CN104504710A - Moore stripe recognition method and device for X-ray grating phase-contrast imaging - Google Patents

Abstract

The invention discloses a method and device for identifying moiré fringes in X-ray grating phase contrast imaging. The method includes: step 1: correcting uneven illumination for the image of moiré fringes to be identified; step 2: correcting uneven illumination after illumination Filter the uniformly corrected moiré image; step 3: binarize the filtered moiré image to obtain a binarized image; step 4: refine the binarized image to extract the binarized image The central line of the moiré fringe in the image; step 5: identifying the precise position of the moiré fringe according to the extracted central line of the moiré fringe. The method provided by the invention realizes the automatic calculation of the moiré fringe angle and direction, avoids the error caused by the subjective factors of the user of the instrument, and greatly improves the adjustment speed of the instrument, and the accuracy is also well guaranteed.

Description

Method and device for identifying moiré fringes in X-ray grating phase contrast imaging

technical field

The invention relates to an automatic detection method for the angle and period of a fringe image, in particular to an automatic identification method for the angle and period of a Moiré fringe in the alignment process of an X-ray grating phase contrast imaging device.

Background technique

For more than 100 years since the German scientist Roentgen first discovered X-rays in 1895, X-rays have been widely used in the field of imaging objects because of their strong penetrating ability. Traditional X-ray imaging methods are mainly based on the absorption of X-rays by objects, and the quality of the final imaging contrast largely depends on the difference in X-ray absorption characteristics of various parts inside the object. In the medical field, since the soft tissue part of the human body has little absorption of X-rays, this means that the application of X-ray absorption imaging methods to the diagnosis of soft tissue lesions in the human body has great limitations.

Since the 1990s, with the development of the third-generation synchrotron radiation facility, hard X-ray phase contrast imaging technology has emerged. At present, a variety of X-ray phase contrast imaging techniques have been developed. Simply put, its mechanism is to use the phase shift of the X-ray after it penetrates the object for imaging. Compared with absorption contrast imaging, the advantage of phase contrast imaging is that the same dose of X-rays penetrates soft tissue, and the change caused by phase shift is much larger than the change caused by radiation intensity absorption, so the obtained X-ray image contrast will be Will be greatly improved, see reference [1].

X-ray grating stepping phase-contrast imaging method is a relatively mature X-ray phase-contrast imaging method at present. Because it can use multicolor and incoherent light generated by general X-ray machines for imaging, it is currently widely used. See References [2]. The widely used X-ray grating phase contrast imaging method was first proposed by Pfeiffer F et al. in 2006. This method uses three gratings with different functions to achieve phase contrast imaging on a general X-ray machine. In the experiment, the main function of the light source grating is to divide the ordinary X-ray light source into a series of independent line light sources. The object sample is placed in front of the phase grating. A single X-ray line source is partially coherent and can produce Talbot effect with the phase grating. Finally, the phase change information is obtained through the analysis grating placed in front of the detector. See reference [3].

A key step in obtaining phase contrast images using this method is the alignment of the phase grating and the analysis grating, and the alignment accuracy has a significant impact on the quality of the acquired image. The alignment method is as follows: firstly adjust the analysis grating to make the grating lines horizontal, and then adjust the phase grating so that the Taber self-imaging of the phase grating coincides completely with the analysis grating. Judging whether the alignment is completed is based on the Talbot self-imaging of the phase grating and the angle and period of the moiré fringes formed by the analysis grating. According to the relevant knowledge of moiré fringes, when the moiré fringes are vertical and their period is equal and tends to infinity, it can be approximately considered that the alignment is completed. However, in current X-ray grating phase-contrast imaging experiments, the angle and period of moiré fringes during alignment are judged by naked eyes. The disadvantages are that there is personal subjective consciousness, the accuracy cannot be guaranteed, and the speed is slow. See reference [4].

references:

[1]Chapman L D, Tomlinson W C, Johnston R E, Washburn D, Pisano E, Gmur N, Zhong Z, Menk R, Arfelli F, Sayers D 1997phys.med.biol.42 2015

[2] Atsushi MOMOSE, Recent Advances in X-ray Phase Imaging, Japanese Journal of Applied Physics, Vol.44, No.9A, 2005, pp.6355-6367

[3] Franz Pfeiffer, Timm Weitkamp, Oliver Bunk, Christian David, Phaseretrieval and differentialphase-contrast imaging with low-brillianceX-raysources, nature physics VOL 2 APRIL 2006

[4] Pavlo Baturin, Mark Shafer, Optimization of grating-basedphase-contrast imaging setup, Medical Imaging 2014: Physics of Medical Imaging, Vol.9033, 90334

Contents of the invention

In order to realize the accurate and fast calculation of the moiré fringe angle and period during the alignment process of X-ray grating phase contrast imaging, so as to improve the alignment accuracy of the instrument and obtain high-quality phase contrast images.

The present invention proposes a method for identifying moiré fringes in X-ray grating phase contrast imaging, which includes:

Step 1: Correct the uneven illumination of the moiré fringe image to be recognized;

Step 2: Filter the moiré fringe image corrected for uneven illumination;

Step 3: binarize the filtered moiré fringe image to obtain a binarized image;

Step 4: Thinning the binarized image to extract the initial position information of each moiré fringe in the binarized image;

Step 5: Identify the precise position of each moiré fringe according to the extracted initial position information of each moiré fringe.

The present invention also proposes an identification device for moiré fringes in X-ray grating phase contrast imaging, which includes:

Correction module: Correct the uneven illumination of the moiré fringe image to be recognized;

Filtering module: filter the moiré fringe image after uneven illumination correction;

Binarization module: binarize the filtered moiré fringe image to obtain a binarized image;

Thinning module: thinning the binarized image to extract the initial position information of each moiré fringe in the binarized image;

Identification module: identify the precise position of each moiré fringe according to the extracted initial position information of each moiré fringe.

Compared with the prior art, the solution provided by the present invention realizes the automation of the calculation of the moiré fringe angle and direction, avoids the error caused by the subjective factors of the instrument user, and the instrument adjustment speed is greatly improved, and the accuracy is also improved. ensure.

Description of drawings

Figure 1 is a schematic diagram of the composition of an X-ray grating step phase contrast imaging system;

Figure 2 is a schematic diagram of several typical relative positions of two gratings and the corresponding Moiré fringes;

Fig. 3 is the flow chart of the identification method of the moiré fringe image in X-ray grating phase contrast imaging in the present invention;

Fig. 4(a)-(e) are schematic diagrams of the software interface and processing steps for realizing the recognition method of the moiré fringe image in the X-ray grating phase contrast imaging of the present invention.

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings.

The principle of moiré fringe generation is as follows: from the Talbot effect, it can be known that the phase grating generates grating self-image at the Talbot distance, we place the analysis grating at a specific Talbot distance, the fringes of the two intersect to form moiré fringes, and place it behind the analysis grating The original image is received by the CCD detector.

Figure 1 shows the composition of the X-ray grating stepping phase contrast imaging system. As shown in Figure 1, the system consists of X-ray light source, light source grating, test sample, phase grating, analysis grating and CCD detector from right to left.

Figure 2 shows several typical relative positions of the analytical grating and phase grating and the corresponding moiré fringes. As shown in Figure 2, the left side of each figure in the first row is a schematic diagram of the analysis grating, the right side is the Talbot self-image of the phase grating, and the second row is the Moiré fringe formed by their superposition.

As shown in Figure 3, the present invention discloses a method for identifying moiré fringe images in X-ray grating phase contrast imaging, which includes:

Step 1: Obtain a fringe image, and correct the uneven illumination on the fringe image; wherein, the fringe image can be a moiré fringe, or a general fringe image;

The X-ray light source in the actual experiment is a point light source, so the obtained fringe image must have uneven illumination. Uneven illumination will degrade the image quality, and the display effect will be worse. More importantly, it will affect the accuracy of the subsequent moiré fringe calculation. Therefore, for the acquired original image, the present invention first needs to correct the uneven illumination.

According to the characteristics of the point light source, it can be seen that the brightness of the center of the image is the largest, and the brightness of each pixel is a function of the distance from the pixel point to the pixel point of the illumination center, and the brightness gradually decays to the surroundings, which conforms to the inverse square law of the distance of the irradiance of the point light source and the illumination of the point light source. The inverse square cosine law of the distance in degrees. Aiming at this feature, the present invention proposes a simple and feasible correction method.

The distance inverse square law of the irradiance of the point light source, that is, assuming that the light intensity of the point light source is I _θ , and the distance from the point light source to the irradiation center of the detector is I, then the illuminance of the irradiation center is And the distance inverse square cosine law of the irradiance of the point light source, that is, assuming that the position of the point light source is not perpendicular to the irradiated surface, the light intensity of the point light source is still assumed to be I _θ , the distance from the point light source to the detector plane is I, and the distance between the point light source and the irradiation surface is The angle between the normal direction of the point is θ, then the illuminance of the irradiation position is Based on this, it is assumed that the gray value matrix of the acquired image is A=(a _ij ) _m×n , and the pixel at the center of the illumination is a _pq , we have Here k is the conversion coefficient from illuminance to image gray value, then the gray value of any pixel at any position is

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; k</span>}\frac{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}{{\mathrm{<span\; class="notranslate">\; I</span>}}^{<span\; class="notranslate">\; \&prime;</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; k</span>}\frac{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; COS\&theta;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; k</span>}\frac{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}{{\mathrm{<span\; class="notranslate">\; I</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; cos</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}$

Where I' is the distance from the light source to the current pixel point (i, j) to be corrected, so we can get the gray value a _ij = a _pq ·cos ³ θ of the current pixel point (i, j). Accordingly, for the original gray value a _ij of the pixel on the acquired image, we modify its gray value to a′ _ij = a _ij /cos ³ θ, where And I can be calculated and measured, assuming that the distance between the current pixel point (i, j) to be corrected and the illumination center is i, j are the pixel coordinates of the current pixel point (i, j) on the original image, p, q are the pixel coordinates of the pixel point (p, q) at the illumination center position, that is $a_{\mathrm{ij}}^{\&prime;}=a_{\mathrm{ij}}\&Center\; Dot;{(I^2/(I^2+{(i-p)}^2+{(j-q)}^2))}^{-\frac{3}{2}}.$

Therefore, specify the illumination center coordinates (p, q) in the calculation, measure the distance I from the light source to the sensor, and correct the uneven illumination for the pixel point (i, j) on the image.

Step 2: Filter the moiré fringe image that has been corrected for uneven illumination.

Due to the limitations of the actual environmental conditions, the characteristics of the CCD itself and other factors, the obtained original image inevitably has noise interference. Common noises in CCD images include salt and pepper noise, pulse noise, Gaussian noise, etc. In addition, for the present invention, the image of grating lines is also noise information. Noise information will have a significant impact on subsequent image processing results, so it is necessary to filter the image.

Common image filtering methods include spatial domain filtering and frequency domain filtering. Spatial domain filtering refers to directly processing the pixel grayscale of the image, and filtering is performed according to the grayscale value characteristics of each pixel. Common spatial domain filtering methods include histogram equalization, median filtering, and mean filtering. The spatial domain filtering method is simple and intuitive, but the filtering effect is often not ideal, so the frequency domain filtering method is preferred in the present invention.

The usual method of frequency domain filtering method is: first perform fast Fourier transform on the image, select the frequency domain filter function to filter, and perform inverse Fourier transform on the filtered image to obtain the filtered image, thereby filtering out noise and improving Image Quality.

Moiré fringes will be formed when the phase grating and the analysis grating interfere. Assume that in the X, Y plane, the coordinate point is expressed as (x, y), and the periods of the two gratings are d ₁ and d ₂ respectively. Let the first The grating is the phase grating or the grating line of the analysis grating is parallel to the Y axis, and the second grating is the analysis grating or the grating line of the phase grating is at an angle θ clockwise to the Y axis. Assuming that the gap between the two gratings is zero, the transmission of the first grating The Fourier transform of the passing function is f ₁ (T), and the Fourier transform of the transmission function of the second grating is f ₂ (T). The light intensity distribution of the interference field formed by them in space is:

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</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">\; 01</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 02</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 02</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&times;</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{<span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 01</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&times;</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{<span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; \{</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{<span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; \{</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{<span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>\end{array}$

Among them, x, y are the coordinates of any point on the moiré fringe, T is the Fourier transform period; a ₀₁ , a _n are the Fourier transform coefficients of the transmission function of the first grating, a ₀₂ , a _m are the second The block grating passes through the Fourier transform coefficient of the function. Analysis shows that the first term on the right side of the above equation does not contain the phase factor, which represents the background light, and the second term contains the frequency component It contains the structural information of the first grating, that is, the phase grating, and the third item contains the frequency component It contains the structural information of the second grating, that is, the analysis grating, and the fourth item contains the sum frequency and difference frequency components of the two gratings, which belong to the moiré fringe information. Therefore, the first and fourth items are useful information that we need to keep, and the second and third items need to be filtered out. Of course, the actual image contains more complex noise frequency components, which should be filtered out during the filtering process.

According to the above-analyzed image frequency information characteristics, the present invention adopts a combination filter combining low-pass and band-pass, the low-pass is used to filter out background components, and the band-pass is used to filter out moiré fringe information. Filter type, ideal filter, exponential filter, Butterworth filter, etc. can be selected in the present invention, wherein the form of ideal filter is relatively simple and the effect meets the requirements, so it is the preferred method used in the present invention. That is, the filter function is H(u, v), and there is

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; others</span>}\end{array}\right.$

Where r ₁ is the filtering radius of the low-pass filter, r ₂ is the filtering radius of the band-pass filter, u, v are the coordinates of points on the filtering plane, u ₀ , v ₀ are the center coordinates of the band-pass filter.

Therefore, it is assumed that the Fourier transform of the image information before filtering is F(u, v), and the Fourier transform of the filtered image should be G(u, v)=F(u, v)H(u, v). Inverse Fourier transform to obtain the filtered image.

Step 3: Binarize the filtered original image.

Binarization, as the name implies, is to divide the image into two parts, the region of interest and the region of no interest. In the present invention, the bright lines of the image are regions of interest, and the region of interest is represented by 1 after binarization, while other regions are represented by 0. The image binarization method based on image segmentation theory has been very mature. Now the commonly used method is thresholding segmentation. The thresholding segmentation algorithm mainly has two steps: determine the required segmentation threshold and compare the segmentation threshold with the pixel value to divide the pixel . Threshold segmentation methods include local threshold method, global threshold method, manual threshold method, etc. Among them, determining the appropriate threshold is the key to image segmentation, and there are various threshold extraction methods. Different threshold segmentation methods are suitable for images with different characteristics. The image information to be processed in the present invention is relatively simple, and after preprocessing, the image quality is relatively good, so most threshold segmentation methods are applicable.

Step 4: Thinning the region of interest of the binarized image to extract the initial position information of the moiré fringe in the image.

After the above processing, the image information has been greatly simplified, but the goal of the present invention is to obtain the precise position of the moiré fringes, so it is necessary to further extract the position information of the moiré fringes, that is, image refinement. Image thinning is to extract the backbone information of the image. Taking moiré fringe extraction as an example, it is to obtain the coordinates and angles of the center point of the moiré fringe.

Step 5: Identify the precise position of the moiré fringes according to the extracted initial position information of the moiré fringes.

The initial position information of the fringes extracted through thinning processing has roughly met the accuracy requirements, but in order to further improve the accuracy, the present invention proposes an iterative calculation method based on the gray variance weight to identify the precise position of the moiré fringes. The method is specifically:

Step 51: Obtain the initial position information of the moiré fringe to be identified currently, set its center point as (x ₀ , y ₀ ), its length as l, and its angle as θ ₀ ;

Step 52: Set the number of iterative calculations, calculate the offset angle α and the number of lines n, take (x ₀ , y ₀ ) as the center, and l as the length, and draw n straight lines to the left and right sides with an inclination α;

Step 53: Set the variance of the gray value of the pixels on each straight line as σ ₁ , σ ₂ , σ ₃ , . . . , σ _2n . At the same time, it can be seen from the previous description that the straight line deflection angle β _i corresponding to each straight line is not difficult to calculate, as ${\mathrm{\&beta;}}_1={\mathrm{\&theta;}}_0+\frac{1}{\mathrm{no}}\mathrm{\&alpha;},{\mathrm{\&beta;}}_2={\mathrm{\&theta;}}_0+\frac{2}{\mathrm{no}}\mathrm{\&alpha;},$ And so on.

Step 54: According to the size of the pixel gray variance on each straight line, assign weights to the inclination angles of each straight line $Q_i=1-\frac{{\mathrm{\&sigma;}}_i}{{\mathrm{\&Sigma;}}_{k=1}^{2\mathrm{no}}{\mathrm{\&sigma;}}_k},$ according to the formula

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; )</span>$

The calculated new angle of the current moiré fringe to be identified;

Step 55: Repeat the iterative calculation process from step 52 to step 54 according to the number of iterative calculations set in step 52, and finally obtain the precise position of the moiré fringe to be identified currently. The precise position of the moiré fringe to be identified currently includes the moiré fringe to be identified currently The coordinates and angles of the center point, the coordinates of the center point are still the coordinates of the center point in the initial position information obtained in step 4, and the angle is the angle optimized by steps 51-55.

The precise position information of each moiré fringe can be obtained by repeatedly performing step 5, and the period of the moiré fringe can be obtained according to the coordinates of the center point of each moiré fringe.

Step 6: Judgment of instrument calibration compliance.

For the calculated moiré fringes, their periods are calculated by subtracting the abscissas of adjacent center points based on the center point. According to actual needs, set the allowable error for the angle and period. When the instrument is adjusted to a certain state, if the calculated angle and period have reached the standard, it can be considered that the instrument alignment has been completed.

The identification method of the above-mentioned moiré fringes of the present invention can be realized through LabVIEW programming.

The present invention utilizes LabVIEW to write software, realizes above-mentioned algorithm (note: " vision and movement " module should have been installed on LabVIEW). All image processing processes are based on image grayscale values, so the "IMAQ ImageToArray" function should be used first to convert the image into a two-dimensional matrix of grayscale values.

Image lighting correction part. The distance from the light source to the sensor and the position of the center of the light are input, and the coordinates of the pixel position and the gray value of the pixel are read from the image, which are brought into the formula as described above. $a_{\mathrm{ij}}^{\&prime;}=a_{\mathrm{ij}}\&CenterDot;{(I^2/({I^2+(i-p)}^2+{(j-q)}^2))}^{-\frac{3}{2}},$ The corrected image grayscale matrix can be obtained, and the corrected image can be obtained by using the "IMAQ ArrayToImage" function. In addition, we can use the "surface" function to draw a three-dimensional image of the gray matrix of the image, and observe the correction effect intuitively.

The part of image filtering uses the hybrid programming technology of LabVIEW and MATLAB. Both LabVIEW and MATLAB programming have their own unique advantages. The graphical programming method of LabVIEW allows developers to focus more on the algorithm itself, while the graphics processing toolbox of MATLAB integrates many image processing functions, which brings great advantages to image processing. Great convenience, so combining LabVIEW and MATLAB programming can greatly improve our programming efficiency. The hybrid programming implementation method of LabVIEW and MATLAB is various, and the method adopted in the present invention is to use " MATLAB script " node to call MATLAB in LabVIEW, and it is positioned at " mathematics > script and formula > script node > MATLAB script ", insert this node Then add the input on the left side, add the output on the right side, enter the MATLAB processing code in the node, and it can be used, which is simple and convenient.

Therefore, in the filtering part, we use the MATLAB script node, and the corrected image grayscale matrix uses the "fft2" function in MATLAB to realize fast two-dimensional Fourier transform, and input the filter center coordinates and filter radius from the front panel to complete the filter function Construct. After the image is filtered, use "ifft2" to realize the inverse Fourier transform to obtain the filtered image.

Binarization part. The filtered image is binarized in this part. In this part, we integrate three methods: "local threshold method", "automatic threshold method" and "manual threshold method". The "local threshold method" is implemented using the "IMAQ Local Threshold" function, the "automatic threshold method" is implemented using the "IMAQAutoBThreshold 2" function, and the "manual threshold method" is implemented using the "IMAQ Threshold" function. The specific input parameters are input by the operator according to the needs of each function and the picture status.

Image thinning is actually composed of two parts: thinning and determining the initial position of fringes. The thinning of the image is realized by the "IMAQ Skeleton" function, and the vein of the stripe can be obtained after the fringe image is processed by this function. However, the vein image may have problems such as bending and burrs, and its specific position information cannot be determined, so we then use the "IMAQ Find Straight Edges 2" function to achieve the preliminary determination of the stripe position. This function is originally used to find the straight edge of the image, but we apply it to the thinned image. By setting appropriate parameters, it can realize the function of finding the straight line in the image and returning the position and angle of the straight line, so it can be used for the preliminary determination of the fringe position.

The precise calculation of the stripe position mainly uses the "IMAQ Line Profile" function, which can return the variance of the gray value of the pixels on the line to a specified line on the image. After obtaining the variance, the specific calculation can be realized by programming as described previously.

After the precise position of the fringe is determined, the allowable error of the angle and variance is input on the front panel, and the position of each fringe is compared with the standard to determine whether the angle and period meet the standard, and two Boolean lights are set on the front panel to indicate the angle and period judgment results respectively. Lights up to indicate compliance.

Fig. 4 (a)-(e) shows the automatic identification method and software implementation of the angle and period of Moiré fringes in a kind of X-ray grating phase-contrast imaging alignment process proposed in the embodiment of the present invention, the present invention proposes The above method is also applicable to stripe recognition of any image containing stripes. The specific implementation is divided into five steps to complete.

As shown in step 1 of Figure 4(a), the first step is correction of uneven illumination. First measure the distance from the light source to the detector and input it. Read in the original moiré fringe image, convert it into a three-dimensional grayscale image to observe its grayscale characteristics, set the abscissa and ordinate of the illumination center in turn according to the observed results, run the software, and the uneven illumination of the image can be corrected . The corrected image and its three-dimensional grayscale image are also displayed in the software to help us observe the correction effect. In addition, we can save the current correction settings by clicking the "Save Correction Parameters" button.

As shown in step 2 of Figure 4(b), the second step is image filtering. The image after illumination correction is the input, and the input image is first subjected to two-dimensional fast Fourier transform, and the output transformed frequency domain image is convenient for us to observe the location of the required frequency components. According to the observed image results, determine the abscissa, ordinate, and filter radius of the three filtering points of the filter in turn. After the setting is completed, run the software to output the filtered frequency domain image and its inverse transformation, and you can observe the filtering effect of the image. The parameters Settings can be further fine-tuned. In addition, we can save the current correction settings by clicking the "Save Filter Parameters" button.

As shown in Step 3 of Figure 4(c), the third step is image binarization. Input the filtered image, choose a binarization method. The method we choose here is the Niblack method in the local threshold method. The specific parameters are set as follows: the Niblack deviation coefficient is 0.2, and the calculation window size is 32 pixels by 32 pixels. In actual operation, we can also choose other binarization methods according to the image quality to obtain the best binarization effect.

As shown in Step 4 of Figure 4(d), the fourth step is image refinement. The image after binarization is used as input, and the range that needs to be refined and measured can be delineated in the image. There are many options for straight line search. The "refinement direction" depends on the direction of the stripes. It can be left and right, or up and down. "kernel size" enters the minimum value, and the "number of lines" in the straight line option should be as large as possible to include all Straight line, other parameters can use default values. In actual operation, other parameter settings can also be adjusted as needed to obtain better results. The number of detected streaks is output in the lower right corner of the software interface.

As shown in Step 5 of Figure 4(e), the fifth step is stripe calculation and qualification determination. The line information found in step 4, such as the position information of the stripe center point, the angle and the length of the line segment, etc. are input to this step, and the line calculation is performed on the image obtained after filtering in step 2 according to the line information. The angle and number of scribed lines are input by the software operator. After the calculation is completed, the final striped lines will be displayed in the filtered image in the form of red lines. We output the angle information of each stripe and the period information between each stripe, and display it in the program in the form of a statistical graph for easy observation. We then set the allowable error δ of the angle (the angle is qualified within ± δ°) and the allowable error Δ of the cycle (if the average value of the cycle is cycle If the angle and period of each stripe are qualified, the Boolean indicator light will be lit. Finally, summarize the information of each stripe, and then determine whether the overall angle and period of the system meet the standard. If the standard is met, the Boolean lights are lit, and both lights are on, which means that the system alignment is completed. If not, choose the appropriate one according to the distribution of the stripe angle and period. According to the calibration method, continue to adjust the position of the grating, and repeat the work of each step.

The specific embodiments described above have further described the purpose, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above descriptions are only specific embodiments of the present invention, and are not intended to limit the present invention. Within the spirit and principles of the present invention, any modifications, equivalent replacements, improvements, etc., shall be included in the protection scope of the present invention.

Claims (10)

1. A method for identifying moiré fringes in X-ray grating phase contrast imaging, comprising: Step 1: Correct the uneven illumination of the moiré fringe image to be recognized; Step 2: Filter the moiré fringe image corrected for uneven illumination; Step 3: binarize the filtered moiré fringe image to obtain a binarized image; Step 4: Thinning the binarized image to extract the initial position information of each moiré fringe in the binarized image; Step 5: Identify the precise position of each moiré fringe according to the extracted initial position information of each moiré fringe. 2. The method according to claim 1, wherein, in the step 1, according to the distance inverse square law of the point light source irradiance and the distance inverse square cosine law of the electric light source irradiance, the moiré fringe image is illuminated unevenly fix. 3. The method according to claim 2, wherein the gray value of any position pixel on the moiré fringe image corrected in the step 1 is calculated as follows: $a_{\mathrm{ij}}^{\&prime;}=a_{\mathrm{ij}}\&CenterDot;{(I^2/(I^2+{(i-p)}^2+{(j-q)}^2))}^{-\frac{3}{2}}$ Wherein, a _ij and a' _ij are the pixel gray values before and after correction of any pixel point (i, j) on the moiré fringe image respectively, and I is the distance from the point light source to the irradiation position of the moiré fringe image detector, p and q are the pixel coordinates of the pixel point (p, q) at the illumination center position, respectively. 4. The method according to any one of claims 1-3, wherein step 2 specifically comprises: Step 21: performing fast Fourier transform on the moiré fringe image corrected for uneven illumination; Step 22: selecting a frequency-domain filter function from the result after the fast Fourier transform for filtering; Step 23: Inverse Fourier transform is performed on the frequency-domain filtered image to obtain a filtered moiré fringe image. 5. The method according to claim 4, wherein the frequency domain filtering function adopted in step 22 is represented as follows: $\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; others</span>}\end{array}\right.$ Where r ₁ is the filtering radius of the low-pass filter, r ₂ is the filtering radius of the band-pass filter, u, v are the coordinates of points on the filtering plane, u ₀ , v ₀ are the center coordinates of the band-pass filter. 6. The method according to any one of claims 1-3, 5, wherein step 5 specifically comprises: Step 51: Obtain the initial position information of the moiré fringe to be identified currently, set the center point of the moiré fringe to be identified currently to be (x ₀ , y ₀ ), the length is l, and the angle is θ ₀ ; Step 52: Set the calculation offset angle α and the number of lines n, take (x ₀ , y ₀ ) as the center, l as the length, and draw n straight lines to the left and right sides with an inclination α; Step 53: Assuming that the variance of the pixel points on each straight line is σ ₁ , σ ₂ , σ ₃ , ..., σ _2n , then calculate the straight line declination angle β _i corresponding to each straight line; Step 54: According to the size of the pixel gray variance on each straight line, assign weights to the inclination angles of each straight line and according to the formula ${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; )</span>$ The calculated new angle of the current moiré fringe to be identified; Step 55: Repeat the iterative calculation process from step 52 to step 54 according to the number of iterative calculations set in step 52, and finally obtain the precise position of the current moiré fringe to be identified. 7. The method according to claim 1, wherein the precise position of the moiré fringe to be identified currently in step 5 comprises a center point and an angle of the moiré fringe to be identified currently. 8. The method of claim 7, wherein the method further comprises: Step 6: According to the calculated angle of each moiré fringe and the period of the moiré fringe, it is judged whether the calibration standard of the instrument is met. 9. An identification device for moiré fringes in X-ray grating phase contrast imaging, comprising: Correction module: Correct the uneven illumination of the moiré fringe image to be recognized; Filtering module: filter the moiré fringe image after uneven illumination correction; Binarization module: binarize the filtered moiré fringe image to obtain a binarized image; Thinning module: thinning the binarized image to extract the initial position information of each moiré fringe in the binarized image; Identification module: identify the precise position of each moiré fringe according to the extracted initial position information of each moiré fringe. 10. The apparatus of claim 9, wherein the identification module identifies the precise location of each moiré fringe as follows: Firstly, the initial position information of the moiré fringe to be identified is obtained, and the center point of the moiré fringe to be identified is (x ₀ , y ₀ ), the length is l, and the angle is θ ₀ ; Set the number of iterative calculations, calculate the offset angle α and the number of lines n, take (x ₀ , y ₀ ) as the center, l as the length, and draw n straight lines inclined to the left and right sides α; set the pixel points on each straight line The variance is σ ₁ , σ ₂ , σ ₃ ,..., σ _2n in turn, then calculate the straight line declination angle β _i corresponding to each straight line; According to the size of the gray variance of the pixels on each straight line, assign weights to the inclination angles of each straight line $Q_i=1-\frac{{\mathrm{\&sigma;}}_i}{{\mathrm{\&Sigma;}}_{k=1}^{2\mathrm{no}}{\mathrm{\&sigma;}}_k},$ and according to the formula ${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; )</span>$ The calculated new angle of the current moiré fringe to be identified; According to the number of iterative calculations set above, the above iterative calculation process is repeated, and finally the precise position of the moiré fringe to be identified is finally obtained.