A method for constructing sub-pixel point-selected Fourier spectrum reference data

Abstract

The present invention proposes a method for constructing sub-pixel point-selected Fourier spectrum reference data, which can be incorporated into experimental methods utilizing Fourier transforms or windowed Fourier transforms. It represents an extension and expansion of the Fourier transform, offering advantages such as simplicity, convenience, and precise reference data construction. While the method is difficult to apply to three-dimensional calculations in the field of optics due to the lack of access to three-dimensional Fourier transform maps, its application in two-dimensional space remains unaffected. This invention represents a new enrichment of the Fourier transform and can facilitate the construction of standard reference data in the field of optomechanics.

Description

Technical Field

[0001] The present invention relates to a method for constructing sub-pixel point-selected Fourier spectrum reference data, and in particular to a method for constructing reference data using a sub-pixel maximum point in a selected Fourier transform spectrum diffraction point area as a reference spectrum, and belongs to the field of photomechanics. Background Art

[0002] As a method that can convert data information from the time domain to the frequency domain, the Fourier transform can represent the infinite superposition of sinusoidal signals of different frequencies. It has simple methods and clear results, and is widely used in fields such as photometry, signal processing, probability statistics, and mathematics. However, since the one-dimensional Fourier transform cannot reflect the changes in frequency over time in the spectrum, and the two-dimensional and three-dimensional Fourier transforms cannot reflect the changes in frequency over length and direction (i.e., time or time domain), the windowed Fourier transform was later developed. The windowed Fourier transform adds a window to the Fourier transform to simultaneously reflect information in the frequency and time domains.

[0003] In the field of photomechanics, the fringe shape corresponding to the diffraction point at the window can be obtained by using a windowed Fourier transform, such as the geometric phase analysis method. In the application process, the fundamental frequency can also be used to generate corresponding reference data to obtain the corresponding deformation information. However, there are many other uses for the fundamental frequency. However, in actual applications, due to the discrete effects of pixels and space, when selecting the fundamental frequency, the actual fundamental frequency cannot be selected, but the maximum point after the actual fundamental frequency is discretized by pixels and space. Therefore, a method for constructing sub-pixel point-selected Fourier spectrum reference data has been developed. This method can directly construct reference data based on the fundamental frequency in the Fourier transform window, thereby facilitating data processing. This method is of great significance for constructing reference data, calculating deformation, etc. Summary of the Invention

[0004] The purpose of the present invention is to propose a method for constructing sub-pixel point-selected Fourier spectrum reference data. The value obtained after Fourier transform represents the content of the wave at that frequency in the input signal. In this patent, this feature of Fourier transform is fully utilized. This patent considers the point with the largest Fourier transform value as the fundamental frequency of the data in the input Fourier transform, and the points with relatively small Fourier transform values ​​around it as deformation information relative to the fundamental frequency. The existing method of measuring deformation or constructing reference data using Fourier transform or windowed Fourier transform is improved, and the properties in the two-dimensional Fourier transform space are used to extend it to the three-dimensional Fourier transform space, while simplifying the operations in the two-dimensional space process.

[0005] The method for constructing sub-pixel point-selected Fourier spectrum reference data proposed in the present invention includes the following steps:

[0006] (1) Perform Fourier transform on data that requires fundamental frequency as a reference;

[0007] (2) Select the corresponding diffraction point on the image obtained by Fourier transform, that is, add window;

[0008] (3) Find the maximum value of the sub-pixel level corresponding to the diffraction point in the window and obtain its corresponding coordinate value;

[0009] (4) Substitute the coordinate value corresponding to the maximum value of the diffraction point for the point-shaped windowed inverse Fourier transform to obtain the fundamental frequency reference data;

[0010] (5) According to the above method, the baseband reference data can be obtained using the following formula: That is, point-wise windowed inverse Fourier transform:

[0011] 1) Two-dimensional point-wise windowed inverse Fourier transform

[0012]

[0013]

[0014] 2) 3D point-wise windowed inverse Fourier transform

[0015]

[0016]

[0017] Where Q(ξ,η) and Q(ξ,η,χ) are Fourier transforms of the image, Q(μ c ,v c )and It is the maximum value point at the sub-pixel level in the Fourier transform diffraction point of the selected area. is the coordinate value corresponding to the maximum value point at the sub-pixel level in the selected Fourier transform diffraction point, and It is the data of the point-wise windowed inverse Fourier transform of the maximum value point at the sub-pixel level.

[0018] The present invention proposes a method for constructing sub-pixel point-selected Fourier spectrum reference data, which can be incorporated into experimental methods utilizing Fourier transforms or windowed Fourier transforms. It represents an extension and expansion of the Fourier transform, offering advantages such as simplicity, convenience, and precise reference data construction. While the method is difficult to apply to three-dimensional calculations in the field of optics due to the lack of access to three-dimensional Fourier transform maps, its application in two-dimensional space remains unaffected. This invention represents a new enrichment of the Fourier transform and can facilitate the construction of standard reference data in the field of optomechanics. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 The present invention is a flowchart of a method for constructing sub-pixel point-selected Fourier spectrum reference data.

[0020] Figure 2 This is a practical flow chart of applying the method of the present invention to the geometric phase method in Example 1.

[0021] Figure 3 In Example 1, the geometric phase method is used to calculate the strain map in an application scenario using the method of the present invention.

[0022] Figure 4 This is an actual strain diagram obtained by applying the method of the present invention to an application scenario in Example 1 using the geometric phase method.

[0023] Figure 5 This is a practical flow chart of the application of the method of the present invention to the moiré inversion method in Example 2.

[0024] Figure 6 In Example 2, the moiré inversion method uses the method of the present invention to calculate the reference grid line lattice fringe pattern in an application scenario.

[0025] Figure 7 This is a reference lattice line diagram calculated by the moiré inversion method in Example 2 using the method of the present invention in an application scenario. DETAILED DESCRIPTION

[0026] The present invention proposes a method for constructing sub-pixel point-selected Fourier spectrum reference data, comprising the following steps:

[0027] (1) Perform Fourier transform on data that requires fundamental frequency as a reference;

[0028] (2) Select the corresponding diffraction point on the image obtained by Fourier transform, that is, add window;

[0029] (3) Find the maximum value of the sub-pixel level corresponding to the diffraction point in the window and obtain its corresponding coordinate value;

[0030] (4) Substitute the coordinate value corresponding to the maximum value of the diffraction point for the point-shaped windowed inverse Fourier transform to obtain the fundamental frequency reference data;

[0031] (5) According to the above method, the baseband reference data can be obtained using the following formula: That is, point-wise windowed inverse Fourier transform:

[0032] 1) Two-dimensional point-wise windowed inverse Fourier transform

[0033]

[0034]

[0035] 2) 3D point-wise windowed inverse Fourier transform

[0036]

[0037]

[0038] Where Q(ξ,η) and Q(ξ,η,χ) are Fourier transforms of the image, Q(μ c ,v c )and It is the maximum value point at the sub-pixel level in the Fourier transform diffraction point of the selected area. is the coordinate value corresponding to the maximum value point at the sub-pixel level in the selected Fourier transform diffraction point, and It is the data of the point-wise windowed inverse Fourier transform of the maximum value point at the sub-pixel level.

[0039] The specific embodiments of the present invention will now be further described.

[0040] In one embodiment of the method of the present invention, when analyzing deformation using the geometric phase analysis method, it is necessary to obtain a deformation phase and a reference phase, wherein the reference phase can be obtained using the method of the present invention. During the geometric phase analysis process, a Fourier transform diffraction point containing deformation phase information is selected, and then a windowed inverse Fourier transform is performed on the diffraction point, and the deformation phase is obtained through unwrapping. Simultaneously, a point-wise windowed inverse Fourier transform is performed on the diffraction point containing deformation phase information, and the fundamental frequency reference phase is obtained through unwrapping. Actual calculations show that using the method of the present invention, the root mean square error of the geometric phase analysis method can be controlled within the range of ±0.001.

[0041] In another embodiment of the present invention, when analyzing moire using the moire inversion method, moire lines and reference lines are required, wherein the reference lines can be obtained using the method of the present invention. During the moire inversion analysis process, Fourier transform diffraction points containing reference line information are selected, and a point-wise windowed inverse Fourier transform is performed on the diffraction points containing deformation information to obtain reference line lattice fringes, which are then post-processed to obtain the reference lines.

Claims

1. A method for constructing sub-pixel level point-selected Fourier spectrum reference data, characterized in that The method comprises the following steps: (1) Perform Fourier transform on data that requires fundamental frequency as a reference; (2) Select the corresponding diffraction point on the image obtained by Fourier transform, that is, add window; (3) Find the maximum value of the sub-pixel level corresponding to the diffraction point in the window and obtain its corresponding coordinate value; (4) Substitute the coordinate value corresponding to the maximum value of the diffraction point into the point-shaped windowed inverse Fourier transform to obtain the fundamental frequency reference data; (5) According to the above method, the baseband reference data can be obtained using the following formula: That is, point-wise windowed inverse Fourier transform: 1) Two-dimensional point-wise windowed inverse Fourier transform 2) 3D point-wise windowed inverse Fourier transform Where Q(ξ,η) and Q(ξ,η,χ) are Fourier transforms of the image, Q(μ c ,v c )and is the maximum value point at the sub-pixel level in the Fourier transform diffraction point of the selected area, μ c ,v c , is the coordinate value corresponding to the maximum value point at the sub-pixel level in the selected Fourier transform diffraction point, and It is the data of the point-wise windowed inverse Fourier transform of the maximum value point at the sub-pixel level.

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