Method for measuring vortex beam atmospheric turbulence distortion wavefront and orbital angular momentum

Abstract

The invention relates to a method for measuring vortex beam atmospheric turbulence distortion wavefront and orbital angular momentum, and belongs to the field of optical measurement. According to the method, a fan-shaped micro-lens array is used as a wavefront sensor, radial and angular decomposition is carried out on displacement vectors of sub-light spots under polar coordinates, distorted wavefront generated when vortex light beams pass through atmospheric turbulence is calculated by utilizing the idea of a related algorithm, and then the distortion wavefront of the vortex light beams is calculated by utilizing angular displacement vector information of a residual wavefront light spot array. And orbital angular momentum information of the vortex light beam is calculated. Compared with a traditional method for measuring vortex light beam atmospheric turbulence distortion by using a probe light beam or deep learning, the method does not need the probe light beam, does not need massive calculation, and can simultaneously calculate the distortion wavefront and orbital angular momentum after the vortex light beam is transmitted through the atmosphere. The method is simple and efficient and has obvious advantages.

Description

Technical Field

[0001] The invention belongs to the field of optical measurement, and in particular relates to a method for measuring atmospheric turbulence distortion wavefront and orbital angular momentum of a vortex light beam. Background Art

[0002] The angular momentum of light is divided into spin angular momentum and orbital angular momentum. Spin angular momentum is reflected by the polarization of light, while orbital angular momentum of light was not known until 1992. This light beam carrying orbital angular momentum (OAM) is also called a vortex beam. It is a light beam with a continuous spiral phase and a circular light field. The magnitude of the orbital angular momentum is ,in It is called the topological charge or mode number. is the reduced Planck constant. Moreover, the modes of the vortex beam are mutually orthogonal and can form a complete set of orthogonal bases. Therefore, orbital angular momentum becomes another basic dimension of light and is applied in various fields. In the field of space optical communication, since the number of modes of the vortex beam can be infinite, it has infinite coding capacity in theory, which gives infinite potential for high information capacity communication and is expected to break through the capacity limit of traditional optical communication.

[0003] In the field of OAM space optical communications, there are two main problems: 1. The orbital angular momentum of the vortex beam diffuses after being transmitted through the atmosphere, causing mode crosstalk; 2. The distorted wavefront detection of the vortex beam after being transmitted through the atmosphere is difficult to detect. At present, the commonly used methods include probe beams and neural networks to solve this problem. The probe beam method is to coaxially transmit the Gaussian beam and the vortex beam, and detect the wavefront distortion of the Gaussian beam at the receiving end to compensate for the wavefront distortion caused by the vortex beam. The neural network method mainly uses convolutional neural networks or other improved network models to establish the corresponding relationship between the light intensity distribution at the receiving end and the turbulence phase, so as to detect the distorted wavefront of the vortex beam transmitted through the atmosphere.

[0004] In the above methods, the orbital angular momentum and the distorted wavefront of atmospheric turbulence cannot be detected at the same time. In addition, the method of using a probe beam increases the complexity of the system. The method based on neural networks and deep learning increases the amount of calculation of the system. In addition, due to the limited samples of network training, the network model may fail in the face of variable atmospheric turbulence in different regions, different times and different climates in practical applications. Therefore, the above two methods are still a certain distance away from practical application. Therefore, an efficient method is needed to realize the measurement of vortex beam atmospheric turbulence distortion wavefront and orbital angular momentum, which will accelerate the development of vortex beam space communication applications. Summary of the invention

[0005] The purpose of the present invention is to solve the shortcomings of the above-mentioned detection method, and proposes a method that can simultaneously detect the atmospheric turbulence wavefront distortion and orbital angular momentum of a vortex beam. After the vortex beam is transmitted through the atmosphere, it is received by the Hartmann wavefront sensor, and the centroid displacement information of its spot array is contributed by the spiral phase and turbulence phase of the vortex beam. By utilizing the phase slope distribution characteristics of the spiral phase in the polar coordinate system and combining the ideas of the relevant algorithms, the distorted wavefront of the atmospheric turbulence of the vortex beam can be obtained from the centroid displacement information of the spot. Then, the magnitude of the orbital angular momentum can be obtained through the mapping relationship between orbital angular momentum and centroid displacement.

[0006] The technical solution adopted by the present invention is: a method for measuring the atmospheric turbulence distortion wavefront and orbital angular momentum of a vortex light beam, the method comprising the following steps:

[0007] Step 1: Using a fan-shaped microlens array to receive signals, obtaining a ring-shaped light spot array;

[0008] Step 2: In the polar coordinate system, calculate the radial and angular centroid displacements of each sub-aperture spot in the spot array, then select a reference sub-aperture on each ring, and calculate the relative centroid displacement column vector G of other sub-aperture spots on the ring relative to the reference sub-aperture spot;

[0009] Step 3, using the relative center of mass displacement column vector G to calculate the Zernike coefficient A of the turbulent distortion wavefront;

[0010] Step 4, calculating the radial and angular centroid displacements of the sub-aperture spot of the restored wavefront;

[0011] Step 5, combining the radial component of the residual wavefront centroid displacement to obtain the Zernike coefficients of defocus and spherical aberration;

[0012] Step 6: Combine the angular component of the residual wavefront centroid displacement to obtain the orbital angular momentum of the vortex beam.

[0013] The present invention has the following beneficial effects:

[0014] The method for measuring the atmospheric turbulence distortion wavefront and orbital angular momentum of a vortex beam of the present invention does not require a probe beam and a complex neural network structure, but only uses a fan-shaped microlens array. Through the single-frame Hartmann spot array information, the turbulence distortion wavefront and orbital angular momentum information can be obtained simultaneously. The structure is simple and the system is highly efficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart of a method for measuring the atmospheric turbulence distortion wavefront and orbital angular momentum of a vortex light beam according to the present invention;

[0016] Figure 2 (a) is a phase slope distribution diagram of the spiral phase;

[0017] Figure 2 (b) Phase slope distribution diagram of the defocused phase;

[0018] Figure 2 (c) Phase slope distribution of primary spherical aberration;

[0019] Figure 2 (d) Phase slope distribution of secondary spherical aberration;

[0020] FIG3 (a) is a schematic diagram of the arrangement of a fan-shaped microlens array;

[0021] FIG3 (b) is a diagram of an annular light spot array on the focal plane of a fan-shaped microlens array;

[0022] Figure 3 (c) The displacement vector diagram of the centroid of the sub-spot decomposed from the radial and angular directions;

[0023] Figure 4 (a) is =5 spiral phase diagram;

[0024] Figure 4 (b) is a turbulent phase diagram;

[0025] Fig. 4 (c) Spiral distortion phase diagram;

[0026] Figure 5 (a) is the restored Zernike coefficient diagram, excluding defocus and spherical aberration;

[0027] Figure 5 (b) is the restored Zernike coefficient diagram, including defocus and spherical aberration;

[0028] Figure 5 (c) is the measured orbital angular momentum diagram. DETAILED DESCRIPTION

[0029] In order to make the purpose, technical scheme and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in each embodiment of the present invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above-mentioned purpose, the present invention adopts the following technical scheme.

[0030] The following is a brief introduction of the use of the correlation algorithm of the present invention in adaptive optics for extended target wavefront detection, in conjunction with the accompanying drawings. In a rectangular coordinate system, since the contribution of the tilt aberration to the centroid displacement of each sub-aperture is the same, the use of the correlation algorithm will subtract the tilt aberration information of the wavefront as a whole, resulting in only being able to detect aberrations other than the tilt. Based on this idea, the present invention analyzes and studies the phase slope distribution of the spiral phase of the vortex beam, as follows:

[0031] (1)

[0032] In the above formula, is the topological charge of the vortex beam, is the characteristic value of OAM, (r, θ) is the polar coordinate, and λ is the wavelength. The distribution of the spiral phase slope is shown in Figure 2(a). The black arrow indicates the slope direction. It can be seen that in the polar coordinate system, the wavefront slope of the vortex beam has nothing to do with the angular coordinate θ, but only with the radial coordinates r and The wavefront slope is circularly symmetric, that is, the slope is the same at the same radius. Based on this characteristic, in the polar coordinate system, combined with the idea of ​​the relevant algorithm, the spiral phase in the spiral distortion wavefront of the vortex beam can be subtracted to obtain the turbulent distortion wavefront.

[0033] The present invention adopts a fan-shaped microlens array, which is more suitable for signal processing in polar coordinate system. Its arrangement is shown in Figure 3(a). A circular array of light spots can be obtained on the focal plane, as shown in Figure 3(b). Since the wavefront information of the received light field contains the turbulent phase and the spiral phase, the centroid displacement information of the Hartmann light spot array also contains the spiral phase and the turbulent phase information. In the polar coordinate system, the radial d is used to calculate the centroid displacement of the light spot of each sub-aperture. r and angular direction d θ Decomposed, as shown in Figure 3(c), the expression is as follows:

[0034] (2)

[0035] In the above formula, (x n,m ,y n,m ) is the coordinate of the (n, m)th pixel in the corresponding subaperture on the camera, I n,m is the intensity information collected by the (n, m)th pixel, (X(i, j), Y(i, j)) is the rectangular coordinate of the center of mass of the spot of the jth sub-aperture on the ith ring. i represents the ith ring, j represents the serial number of the sub-aperture on each ring, are the radial and angular centroid displacements of the jth subaperture on the ith ring, respectively, and θ is the angle between the center of the subaperture and the origin of the coordinate system and the horizontal coordinate.

[0036] Then, the subaperture centroid information on each ring is subtracted from the reference subaperture centroid information of each ring to obtain the relative centroid displacement column vector G, which can be expressed as follows:

[0037] (3)

[0038] In the above formula, represents the relative centroid displacement of the jth subaperture of the ith ring, The first subaperture of the ith ring is used as a reference. The relative displacement of each subaperture corresponding to each order Zernike polynomial can be expressed as follows:

[0039] (4)

[0040] In the above formula, are the radial and angular displacements of the centroid of the k-th order Zernike aberration in the j-th subaperture of the ith ring, respectively. Therefore, the Zernike coefficient A of the turbulent distortion wavefront can be obtained as follows:

[0041] (5)

[0042] In the above formula, is the restoration matrix, which is the inverse matrix of D. Since the phase slopes and phase slopes of defocus and spherical aberration are also circularly symmetric, as shown in Figure 2(b), Figure 2(c) and Figure 2(d). Therefore, the Zernike coefficients obtained by the calculation of formulas (2) to (5) do not include defocus and spherical aberration. At this time, the restored wavefront can be expressed as:

[0043] (6)

[0044] in, is the i-th term of the Zernike coefficient A of the turbulent distortion wavefront, represents the i-th order Zernike aberration, and the restored wavefront matrix The corresponding subaperture displacement is expressed as:

[0045] (7)

[0046] In the above formula, S is the area where the jth subaperture of the i-th ring is located, represents the Fourier transform, is the centroid displacement of each sub-aperture of the restored wavefront in rectangular coordinates. Formula (2) can be used to obtain the radial and angular centroid displacement of each sub-aperture ( ).

[0047] After the centroid displacement introduced by the restored wavefront is subtracted from the detected initial spot centroid information, the centroid displacement of the residual wavefront can be obtained as follows:

[0048] (8)

[0049] As shown by the black arrows in Figure 2(a)-(d), the phase slopes of defocus and spherical aberration are distributed radially, and the spiral phase slope is distributed angularly, and they are orthogonal to each other. Therefore, the angular component of the spot displacement vector of the residual wavefront is provided by the spiral phase, and the radial component is provided by the defocus and spherical aberration. Therefore, by extracting the radial component of the residual wavefront centroid displacement vector, the Zernike coefficients of defocus and spherical aberration can be obtained, and the expressions are as follows:

[0050] (9)

[0051] In the above formula, is the radial component of the displacement of the centroid of the residual wavefront, is a restoration matrix containing only defocus and spherical aberration, which can be obtained by formula (4) by replacing the Zernike aberration in the matrix with defocus and spherical aberration. Combining formulas (5) and (9), the Zernike coefficient of the turbulent distortion wavefront after the vortex beam is transmitted through the atmosphere can be detected.

[0052] According to formula (1), the phase slope of the vortex beam is related to the topological charge The topological charge is the eigenvalue of orbital angular momentum, so when mapped to the displacement of the center of mass, the topological charge It can be expressed as:

[0053] (10)

[0054] In the above formula, d is the spot displacement. For the entire spot array, the topological charge of the vortex beam is It can be obtained by the following formula:

[0055] (11)

[0056] In the above formula, is the angular component of the displacement of the centroid of the residual wavefront, is the restoration matrix containing only the spiral phase, which can be obtained by formula (4) by replacing the Zernike aberration in the matrix with =1 spiral phase.

[0057] In summary, by using a fan-shaped microlens array, in a polar coordinate system, combined with the idea of ​​relevant algorithms, and using single-frame data, it is possible to detect the turbulent phase information and orbital angular momentum information of the vortex light beam after it is transmitted through the atmosphere.

[0058] Example 1: Vortex beam topological charge =5, atmospheric coherence length r0=10cm, receiving aperture 600mm, obstruction ratio 0.286.

[0059] In this embodiment, the topological charge of the emitted vortex beam is =5, and its spiral phase is shown in Figure 4(a). The atmospheric coherence length r0=10cm, and the turbulent phase is shown in Figure 4(b). A telescope with a 600mm aperture and an obscuration ratio of 0.286 is used as the receiving telescope. After the vortex beam is transmitted through the atmosphere, the phase distribution at the receiving telescope is shown in Figure 4(c). Compared with the initial spiral phase, the spiral phase is distorted. Since the wavefront at the receiving telescope is a spirally distorted wavefront, the Hartmann wavefront sensor calibrated with a plane wavefront cannot detect the turbulent distorted wavefront.

[0060] The algorithm flow chart of the present invention is as follows: Figure 1 As shown, first calculate the centroid displacement of the annular spot, then select a reference sub-aperture for each ring, calculate the relative displacement of other sub-aperture spots on the ring, and calculate the Zernike coefficient of the turbulent distortion wavefront by formula (4). Then calculate the centroid displacement of the sub-aperture spot of the restored wavefront, calculate the difference with the centroid displacement of the initial spot, and obtain the centroid displacement of the residual wavefront. According to formula (5), combined with the radial component of the centroid displacement of the residual wavefront, the Zernike coefficients of defocus and spherical aberration are obtained. According to formula (7), combined with the angular component of the centroid displacement of the residual wavefront, the orbital angular momentum of the vortex beam is obtained.

[0061] The calculation results are shown in Figure 5(a)-(c), and the Zernike coefficients of the first 35 orders are restored. Figure 5(a) shows the Zernike coefficients obtained by formula (4). The 3rd, 10th, and 21st orders are defocus, primary spherical aberration, and secondary spherical aberration, respectively, and the restored Zernike coefficients are zero. Combined with formula (5), the Zernike coefficients of defocus and spherical aberration can be calculated, as shown in Figure 5(b). The restored results are basically consistent with the initial Zernike coefficients. The measured orbital angular momentum result is shown in Figure 5(c), which is completely consistent with the orbital angular momentum of the emitted vortex beam. Since the present invention processes the turbulent distortion wavefront and the spiral phase separately, the eigenmode of the vortex beam can be directly detected without considering the influence of mode crosstalk caused by atmospheric turbulence.

[0062] The above embodiments show that the present invention can detect the distorted wavefront and orbital angular momentum of a vortex light beam after it is transmitted through the atmosphere without the need for complex structures and probe beams.

[0063] The present invention is not limited to the above-mentioned specific implementation modes. Any modifications and changes to the present invention within the spirit and principle of the present invention should also fall within the protection scope of the claims of the present invention.

Claims

1. A method for measuring the atmospheric turbulence distortion wavefront and orbital angular momentum of a vortex beam, characterized in that: The method comprises the following steps: Step 1: Using a fan-shaped microlens array to receive signals, obtaining a ring-shaped light spot array; Step 2: In the polar coordinate system, calculate the radial and angular centroid displacements of each sub-aperture spot in the spot array, then select a reference sub-aperture on each ring, and calculate the relative centroid displacement column vector G of other sub-aperture spots on the ring relative to the reference sub-aperture spot; Step 3, using the relative center of mass displacement column vector G to calculate the Zernike coefficient matrix A of the turbulent distortion wavefront; Step 4, calculating the centroid displacement of the sub-aperture spot of the restored wavefront, calculating the difference with the centroid displacement of the initial spot, obtaining the centroid displacement of the residual wavefront, and further obtaining the radial component and angular component of the centroid displacement of the residual wavefront; Step 5, combining the radial component of the residual wavefront centroid displacement to obtain the Zernike coefficients of defocus and spherical aberration; Step 6: Combine the angular component of the residual wavefront centroid displacement to obtain the orbital angular momentum of the vortex beam.

2. The method according to claim 1, characterized in that In step 2, the relative center of mass displacement column vector G in the polar coordinate system is calculated as follows: In the polar coordinate system, the centroid displacement of each sub-aperture spot is decomposed radially and angularly, and the expression is as follows: (2) In the above formula, (x n,m ,y n,m ) is the coordinate of the (n, m)th pixel in the corresponding subaperture on the camera, I n,m is the intensity information collected by the (n, m)th pixel, (X(i, j), Y(i, j)) is the rectangular coordinate of the center of mass of the spot of the jth subaperture on the ith ring, i represents the ith ring, j represents the sequence number of the subaperture on each ring, , are the radial and angular centroid displacements of the jth sub-aperture spot on the ith ring, respectively, and θ is the angle between the center of the sub-aperture and the origin of the coordinate system and the horizontal coordinate; Then, the relative centroid displacement column vector G of the other sub-aperture spots on the ring relative to the reference sub-aperture is expressed as follows: (3) In the above formula, represents the centroid displacement of the jth subaperture on the ith ring, represents the centroid displacement of the first subaperture of the ith ring as the reference subaperture, , They represent the radial and angular components of the displacement of the light spot of the jth sub-aperture on the ith ring relative to the centroid.

3. The method according to claim 2, characterized in that In step 3, the relative centroid displacement matrix D of each sub-aperture corresponding to each order of Zernike aberration is expressed as follows: (4) in, denote the radial and angular centroid displacements of the k-th order Zernike aberration in the j-th subaperture of the ith ring, respectively. Then, the Zernike coefficient matrix A of the turbulent distortion wavefront is calculated by the following formula; (5) In the above formula, is the restoration matrix, which is the inverse matrix of D.

4. The method according to claim 3, characterized in that In step 4, the wavefront matrix is ​​restored It is expressed as: (6) in, is the i-th term of the Zernike coefficient A of the turbulent distortion wavefront, represents the i-th order Zernike aberration, and the restored wavefront matrix The corresponding subaperture displacement is expressed as: (7) In the above formula, S is the area where the jth subaperture of the i-th ring is located, represents the Fourier transform, , is the centroid displacement of each sub-aperture of the restored wavefront in rectangular coordinates. According to formula (2), the radial displacement of each sub-aperture is obtained. and angular displacement ; Then the difference with the initial spot centroid displacement is calculated to obtain the centroid displacement of the residual wavefront, and the radial component and angular component of the centroid displacement of the residual wavefront are obtained as follows: (8)。 5. The method according to claim 4, characterized in that In step 5, the Zernike coefficients of defocus and spherical aberration are obtained by combining the radial component of the residual wavefront centroid displacement according to the following formula: (9) In the above formula, is the radial component of the displacement of the centroid of the residual wavefront, is the restoration matrix containing only defocus and spherical aberration, by replacing the matrix D + The Zernike aberration in is replaced by defocus and spherical aberration to obtain.

6. The method according to claim 5, characterized in that Step 6: According to the following formula, the orbital angular momentum of the vortex beam is obtained by combining the angular component of the displacement of the center of mass of the residual wavefront; (11) In the above formula, is the topological charge, is the eigenvalue of orbital angular momentum, is the angular component of the displacement of the centroid of the residual wavefront, is the restored matrix containing only the spiral phase, which is obtained by replacing the Zernike aberration in the matrix D+ with =1 is obtained.

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