A method for electromagnetic field angle measurement based on spatial distribution of wavefront polarization state

Abstract

This paper proposes an electromagnetic field angle measurement method based on the spatial distribution of wavefront polarization states. This method aims to address the problem of single-pulse electromagnetic field angle measurement when the spatial distribution of polarization states is inconsistent. The method can eliminate errors introduced by spatial polarization inconsistencies. By processing the electromagnetic field amplitude and phase data output by a dual-polarization digital array, the method extracts the four Stokes parameters of the electromagnetic field to describe the polarization state and its spatial distribution. This method then calculates the geometric phase and derives an accurate formula for calculating the electromagnetic wave's incident angle.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and in particular relates to an electromagnetic field angle measurement method based on the spatial distribution of wavefront polarization states. Background Art

[0002] In the field of radio frequency detection and perception, angle measurement is an important function. By measuring the spatial azimuth and elevation angles of the electromagnetic wave emission source relative to the receiver, it effectively supports applications such as wireless communication, target positioning, active detection, passive perception, and precision measurement, which has far-reaching significance for economic development.

[0003] With the advancement of electromagnetic wave receiving array device technology, the emergence of dual-polarization digital arrays has enabled the simultaneous detection and processing of electromagnetic field information from both polarization channels. Larger arrays and a greater number of elements provide high-resolution and precise spatial sampling of the electromagnetic field. High-computing chips enable large-scale, real-time data processing. Leveraging the increased computing power of chips, how to deeply mine the massive amounts of data generated by these new hardware has become a significant research topic. This data also provides opportunities for new angle measurement methods.

[0004] In scenes with dense reflectors, such as those at low altitudes in cities, after electromagnetic waves are reflected by objects with complex surface features, the spatial distribution of the wavefront polarization state (SOP) will be modulated by the reflector, resulting in different local polarization states at different positions on the wavefront plane. Therefore, it is no longer possible to accurately describe the entire incident electromagnetic field with a single polarization state. Instead, it is necessary to introduce the spatial distribution of the polarization state to describe it, that is, to characterize the polarization state as a variable that changes with spatial position. Existing single-pulse angle measurement methods (such as sum-difference beam amplitude ratio angle measurement, interference angle measurement, etc.) all assume at the input that the polarization state (polarization) of all positions on the electromagnetic field wavefront is consistent. These angle measurement methods for single-polarization electromagnetic fields cannot properly solve the aforementioned angle measurement problem of electromagnetic fields with spatial distribution of polarization states, nor can they fully utilize the spatial distribution information of polarization states received by the dual-polarization digital array to improve angle measurement performance.

[0005] In summary, for electromagnetic fields with non-uniform spatial distribution of polarization states, dual-polarization digital arrays provide a detection method, but there is no corresponding angle measurement method. A new and effective angle measurement method needs to be proposed. Summary of the Invention

[0006] This paper proposes an electromagnetic field angle measurement method based on the spatial distribution of wavefront polarization states. This method aims to address the problem of single-pulse electromagnetic field angle measurement when the spatial distribution of polarization states is inconsistent. The method can eliminate errors introduced by spatial polarization inconsistencies. By processing the electromagnetic field amplitude and phase data output by a dual-polarization digital array, the method extracts the four Stokes parameters of the electromagnetic field to describe the polarization state and its spatial distribution. This method then calculates the geometric phase and derives an accurate formula for calculating the electromagnetic wave's incident angle.

[0007] This method is a single-pulse angle measurement method that requires only a single dual-polarization channel electromagnetic field amplitude and phase measurement data, and in principle supports rapid real-time angle measurement. This method fully considers and corrects the influence of the spatial distribution of polarization states on electromagnetic field angle measurement. It can handle electromagnetic fields with arbitrary polarization state distributions. In scenes with numerous reflectors and complex surface features, such as low-altitude urban areas, it effectively eliminates the additional error terms introduced by complex polarization state distributions.

[0008] This method is compatible. When the polarization state of the electromagnetic field to be measured satisfies consistency, the polarization distribution correction term in this method will be correspondingly reset to zero, thereby being compatible with the electromagnetic field situation with consistent polarization.

[0009] The present invention provides an electromagnetic field angle measurement method based on the spatial distribution of wavefront polarization states, the method comprising the following steps:

[0010] Step 1: Extraction of Stokes parameters of electromagnetic field wavefront

[0011] Step 1.1: For all digital array elements, calculate the Stokes parameters of each element based on the electromagnetic field complex amplitude measurements of the two polarization channels and temporarily store them for use in step 2. The four Stokes parameters S0 to S3 are calculated for each element, and the calculation formula is shown in Equation (2).

[0012] Assume that the rectangular coordinates of the dual-polarization digital array element are (x, y), the polarization receiving directions are horizontal and vertical, the horizontal direction is subscripted H, and the vertical direction is subscripted V. Then the output electromagnetic field amplitude and phase data of the dual-polarization digital array can be expressed as the following complex vector form:

[0013]

[0014] Among them, “|>” is a right arrow, indicating a column vector, where the vector elements are arranged in a column. is the horizontal polarization component of the electromagnetic field, is the vertical polarization component of the electromagnetic field; the above formula is the input parameter representation of this method. According to the definition in formula (1), the Stokes parameter can be calculated by the following formula:

[0015]

[0016] The parameter δ in formula (2)s (x,y) is the horizontal polarization component of the electromagnetic field With vertical polarization component The phase difference between them is as follows:

[0017]

[0018] Where arg[] represents the complex angle of the complex number.

[0019] The default dual-polarization channels in formula (2) are horizontal polarization and vertical polarization.

[0020] Preferably, when the dual-polarization channels of the digital array use left-hand / right-hand polarization, or 45° / 135° polarization, a simple linear transformation is first performed to calculate the equivalent horizontal / vertical polarization components, which are then substituted into equation (2) to calculate the Stokes parameters. The matrix form of the linear transformation is the Pauli matrix.

[0021] Step 1.2: Based on the Stokes parameters, the polarization state at each array element can be plotted to obtain the polarization distribution of the entire electromagnetic field.

[0022] The four Stokes parameters in formula (2) are sufficient to fully describe the polarization state of any electromagnetic field. The present invention mainly considers the situation where the polarization state is non-uniform and has a complex spatial distribution, so it is necessary to consider the changes of each Stokes parameter with (x, y).

[0023] Figure 2 The paper shows three typical digital array element position distributions and the polarization state at each element position, which is called a polarization distribution diagram. The polarization distribution diagram can be used to completely describe the polarization state distribution of any electromagnetic field wavefront. Figure 2 In the figure, linear polarization is represented by a line segment, elliptical polarization is represented by an ellipse, the arrow represents the handedness of the elliptical polarization, and the amplitude of the electromagnetic field received by each array element is represented by the size of the line segment / ellipse. The present invention supports various forms of digital array element position distribution, such as rectangular distribution, triangular distribution, radial distribution, etc., respectively. Figure 2 (left, middle, right) as shown. Figure 2 It can be seen from the three typical polarization distributions given in that the polarization states at different array element positions are significantly different. For this special electromagnetic field, the single-pulse angle measurement method proposed in the present invention can be used.

[0024] Step 2: Calculate the geometric phase and polarization state pointing angle

[0025] This step is based on the Stokes parameters derived in step 1 to calculate the geometric phase ψ(x,y) and the polarization state pointing angle ψ S (x,y), as the key intermediate variable used in the subsequent angle measurement method, (x,y) is the rectangular coordinate of the dual-polarization digital array element.

[0026] Step 2.1: The present invention selects the right-handed circular polarization state as a reference for calculating the geometric phase. According to the definition of the input electromagnetic field vector in step 1, the right-handed circular polarization state can be expressed as the following vector:

[0027]

[0028] Furthermore, the geometric phase ψ(x,y) is defined as the complex angle of the inner product of the electromagnetic field vector and the right-handed circular polarization state vector. The calculation formula is as follows:

[0029] ψ(x,y)=arg[E R |E(x,y)>] (5)

[0030] Among them, “|>” is a right arrow, indicating a column vector, with the vector elements arranged in a column; “<|” is a left arrow, indicating a row vector, with the vector elements arranged in a row; the multiplication of a row vector and a column vector is expressed as “<|>”, and the result of the multiplication is a number; <E R | is a row vector, is a column vector |E R > the conjugate transpose of,

[0031] Step 2.2: Define the polarization pointing angle ψ S (x,y), the calculation formula is as follows:

[0032]

[0033] Step 3: Calculate the topological charge distribution at different positions of the electromagnetic field

[0034] To distinguish it from (x, y), the two-dimensional rectangular coordinate (u, v) is introduced, and the electromagnetic field topological charge distribution C(u, v) is calculated below.

[0035] Step 3.1. Select a set of two-dimensional rectangular coordinates (u, v) from the rectangular coordinate system. (u, v) is used as the origin of the polar coordinate system to calculate the electromagnetic field topological charge distribution C(u, v);

[0036] Step 3.2, performing coordinate transformation on the first Stokes parameter S0(x, y) and the fourth Stokes parameter S3(x, y) obtained in step 1;

[0037] The transformation from the rectangular coordinate system with (0,0) as the origin to the polar coordinate system with (u,v) as the origin is as follows:

[0038]

[0039] Where (r, φ) is the polar coordinate system, r is the polar diameter in the polar coordinate system, and φ is the polar angle in the polar coordinate system;

[0040] Step 3.3: The geometric phase ψ(x,y) and polarization state pointing angle ψ obtained in step 2 are S (x,y) coordinate conversion;

[0041] The transformation from the rectangular coordinate system with (0,0) as the origin to the polar coordinate system with (u,v) as the origin is as follows:

[0042]

[0043] Among them, (r, φ) is the polar coordinate system coordinate;

[0044] The distribution of each variable in polar coordinates in equations (7) and (8) is obtained through two-dimensional interpolation calculation, where the superscript (u, v) represents the origin of the polar coordinates.

[0045] Preferably, the specific interpolation method may be nearest neighbor interpolation, two-dimensional bilinear interpolation, or the like.

[0046] Preferably, in step 3.3, the geometric phase ψ(x,y) and polarization state pointing angle ψ obtained in step 2 are S When performing coordinate transformation (x, y), first calculate the sine and cosine of the geometric phase and polarization pointing angle, and then perform the coordinate transformation. The steps are as follows:

[0047] Step 3.3.1. Calculate the sine and cosine of the geometric phase and polarization pointing angle calculated in step 2 and store them temporarily for use in step 3.3.2. This is to avoid phase entanglement during the coordinate transformation in step 3.3.2. The calculation formula is as follows:

[0048]

[0049] Step 3.3.2: Perform the same coordinate transformation as in step 3.2 on the calculated geometric phase and sine / cosine of the polarization pointing angle. The transformation formula is as follows:

[0050]

[0051] Interpolation methods can be selected from nearest neighbor interpolation, two-dimensional bilinear interpolation, etc.

[0052] Step 3.4, calculate the electromagnetic field topological charge distribution C(u,v);

[0053] The calculation formula is as follows:

[0054]

[0055] In the above formula, the superscripts u, v and polar coordinates r, φ are omitted for simplicity. The parameters S0, S3, ψ, ψ on the right side of the equation are SThey represent the corresponding parameters on the left side of equations (7) and (8). ∫∫ represents the full plane integral. It should be noted that the second term in the brackets of the numerator of equation (9) is the polarization distribution correction term. When the polarization state of the electromagnetic field wavefront to be measured is consistent, the polarization state pointing angle ψ in equation (6) is S is a constant, and the polarization pointing angle ψ in formula (9) S The partial derivative of is always equal to zero, and only the first term in the square brackets in the numerator of formula (9) contributes.

[0056] Preferably, when the sine and cosine of the geometric phase and the polarization state pointing angle are first calculated and then the coordinate transformation is performed in step 3.3, the partial derivative of the geometric phase and the partial derivative of the polarization state pointing angle in the numerator of formula (9) should be processed as follows:

[0057]

[0058] In the above equation, Δφ is the polar angle scale value in the polar coordinate system after coordinate transformation. Substituting equation (13) into equation (9) completely transforms the integral into multiplication, addition, subtraction, and summation to calculate C(u,v).

[0059] Step 4: Calculate the incident angle of the electromagnetic wave to be measured, and calculate the azimuth and elevation angles;

[0060] The azimuth and elevation angles are calculated using the following formulas:

[0061]

[0062] In formula (10), k is the magnitude of the electromagnetic field wave vector, which is a scalar quantity and its value is equal to 2π / λ, where λ is the wavelength of the electromagnetic wave;

[0063] Repeat steps 3 and 4, recalculating for different (u, v).

[0064] The beneficial effects of the present invention are:

[0065] This invention addresses the problem of measuring angles using electromagnetic waves with complex polarization patterns and is a single-pulse angle measurement method. Compared with existing technologies, it has the following characteristics and advantages:

[0066] 1. Current angle measurement methods can only handle electromagnetic fields with a single polarization. Non-uniform polarization distributions can introduce angle measurement errors. No method is currently available that can handle angle measurement in complex electromagnetic fields with arbitrary polarization distributions. This invention can analytically separate and eliminate the influence of arbitrary polarization distributions on angle measurement, resulting in accurate angle measurement results.

[0067] 2. In complex scenarios, such as urban areas, where reflective objects are densely packed and reflective surfaces are made of varying materials, these objects can easily introduce additional spatial modulation effects to the electromagnetic field's polarization state. To address this type of angle measurement problem, the present invention is universal and can calculate the angle of incidence for electromagnetic fields with arbitrary spatial distributions of polarization states. Furthermore, the present invention is compatible with simple scenarios where polarization states are uniform.

[0068] 3. The present invention can conduct more in-depth mining of the output data of the dual-polarization digital array. With the further popularization of the dual-polarization digital array and high-performance real-time processors, it will have a wider application prospect. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 Flowchart of the electromagnetic field angle measurement method provided by the present invention

[0070] Figure 2 Three polarization distribution diagrams DETAILED DESCRIPTION

[0071] The technical solutions provided by the present invention will be described in detail below with reference to specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0072] Example 1:

[0073] The present invention provides an electromagnetic field angle measurement method based on the spatial distribution of wavefront polarization states, the method comprising the following steps:

[0074] Step 1: Calculate the Stokes parameters based on the dual-polarized electromagnetic field vector

[0075] Step 1.1: For all digital array elements, calculate the Stokes parameters of each element based on the electromagnetic field complex amplitude measurements of the two polarization channels and temporarily store them for use in step 2. The four Stokes parameters S0 to S3 are calculated for each element, and the calculation formula is shown in Equation (2).

[0076] Equation (2) assumes horizontal and vertical polarization for the dual-polarization channels. If the digital array's dual-polarization channels in actual applications use left-hand / right-hand polarization, or 45° / 135° polarization, first calculate the equivalent horizontal / vertical polarization components through a simple linear transformation, then substitute them into Equation (2) to calculate the Stokes parameters. The matrix form of the linear transformation is a Pauli matrix.

[0077] Step 1.2: Based on the Stokes parameters, the polarization state at each array element can be plotted to obtain the polarization distribution of the entire electromagnetic field.

[0078] Figure 2The paper shows three typical digital array element position distributions and the polarization state at each element position, which is called a polarization distribution diagram. The polarization distribution diagram can be used to completely describe the polarization state distribution of any electromagnetic field wavefront. Figure 2 In the figure, linear polarization is represented by a line segment, elliptical polarization is represented by an ellipse, the arrow represents the handedness of the elliptical polarization, and the amplitude of the electromagnetic field received by each array element is represented by the size of the line segment / ellipse. The present invention supports various forms of digital array element position distribution, such as rectangular distribution, triangular distribution, radial distribution, etc., respectively. Figure 2 (left, middle, right) as shown. Figure 2 It can be seen from the three typical polarization distributions given in that the polarization states at different array element positions are significantly different. For this special electromagnetic field, the single-pulse angle measurement method proposed in the present invention can be used.

[0079] Step 2: Calculate the geometric phase and polarization state pointing angle

[0080] Step 2.1: Based on the Stokes parameters S0-S3 calculated in step 1, calculate the geometric phase ψ(x,y) for each array element and store it temporarily for use in step 3. The calculation formula of the geometric phase is shown in equation (5).

[0081] Step 2.2: Based on the Stokes parameters S0 to S3 calculated in step 1, calculate the polarization pointing angle ψ for each array element. S (x, y) and temporarily save it for use in step 3. The calculation formula of the polarization state pointing angle is shown in formula (6).

[0082] Step 3: Calculate the electromagnetic field topological charge distribution

[0083] Step 3.1. Select a set of two-dimensional rectangular coordinate grid points (u, v) for calculating the electromagnetic field topological charge distribution C(u, v).

[0084] A set of two-dimensional rectangular coordinates (u, v) is selected from the rectangular coordinate system, and (u, v) is used as the origin of the polar coordinate system. The density of the grid points can be roughly equivalent to the density of the digital array elements. When the digital array elements are distributed in a rectangular shape (such as Figure 2 Left), the above two-dimensional rectangular coordinate grid (u, v) can coincide with the position (x, y) of the digital array element. When the digital array elements are distributed in other positions (such as Figure 2 The two-dimensional rectangular coordinate grid points (u, v) do not coincide with the digital array element positions (x, y).

[0085] Step 3.2, performing coordinate transformation on the first Stokes parameter S0(x, y) and the fourth Stokes parameter S3(x, y) calculated in step 1;

[0086] Transform from the rectangular coordinate system with (0,0) as the origin to the polar coordinate system with (u,v) as the origin. The conversion rule is as shown in formula (7). The interpolation method can be selected from nearest neighbor interpolation, two-dimensional bilinear interpolation, etc., to obtain the transformed S0 u,v (r,φ) and S3 u,v (r,φ).

[0087] Step 3.3: The geometric phase ψ(x,y) and polarization state pointing angle ψ obtained in step 2 are S (x,y) coordinate conversion;

[0088] The transformation from the rectangular coordinate system with (0,0) as the origin to the polar coordinate system with (u,v) as the origin is as shown in formula (8).

[0089] Step 3.4, calculate the electromagnetic field topological charge distribution C(u,v);

[0090] The calculation formula is as follows (9)

[0091] Step 4: Calculate the incident angle of the electromagnetic field.

[0092] According to C(u,v) calculated in step 3, substitute it into formula (10) to calculate the azimuth and elevation angles of the electromagnetic wave source.

[0093] Repeat steps 3 and 4, recalculating for different (u, v).

[0094] Example 2:

[0095] The present invention provides an electromagnetic field angle measurement method based on the spatial distribution of wavefront polarization states, the method comprising the following steps:

[0096] Steps 1 and 2 are the same as those in Example 1.

[0097] Step 3: Calculate the electromagnetic field topological charge distribution

[0098] Step 3.1. Select a set of two-dimensional rectangular coordinate grid points (u, v) for calculating the electromagnetic field topological charge distribution C(u, v).

[0099] A set of two-dimensional rectangular coordinates (u, v) is selected from the rectangular coordinate system, and (u, v) is used as the origin of the polar coordinate system. The density of the grid points can be roughly equivalent to the density of the digital array elements. When the digital array elements are distributed in a rectangular shape (such as Figure 2 Left), the above two-dimensional rectangular coordinate grid (u, v) can coincide with the position (x, y) of the digital array element. When the digital array elements are distributed in other positions (such as Figure 2 The two-dimensional rectangular coordinate grid points (u, v) do not coincide with the digital array element positions (x, y).

[0100] Step 3.2, performing coordinate transformation on the first Stokes parameter S0(x, y) and the fourth Stokes parameter S3(x, y) calculated in step 1;

[0101] Transform from the rectangular coordinate system with (0,0) as the origin to the polar coordinate system with (u,v) as the origin. The conversion rule is as shown in formula (7). The interpolation method can be selected from nearest neighbor interpolation, two-dimensional bilinear interpolation, etc., to obtain the transformed S0 u,v (r,φ) and S3 u,v (r,φ).

[0102] Step 3.3: The geometric phase ψ(x,y) and polarization state pointing angle ψ obtained in step 2 are S (x,y) coordinate conversion;

[0103] Step 3.3.1. Calculate the sine and cosine of the geometric phase and polarization pointing angle calculated in step 2 and store them temporarily for use in step 3.3.2. This is to avoid phase entanglement during the coordinate transformation in step 3.3.2. The calculation formula is as follows:

[0104]

[0105] Step 3.3.2: Perform the same coordinate transformation as in step 3.2 on the calculated geometric phase and sine / cosine of the polarization pointing angle. The transformation formula is as follows:

[0106]

[0107] Interpolation methods can be selected from nearest neighbor interpolation, two-dimensional bilinear interpolation, etc.

[0108] Step 3.4: Calculate the topological charge distribution C(u,v). For each pair of coordinate points (u,v), it is necessary to calculate it independently. The calculation steps are as follows:

[0109] The topological charge C(u,v) is calculated according to formula (9). The partial derivatives of the geometric phase and the polarization pointing angle in the numerator of formula (9) should be processed as follows:

[0110]

[0111] In the above equation, Δφ is the polar angle scale value in the polar coordinate system after coordinate transformation. Substituting equation (13) into equation (9) completely transforms the integral into multiplication, addition, subtraction, and summation to calculate C(u,v).

[0112] Step 4: Calculate the incident angle of the electromagnetic field.

[0113] According to C(u,v) calculated in step 3, substitute it into formula (10) to calculate the azimuth and elevation angles of the electromagnetic wave source.

[0114] Repeat steps 3 and 4, recalculating for different (u, v).

[0115] The above description is only the best specific implementation of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed in the present invention should be covered by the scope of protection of the present invention.

[0116] The contents not described in detail in the specification of the present invention belong to the common knowledge of professionals in this field.

Claims

1. A method for electromagnetic field angle measurement based on the spatial distribution of wavefront polarization states, characterized in that: The steps of this method are as follows: Step 1: Extraction of Stokes parameters of electromagnetic field wavefront Step 1.

1. For all digital array elements, calculate the Stokes parameters of each element based on the electromagnetic field complex amplitude measurements of the two polarization channels and temporarily store them for use in Step 2. Calculate the four Stokes parameters S0 to S3 for each element. Step 1.2: Plot the polarization state of each array element based on the Stokes parameters to obtain the polarization distribution of the entire electromagnetic field. Step 2: Calculate the geometric phase and polarization state pointing angle This step is based on the Stokes parameters derived in step 1 to calculate the geometric phase ψ(x,y) and the polarization state pointing angle ψ S (x,y), as the key intermediate variable used in the subsequent angle measurement method, (x,y) is the rectangular coordinate of the dual-polarization digital array element; Step 3: Calculate the topological charge distribution at different locations of the electromagnetic field To distinguish it from (x, y), we introduce the two-dimensional rectangular coordinate (u, v). The electromagnetic field topological charge distribution C(u, v) is calculated below. Step 3.

1. Select a set of two-dimensional rectangular coordinates (u, v) from the rectangular coordinate system. (u, v) is used as the origin of the polar coordinate system to calculate the electromagnetic field topological charge distribution C(u, v); Step 3.2, performing coordinate transformation on the first Stokes parameter S0(x, y) and the fourth Stokes parameter S3(x, y) obtained in step 1; Step 3.3: The geometric phase ψ(x,y) and polarization state pointing angle ψ obtained in step 2 are S (x,y) coordinate conversion; Step 3.4, calculate the electromagnetic field topological charge distribution C(u,v); Step 4: Calculate the incident angle of the electromagnetic wave to be measured, and calculate the azimuth and elevation angles; Repeat steps 3 and 4, recalculating for different (u, v).

2. The method according to claim 1, characterized in that Step 1.1 is as follows: Assume that the rectangular coordinates of the dual-polarization digital array element are (x, y), the polarization receiving directions are horizontal and vertical, the horizontal direction is subscripted H, and the vertical direction is subscripted V. Then the output electromagnetic field amplitude and phase data of the dual-polarization digital array are expressed as the following complex vector form: Among them, "|>" is a right arrow, indicating a column vector, where the vector elements are arranged in a column. is the horizontal polarization component of the electromagnetic field, is the vertical polarization component of the electromagnetic field; the above formula is the input parameter representation of this method; according to the definition in formula (1), the Stokes parameter is calculated by the following formula: The parameter δ in formula (2) s (x,y) is the horizontal polarization component of the electromagnetic field With vertical polarization component The phase difference between them is as follows: Where arg[] represents the complex angle of the complex number.

3. The method according to claim 2, characterized in that Step 2 is specifically as follows: Step 2.1, the present invention selects the right-handed circular polarization state as a reference for calculating the geometric phase; according to the definition of the input electromagnetic field vector in step 1, the right-handed circular polarization state is expressed as the following vector: Furthermore, the geometric phase ψ(x,y) is defined as the complex angle of the inner product of the electromagnetic field vector and the right-handed circular polarization state vector. The calculation formula is as follows: ψ(x,y)=arg[ <E R |E(x,y)>] (5) Among them, "|>" is a right arrow, indicating a column vector, with vector elements arranged in a column; "<|" is a left arrow, indicating a row vector, with vector elements arranged in a row; the multiplication of a row vector and a column vector is expressed as "<|>", and the result of the multiplication is a number; <E R | is a row vector, is a column vector |E R > the conjugate transpose of, Step 2.2: Define the polarization pointing angle ψ S (x,y), the calculation formula is as follows:

4. The method according to claim 3, characterized in that In step 3.2, the transformation from the rectangular coordinate system with (0,0) as the origin to the polar coordinate system with (u,v) as the origin is carried out according to the following transformation rules: Where (r, φ) is the polar coordinate system, r is the polar diameter in the polar coordinate system, and φ is the polar angle in the polar coordinate system.

5. The method according to claim 4, characterized in that In step 3.3, the transformation from the rectangular coordinate system with (0,0) as the origin to the polar coordinate system with (u,v) as the origin is carried out according to the following transformation rules: Among them, (r, φ) is the polar coordinate system coordinate; The distribution of each variable in polar coordinates in equations (7) and (8) is obtained through two-dimensional interpolation calculation, where the superscript (u, v) represents the origin of the polar coordinates.

6. The method according to claim 5, characterized in that In step 3.4, the calculation formula is as follows: In the above formula, the superscripts u, v and polar coordinates r, φ are omitted, and the parameters S0, S3, ψ, ψ on the right side of the equation are S They represent the corresponding parameters on the left side of equations (7) and (8) respectively; ∫∫ represents the full plane integral; the second term in the brackets of the numerator of equation (9) is the polarization distribution correction term; when the polarization state of the electromagnetic field wavefront to be measured is consistent, the polarization state pointing angle ψ in equation (6) S is a constant, and the polarization pointing angle ψ in formula (9) S The partial derivative of is always equal to zero, and only the first term in the square brackets in the numerator of formula (9) contributes.

7. The method according to claim 4, characterized in that In step 3.3, the geometric phase ψ(x,y) and polarization state pointing angle ψ obtained in step 2 are S When performing coordinate transformation (x, y), first calculate the sine and cosine of the geometric phase and polarization pointing angle, and then perform the coordinate transformation. The steps are as follows: Step 3.3.

1. Calculate the sine and cosine of the geometric phase and polarization pointing angle calculated in step 2 and store them temporarily for use in step 3.3.

2. This is to avoid phase entanglement during the coordinate transformation in step 3.3.

2. The calculation formula is as follows: Step 3.3.2: Perform the same coordinate transformation as in step 3.2 on the calculated geometric phase and sine / cosine of the polarization pointing angle. The transformation formula is as follows:

8. The method according to claim 7, characterized in that In step 3.4, the calculation formula is as follows: In the above formula, the superscripts u, v and polar coordinates r, φ are omitted, and the parameters S0, S3, ψ, ψ on the right side of the equation are S They represent the corresponding parameters on the left side of equations (7) and (8) respectively; ∫∫ represents the full plane integral; the second term in the brackets of the numerator of equation (9) is the polarization distribution correction term; when the polarization state of the electromagnetic field wavefront to be measured is consistent, the polarization state pointing angle ψ in equation (6) S is a constant, and the polarization pointing angle ψ in formula (9) S The partial derivative is always zero, and only the first term in the square brackets in the numerator of formula (9) contributes; When the sine and cosine of the geometric phase and polarization pointing angle are first calculated and then the coordinate transformation is performed in step 3.3, the partial derivatives of the geometric phase and the partial derivatives of the polarization pointing angle in the numerator of equation (9) should be processed as follows: In the above formula, △φ is the polar angle graduation value in the polar coordinate system after coordinate transformation; Substituting formula (13) into formula (9), the integral is completely converted into multiplication, addition, subtraction and summation to calculate C(u,v).

9. The method according to claim 1, characterized in that The azimuth and elevation angles in step 4 are calculated using the following formulas: In formula (10), k is the magnitude of the electromagnetic field wave vector, which is a scalar quantity and its value is equal to 2π / λ, where λ is the wavelength of the electromagnetic wave.

10. The method according to claim 2, characterized in that When the dual-polarization channel of the digital array uses left-hand / right-hand polarization, or 45° / 135° polarization, the equivalent horizontal / vertical polarization components are first calculated through a simple linear transformation, and then substituted into equation (2) to calculate the Stokes parameters; the matrix form of the linear transformation is the Pauli matrix.

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