same time on both sides to obtain:

lnI _n (i,j)＝γ{I _b (i,j)+I _m (i,j)cos[φ(i,j)+δ _n ]} (9)

it can be deduced that:

wrap phase is derived from the last:

it is clear from the equation that the proposed exponential grating model calculates the phase independently of the gamma value. Therefore, the method provides a direct and effective solution, does not need other extra calculation and auxiliary forms, and well solves the nonlinear error of the system.

In order to more intuitively show the intensity difference between the index grating and the traditional grating image, a computer is used for generating corresponding grating images, for example, fig. 2 is respectively a traditional sinusoidal grating, an index grating, a nonlinear sinusoidal grating modulated by a nonlinear effect and a nonlinear index grating, wherein the gamma value is 2.2, fig. 3 is a cross-sectional view of the 100 th line of the several grating images after intensity normalization, a straight line is represented as a sinusoidal grating, a dotted line is represented as an index grating, an asterisk line is represented as a nonlinear sinusoidal grating, and a circle line is represented as a nonlinear index grating.

Principal Component Analysis (PCA), a commonly used multivariate Analysis method, converts a plurality of related variables into a small number of independent important variables using orthogonal linear transformation. Vargas et al [ ] first applied the PCA technique to the phase solution of phase-shifting interferometry and achieved good results. Compared with other methods, the method is simple, convenient and easy to implement. Which researchers have subsequently introduced into grating projection techniques for reconstruction of the wrapped phase. The principle of solving the phase by the PCA method is briefly described below.

To facilitate the derivation of the principle of PCA, the present embodiment expresses the light intensity of the nth phase-shift grating pattern as:

because the light intensity of each grating pattern collected by the detectors such as the CCD is a two-dimensional pixel matrix, for the convenience of description, the light intensity is reconstructed into a one-dimensional row vector, and the reconstructed nth grating pattern can be represented as:

the reconstructed grating pattern has an intensity of 1 × K line vector, K being the total number of pixels in each grating pattern, K =1,2 \8230, and K, the subscript K indicating the number of pixels.

Any one raster pattern may consist of two orthogonal signals, i.e.

And

k is the coordinate of each pixel point after reconstruction. The weights of the different orthogonal signals form different raster patterns. Therefore, the PCA method can be used for extracting two orthogonal signals in the phase shift grating pattern, and the phase to be measured is reconstructed through an arctangent function. The principle of the algorithm to reconstruct the phase is described below.

The collected N raster images are expressed as a matrix

x＝[I _1,k ,I _2,k ,…,I _N,k ] ^T (14)

Substituting equation (12) into equation (14) yields

Due to the background item a _k Is a smooth dc signal, which can be extracted from the raster pattern by the time domain averaging method:

the grating pattern after filtering the background term is

Can be expressed as

Wherein the content of the first and second substances,

let c _n ＝cos(δ _n ),s _n ＝sin(δ _n ),

Matrix array

An element in (1) can be written as

The covariance matrix can thus be written as

By expanding equation (17), one obtains

Let A _i,j ＝c _i c _j ,F _i,j ＝s _i s _j ,E _i,j ＝c _i s _j +c _j s _i The formula (3-41) can be rewritten as

If the number of stripes in the phase shift grating pattern is more than one, the following approximation condition holds

In combination with the approximation condition, the covariance matrix can be simplified to

C＝αA+βF

Wherein the content of the first and second substances,

for the same sequence of phase-shifted grating patterns, α and β are generally considered to be constant. A and F are N × N matrices

A＝[cos(δ ₁ ) cos(δ ₂ ) … cos(δ _N )] ^T ·[cos(δ ₁ ) cos(δ ₂ ) … cos(δ _N )] (22)

F＝[sin(δ ₁ ) sin(δ ₂ ) … sin(δ _N )] ^T ·[sin(δ ₁ ) sin(δ ₂ ) … sin(δ _N )] (23)

Since both matrices a and F are obtained by multiplying a matrix by its own transpose matrix, both ranks a and F are 1, and both a and F have only one eigenvalue and eigenvector. The eigenvalues of the matrices A and F are respectively

The corresponding feature vectors are respectively

Thus, the covariance matrix C has a rank of 2 and two eigenvectors, which can be approximated as follows if the phase shift amount of the raster pattern is uniformly distributed in the range of [0,2 π ]

Thus, it is possible to provide

Aw _F ＝0,Fw _A ＝0 (27)

In this case, the two eigenvalues of the covariance matrix are λ ₁ ＝αλ _A ,λ ₂ ＝βλ _F With the corresponding feature vector as w ₁ ＝w _A ,w ₂ ＝w _F . Through the two sets of eigenvalues and eigenvectors, the covariance matrix C can be diagonal into a diagonal matrix D, and the corresponding orthogonal transformation matrix is U. And the diagonal matrix D has only two non-zero elements, D ₁₁ ＝λ ₁ ,D ₂₂ ＝λ ₂ And the first and second rows of the transformation matrix U are each w ₁ ,w ₂ After the matrix U is obtained, the first principal component and the second principal component of the raster pattern can be obtained through Hotelling transformation, and the approximation condition (26) is combined to obtain the first principal component and the second principal component of the raster pattern

According to the above formula, the phase to be measured can be obtained by the arc tangent function

Therefore, the phase to be measured in the grating pattern can be conveniently obtained by the PCA method.

In the embodiment, a PCA method is introduced into the index grating model, and the phase is solved by the PCA method. Equation (10) can be further rewritten as:

ln _n (i,j)＝γI _b (i,j)+γI _m (i,j)cos[φ(i,j)]cosδ _n -γI _m (i,j)sin[φ(i,j)]sinδ _n ] (31)

the following (i, j) are omitted for simplicity by combining the formula (31). Set to I' _n ＝lnI _n ，α＝γI _b ，α _n ＝cosδ _n ，β _n ＝-sinδ _n ，I _c ＝γI _m cos[φ]，I _s ＝γI _m sin[φ]It is possible to obtain:

I′ _n ＝α+α _n I _c +β _n I _s (32)

will be the background intensity term

Equation (32) may be written as:

I″ _n ＝I′ _n -α＝α _n I _c +β _n I _s (34)

equation (34) indicates that a raster pattern without a background intensity term can be decomposed into two uncorrelated orthogonal signals I _c And I _s In linear combination, i.e.

Where X and Y are the width and height of the raster image, respectively. Thus, the exponential grating model can be solved using the PCA method.

The grating phase extraction method of the grating projection imaging system of the embodiment includes:

step one, forming a matrix X by N collected index grating images;

step two, constructing a covariance matrix C according to the matrix X:

D＝ACA ^T (37)

wherein the content of the first and second substances,

is an indexAfter the background item is removed from the raster image, A is orthogonal transformation matrix, D is N row H x W column, [ 2 ]] ^T Representing a transposition;

step three, acquiring a principal component matrix:

the principal components of the first two maximum eigenvalues in Y are respectively I _c And I _s According to I _c And I _s The phase of the index grating is obtained as follows:

where (i, j) is the camera pixel coordinate.

I _c And I _s Contains gamma, and is eliminated in the process of solving the wrapping phase, so that the whole model is not influenced by the nonlinear gamma effect. And the PCA algorithm is adopted to calculate the wrapping phase, so that the phase error caused by the gamma effect is eliminated. Obviously, the proposed exponential grating model is independent of gamma value, and is applicable to any multi-step phase shift algorithm. Thus, it provides a direct, simple and effective solution to eliminate non-linearity errors without requiring any additional three-dimensional shape measurement calculations. After the wrapped phase is obtained, the corresponding absolute phase can be calculated by using a phase unwrapping method.

This embodiment describes the reconstruction of the exponential grating phase using the PCA method for eliminating non-linearity errors. However, the problem that the exponential grating model is sensitive to noise is not improved by the algorithm, so that the embodiment provides a PCA phase reconstruction method for neighborhood space information expansion to reduce the influence of noise on phase accuracy.

In this embodiment, a simple modification of the above-mentioned PCA-based phase reconstruction method is proposed to improve its accuracy. The basic idea is to take into account the spatial relationship of neighboring pixels in the decomposition process. Since the inherent properties of the grating determine its specific structure, the adjacent pixels of the grating image also have specific properties. To take advantage of this relationship, the present embodiment extends the data matrix of the PCA method, which can separate random noise well because the noise does not follow the particular structure of the fringes.

The adjacent relation between the random noise and each pixel point in the grating image is different. Therefore, the noise-related components should be dispersed over all the feature vectors after decomposition. Since only the first two eigenvectors are needed for phase extraction, their signal-to-noise ratio increases as the number of eigenvectors increases. That is, the energy of the noise at each eigenvalue is reduced due to its spread over the other eigenvalues, while the energy of the grating components is concentrated on the first two eigenvalues. Therefore, as more data vectors are connected into the expanded data matrix, the correlation error caused by the influence of random noise on the extracted phase is reduced.

Based on the above discussion, the present embodiment proposes a PCA exponential grating phase extraction method that expands spatial information to a data matrix, thereby reducing an extraction error, the method including the steps of:

1. after N raster images are processed by the formula (13), each pixel is connected to form a one-dimensional column vector

(expand the two-dimensional map into a one-dimensional vector), where i, j denote the pixel locations and N denotes the number of images.

2. And connecting the processed vectors in series to form an N-dimensional data matrix as shown in a formula (10):

X＝[I _1,i,j ,I _2,i,j ,…,I _N,i,j ] ^T (40)

3. a neighborhood M range centered around the camera pixel coordinate (i, j) is selected, such as the 5 neighborhood or the 9 neighborhood as shown in fig. 4.

4. Establishing a spatial neighborhood matrix, adding neighborhood information into the data matrix in the form of column vectors,

when the M is less than or equal to 5,

when the M is less than or equal to 9,

at this time, the data matrix becomes

This matrix is an MN dimensional matrix.

Solving the phases in the second step and the third step;

simulation and experiment:

in order to verify the effectiveness of the neighborhood extension PCA method for solving the index grating, a simulated grating pattern is used for carrying out simulation test on the method, the simulation test is divided into two parts, the first part is used for testing the effectiveness of the index grating for overcoming nonlinear errors, and the second part is used for testing the influence of noise reduction on the neighborhood extension PCA method for solving the index grating.

Firstly, MATLAB is used to respectively generate a noiseless four-step sinusoidal grating and an exponential grating sequence with the size of 500 × 500 pixels, the period T of 100 and the gamma value of 2.2, a four-step phase shift method is used to solve the phase of the sinusoidal grating sequence, a four-step phase shift method and a PCA method are used to solve the phase of the exponential grating sequence, the result is shown in fig. 5, the left side is a wrapped phase diagram obtained by the conventional grating and exponential grating sequence, and the right side is a central cross-sectional diagram of the wrapped phase diagram. From the right graph, it can be clearly seen that the conventional sinusoidal grating sequence is affected by the nonlinear gamma effect, and the wrapped phases obtained by respectively solving the exponential gratings in the two ways are not affected by the nonlinear gamma effect. The obtained wrapped phase is subjected to phase expansion to obtain an absolute phase diagram, fig. 6 is the absolute phase diagram obtained by the conventional sinusoidal grating, fig. 7 is the absolute phase diagram obtained by the exponential grating, and fig. 8 is a cross-section comparison diagram of the absolute phase of the two grating modes.

The ideal phase value is subtracted from the obtained absolute phase value to obtain phase error maps of two grating sequences, as shown in fig. 9, which is a phase error contrast map of two grating modes. The traditional sinusoidal grating projection method is influenced by the nonlinear gamma effect, and the phase error of the sinusoidal fringe sequence can reach 0.08rad at most. Therefore, it can be obtained from the above experiment that the experimental result is consistent with the analysis result of the above exponential grating for the method of eliminating gamma effect, the method is not affected by the nonlinear gamma effect, and the accurate phase can be obtained.

The second part of experiment is to verify that the proposed neighborhood extension PCA solves the influence of noise suppression by the exponential grating method. MATLAB is utilized to respectively generate index grating sequences with the size of 500 multiplied by 500 pixels, the period T of 100 and the gamma value gamma of 2.2, noise with the standard deviation sigma of 0.01 to 0.1 and the interval of 0.01 is respectively added to generate ten groups of grating sequences, phase solution is respectively carried out by a phase shift method, a PCA method and an extended neighborhood PCA method (according to the difference of neighborhood pixels, the method is respectively called PCA-5 and PCA-9), an ideal phase is subtracted from a phase value to obtain a phase error, and then the influence of the noise on the methods is compared.

Fig. 10 shows exponential gratings generated by adding noise of different σ values, and phase-unwrapping processing is performed on grating sequence charts of different noise, and fig. 11 shows phase error charts obtained by various methods in the case where σ = 0.1. As can be seen, the phase shift method and the PCA method gave similar results, which is consistent with the previous analysis. On the other hand, the results obtained by the proposed PCA-5 and PCA-9 methods have smaller errors than the previous algorithm, and it is also obvious that PCA-9 has stronger noise suppression capability than PCA-5.

TABLE 1 phase error (rad) for each method at different noise

It can be further seen from table 1 that, under the same noise condition, the phase error of the PCA method is slightly higher than that of the phase shift method, the PCA-5 and PCA-9 methods effectively suppress the influence of noise, the phase error is greatly reduced, the noise suppression capability of the PCA-9 is stronger than that of the PCA-5, the experimental result completely conforms to the inference of the method in the previous section, when more adjacent pixels are integrated in the extended data matrix, the method can eliminate more noise, and the noise suppression capability of the proposed method is verified. Table 2 shows the running time of each method, and it can be seen from the table that the time of the phase shift method is shortest, and the time of the PCA method is longer, on the other hand, as the number of adjacent pixels in the extended data matrix increases, the method requires more computing resources, so the time is greatly increased, theoretically, the noise suppression by the neighborhood re-expansion (such as PCA-13) is better, but the computing time is also correspondingly rapidly increased, and in order to meet the needs of the whole three-dimensional reconstruction system, PCA-5 and PCA-9 are two methods with the best comprehensive performance.

TABLE 2 run times of the methods

The performance of the method is verified by using a white board, two groups of grating images are respectively projected onto the white board and are collected by a camera and then processed, as shown in the figure, the collected grating images are an example, and it can be obviously seen that the difference of the obtained images is larger because the two gratings are generated in different modes.

The conventional grating obtains the wrapped phase by adopting a four-step phase shift algorithm, the exponential grating solves the phase by adopting the PCA algorithm introduced earlier, and then the absolute phase of the plate is obtained by using a phase unwrapping algorithm, which are respectively shown as the following figures:

it is obvious from fig. 12 and fig. 13 that due to the existence of the nonlinear effect of the projector, the absolute phase diagram solved by the conventional grating has obvious fluctuating errors, which will cause great influence on the measurement result, while the exponential grating has no nonlinear error because the gamma is eliminated in the solving process, so that the obtained effect is greatly improved compared with the sinusoidal grating, but the accuracy is still not high because of the sensitivity to noise. In order to reduce the influence of noise on the phase, the phase of the exponential grating is solved by using the proposed neighborhood expansion PCA method, 5 neighborhood and 9 neighborhood methods are respectively used and compared with the reference phase of a white board to obtain the root mean square error (RMS) of the reference phase, the obtained error map and numerical values can obviously show that the phase error is obviously improved to 25% after the neighborhood is expanded, which well shows that the proposed method has obvious inhibition effect on the noise when solving the exponential grating and can eliminate the nonlinear error of a projector at the same time, but the improvement degree between the 5 neighborhood and the 9 neighborhood is not obvious, so that a 5 neighborhood mode is selected in practical application, and a better balance can be achieved in time and precision. Because the method is improved only in the solving process, the whole system is not required to calibrate the nonlinearity and specific prior information, and the use is more convenient and concise.

Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It is to be understood that features described in different dependent claims and in this embodiment may be combined in ways other than those described in the original claims. It is also to be understood that features described in connection with individual embodiments may be used in other described embodiments.

Claims

1. A method for extracting a grating phase of a grating projection imaging system, the method comprising:

step one, forming a matrix X by N acquired index grating images;

step two, constructing a covariance matrix C according to the matrix X:

D＝ACA ^T

wherein, the first and the second end of the pipe are connected with each other,

step three, acquiring a principal component matrix:

wherein, (i, j) is a camera pixel coordinate;

the first step comprises the following steps:

selecting a neighborhood M range with coordinates i, j as a center, adding neighborhood M range information into a data matrix in a column vector form, wherein the data matrix is changed into:

the matrix X is an MN-dimensional matrix.

2. The grating phase extracting method of the grating projection imaging system of claim 1, wherein when M is 5,

3. the grating phase extracting method of the grating projection imaging system of claim 1, wherein when M is 9,