1. A moire fringe information extraction method based on wavelet transformation is characterized by comprising the following steps:

step 1: preprocessing the intensity of a moire fringe light field under the primary filtering, and deducing an expression of a moire fringe phase;

step 2: the Gabor wavelet transform is applied to the intensity of the Moire fringe, and the Gabor wavelet can be regarded as a filter with the center frequency of (u, v) due to the filtering characteristic of the Gabor wavelet;

and step 3: according to a moire fringe light intensity expression, a Gabor wavelet filter with the center frequency of (0, f) is selected to filter a moire fringe image, and the output result is in a complex form;

and 4, step 4: respectively convolving the moire fringe light intensity by using the real part and the imaginary part of the Gabor wavelet function to obtain the main amplitude angle of the output result in the step 3; combining the moire fringe phase in the step 1 with the main amplitude angle expression output by filtering in the step to obtain the moire fringe phase extracted by the Gabor wavelet transform method;

and 5: and (4) performing phase unwrapping on the moire fringe phase obtained in the step (4) by using a multiple grid method.

2. The wavelet transform-based moire fringe information extraction method as claimed in claim 1, wherein step 1 specifically comprises: the intensity of the moire fringe light field under the first-order filtering is as follows:

wherein, x and y are respectively the displacement of each point on the moire fringe pattern from the x direction and the y direction of the image center; alpha is grating G₁And G₂The included angle of the grid line direction; a is₀、a₁Respectively at grating G under kirchhoff boundary conditions₁Coefficients of a first term and a second term of an expression of the order form of the complex amplitude of the light wave of the rear surface; d is a grating constant, and the grating coefficients of the two gratings are the same; phi (x, y) is the moire fringe phase caused by the measured field disturbance;

the moire fringe phase under the first-order filtering is preprocessed, and equation (1) can be expressed as follows after removing the direct-current component:

1 in the formula (2)Obtaining:

I(x,y)＝2a₀ ²a₁ ²cos[fy+φ(x,y)]. (3)

furthermore, equation (3) can be written as:

I(x,y)＝2a₀ ²a₁ ²[c(x,y)cos(fy)+s(x,y)sin(fy)], (4)

wherein the content of the first and second substances,

c²(x,y)+s²(x,y)＝1, (5)

c (x, y), s (x, y) are intermediate quantities set for the convenience of deriving the phase expression.

Obtaining a mathematically preprocessed moire fringe phase:

。

3. the wavelet transform-based moire fringe information extraction method as claimed in claim 1, wherein step 2 specifically comprises: the gabor wavelet transform is applied to the intensity of the moire fringes, and can be expressed as:

G_uv[I(x,y)]＝h_uv(x,y)*I(x,y), (7)

wherein the symbol denotes a convolution operation, h_uv(x, y) represents a two-dimensional Gabor wavelet function, h due to the nature of the Gabor wavelet transform_uv(x, y) can be regarded as a grating with an amplitude of a gaussian line and an equal phase plane as a plane, namely a band-pass filter with a center frequency tuned to (u, v), and the specific expression is as follows:

h_uv(x,y)＝g(x,y)exp[2πj(ux+vy)], (8)

wherein u and v are coefficients defined by a two-dimensional gabor wavelet function, g (x, y) is a two-dimensional gaussian function, σ is a scale function, and λ is the incident laser wavelength.

4. The wavelet transform-based moire fringe information extraction method as claimed in claim 1, wherein step 3 specifically comprises: filtering the moire fringe image by using a gabor wavelet filter with the center frequency of (0, f) to obtain a filtering output:

G_(0,f)[I(x,y)]＝k_r(x,y)+jk_i(x,y), (10)

wherein k is_r(x, y) and k_i(x, y) are the real and imaginary parts of the filtered output, respectively.

5. The wavelet transform-based moire fringe information extraction method as claimed in claim 1, wherein step 4 specifically comprises: convolving the moire fringe intensity with the real part and the imaginary part of the gabor wavelet function, respectively, to obtain the real part and the imaginary part of the filtering output in equation (10), respectively:

wherein h is_rIs the real part of the Gabor wavelet function, h_iIs the imaginary part of the gabor wavelet function;

since phi (x, y) has the characteristics of low frequency, narrow band, etc., as long as the spatial scale selected for g (x, y) is small enough and the bandwidth of g (x, y) is wide enough to contain phi (x, y), within this spatial scale, phi (x, y) can be considered as a constant, so we can obtain:

finally, the main argument of the filtering output after gabor wavelet transform is:

combining equation (6), we can get the moire fringe phase phi (x, y) under the first-order filtering:

6. the wavelet transform-based moire fringe information extraction method as claimed in claim 1, wherein step 5 specifically comprises: and performing phase unwrapping on the extracted moire fringe phase by adopting a multiple grid method based on a least square (LMS) phase estimation algorithm.

Background

Moire chromatographic technique is a branch of optical computer chromatographic technique, has the advantages of real-time, stability and non-contact, etc., and has wide application in the aspect of flow field detection. When the moire chromatography technology is used for measuring key parameters of a high-temperature complex flow field, in order to ensure the measurement accuracy, the accuracy of extracting fringe phase information needs to be ensured as much as possible. Up to now, it is more common to extract moire phase information by fourier transform in actual measurement. Therefore, finding a simpler and more accurate fringe phase information extraction method has important significance for the application of the moire chromatography technology in the field of flow field measurement.

Disclosure of Invention

Aiming at the defects in the prior art, the invention provides a high-precision and easy-to-implement wavelet transform-based moire fringe phase information extraction method, so as to be used for refractive index reconstruction and key parameter measurement of a further measured flow field.

In order to achieve the purpose, the invention adopts the following technical scheme:

a moire fringe information extraction method based on wavelet transformation comprises the following steps:

step 1: preprocessing the intensity of a moire fringe light field under the primary filtering, and deducing an expression of a moire fringe phase;

step 2: the Gabor wavelet transform is applied to the intensity of the Moire fringe, and the Gabor wavelet can be regarded as a filter with the center frequency of (u, v) due to the filtering characteristic of the Gabor wavelet;

and step 3: according to a moire fringe light intensity expression, a Gabor wavelet filter with the center frequency of (0, f) is selected to filter a moire fringe image, and the output result is in a complex form;

and 4, step 4: respectively convolving the moire fringe light intensity by using the real part and the imaginary part of the Gabor wavelet function to obtain the main amplitude angle of the output result in the step 3; combining the moire fringe phase in the step 1 with the main amplitude angle expression output by filtering in the step to obtain the moire fringe phase extracted by the Gabor wavelet transform method;

and 5: and (4) performing phase unwrapping on the moire fringe phase obtained in the step (4) by using a multiple grid method.

Further, step 1 specifically comprises: the intensity of the moire fringe light field under the first-order filtering is as follows:

wherein, x and y are respectively the displacement of each point on the moire fringe pattern from the x direction and the y direction of the image center; alpha is grating G₁And G₂The included angle of the grid line direction; a is₀、a₁Respectively at grating G under kirchhoff boundary conditions₁Coefficients of a first term and a second term of an expression of the order form of the complex amplitude of the light wave of the rear surface; d is a grating constant, and the grating coefficients of the two gratings are the same; phi (x, y) is the moire fringe phase caused by the measured field disturbance;

the moire fringe phase under the first-order filtering is preprocessed, and equation (1) can be expressed as follows after removing the direct-current component:

1 in the formula (2)Obtaining:

I(x,y)＝2a₀ ²a₁ ²cos[fy+φ(x,y)]. (3)

furthermore, equation (3) can be written as:

I(x,y)＝2a₀ ²a₁ ²[c(x,y)cos(fy)+s(x,y)sin(fy)], (4)

wherein the content of the first and second substances,

c²(x,y)+s²(x,y)＝1, (5)

c (x, y), s (x, y) are intermediate quantities set for the convenience of deriving the phase expression.

Obtaining a mathematically preprocessed moire fringe phase:

further, step 2 specifically comprises: the gabor wavelet transform is applied to the intensity of the moire fringes, and can be expressed as:

G_uv[I(x,y)]＝h_uv(x,y)*I(x,y), (7)

wherein the symbol denotes a convolution operation, h_uv(x, y) represents a two-dimensional Gabor wavelet function, h due to the nature of the Gabor wavelet transform_uv(x, y) can be regarded as a grating with an amplitude of a gaussian line and an equal phase plane as a plane, namely a band-pass filter with a center frequency tuned to (u, v), and the specific expression is as follows:

h_uv(x,y)＝g(x,y)exp[2πj(ux+vy)], (8)

wherein u and v are coefficients defined by a two-dimensional gabor wavelet function, g (x, y) is a two-dimensional gaussian function, σ is a scale function, and λ is the incident laser wavelength.

Further, step 3 specifically comprises: filtering the moire fringe image by using a gabor wavelet filter with the center frequency of (0, f) to obtain a filtering output:

G_(0,f)[I(x,y)]＝k_r(x,y)+jk_i(x,y), (10)

wherein k is_r(x, y) and k_i(x, y) are the real and imaginary parts of the filtered output, respectively.

Further, step 4 specifically includes: convolving the moire fringe intensity with the real part and the imaginary part of the gabor wavelet function, respectively, to obtain the real part and the imaginary part of the filtering output in equation (10), respectively:

wherein h is_rIs the real part of the Gabor wavelet function, h_iIs the imaginary part of the gabor wavelet function;

since phi (x, y) has the characteristics of low frequency, narrow band, etc., as long as the spatial scale selected for g (x, y) is small enough and the bandwidth of g (x, y) is wide enough to contain phi (x, y), within this spatial scale, phi (x, y) can be considered as a constant, so we can obtain:

finally, the main argument of the filtering output after gabor wavelet transform is:

combining equation (6), we can get the moire fringe phase phi (x, y) under the first-order filtering:

further, step 5 specifically comprises: and performing phase unwrapping on the extracted moire fringe phase by adopting a multiple grid method based on a least square (LMS) phase estimation algorithm.

The invention has the beneficial effects that: the invention provides a moire fringe information extraction method based on wavelet transformation, wherein moire fringe phase information extracted based on Gabor wavelet transformation is smoother on the whole, the number of noise points can be effectively reduced, the outline is clearer, the accuracy is high, and the operation is simple and convenient.

Drawings

FIG. 1 is an optical path setup of a Moire polarization analyzer, in which 1-laser; 2-the first lens, 3-the second lens, 2 and 3 jointly form a beam expanding collimation system; 4-field to be measured; 5-a first Ronchi grating and 6-a second Ronchi grating; 7-a first imaging lens, 8-a filter, 9-a second imaging lens, and 10-a receiving screen;

FIG. 2(a) shows moire fringes before being heated by an electric soldering iron, and FIG. 2(b) shows moire fringes after being heated by an electric soldering iron;

fig. 3(a) is a phase diagram of a flow field of the heating electric iron extracted by gabor wavelet transform, and fig. 3(b) is a phase diagram of a flow field of the heating electric iron extracted by fourier transform;

FIG. 4(a) shows moire fringes before candle ignition, and FIG. 4(b) shows moire fringes after candle ignition;

fig. 5(a) is a phase diagram of a flow field of a burning candle extracted by gabor wavelet transform, and fig. 5(b) is a phase diagram of a flow field of a burning candle extracted by fourier transform.

Detailed Description

The present invention will now be described in further detail with reference to the accompanying drawings.

As shown in figure 1, the experimental device of the invention comprises a laser 1, a field to be measured 4, a first Ronchi grating 5 and a second Ronchi grating 6, namely G, which are sequentially arranged and are composed of a beam expanding collimation system 2 and a beam expanding collimation system 3₁，G₂The first imaging lens 7, the filter 8 and the second imaging lens 9 present a moire fringe deflection pattern on the receiving screen 10, the grating constant is d, the grating coefficients of the two gratings are the same, the grating pitch is Δ, and Δ should satisfy the talbot distance for obtaining better fringe contrast, that is, Δ ═ jd²The grid line directions of the two gratings respectively form included angles of + alpha/2 and-alpha/2 with the y axis, and alpha is a grating G₁And G₂Included angle of grid line direction of slave grating G₂Is a typical 4-f system to the receiving screen 10. The moire fringes of the measured flow field can be obtained by the device of fig. 1, and are acquired by a Charge Coupled Device (CCD) and transmitted to a computer for phase information extraction. Two types of typical measured flow fields are selected for experiments, and the feasibility and the superiority of the phase information extraction method are proved.

A moire fringe information extraction method based on wavelet transformation comprises the following steps:

step 1: preprocessing the intensity of a moire fringe light field under the primary filtering, and deducing an expression of a moire fringe phase, which specifically comprises the following steps:

the intensity of the moire fringe light field under the first-order filtering is as follows:

wherein, x and y are respectively the displacement of each point on the moire fringe pattern from the x direction and the y direction of the image center; a is₀、a₁Respectively at grating G under kirchhoff boundary conditions₁Coefficients of a first term and a second term of an expression of the order form of the complex amplitude of the light wave of the rear surface; phi (x, y) is the moire fringe phase caused by the measured field disturbance;

the moire fringe phase under the first-order filtering is preprocessed, and equation (1) can be expressed as follows after removing the direct-current component:

1 in the formula (2)Obtaining:

I(x,y)＝2a₀ ²a₁ ²cos[fy+φ(x,y)]. (3)

furthermore, equation (3) can be written as:

I(x,y)＝2a₀ ²a₁ ²[c(x,y)cos(fy)+s(x,y)sin(fy)], (4)

wherein the content of the first and second substances,

c²(x,y)+s²(x,y)＝1, (5)

c (x, y), s (x, y) are intermediate quantities set for the convenience of deriving the phase expression.

Obtaining a mathematically preprocessed moire fringe phase:

step 2: the gabor wavelet transform is applied to the moire fringe light intensity, and due to the filtering characteristics of the gabor wavelet, the gabor wavelet can be regarded as a filter with the center frequency (u, v), which specifically comprises the following steps: the gabor wavelet transform is applied to the intensity of the moire fringes, and can be expressed as:

G_uv[I(x,y)]＝h_uv(x,y)*I(x,y), (7)

wherein the symbol denotes a convolution operation, h_uv(x, y) represents a two-dimensional Gabor wavelet function, h due to the nature of the Gabor wavelet transform_uv(x, y) can be regarded as a grating with an amplitude of a gaussian line and an equal phase plane as a plane, namely a band-pass filter with a center frequency tuned to (u, v), and the specific expression is as follows:

h_uv(x,y)＝g(x,y)exp[2πj(ux+vy)], (8)

wherein u and v are coefficients defined by a two-dimensional gabor wavelet function, g (x, y) is a two-dimensional gaussian function, σ is a scale function, and λ is the incident laser wavelength.

And step 3: according to a moire fringe light intensity expression, a Gabor wavelet filter with the center frequency of (0, f) is selected to filter a moire fringe image, and the output result is in a complex form, specifically:

filtering the moire fringe image by using a gabor wavelet filter with the center frequency of (0, f) to obtain a filtering output:

G_(0,f)[I(x,y)]＝k_r(x,y)+jk_i(x,y), (10)

wherein k is_r(x, y) and k_i(x, y) are the real and imaginary parts of the filtered output, respectively.

And 4, step 4: respectively convolving the moire fringe light intensity by using the real part and the imaginary part of the Gabor wavelet function to obtain the main amplitude angle of the output result in the step 3; combining the moire fringe phase in the step 1 with the main argument expression output by filtering in the step to obtain the moire fringe phase extracted by the gabor wavelet transform method, which specifically comprises the following steps:

convolving the moire fringe intensity with the real part and the imaginary part of the gabor wavelet function, respectively, to obtain the real part and the imaginary part of the filtering output in equation (10), respectively:

wherein h is_rIs the real part of the Gabor wavelet function, h_iIs the imaginary part of the gabor wavelet function;

since phi (x, y) has the characteristics of low frequency, narrow band, etc., as long as the spatial scale selected for g (x, y) is small enough and the bandwidth of g (x, y) is wide enough to contain phi (x, y), within this spatial scale, phi (x, y) can be considered as a constant, so we can obtain:

finally, the main argument of the filtering output after gabor wavelet transform is:

combining equation (6), we can get the moire fringe phase phi (x, y) under the first-order filtering:

and 5: and (4) performing phase unwrapping on the moire fringe phase extracted in the step (4) by adopting a multiple grid method based on a least square (LMS) phase estimation algorithm.

As shown in fig. 2(a) and 2(b), the moire fringes appear when the electric soldering iron is not heated, and the moire fringes are bent after the electric soldering iron is heated; as shown in fig. 4(a) and 4(b), the candle exhibits moire fringes when unlit, and the moire fringes bend after the candle is lit.

The results of extracting moire fringe phase information for two typical flow fields, the electric soldering iron and the candle burning field, are shown in fig. 3 and 5. In order to see the advantages of the Gabor wavelet transform in phase information extraction, results under the condition that more Fourier transforms are used are given for comparison. As can be seen, the moire fringe phase information extracted based on the Gabor wavelet transform is smoother on the whole, the number of noise points is effectively reduced, and the outline is clearer. The results of extracting moire fringe phase information for two typical flow fields, electric soldering iron and candle burning field, using gabor wavelet transform are shown in fig. 3(a) and fig. 5 (a). In order to see the advantages of the gabor wavelet transform in the phase information extraction and simultaneously give the results under the existing more Fourier transform, the moire fringe phase information extracted based on the gabor wavelet transform is smoother as a whole, the number of noise points is effectively reduced, and the outline is clearer as compared with the moire fringe phase information extracted based on the gabor wavelet transform in fig. 3(b) and fig. 5 (b)).

The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.