CN108279069B - A kind of optical phase difference demodulation method based on spiral shape interference image Feature Extraction Technology - Google Patents

Abstract

The invention provides an optical phase difference demodulation method based on the feature extraction technology of helical interference image, which can demodulate the optical phase difference between two light beams. Including: acquiring the spiral interference image formed by the interference of the orbital angular momentum beam and the Gaussian beam; extracting the common feature image, which is used to analyze a series of spiral interference images corresponding to different optical phase differences to obtain their common feature image; feature demodulation , map the spiral interference image to the two-dimensional space with the common feature image as the base vector, obtain the coordinate value of the spiral interference image in the two-dimensional space, and realize the data dimension reduction of the spiral interference image; optical phase difference calculation, Optical phase difference is calculated using coordinate values in two-dimensional space. The spiral interference image of the present invention is convenient for feature extraction, and by reducing the dimension of the data of the spiral interference image, the efficiency of signal demodulation is improved, and the influence of beam power fluctuation on the optical phase difference demodulation result can be effectively avoided.

Description

An Optical Phase Difference Demodulation Based on Spiral Interference Image Feature Extraction Technology method

technical field

The invention relates to the field of applied optics, in particular to an optical phase difference demodulation method based on a feature extraction technology of helical interference images.

Background technique

With the increasing demand for information, optical detection technology has received extensive attention due to its high-precision measurement performance. Optical interferometer is an optical detection instrument that uses the interference effect of light to obtain the physical quantity to be measured. Optical interferometer is used in many precision measurement fields such as astronomy, optics, engineering measurement, oceanography, seismology, spectral analysis, quantum physics, etc. widely used. Signal demodulation methods commonly used in optical interferometers include intensity demodulation and wavelength demodulation. In comparison, the intensity demodulation method is more intuitive, its structure is simple and the cost is low, but the intensity demodulation is easily affected by the fluctuation of the light source power, which causes deviations in the measurement results. Wavelength demodulation realizes the demodulation of the sensing signal by changing the position of the characteristic wavelength in the reflection or transmission spectrum. The position of the characteristic wavelength depends on the modulation effect of the parameter to be measured on the characteristics of the sensing structure, and the fluctuation of the light source power only affects the absolute intensity of the spectrum. without affecting the relative intensity distribution. This method can exclude the influence of light source power fluctuations. However, in the spectrum measurement, the spectrum analyzer is indispensable. At present, the spectrometer is large and expensive.

SUMMARY OF THE INVENTION

According to the technical problem proposed above, an optical phase difference demodulation method of an optical interferometer with simple structure, high demodulation efficiency and convenient feature extraction is provided. The invention mainly utilizes the image feature extraction technology, extracts common feature images by processing a series of spiral interference images, uses the extracted common feature images to transform the spiral interference images that need to be analyzed, and maps the spiral interference images to common feature images. The feature image is a two-dimensional space of base vectors, and the optical phase difference is calculated by using the coordinate values in the low-dimensional space to realize optical phase difference demodulation.

The technical means adopted in the present invention are as follows:

An optical phase difference demodulation method based on a feature extraction technology of a spiral interference image, comprising: a step of acquiring a spiral interference image and a step of extracting a feature of the spiral interference image,

The step of acquiring the helical interference image refers to: the helical interference image is formed by the interference of the orbital angular momentum beam and the Gaussian beam, and there are helical interference fringes in the helical interference pattern, wherein,

the helical interference image changes with an optical phase difference between the two beams, the optical phase difference being the optical phase difference between the orbital angular momentum beam and the Gaussian beam;

The step of extracting the features of the spiral interference image refers to the steps of extracting a common feature image, feature demodulation and optical phase difference calculation;

The step of extracting the common feature image is to extract common feature images of a series of spiral interference images corresponding to different optical phase differences;

The step of feature demodulation is to map the spiral interference image to the two-dimensional space with the common feature image as the base vector, and to obtain the coordinate value of the spiral interference image in the two-dimensional space, which is used to represent the spiral interference image. Characteristics;

The step of calculating the optical phase difference is to use the coordinate values in the two-dimensional space to calculate the optical phase difference, so as to realize the demodulation of the optical phase difference.

Further, the topological charge of the orbital angular momentum beam is +1 or -1.

Further, the topological charge number of the Gaussian beam is 0, and the light intensity distribution of the Gaussian beam along the radial direction satisfies a Gaussian function.

The extracting common feature images includes the following steps:

S401: Rearrange the spiral-shaped interference image matrix into a column vector, where the size of the spiral-shaped interference image matrix is N×N, and can be expressed in the following form:

Among them, each element in the matrix represents the gray value of the corresponding image pixel,

The column vector size is N ² ×1, and can be expressed in the following form:

Ψ _m represents the one-dimensional column vector corresponding to a pair of interference images;

S402: Rearrange M spiral interference images corresponding to different optical phase differences into M one-dimensional column vectors according to the method in S401, which are respectively represented as Ψ ₁ , Ψ ₂ ,...Ψ _M , and calculate M one-dimensional column vectors by the following formula Average vector of dimension column vectors:

The data matrix Φ is calculated by the following formula:

S403: Calculate the covariance matrix C=Φ ^T Φ of the data matrix described in S402;

S404: Calculate the eigenvalues of the covariance matrix and the eigenvectors of the covariance matrix described in S403;

S405: Select the eigenvalues of the two largest covariance matrices and their corresponding eigenvectors V ₁ , V ₂ of the two covariance matrices from the eigenvalues of the covariance matrix and the eigenvectors of the covariance matrix;

S406: Calculate the common feature images U ₁ and U ₂ by using the following formulas to calculate the eigenvectors V ₁ , V ₂ of the two covariance matrices described in S405 and the data matrix Φ described in S402:

[U ₁ U ₂ ]=Φ×[V ₁ V ₂ ].

Further, the feature demodulation includes the following steps:

S501: Rearrange a pair of helical interference images that need to be demodulated by optical phase difference into column vectors according to the method in S401, and represent the rearrangement into column vectors as Ψ _i , and the need to perform optical phase difference A pair of helical interference images for differential demodulation may be one of the M spiral interference images corresponding to different optical phase differences described in S402, or may be obtained under the same conditions of the same size. Another spiral interference image of , the size of the spiral interference image matrix is N×N, rearranged into a column vector Ψ _i of size N ² × 1;

S502: subtract the average vector described in S402 from the Ψ _i , and express the obtained result as Φ _i , so the described

S503: The Φ _i is mapped to a two-dimensional space with the common feature images U ₁ and U ₂ as base vectors, and the coordinate value Ω _i of Φ _i in the two-dimensional space is calculated by the following formula, Ω _i =[ω ₁ ω ₂ ] ^T :

Further, the optical phase difference calculation includes the following steps:

S601: Convert the coordinate value Ω _i in S503 into the coordinate value [ω _r ω _θ ] in the cylindrical coordinate system by the following formula:

Among them, ω _r is the radial coordinate value of the coordinate value Ω _i , and ω _θ is the angular coordinate value of the coordinate value Ω _i .

S602: Calculate the optical phase difference φ between the orbital angular momentum beam and the Gaussian beam by the following formula:

φ=π/2-ω _θ .

The present invention has the following advantages:

1. The present invention introduces an orbital angular momentum beam and interferes with the Gaussian beam to obtain a spiral interference image with obvious features, which is convenient for feature extraction.

2. The feature extraction technology adopted in the present invention can represent the features of the spiral interference image with two-dimensional spatial coordinates, and the efficiency of signal demodulation is improved by reducing the dimension of the data of the spiral interference image.

3. The present invention can effectively avoid the influence of the beam power fluctuation on the optical phase difference demodulation result.

For the above reasons, the present invention can be widely applied in the optical field.

Description of drawings

In order to illustrate the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description These are some embodiments of the present invention, and for those of ordinary skill in the art, other drawings can also be obtained from these drawings without any creative effort.

FIG. 1 is a Gaussian beam (a), an orbital angular momentum beam (b) and a helical interference image (c) according to the present invention.

Figure 2 shows the helical interference pattern of the present invention as a function of the optical phase difference between the orbital angular momentum beam and the Gaussian beam, and the optical phase differences are 0 degrees (a), 45 degrees (b), 90 degrees (c), and 135 degrees, respectively. (d), 180 degrees (e), 225 degrees (f), 270 degrees (g), 315 degrees (h), and 360 degrees (a).

FIG. 3 is two common feature images extracted by the present invention through (a) and (b) two pairs of spiral interference images corresponding to different optical phase differences.

Fig. 4 shows the coordinate values [ω ₁ ,ω ₂ ] of the corresponding helical interference image mapped in the two-dimensional space when the optical phase difference φ between the orbital angular momentum beam and the Gaussian beam varies from 0 degrees to 360 degrees. Schematic diagram of position change.

FIG. 5 is a schematic diagram of the corresponding relationship between the angular coordinate value ω _θ of the coordinate value of the helical interference image mapped in the two-dimensional space and the optical phase difference φ.

Detailed ways

In order to make the purposes, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments These are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

Example 1

As shown in Fig. 1, the helical interference image (Fig. 1c) is formed by the interference of a Gaussian beam (Fig. 1a) and an orbital angular momentum beam (Fig. 1b). The size of the spiral interference image in this embodiment is 500×500, and there are spiral-shaped fringes in the spiral interference image (FIG. 1c).

The orbital angular momentum beam topological charge is +1. (Fig. 1b).

The topological charge of the Gaussian beam is 0, and the intensity distribution of the Gaussian beam along the radial direction satisfies the Gaussian function (Fig. 1a).

As shown in Figure 2, there are 32 spiral interference images used for extracting common feature images in this embodiment, the corresponding optical phase difference variation range is 0 degrees to 360 degrees, and the optical phase difference variation interval is 11.25 degrees. Figure 2 Eight of the 32 helical interference images are presented in (a–h), all of which are 500 × 500 in size.

Extracting common feature images specifically includes the following steps:

S401: Rearrange the spiral interference image matrix into a column vector, where the size of the spiral interference image matrix is 500×500, and can be expressed in the following form:

where N=500

The size of the column vector is 250000×1, and can be expressed in the following form, where N=500:

S402: Rearrange the 32 spiral interference images corresponding to different optical phase differences into M one-dimensional column vectors according to the method in S401, which are expressed as Ψ ₁ , Ψ ₂ ,...Ψ ₃₂ , and calculate these 32 one-dimensional column vectors the mean vector of

Then, the data matrix Φ is calculated according to the following formula:

S403: Calculate the covariance matrix C=Φ ^T Φ of the data matrix in S402.

S404: Calculate the eigenvalues of the covariance matrix and the eigenvectors of the covariance matrix described in S403.

S405: Extract the eigenvalues of the two largest covariance matrices and their corresponding eigenvectors V ₁ , V ₂ of the two covariance matrices from the eigenvalues of the covariance matrix and the eigenvectors of the covariance matrix.

S406: Use the eigenvectors V ₁ , V ₂ of the two covariance matrices described in S405 and the data matrix Φ described in S402 to calculate the common feature images U ₁ and U ₂ , and the calculation formula is as follows:

[U ₁ U ₂ ]=Φ×[V ₁ V ₂ ]

As shown in Figure 3, U ₁ and U ₂ are transformed into a two-dimensional matrix with a size of 500 × 500 according to the reverse arrangement process of step S401, and the distribution characteristics of the common feature images can be seen more clearly (Figure 3a, Figure 3b) .

The feature demodulation specifically includes the following steps:

S501: Rearrange a pair of helical interference images that need to be demodulated by optical phase difference into column vectors according to the method in S401, and represent the rearrangement into column vectors as Ψ _i , and the need to perform optical phase difference A pair of helical interference images for differential demodulation may be one of the M spiral interference images corresponding to different optical phase differences described in S402, or may be obtained under the same conditions of the same size. Another spiral interference image of , the size of the spiral interference image matrix is 500 × 500, rearranged into a column vector Ψ _i of size 250000 × 1.

S502: subtract the average vector described in S402 from the Ψ _i and express the obtained result as Φ _i , so the stated

S503: Map the Φ _i to a two-dimensional space with the common feature images U ₁ and U ₂ as base vectors, the coordinate value of Φ _i in the two-dimensional space is Ω _i =[ω ₁ ω ₂ ] ^T , the The coordinate value calculation formula is as follows:

When the optical phase difference φ between the orbital angular momentum beam and the Gaussian beam varies from 0 degrees to 360 degrees, the position changes of the coordinates [ω ₁ ,ω ₂ ] in the two-dimensional space corresponding to the helical interference image are shown in Figure 4 As shown, the coordinate values [ω ₁ , ω ₂ ] are distributed on a circle with the origin of the two-dimensional coordinate as the center of the circle, and the coordinate values [ω ₁ , ω ₂ ] vary from 0 degrees to 360 degrees with φ The time change rotates counterclockwise.

The optical phase difference calculation specifically includes the following steps:

S601: Convert the coordinate value Ω _i described in S503 into a coordinate value [ω _r ω _θ ] in the cylindrical coordinate system, where ω _r is the radial coordinate value of the coordinate value Ω _i , and ω _θ is the coordinate value Ω _i The angular coordinate value of , can be calculated by the following formula:

S602: The optical phase difference φ between the orbital angular momentum beam and the Gaussian beam can be calculated by using the angular coordinate value ω _θ of the coordinate value Ω _i :

φ=π/2-ω _θ

As shown in Figure 5, when the optical phase difference varies from 0° to 360°, a spiral interference image is obtained every 5°, and the angular coordinate value ω _θ of the corresponding coordinate value Ω _i is calculated, Using the corresponding relationship between the angular coordinate value ω _θ of the coordinate value in the two-dimensional space mapped by the helical interference image and the optical phase difference ϕ (Fig. 5), the calculation formula of the optical phase difference ϕ in S602 is satisfied, and it can be proved that this Validity of the method in this example.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, but not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: The technical solutions described in the foregoing embodiments can still be modified, or some or all of the technical features thereof can be equivalently replaced; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the technical solutions of the embodiments of the present invention. scope.

Claims (6)

1. a kind of optical phase difference demodulation method based on spiral shape interference image Feature Extraction Technology characterized by comprising The step of the step of obtaining spiral shape interference image and extraction spiral shape interference image feature,

The step of acquisition spiral shape interference image refers to: spiral shape interference image is by orbital angular momentum light beam and Gaussian beam Interference is formed, and has spiral-shaped interference fringe in the spiral shape interference pattern, wherein

The spiral shape interference image changes with the optical phase difference between two light beams, and the optical phase difference is described Optical phase difference between orbital angular momentum light beam and Gaussian beam；

The step of extraction spiral shape interference image feature, refers to: extracting common trait image, feature demodulation optical phase The step of difference calculates；

The step of described extraction common trait image is the spiral shape interference image to a series of different optical phase differences of correspondences Common trait image extract；

The step of feature demodulates is mapped to spiral shape interference image using common trait image as the two dimension of base vector Space finds out coordinate value of the spiral shape interference image in two-dimensional space, for indicating the feature of spiral shape interference image；

The step of optical phase difference calculates is to utilize the coordinate value calculating optical phase difference in two-dimensional space.

2. the optical phase difference demodulation method of spiral shape interference image Feature Extraction Technology according to claim 1, special Sign is that the orbital angular momentum light beam topological charge number is+1 or -1.

3. the optical phase difference demodulation method of spiral shape interference image Feature Extraction Technology according to claim 1, special Sign is that the Gaussian beam topological charge number is 0, and radially light distribution meets Gaussian function to the Gaussian beam.

4. the optical phase difference demodulation method of spiral shape interference image Feature Extraction Technology according to claim 1, special Sign is, the extraction common trait image the following steps are included:

S401: spiral shape interference image matrix is rearranged as column vector, the size of the spiral shape interference image matrix For N × N, and form can be expressed as:

Wherein, in matrix each element representation correspondence image pixel gray value,

The column vector is having a size of N²× 1, and form can be expressed as:

Ψ_mWhat is indicated is the corresponding dimensional vector of a pair interference image；

S402: the spiral shape interference image that M width corresponds to different optical phase differences is rearranged into M one by the method in S401 Dimensional vector is expressed as Ψ₁,Ψ₂,…Ψ_M, it is calculated by the following formula the average vector of a M dimensional vectors

Data matrix Φ is calculated by following formula:

S403: the covariance matrix C:C=Φ of data matrix described in S402 is calculated^TΦ；

S404: the characteristic value of covariance matrix and the feature vector of covariance matrix described in S403 are calculated；

S405: two maximum covariances are chosen in the characteristic value of the covariance matrix and the feature vector of covariance matrix The feature vector V of the characteristic value of matrix and its corresponding two covariance matrixes₁,V₂；

S406: by the feature vector V of two covariance matrixes described in S405₁,V₂And data matrix Φ described in S402 Common trait image U is calculated by following formula₁And U₂:

[U₁ U₂]=Φ × [V₁ V₂]。

5. the optical phase difference demodulation method of spiral shape interference image Feature Extraction Technology according to claim 4, special Sign is, the characteristic solution tune the following steps are included:

S501: the secondary spiral shape interference image for needing to carry out optical phase difference demodulation is rearranged according to the method in S401 Ψ is expressed as column vector as column vector, and by described rearranging_i, described needs to carry out optical phase difference demodulation A secondary spiral shape interference image can be M width described in S402 correspond to different optical phase differences spiral shape interference image it In a width spiral shape interference image, be also possible to same size obtain under the same conditions an other width spiral shapes interference The size of image, spiral shape interference image matrix is N × N, is rearranged as column vector Ψ_iHaving a size of N²×1；

S502: by the Ψ_iAverage vector described in S402 is subtracted, and obtained result is expressed as Φ_i, described

S503: the Φ_iIt is mapped to common trait image U₁And U₂For the two-dimensional space of base vector, pass through following formula meter Calculate Φ_iCoordinate value Ω in two-dimensional space_i, Ω_i=[ω₁ω₂]^T:

6. the optical phase difference demodulation method of spiral shape interference image Feature Extraction Technology according to claim 5, special Sign is, the optical phase difference calculate the following steps are included:

S601: by following formula by the coordinate value Ω in S503_iCoordinate value [the ω being converted into cylindrical coordinate_r ω_θ]:

Wherein, ω_rFor coordinate value Ω_iRadial coordinate value, ω_θFor coordinate value Ω_iAngular coordinate value.

S602: the optical phase difference φ being calculated by the following formula between orbital angular momentum light beam and Gaussian beam:

φ=pi/2-ω_θ。