CN113686452B - Multi-optical vortex light beam topological value detection method based on shack Hartmann wavefront sensor - Google Patents

Multi-optical vortex light beam topological value detection method based on shack Hartmann wavefront sensor Download PDF

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CN113686452B
CN113686452B CN202110993027.5A CN202110993027A CN113686452B CN 113686452 B CN113686452 B CN 113686452B CN 202110993027 A CN202110993027 A CN 202110993027A CN 113686452 B CN113686452 B CN 113686452B
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刘华锋
王岱崟
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Abstract

The invention discloses a multi-vortex light beam topological value detection method based on deep learning and a shack Hartmann wave-front sensor, which uses the thought of an intensity ridge extraction method for reference, skillfully converts the extraction of a closed loop under the condition of multi-vortex into a semantic segmentation problem, and is realized by using a deep learning method of U-Net, thereby avoiding the influence of an interfusion part between optical vortices on the acquisition of the closed loop. In addition, in order to solve the dilemma that training data cannot be obtained under the condition of multiple optical vortexes, the invention provides a data generation method, namely, the multiple optical vortexes data can be generated in a large batch for network training by finely processing the single optical vortexes data; in the design of the method, a dice loss function is selected as a loss function based on scene analysis, and the post-processing of closed operation is introduced to improve the performance of the algorithm. A large number of experimental results show that the method can realize the simultaneous and accurate topological value detection of each optical vortex in the multi-optical-vortex beam.

Description

Multi-optical vortex light beam topological value detection method based on shack Hartmann wavefront sensor
Technical Field
The invention belongs to the technical field of vortex beam detection, and particularly relates to a multi-optical vortex beam topology value detection method based on deep learning and a shack Hartmann wavefront sensor.
Background
There are many vortex phenomena in nature, such as tornadoes, vortices in the ocean, and the like. Optical vortex is called optical vortex for short, and particularly refers to the vortex phenomenon in an optical field; for a beam containing one or more optical vortices, we generally call it a vortex beam. In recent years, vortex beams have received much attention and research due to their characteristics, and have been successfully used in many fields. Since photons in vortex-rotating beams carry orbital angular momentum, vortex beams can be used to manipulate microscopic particles and are considered one of the most powerful tools for exploring the microscopic world; because the vortex light beams have natural orthogonality, the vortex light beams with different modes can carry out independent information coding and information transmission simultaneously, and therefore the communication speed is improved by times or even tens of times. In addition, the vortex light beam is also applied to the fields of optical detection, optical remote sensing and the like, and in numerous applications of the vortex light beam, a key parameter, namely a topological value is always inseparable from the application principle of the vortex light beam; therefore, how to realize accurate and efficient vortex light beam topology value detection is a fundamental stone for vortex light beam related application.
Research on detection of the topological values of vortex beams has been established for decades: since the Fired proves the existence of the optical vortex in the angle of numerical operation, how to realize high-precision topological value detection is always the core of the relevant research of vortex beams. From the earliest topological value detection method based on interference to the later topological value detection method based on diffraction and mode decomposition, the accuracy of the topological value detection is increasingly improved, and the capability of the detection method for resisting environmental disturbance is gradually enhanced; however, these methods rely on complex optical systems or are limited to more stringent preconditions for topology value detection. In recent years, with the vigorous development of adaptive optics, a shack hartmann wavefront sensor, an important device in the adaptive optics, is proved to be used for detecting the topological value of a vortex light beam; due to the flexible, convenient and accurate characteristics of the shack Hartmann wavefront sensor, the topological value detection method based on the shack Hartmann wavefront sensor is not only not output to other topological value detection methods in the precision level, but also greatly simplifies a detection system and is free from the limitation of the limitation condition, so that the method gradually becomes one of mainstream topological value detection methods.
A number of innovative works have also been proposed in succession, such as the methods described in the documents [ Chen M, Roux F S, Olivier J C.Detection of phase singulates with a Shack-Hartmann wave front sensor [ J ]. Journal of the Optical Society of America A,2007,24(7):1994 2002] and the documents [ Huang H, Luo J, Matsui Y, et al, elevation-connected vortex method for access position detection of Optical vortices using Shack-Hartmann wave front sensor [ J ]. Optical Engineering,2015,54(11):111302], however these methods are applicable to single vortex light beams only without exception, and in practical applications such as Optical communication, multiple vortices are usually included in the same light beam. Therefore, how to realize the simultaneous and accurate topological value detection of each optical vortex in the optical beam with multiple optical vortex is a difficult problem to be solved urgently.
Disclosure of Invention
In view of the above, the invention provides a multi-optical vortex light beam topological value detection method based on deep learning and a shack Hartmann wavefront sensor, which uses the thought of an intensity ridge extraction method for reference, skillfully converts the extraction of an intensity ridge into a semantic segmentation problem, and simultaneously designs the method based on a deep neural network of U-Net, thereby realizing the simultaneous and accurate topological value detection of a plurality of optical vortices.
A multi-optical vortex light beam topological value detection method based on deep learning and a shack Hartmann wavefront sensor comprises the following steps:
(1) collecting a multi-optical vortex light beam image by using a shack Hartmann wavefront sensor, and obtaining an average phase slope distribution diagram of the multi-optical vortex light beam image;
(2) calculating according to the multi-optical vortex light beam image to obtain corresponding intensity and distribution diagram Isum；
(3) Training a network model based on U-Net structure for intensity and distribution diagram IsumDividing two regions inside the intensity ridge (including the area above the intensity ridge) and outside the intensity ridge;
(4) performing boundary extraction and processing on the segmentation result to obtain a closed loop of the light vortex by light vortex;
(5) and calculating the rotation value of the obtained light vortex-by-light vortex closed loop by using a generalized contour sum method, thereby obtaining the topological value of each light vortex.
Further, in the step (1), after the multi-optical vortex light beam image is collected by using the shack Hartmann wavefront sensor, the background noise of the multi-optical vortex light beam image needs to be removed.
Further, the intensity and distribution profile I is calculated in the step (2) by the following formulasum；
Figure BDA0003229053780000031
Wherein: i (xi, eta) represents the intensity of the coordinate point (xi, eta) in the multi-light vortex light beam image, Isum(i, j) denotes a shack Hartmann wavefront sensor lens arrayIntensity sum value theta of corresponding area of ith row and jth column lensijAnd all coordinate points in the corresponding area of the ith row and the jth column lens in the lens array are represented as a set.
Further, training data required in the process of training the network model in the step (3) is obtained in the following manner;
3.1 preparing an input-output pair of single vortex images, which comprises an input image and an output image, wherein the input image is an intensity and distribution map of single vortex far-field distribution, the output image is a binary image, the intensity value of a point in an intensity ridge (including the point on the intensity ridge) is 1, the intensity value of a point outside the intensity ridge is 0, and the intensity ridge is determined by a mean brightest intensity ring method of watershed transform prior;
3.2, cutting the input and output pairs of the single eddy image in a unified area, wherein the cutting boundary is a circumscribed rectangle of a bright area in the intensity and distribution diagram;
3.3 generating a blank multi-vortex image pair with the pixel values of 0, equally dividing the blank multi-vortex image pair into 4 areas of 2 multiplied by 2, then generating a random number with the value range of [0,1] for each area, and taking whether the random number is more than 0.5 as a judgment mark for inserting the cut image pair in the area;
3.4 for any region to be inserted, randomly selecting a pair from all the cut image pairs, and inserting the pair into a blank multi-optical vortex image pair to obtain an input image for model training and a truth label image.
Further, the insertion position of the cut image pair in the step 3.4 is determined by the following formula;
Figure BDA0003229053780000032
Figure BDA0003229053780000033
wherein: (x, y) represents the coordinates of the position of insertion of the pair of cut images, (x)c,yc) To representThe coordinate of the center point of the region to be inserted, H and W are the height and width of the region to be inserted respectively, H and W are the height and width of the pair of cut images respectively, floor () is a downward integer operator, and rand () represents a random number generation operator in a bracket interval.
Further, the loss function expression adopted in the training process of the network model in the step (3) is as follows:
Figure BDA0003229053780000041
wherein: DiceLoss represents a dice loss function, Y' and Y are a segmentation result graph output by the network model and a truth label image corresponding to the segmentation result graph respectively, and | | represents an image area operator.
Further, in the step (4), boundary extraction is performed on the segmentation result to obtain closed loops of the light vortex by light vortex, and then a closed operation is performed on each closed loop to avoid the shape of the closed loop from being too uneven.
Further, the generalized profile and method in the step (5) calculates a value of the vorticity of the light-vortex-by-light closed loop based on the following expression;
Figure BDA0003229053780000042
wherein: cir, K is the rotation value of the optical vortex-by-optical closed loop, K is the number of points on the optical vortex-by-optical closed loop,
Figure BDA0003229053780000043
and
Figure BDA0003229053780000044
respectively, the phase slope and the path vector S at the kth point on the optical vortex-by-vortex closed loopx,kAnd Sy,kRespectively phase slope
Figure BDA0003229053780000045
Component in horizontal and vertical directions,/x,kAnd ly,kAre respectively path vectors
Figure BDA0003229053780000046
Components in the horizontal and vertical directions.
Further, the phase slope
Figure BDA0003229053780000047
Sum path vector
Figure BDA0003229053780000048
The component expression of (a) is as follows:
Figure BDA0003229053780000049
Figure BDA00032290537800000410
wherein:
Figure BDA00032290537800000411
indicating the coordinates at the kth point on the optical vortex-by-vortex closed loop,
Figure BDA00032290537800000412
and
Figure BDA00032290537800000413
are respectively coordinates
Figure BDA00032290537800000414
The average phase slope at a point is the component in the horizontal and vertical directions.
Further, in the step (5), a topological value of each optical vortex is calculated by the following formula;
Figure BDA00032290537800000415
wherein: cir is the rotation value of the optical vortex-by-optical vortex closed loop, and TC is the topological value of the corresponding optical vortex.
The topological value detection method based on deep learning and the shack Hartmann wavefront sensor can simultaneously and accurately detect the topological values of a plurality of optical vortexes in the vortex optical beam, so that the method has a high practical application value. Taking the application scenario of optical communication based on vortex beams as an example, vortex beams with different topological values in the application scenario correspond to different channels, and information can be independently encoded; in order to greatly increase the information transmission rate, in actual transmission, a plurality of vortex light beams with different topological values are coupled into the same light beam to be transmitted simultaneously. Therefore, in order to acquire accurate target information at a signal receiving end, the topological value of each optical vortex in the received light beam needs to be simultaneously and accurately identified so as to realize decoupling among different channels and finally decode the target information.
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FIG. 1 is a schematic flow chart of a multi-optical vortex beam topology value detection method according to the present invention.
FIG. 2 is an intensity and distribution plot of a multi-vortex beam image.
FIG. 3 is a single vortex input output versus image.
Fig. 4(a) is a single-vortex input-output pair image after cropping, in which the gray portion is the area cropped away.
Fig. 4(b) is a generated blank multi-vortex image pair, which is equally area-divided into four regions to be inserted.
Fig. 4(c) shows a finally generated multiple optical vortex input-output pair image.
Fig. 5 is a schematic diagram of a light-vortex-by-light closed loop extracted from a segmentation result graph.
Detailed Description
In order to more specifically describe the present invention, the following detailed description is provided for the technical solution of the present invention with reference to the accompanying drawings and the specific embodiments.
As shown in fig. 1, the method for detecting the topology value of the multi-optical vortex light beam based on the deep learning and shack hartmann wavefront sensor of the present invention includes the following steps:
s1, multiple optical vortex light beams are incident into a shack Hartmann wavefront sensor to collect multiple optical vortex images, and then an average phase slope distribution diagram of the multiple optical vortices is obtained.
S2, calculating the collected multi-optical vortex image by the following formula to obtain the intensity and distribution diagram I shown in the figure 2sum：
Figure BDA0003229053780000061
S3, in combination with a network training mode, the intensity and distribution map is divided into two areas, namely an intensity intraridge area (including an intensity intraridge area) and an intensity extraridge area, by using the U-Net, and the specific steps are as follows:
s3.1 preparation of training data:
firstly, preparing input-output pairs of single eddy images: the input image is a single eddy far-field distribution intensity and distribution diagram; the output image is a binary image, the intensity value of the point in the intensity ridge (including the point on the intensity ridge) is 1, the intensity value of the point outside the intensity ridge is 0, the intensity ridge is determined by the mean brightest intensity ring method of watershed transform prior, and the input and output pair obtained under the condition of single vortex is shown in fig. 3.
The single vortex input-output pair obtained above is then cropped in a uniform region with the cropping boundary being a circumscribed rectangle of the bright areas in the intensity and profile to generate an image pair as shown in fig. 4 (a).
A blank multi-vortex image pair having pixel values of 0 is generated and equally divided into four regions as shown in fig. 4 (b).
And generating a random number with the value range of [0,1] for each area, and taking whether the random number is larger than 0.5 as a judgment mark for inserting the cut image pair in the area.
And finally, for each region to be inserted, randomly extracting a pair from all the cut image pairs, and inserting the pair into the blank multi-optical vortex image pair, wherein the insertion position is determined by the following formula:
Figure BDA0003229053780000062
Figure BDA0003229053780000063
the resulting multi-vortex image pair is shown in fig. 4 (c).
S3.2 preparation of verification data: the input-output pair in the case of a single vortex is taken as the validation data.
And S3.3, initializing the network by using a kaiming initialization mode, and training the network by using training data. In order to continuously update the parameters of the network to improve the performance of the network, the network is supervised by using a loss function with true values continuously in the network training process, and then a back propagation algorithm is combined to enable supervision signals to be transmitted from the loss function to the shallow layer of the network layer by layer so as to guide the network to perform overall optimization and parameter updating. The loss function used for network supervision is as follows:
Figure BDA0003229053780000064
and S3.4, after each round of training is finished, verifying the current network performance by using the verification data set, and storing the network parameters under the optimal performance.
And S4, performing boundary extraction of light vortexes on the segmentation result by using a bwboundaries function embedded in the MATLAB, performing post-processing on the extracted boundary by using an close function embedded in the MATLAB, and after the post-processing, wherein the intensity ridge of each light vortex is shown in figure 5.
And S5, calculating the rotation value of the intensity ridge obtained in the last step by utilizing a generalized contour sum method, and further obtaining a topological value of each optical vortex.
The generalized contour sum method solves the expression for the rotation value of the closed loop as follows:
Figure BDA0003229053780000071
wherein: cir is the calculated rotation, K is the number of points on the closed loop,
Figure BDA0003229053780000072
respectively, the phase slope and the path vector at the k-th point on the closed loop.
Phase slope (S)x,k,Sy,k) Sum path vector (l)x,k,ly,k) The calculation formula of (a) is as follows:
Figure BDA0003229053780000073
Figure BDA0003229053780000074
wherein:
Figure BDA0003229053780000075
representing the coordinates at the kth point on the closed loop,
Figure BDA0003229053780000076
and
Figure BDA0003229053780000077
the components of the average phase slope at that point along the horizontal and vertical directions, respectively.
And finally, solving the topological value TC of the optical vortex by the following formula:
Figure BDA0003229053780000078
in order to verify that the method can effectively detect the topological value of the multi-optical vortex light beam, the vortex light beam containing 4 optical vortices with equal topological values is generated, and the topological value is changed from +/-1 to +/-10. The method is used for detecting the topological value of the multi-optical vortex light beam under each topological value, and experimental results show that the method obtains 100% detection accuracy under all topological value conditions, so that the method can accurately and effectively detect the topological value of the multi-optical vortex light beam.
The previous description of the specific embodiments is provided to enable any person skilled in the art to make or use the present invention. It will be readily apparent to those skilled in the art that various modifications to the specific embodiments described above may be made, and the generic principles described herein may be applied to other embodiments without the use of the inventive faculty. Therefore, the present invention is not limited to the above embodiments, and those skilled in the art should make improvements and modifications to the present invention based on the disclosure of the present invention within the protection scope of the present invention.

Claims (7)

1. A multi-optical vortex light beam topological value detection method based on deep learning and a shack Hartmann wavefront sensor comprises the following steps:
(1) collecting a multi-optical vortex light beam image by using a shack Hartmann wavefront sensor, and obtaining an average phase slope distribution diagram of the multi-optical vortex light beam image;
(2) calculating according to the multi-optical vortex light beam image to obtain corresponding intensity and distribution diagram Isum；
(3) Training a network model based on U-Net structure for intensity and distribution diagram IsumDividing two areas, namely an inner area of the intensity ridge and an outer area of the intensity ridge; training data required in the process of training the network model is obtained in the following mode;
3.1 preparing an input-output pair of the single vortex image, which comprises an input image and an output image, wherein the input image is an intensity and distribution map of single vortex far-field distribution, the output image is a binary image, the intensity value of an inner point of an intensity ridge is 1, the intensity value of an outer point of the intensity ridge is 0, and the intensity ridge is determined by a mean brightest intensity ring method of watershed transform prior;
3.2, cutting the input and output pairs of the single eddy image in a unified area, wherein the cutting boundary is a circumscribed rectangle of a bright area in the intensity and distribution diagram;
3.3 generating a blank multi-vortex image pair with the pixel values of 0, equally dividing the blank multi-vortex image pair into 4 areas of 2 multiplied by 2, then generating a random number with the value range of [0,1] for each area, and taking whether the random number is more than 0.5 as a judgment mark for inserting the cut image pair in the area;
3.4 for any region to be inserted, randomly selecting a pair from all the cut image pairs, and inserting the pair into a blank multi-optical vortex image pair to obtain an input image and a truth label image for model training; wherein the insertion position of the cut image pair is determined by the following formula;
Figure FDA0003579395730000011
Figure FDA0003579395730000012
wherein: (x, y) represents the coordinates of the position of insertion of the pair of cut images, (x)c,yc) Representing the coordinate of the central point of the region to be inserted, H and W are respectively the height and width of the region to be inserted, H and W are respectively the height and width of the pair of cut images, floor () is a downward integer operator, and rand () represents a random number generation operator in a bracket interval;
the loss function expression adopted in the process of training the network model is as follows:
Figure FDA0003579395730000021
wherein: DiceLoss represents a dice loss function, Y' and Y are a segmentation result graph output by a network model and a corresponding truth label image thereof respectively, and | | represents an image area operator;
(4) performing boundary extraction and processing on the segmentation result to obtain a closed loop of the light vortex by light vortex;
(5) and calculating the rotation value of the obtained light vortex-by-light vortex closed loop by using a generalized contour sum method, thereby obtaining the topological value of each light vortex.
2. The method for detecting the topological value of the multi-optical vortex beam according to claim 1, wherein: in the step (1), after the multi-optical vortex light beam image is collected by using the shack Hartmann wavefront sensor, the background noise of the multi-optical vortex light beam image needs to be removed.
3. The method for detecting the topological value of the multi-optical vortex beam according to claim 1, wherein: in the step (2), the intensity and distribution profile I is calculated by the following formulasum；
Figure FDA0003579395730000022
Wherein: i (xi, eta) represents the intensity of the coordinate point (xi, eta) in the multi-light vortex light beam image, Isum(i, j) represents the intensity and value of the corresponding area of the ith row and jth column lens in the shack Hartmann wavefront sensor lens array, thetaijAnd all coordinate points in the corresponding area of the ith row and the jth column lens in the lens array are represented as a set.
4. The method for detecting the topological value of the multi-optical vortex beam according to claim 1, wherein: in the step (4), boundary extraction is performed on the segmentation result to obtain closed loops of the light vortex by light vortex, and then closed operation is performed on each closed loop to avoid the shape of the closed loop from being too uneven.
5. The method for detecting the topological value of the multi-optical vortex beam according to claim 1, wherein: calculating the rotation degree value of the light-vortex-by-light closed loop based on the following expression by the generalized contour sum method in the step (5);
Figure FDA0003579395730000023
wherein: cir, K is the rotation value of the optical vortex-by-optical closed loop, K is the number of points on the optical vortex-by-optical closed loop,
Figure FDA0003579395730000024
and
Figure FDA0003579395730000025
respectively, the phase slope and the path vector S at the kth point on the optical vortex-by-vortex closed loopx,kAnd Sy,kRespectively phase slope
Figure FDA0003579395730000026
Component in horizontal and vertical directions,/x,kAnd ly,kAre respectively path vectors
Figure FDA0003579395730000027
Components in the horizontal and vertical directions.
6. The method for detecting the topological value of the multi-optical vortex beam according to claim 5, wherein: the phase slope
Figure FDA0003579395730000031
Sum path vector
Figure FDA0003579395730000032
The component expression of (a) is as follows:
Figure FDA0003579395730000033
Figure FDA0003579395730000034
wherein:
Figure FDA0003579395730000035
indicating the coordinates at the kth point on the optical vortex-by-vortex closed loop,
Figure FDA0003579395730000036
and
Figure FDA0003579395730000037
are respectively coordinates
Figure FDA0003579395730000038
The average phase slope at a point is the component in the horizontal and vertical directions.
7. The method for detecting the topological value of the multi-optical vortex beam according to claim 1, wherein: calculating a topological value of each optical vortex in the step (5) by the following formula;
Figure FDA0003579395730000039
wherein: cir is the rotation value of the optical vortex-by-optical vortex closed loop, and TC is the topological value of the corresponding optical vortex.
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