A method and system for optimizing a dual-focus optical system based on fundamental mode Gaussian beam

Abstract

The invention relates to a method and system for optimizing a bifocal optical system based on a fundamental mode Gaussian beam, and the method comprises the following steps: deriving a light intensity distribution formula on an axis of a fundamental mode Gaussian beam after the beam passes through the bifocal optical system; obtaining a light intensity distribution diagram on an axis of the beam after the beam passes through the bifocal optical system; dividing the light intensity distribution diagram on the axis into a plurality of intervals, taking a median for each interval on the axis of the light intensity distribution diagram on the axis, and taking the median of each interval as the light intensity value of the corresponding interval; creating a light intensity correction model, measuring the light intensity values ​​of a plurality of designated points in real time, and calculating the corresponding theoretical light intensity values ​​of the plurality of designated points, inputting the light intensity values ​​of the plurality of designated points measured in real time and the corresponding theoretical light intensity values ​​into the light intensity correction model for training, and then inputting the median of each interval into the light intensity correction model, and outputting a corrected value of the median of each interval; and performing light intensity compensation processing on each interval based on the difference between the corrected median and a preset standard value, thereby improving the stability of the optical system.

Description

Technical Field

[0001] The invention belongs to the technical field of laser optics, and in particular relates to a method for optimizing a dual-focus optical system based on a fundamental mode Gaussian beam. Background Art

[0002] The fundamental mode Gaussian beam is one of the most important basic beams. The intensity distribution of the fundamental mode Gaussian beam is a circular spot, with the strongest light intensity at the center and gradually weakening toward the edge, showing a Gaussian distribution. This distribution characteristic gives the fundamental mode Gaussian beam high spatial coherence and geometric optical properties. In addition, its equiphase surface is a spherical surface with a continuously changing center of curvature, and the amplitude and intensity maintain a Gaussian distribution within the cross section. The fundamental mode Gaussian beam can be regarded as a non-uniform spherical wave around its propagation axis. As the transmission distance increases, the beam will diverge according to a certain rule, but its divergence angle is relatively small, so that the beam can still maintain a high power density at a long distance.

[0003] At a certain Fresnel number, when the wavelength is λ After the fundamental mode Gaussian beam passes through the bifocal optical system composed of Fresnel zone plate and thin lens, a wavy light intensity distribution diagram is formed on the axis. The light intensity at each point on the axis is not the same, and the different light intensity distribution on the axis will affect the stability of the optical system. Therefore, how to optimize the optical system and improve its stability based on the wavy light intensity distribution on the axis after the fundamental mode Gaussian beam passes through the bifocal optical system composed of Fresnel zone plate and thin lens is a technical problem that needs to be solved urgently. Summary of the invention

[0004] The purpose of the present invention is to provide a method for optimizing a bifocal optical system based on a fundamental mode Gaussian beam, so as to optimize the optical system and improve its stability based on the wavy light intensity distribution formed on the axis after the fundamental mode Gaussian beam passes through the bifocal optical system composed of a Fresnel zone plate and a thin lens.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0006] In a first aspect, a method for optimizing a dual-focus optical system based on a fundamental mode Gaussian beam is provided, comprising the following steps:

[0007] S1: Based on the generalized Huygens-Fresnel diffraction integral formula, the formula for the axial light intensity distribution of a fundamental mode Gaussian beam with a wavelength of λ after passing through a bifocal optical system consisting of a Fresnel zone plate and a thin lens is derived;

[0008] S2: based on the on-axis light intensity distribution formula, obtaining an on-axis light intensity distribution diagram of a fundamental mode Gaussian beam with a wavelength of λ after passing through the bifocal optical system composed of the Fresnel zone plate and the thin lens;

[0009] S3: Divide the light intensity distribution diagram on the axis into a number of intervals in the direction of the axis, and the division standard of the several intervals is: the difference between the light intensity value corresponding to the left endpoint and the light intensity value corresponding to the right endpoint of each interval is n% of the light intensity corresponding to the left endpoint;

[0010] S4: taking the median of each interval on the axial direction of the light intensity distribution diagram on the axis, and mapping each interval to the median of each interval, and taking the median of each interval as the light intensity value of the corresponding interval;

[0011] S5: Create a light intensity correction model, measure the light intensity values ​​of several designated points in real time, and calculate the corresponding theoretical light intensity values ​​of the several designated points based on the light intensity distribution formula on the axis in step S1, and input the light intensity values ​​of the several designated points measured in real time and the corresponding theoretical light intensity values ​​into the light intensity correction model for training, and then input the median value of each interval into the light intensity correction model, and output the correction value of the median value of each interval;

[0012] S6: Calculate the difference between the corrected median value of each interval and the preset standard value, and perform light intensity compensation processing on each interval based on the difference between the corrected median value of each interval and the preset standard value.

[0013] Preferably, the specific process of dividing the light intensity distribution diagram on the axis into a plurality of intervals in the direction of the axis in step S3 is as follows:

[0014] S31: Set the starting endpoint on the axis as the left endpoint of the first interval, and set the light intensity value of the starting value on the axis to I 0, then the right endpoint of the first interval is the first light intensity value to the right of the starting endpoint. I The point on the axis corresponding to 0*(1+n%) or the first light intensity value is I The point on the axis corresponding to 0*(1-n%);

[0015] S32: Taking the right endpoint of the first interval as the left endpoint of the second interval, calculating the right endpoint of the second interval, the right endpoint of the second interval being the first light intensity value to the right of the left endpoint of the second interval I 0*(1+n%) 2 or I 0*(1-n 2 %)or I 0*(1-n%) 2 The corresponding point on the axis;

[0016] S33: Taking the right endpoint of the second interval as the left endpoint of the third interval, calculating the right endpoint of the third interval, the right endpoint of the third interval being the first light intensity value to the right of the left endpoint of the third interval I 0*(1+n%) 3 orI 0*(1+n%) 2 *(1-n%) or I 0*(1-n 2 %)*(1+n%) or I 0*(1-n 2 %)*(1-n%) or I 0*(1-n%) 2 *(1+n%) or I 0*(1-n%) 3 ;

[0017] S34: Calculate the left and right endpoints of the fourth interval to the nth interval in this way, where the left endpoint of the nth interval is the right endpoint of the n-1th interval, and the right endpoint of the nth interval is the point on the axis corresponding to the first light intensity value to the right endpoint of the n-1th interval multiplied by (1+n%) or (1-n%).

[0018] Preferably, the light intensity value of the starting value corresponding to the first interval is I 0, then the light intensity value I 0*(1+n%) or light intensity value I The n% in 0*(1-n%) represents the rate of change of the light intensity value at the right endpoint of the interval relative to the light intensity value at the left endpoint, and n% is set to the critical value of the degree of light intensity change that can be perceived by the human eye.

[0019] Preferably, the process of taking the median of a certain interval on the axis in step S4 is as follows:

[0020] S41: Take the minimum value of the light intensity values ​​corresponding to each point in a certain interval, recorded as I min , take the maximum value of the light intensity values ​​corresponding to each point in the interval, recorded as I max , then the median value of the light intensity in this interval is ( I min + I max ) / 2;

[0021] S42: median the other intervals on the axis of the light intensity distribution diagram on the axis respectively, and the process of medianizing the other intervals is the same as the process of medianizing in step S41.

[0022] Preferably, the light intensity correction model in step S5 is a deep belief network model, which includes an input layer, multiple hidden layers and an output layer, wherein the input layer is a visible layer, used to receive the light intensity values ​​of several specified points measured in real time and the corresponding theoretical light intensity values, each hidden layer is composed of multiple neurons, and the multiple neurons capture the relationship between the light intensity values ​​of several specified points measured in real time and the corresponding theoretical light intensity values ​​by learning the probability distribution of the light intensity values ​​of several specified points measured in real time and the corresponding theoretical light intensity values, and the output layer is used to map the theoretical median of each interval to the corrected median based on the captured relationship between the light intensity values ​​of several specified points measured in real time and the corresponding theoretical light intensity values.

[0023] Preferably, the training process of the light intensity correction model in step S5 is:

[0024] S51: training each layer in the light intensity correction model independently, wherein each layer learns the representation of the correction value between the light intensity values ​​of a plurality of designated points measured in real time and the corresponding theoretical light intensity values, and the training is performed from the bottom layer to the top layer;

[0025] S52: Using a back propagation algorithm to perform network fine-tuning on the trained light intensity correction model;

[0026] In the process of fine-tuning the network of the light intensity correction model, the parameters of each layer of the light intensity correction model are optimized by a gradient descent algorithm.

[0027] In a second aspect, a bifocal optical system optimization system based on a fundamental mode Gaussian beam is provided, which is used to implement any one of the bifocal optical system optimization methods based on a fundamental mode Gaussian beam, including a light intensity distribution formula acquisition module, a light intensity distribution map drawing module, an interval division module, an interval median calculation module, a light intensity measurement module, a model creation module, a light intensity correction model, and a light intensity compensation module, wherein the light intensity distribution formula acquisition module is connected to the light intensity distribution map drawing module, the light intensity distribution map drawing module is connected to the interval division module, the interval division module is connected to the interval median calculation module, the interval median calculation module and the light intensity measurement module are connected to the light intensity correction model, the model creation module is connected to the light intensity correction model, and the light intensity correction model is connected to the light intensity compensation module;

[0028] The light intensity distribution formula acquisition module is used to obtain the light intensity distribution formula on the axis of a fundamental mode Gaussian beam with a wavelength of λ after passing through a bifocal optical system composed of a Fresnel zone plate and a thin lens;

[0029] The light intensity distribution diagram drawing module is used to draw the light intensity distribution diagram on the axis of the fundamental mode Gaussian light beam with a wavelength of λ after passing through the bifocal optical system composed of the Fresnel zone plate and the thin lens based on the light intensity distribution formula on the axis;

[0030] The interval division module is used to divide the light intensity distribution diagram on the axis into a number of intervals in the direction of the axis, and the division standard of the several intervals is: the difference between the light intensity value corresponding to the left endpoint and the light intensity value corresponding to the right endpoint of each interval is n% of the light intensity corresponding to the left endpoint;

[0031] The interval median calculation module is used to calculate the median of the light intensity values ​​of the divided intervals;

[0032] The light intensity measurement module is used to measure the light intensity values ​​of several designated points in real time;

[0033] The model creation module is used to create a light intensity correction model;

[0034] The light intensity correction model is used to input the light intensity values ​​of several designated points measured in real time and the corresponding theoretical light intensity values ​​into the light intensity correction model for training, and then input the median value of each interval into the light intensity correction model to output the correction value of the median value of each interval;

[0035] The light intensity compensation module is used to compensate the light intensity of each interval by outputting a correction value of the median of each interval based on the light intensity correction model.

[0036] The beneficial effects of the present invention include:

[0037] The present invention provides a dual-focus optical system optimization method based on a fundamental mode Gaussian beam, which derives the on-axis light intensity distribution formula of the fundamental mode Gaussian beam after passing through the dual-focus optical system; and obtains the on-axis light intensity distribution diagram of the fundamental mode Gaussian beam after passing through the dual-focus optical system; divides the on-axis light intensity distribution diagram into a plurality of intervals, takes the median of each interval on the axis of the on-axis light intensity distribution diagram, and takes the median of each interval as the light intensity value of the corresponding interval; creates a light intensity correction model, measures the light intensity values ​​of a plurality of designated points in real time and calculates the corresponding theoretical light intensity values ​​of the plurality of designated points, inputs the light intensity values ​​of the plurality of designated points measured in real time and the corresponding theoretical light intensity values ​​into the light intensity correction model for training, then inputs the median of each interval into the light intensity correction model, and outputs the corrected value of the median of each interval; and performs light intensity compensation processing on each interval based on the difference between the corrected median and a preset standard value.

[0038] Firstly, the on-axis light intensity distribution diagram of the fundamental mode Gaussian beam after passing through the bifocal optical system is obtained by the on-axis light intensity distribution formula of the fundamental mode Gaussian beam after passing through the bifocal optical system, and the diagram is divided into several intervals. Then, the median calculation is performed based on the intervals, and then the light intensity compensation is performed on each interval according to the median, so as to avoid compensating the light intensity of all points in the on-axis light intensity distribution diagram, which greatly reduces the amount of calculation and the light intensity compensation points, and improves the light intensity compensation efficiency.

[0039] Secondly, by creating a light intensity correction model, measuring the light intensity values ​​of several specified points in real time and calculating the corresponding theoretical light intensity values ​​of several specified points, the real-time measured light intensity values ​​of several specified points and the corresponding theoretical light intensity values ​​are input into the light intensity correction model for training, and then the median of each interval is input into the light intensity correction model, and the correction value of the median of each interval is output, which effectively avoids the difference between the theoretical light intensity distribution on the axis and the actual light intensity distribution, resulting in inaccurate subsequent light intensity compensation, thereby improving the accuracy of light intensity compensation, and then improving the stability of the optical system, thereby achieving optimization of the optical system.

[0040] Thirdly, by setting the division criteria of several intervals as the difference between the light intensity value corresponding to the left endpoint and the light intensity value corresponding to the right endpoint of each interval is n% of the light intensity corresponding to the left endpoint, where n% is the critical value of the degree of light intensity change that can be perceived by the human eye. In other words, although the light intensity distribution diagram is divided into intervals, the interval division criteria are critical values ​​that cannot be perceived by the human eye. On the one hand, the amount of calculation and light intensity compensation points are greatly reduced, and the light intensity compensation efficiency is improved. On the other hand, it can ensure that the degree of division does not affect the performance of the optical system.

[0041] Finally, by creating a light intensity correction model, training and optimizing the light intensity correction model, the light intensity correction model is made accurate, ensuring that the light intensity correction model is accurate for the specified point and thus ensuring the accuracy of subsequent light intensity compensation. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a schematic flow chart of the method for optimizing a dual-focus optical system based on a fundamental mode Gaussian beam of the present invention.

[0043] Figure 2 A simplified schematic diagram of a bifocal optical system consisting of a Fresnel zone plate and a thin lens.

[0044] Figure 3 Schematic diagram of the on-axis light intensity distribution of the fundamental mode Gaussian beam after passing through the Fresnel zone plate. DETAILED DESCRIPTION

[0045] The following is combined with Figure 1~Figure 3 The present invention is further described in detail:

[0046] Example 1

[0047] See attached Figure 1 As shown, a method for optimizing a dual-focus optical system based on a fundamental mode Gaussian beam comprises the following steps:

[0048] S1: Based on the generalized Huygens-Fresnel diffraction integral formula, the on-axis light intensity distribution formula of a fundamental mode Gaussian beam with a wavelength of λ after passing through a bifocal optical system composed of a Fresnel zone plate and a thin lens is derived. The light intensity distribution formula is a theoretical formula derived based on the generalized Huygens-Fresnel diffraction integral formula.

[0049] S2: Based on the on-axis light intensity distribution formula, the on-axis light intensity distribution diagram of the fundamental mode Gaussian beam with a wavelength of λ after passing through the bifocal optical system composed of the Fresnel zone plate and the thin lens is obtained. Since the above-mentioned light intensity distribution formula is a theoretical formula, the subsequent light intensity distribution diagram obtained based on the theoretical formula is also a theoretical light intensity distribution diagram after a specific wavelength λ passes through a specific bifocal optical system. The light intensity distribution diagram can be found in Figure 3 ;

[0050] S3: Divide the light intensity distribution diagram on the axis into a number of intervals in the direction of the axis, and the division standard of the several intervals is: the difference between the light intensity value corresponding to the left endpoint and the light intensity value corresponding to the right endpoint of each interval is n% of the light intensity corresponding to the left endpoint, and the division standard of the several intervals is set as the difference between the light intensity value corresponding to the left endpoint and the light intensity value corresponding to the right endpoint of each interval is n% of the light intensity corresponding to the left endpoint, where n% is the critical value of the degree of light intensity change that can be perceived by the human eye, that is to say, although the light intensity distribution diagram is divided into intervals, the division standard of the intervals is the critical value that cannot be perceived by the human eye, which greatly reduces the amount of calculation and the light intensity compensation point on the one hand, and improves the light intensity compensation efficiency, and on the other hand, it can ensure that the division degree does not affect the performance of the optical system.

[0051] S4: Take the median of each interval on the axis of the intensity distribution diagram on the axis, and map each interval to the median of each interval, and take the median of each interval as the intensity value of the corresponding interval. The reason for taking the median of the divided interval is that the median of the interval reflects the average intensity level of the interval to a certain extent, so it is reasonable to take the median as the intensity value of the interval. And the intensity distribution diagram on the axis of the fundamental mode Gaussian beam after passing through the bifocal optical system is obtained by the intensity distribution formula on the axis after the fundamental mode Gaussian beam passes through the bifocal optical system, and is divided into several intervals, and then the median is calculated based on the interval, and then the intensity compensation is performed on each interval according to the median, so as to avoid compensating the intensity of all points in the intensity distribution diagram on the axis, greatly reducing the amount of calculation and the intensity compensation points, and improving the efficiency of intensity compensation.

[0052] S5: Create a light intensity correction model, measure the light intensity values ​​of several designated points in real time, and calculate the corresponding theoretical light intensity values ​​of the designated points based on the light intensity distribution formula on the axis in step S1, and input the light intensity values ​​of several designated points measured in real time and the corresponding theoretical light intensity values ​​into the light intensity correction model for training, and then input the median of each interval into the light intensity correction model, and output the correction value of the median of each interval. Since the aforementioned light intensity distribution diagram is obtained based on the theoretical light intensity distribution formula, the light intensity distribution diagram here is also theoretical, but in practice, due to the difference between the environment or the Fresnel zone plate or the thin lens and the theory, the actual light intensity distribution on the axis of the fundamental mode Gaussian beam with a wavelength of λ after passing through the bifocal optical system composed of the Fresnel zone plate and the thin lens is also different from the theoretical light intensity distribution. Therefore, by creating a light intensity correction model, training and optimizing the light intensity correction model, the light intensity correction model is accurate, ensuring that the light intensity correction model has accuracy for the light intensity correction amount of the designated point, thereby ensuring the accuracy of the subsequent light intensity compensation.

[0053] S6: Calculate the difference between the corrected median of each interval and the preset standard value, and perform light intensity compensation processing on each interval based on the difference between the corrected median of each interval and the preset standard value. Since steps S1-S5 first obtain the theoretical light intensity distribution diagram, then divide the intervals, then calculate the median, and perform light intensity correction through the light intensity correction model, and finally perform light intensity compensation processing, the accuracy of light intensity compensation is guaranteed and the optimization of the optical system is achieved.

[0054] The wavelength is The fundamental mode Gaussian beam passes through the bifocal optical system composed of the Fresnel zone plate and thin lens, such as Figure 2 As shown, the number of half-wave zones of the Fresnel zone plate is Take the annular aperture of 2 as an example, the aperture is located on the incident surface RP 1, and behind it is a thin lens with a focal length of , whose axial geometric focus is , and point is located on the exit surface RP The on-axis observation point at 2 is at a distance from the geometric focus of z , assuming that the optical system is in a refractive index n = 1. Figure 2 Intermediate incident surface RP 1 to the exit surface RP 2 optical system, its transformation matrix is ​​expressed as:

[0055] (1);

[0056] In cylindrical coordinates Lower, incident surface RP The field distribution of a Gaussian beam on plane 1 is:

[0057] (2);

[0058] in, is the complex parameter of the incident fundamental mode Gaussian beam, A 0 is a complex constant, w 0 is the waist width of the fundamental mode Gaussian beam, is the wave number, r 0 is the radial coordinate.

[0059] When the number of half-wave zones of the Fresnel zone plate is an even number M =2, for the exit surface RP Observation point on 2 P , in the case of rotational symmetry, the field distribution on the incident surface can be obtained from the generalized Huygens-Fresnel diffraction integral formula, and because P The point is located on the axis field, that is r= 0, then the cylindrical coordinate form of its output field distribution is:

[0060] (3);

[0061] In the formula, L Center of annular aperture O To the observation point P The distance from Figure 2 Knowable ; After calculation:

[0062] (4);

[0063] Where: , ; is the Fresnel number of the fundamental mode Gaussian beam. The Fresnel numbers involved in the following discussions in this chapter are all the Fresnel numbers of this fundamental mode Gaussian beam.

[0064] When the number of half-wave zones of the Fresnel zone plate is an odd number, the output field distribution at the observation point is:

[0065] (5)

[0066] Substituting equation (1) into equation (5), after complex calculations, we get:

[0067] (6)

[0068] Consider the diffraction of the fundamental mode Gaussian beam by the Fresnel zone plate:

[0069] The radius of the ring plate on the Fresnel zone plate is:

[0070] (7)

[0071] in, M is the number of Fresnel half-wave zones, r M is the radius of the last half-wave band.

[0072] Substituting (7) into (4), we can get: M When is an even number, P The point emission field distribution is:

[0073] (8)

[0074] In the formula, α = r M 2 / w 0 2 Defined as the truncation parameter.

[0075] Substituting equation (3-7) into equation (3-6), we can get the value of the half-wave zone number of the Fresnel zone plate. M When is an odd number, P The point emission field distribution is:

[0076] (9)

[0077] Finally, summing the alternating exponentials in (8) and (9), we obtain P The field distribution expression of a point is:

[0078] (10)

[0079] The light intensity distribution on the axis is:

[0080] (11)

[0081] In the above formula, is the wavelength of the plane wave, M is the number of half-wave zones of the Fresnel zone plate, r 1. r 2. r 3 are the radius of the annular wave band, f is the focal length of the thin lens, F is the on-axis geometric focus of the thin lens, P The point is located on the exit surface RP The on-axis observation point at 2, z for P Point and geometric focus F The distance between n is the refractive index,E () is on the axis P The output field distribution value of the point, A, B, C, D are matrix elements, i is an imaginary unit, E* ()for E () Take the conjugate. After taking the conjugate, the content in the phase disappears, and only the intensity distribution of the light field remains, which is I , A 0 is a complex constant, w 0 is the waist width of the fundamental mode Gaussian beam, k is the wave number, r 0 is the radial coordinate, r M is the radius of the last half-wave band, L Center of annular aperture O To the observation point P The distance q 0 is the complex parameter of the fundamental mode Gaussian beam related to the incident beam, , u is a dimensionless parameter. In calculus, dx Indicates the independent variable x The differential of d r0 is the independent variable r0 A very small change in r0 The differential of .

[0082] Example 2

[0083] On the basis of Embodiment 1, the specific process of dividing the light intensity distribution diagram on the axis into a plurality of intervals in the direction of the axis in step S3 is as follows:

[0084] S31: Set the starting endpoint on the axis as the left endpoint of the first interval, and set the light intensity value of the starting value on the axis to I 0, then the right endpoint of the first interval is the first light intensity value to the right of the starting endpoint. I The point on the axis corresponding to 0*(1+n%) or the first light intensity value is I The point on the axis corresponding to 0*(1-n%);

[0085] S32: Taking the right endpoint of the first interval as the left endpoint of the second interval, calculating the right endpoint of the second interval, the right endpoint of the second interval being the first light intensity value to the right of the left endpoint of the second interval I 0*(1+n%) 2 or I 0*(1-n 2 %)or I 0*(1-n%) 2 The corresponding point on the axis;

[0086] S33: Taking the right endpoint of the second interval as the left endpoint of the third interval, calculating the right endpoint of the third interval, the right endpoint of the third interval being the first light intensity value to the right of the left endpoint of the third interval I 0*(1+n%) 3 or I 0*(1+n%) 2 *(1-n%) or I 0*(1-n 2 %)*(1+n%) or I 0*(1-n 2 %)*(1-n%) or I 0*(1-n%) 2 *(1+n%) or I 0*(1-n%) 3 ;

[0087] S34: Calculate the left and right endpoints of the fourth interval to the nth interval in this way, where the left endpoint of the nth interval is the right endpoint of the n-1th interval, and the right endpoint of the nth interval is the point on the axis corresponding to the first light intensity value to the right endpoint of the n-1th interval multiplied by (1+n%) or (1-n%).

[0088] The division criteria for several intervals are set such that the difference between the light intensity value corresponding to the left endpoint and the light intensity value corresponding to the right endpoint of each interval is n% of the light intensity corresponding to the left endpoint, where n% is the critical value of the degree of light intensity change that can be perceived by the human eye. In other words, although the light intensity distribution diagram is divided into intervals, the interval division criteria are critical values ​​that cannot be perceived by the human eye. On the one hand, the amount of calculation and the light intensity compensation point are greatly reduced, and the light intensity compensation efficiency is improved. On the other hand, it can ensure that the degree of division does not affect the performance of the optical system.

[0089] In this embodiment, the light intensity value of the starting value corresponding to the first interval is I 0, then the light intensity value I 0*(1+n%) or light intensity value I The n% in 0*(1-n%) represents the rate of change of the light intensity value at the right endpoint of the interval relative to the light intensity value at the left endpoint, and n% is set to the critical value of the degree of light intensity change that can be perceived by the human eye.

[0090] The process of taking the median of a certain interval on the axis in step S4 is as follows:

[0091] S41: Take the minimum value of the light intensity values ​​corresponding to each point in a certain interval, recorded as I min, take the maximum value of the light intensity values ​​corresponding to each point in the interval, recorded as I max , then the median value of the light intensity in this interval is ( I min + I max ) / 2;

[0092] S42: median the other intervals on the axis of the light intensity distribution diagram on the axis respectively, and the process of medianizing the other intervals is the same as the process of medianizing in step S41.

[0093] Example 3

[0094] On the basis of Example 1 or Example 2, the light intensity correction model in step S5 is a deep belief network model, which includes an input layer, multiple hidden layers and an output layer, the input layer is a visible layer, used to receive the real-time measurement of light intensity values ​​of several specified points and the corresponding theoretical light intensity values, each hidden layer is composed of multiple neurons, and the multiple neurons capture the relationship between the real-time measurement of light intensity values ​​of several specified points and the corresponding theoretical light intensity values ​​by learning the probability distribution of the real-time measurement of light intensity values ​​of several specified points and the corresponding theoretical light intensity values, and the output layer is used to map the theoretical median of each interval to the corrected median based on the captured relationship between the real-time measurement of light intensity values ​​of several specified points and the corresponding theoretical light intensity values.

[0095] The training process of the light intensity correction model in step S5 is:

[0096] S51: Each layer in the light intensity correction model is trained independently. Each layer learns the representation of the correction value between the real-time measured light intensity values ​​of several specified points and the corresponding theoretical light intensity values, and the training is performed from the bottom layer to the top layer, which effectively ensures the effectiveness of the training.

[0097] S52: Use the back-propagation algorithm to perform network fine-tuning on the trained light intensity correction model, wherein in the process of performing network fine-tuning on the light intensity correction model, the parameters of each layer of the light intensity correction model are optimized by the gradient descent algorithm to ensure that the model can better adapt to the training data and improve the prediction or classification accuracy of specific tasks.

[0098] A bifocal optical system optimization system based on a fundamental mode Gaussian beam is used to implement any one of the bifocal optical system optimization methods based on a fundamental mode Gaussian beam, including a light intensity distribution formula acquisition module, a light intensity distribution map drawing module, an interval division module, an interval median calculation module, a light intensity measurement module, a model creation module, a light intensity correction model, and a light intensity compensation module. The light intensity distribution formula acquisition module is connected to the light intensity distribution map drawing module, the light intensity distribution map drawing module is connected to the interval division module, the interval division module is connected to the interval median calculation module, the interval median calculation module and the light intensity measurement module are connected to the light intensity correction model, the model creation module is connected to the light intensity correction model, and the light intensity correction model is connected to the light intensity compensation module.

[0099] The light intensity distribution formula acquisition module is used to obtain the light intensity distribution formula on the axis after the fundamental mode Gaussian beam with a wavelength of λ passes through the bifocal optical system composed of a Fresnel zone plate and a thin lens. The light intensity distribution graph drawing module is used to draw the light intensity distribution graph on the axis after the fundamental mode Gaussian beam with a wavelength of λ passes through the bifocal optical system composed of a Fresnel zone plate and a thin lens based on the light intensity distribution formula on the axis. The interval division module is used to divide the light intensity distribution graph on the axis into a plurality of intervals in the direction of the axis, and the division standard of the plurality of intervals is: the difference between the light intensity value corresponding to the left endpoint and the light intensity value corresponding to the right endpoint of each interval is n% of the light intensity corresponding to the left endpoint. The interval median calculation module is used to calculate the median of the light intensity values ​​of the divided intervals. The light intensity measurement module is used to measure the light intensity values ​​of a plurality of specified points in real time. The model creation module is used to create a light intensity correction model. The light intensity correction model is used to input the light intensity values ​​of several designated points measured in real time and the corresponding theoretical light intensity values ​​into the light intensity correction model for training, and then input the median value of each interval into the light intensity correction model to output the correction value of the median value of each interval. The light intensity compensation module is used to compensate the light intensity of each interval based on the correction value of the median value of each interval output by the light intensity correction model.

[0100] In summary, the present invention provides a method for optimizing a bifocal optical system based on a fundamental mode Gaussian beam, derives the formula for the on-axis light intensity distribution of the fundamental mode Gaussian beam after it passes through the bifocal optical system; and obtains a light intensity distribution diagram of the fundamental mode Gaussian beam on the axis after it passes through the bifocal optical system; divides the on-axis light intensity distribution diagram into a number of intervals, and takes the median of each interval on the axis of the on-axis light intensity distribution diagram, and uses the median of each interval as the light intensity value of the corresponding interval; creates a light intensity correction model, and measures the light intensity values ​​of a number of specified points in real time and calculates the corresponding theoretical light intensity values ​​of the number of specified points, inputs the real-time measured light intensity values ​​of the number of specified points and the corresponding theoretical light intensity values ​​into the light intensity correction model for training, and then inputs the median of each interval into the light intensity correction model, and outputs the corrected value of the median of each interval; and performs light intensity compensation processing on each interval based on the difference between the corrected median and the preset standard value.

[0101] The intensity distribution diagram of the fundamental mode Gaussian beam on the axis after passing through the bifocal optical system is obtained by the intensity distribution formula of the fundamental mode Gaussian beam on the axis after passing through the bifocal optical system, and is divided into several intervals, and then the median calculation is performed based on the interval, and then the intensity compensation is performed for each interval according to the median, so as to avoid compensating the intensity of all points in the intensity distribution diagram on the axis, greatly reducing the amount of calculation and the intensity compensation points, and improving the efficiency of intensity compensation. By creating an intensity correction model, measuring the intensity values ​​of several specified points in real time and calculating the corresponding theoretical intensity values ​​of several specified points, the intensity values ​​of several specified points measured in real time and the corresponding theoretical intensity values ​​are input into the intensity correction model for training, and then the median of each interval is input into the intensity correction model, and the correction value of the median of each interval is output, which effectively avoids the difference between the theoretical intensity distribution on the axis and the actual intensity distribution, resulting in inaccurate subsequent intensity compensation, thereby improving the accuracy of intensity compensation, thereby improving the stability of the optical system, and realizing the optimization of the optical system. By setting the division criteria of several intervals as n% of the light intensity corresponding to the left endpoint and the right endpoint of each interval, the difference between the light intensity value corresponding to the left endpoint is n%, where n% is the critical value of the degree of light intensity change that can be perceived by the human eye. In other words, although the light intensity distribution diagram is divided into intervals, the interval division criteria are critical values ​​that cannot be perceived by the human eye. On the one hand, the amount of calculation and light intensity compensation points are greatly reduced, and the light intensity compensation efficiency is improved. On the other hand, it can ensure that the degree of division does not affect the performance of the optical system. By creating a light intensity correction model, training and optimizing the light intensity correction model, the light intensity correction model is accurate, ensuring that the light intensity correction model is accurate for the light intensity correction amount of the specified point, thereby ensuring the accuracy of subsequent light intensity compensation.

Claims

1. A method for optimizing a dual-focus optical system based on a fundamental mode Gaussian beam, characterized in that: The following steps are involved: S1: Based on the generalized Huygens-Fresnel diffraction integral formula, the formula for the axial light intensity distribution of a fundamental mode Gaussian beam with a wavelength of λ after passing through a bifocal optical system consisting of a Fresnel zone plate and a thin lens is derived; S2: based on the on-axis light intensity distribution formula, obtaining an on-axis light intensity distribution diagram of a fundamental mode Gaussian beam with a wavelength of λ after passing through the bifocal optical system composed of the Fresnel zone plate and the thin lens; S3: Divide the light intensity distribution diagram on the axis into a number of intervals in the direction of the axis, and the division standard of the several intervals is: the difference between the light intensity value corresponding to the left endpoint and the light intensity value corresponding to the right endpoint of each interval is n% of the light intensity corresponding to the left endpoint; S4: taking the median of each interval on the axial direction of the light intensity distribution diagram on the axis, and mapping each interval to the median of each interval, and taking the median of each interval as the light intensity value of the corresponding interval; S5: Create a light intensity correction model, measure the light intensity values ​​of several designated points in real time, and calculate the corresponding theoretical light intensity values ​​of the several designated points based on the light intensity distribution formula on the axis in step S1, and input the light intensity values ​​of the several designated points measured in real time and the corresponding theoretical light intensity values ​​into the light intensity correction model for training, and then input the median value of each interval into the light intensity correction model, and output the correction value of the median value of each interval; S6: Calculate the difference between the corrected median value of each interval and the preset standard value, and perform light intensity compensation processing on each interval based on the difference between the corrected median value of each interval and the preset standard value.

2. The method for optimizing a dual-focus optical system based on a fundamental mode Gaussian beam according to claim 1, characterized in that: The specific process of dividing the light intensity distribution diagram on the axis into a plurality of intervals in the direction of the axis in step S3 is as follows: S31: Set the starting endpoint on the axis as the left endpoint of the first interval, and set the light intensity value of the starting value on the axis to I 0, then the right endpoint of the first interval is the first light intensity value to the right of the starting endpoint. I The point on the axis corresponding to 0*(1+n%) or the first light intensity value is I The point on the axis corresponding to 0*(1-n%); S32: Taking the right endpoint of the first interval as the left endpoint of the second interval, calculating the right endpoint of the second interval, the right endpoint of the second interval being the first light intensity value to the right of the left endpoint of the second interval I 0*(1+n%) 2 or I 0*(1-n 2 %)or I 0*(1-n%) 2 The corresponding point on the axis; S33: Taking the right endpoint of the second interval as the left endpoint of the third interval, calculating the right endpoint of the third interval, the right endpoint of the third interval being the first light intensity value to the right of the left endpoint of the third interval I 0*(1+n%) 3 or I 0*(1+n%) 2 *(1-n%) or I 0*(1-n 2 %)*(1+n%) or I 0*(1-n 2 %)*(1-n%) or I 0*(1-n%) 2 *(1+n%) or I 0*(1-n%) 3 ; S34: Calculate the left and right endpoints of the fourth interval to the nth interval in this way, where the left endpoint of the nth interval is the right endpoint of the n-1th interval, and the right endpoint of the nth interval is the point on the axis corresponding to the first light intensity value to the right endpoint of the n-1th interval multiplied by (1+n%) or (1-n%).

3. The method for optimizing a bifocal optical system based on a fundamental mode Gaussian beam according to claim 2, characterized in that: The light intensity value of the initial value corresponding to the first interval I 0, then the light intensity value I 0*(1+n%) or light intensity value I The n% in 0*(1-n%) represents the rate of change of the light intensity value at the right endpoint of the interval relative to the light intensity value at the left endpoint.

4. The method for optimizing a dual-focus optical system based on a fundamental mode Gaussian beam according to claim 1, characterized in that: The process of taking the median of a certain interval on the axis in step S4 is as follows: S41: Take the minimum value of the light intensity values ​​corresponding to each point in a certain interval, recorded as I min , take the maximum value of the light intensity values ​​corresponding to each point in the interval, recorded as I max , then the median value of the light intensity in this interval is ( I min + I max ) / 2; S42: median the other intervals on the axis of the light intensity distribution diagram on the axis respectively, and the process of medianizing the other intervals is the same as the process of medianizing in step S41.

5. The method for optimizing a dual-focus optical system based on a fundamental mode Gaussian beam according to claim 1, characterized in that: The light intensity correction model in step S5 is a deep belief network model, which includes an input layer, multiple hidden layers and an output layer. The input layer is a visible layer, which is used to receive the light intensity values ​​of several specified points measured in real time and the corresponding theoretical light intensity values. Each hidden layer is composed of multiple neurons. The multiple neurons capture the relationship between the light intensity values ​​of several specified points measured in real time and the corresponding theoretical light intensity values ​​by learning the probability distribution of the light intensity values ​​of several specified points measured in real time and the corresponding theoretical light intensity values. The output layer is used to map the theoretical median of each interval to the corrected median based on the captured relationship between the light intensity values ​​of several specified points measured in real time and the corresponding theoretical light intensity values.

6. The method for optimizing a dual-focus optical system based on a fundamental mode Gaussian beam according to claim 5, characterized in that: The training process of the light intensity correction model in step S5 is: S51: training each layer in the light intensity correction model independently, wherein each layer learns the representation of the correction value between the light intensity values ​​of a plurality of designated points measured in real time and the corresponding theoretical light intensity values, and the training is performed from the bottom layer to the top layer; S52: Using a back propagation algorithm to perform network fine-tuning on the trained light intensity correction model; In the process of fine-tuning the network of the light intensity correction model, the parameters of each layer of the light intensity correction model are optimized by a gradient descent algorithm.

7. A bifocal optical system optimization system based on fundamental mode Gaussian beam, used to implement a bifocal optical system optimization method based on fundamental mode Gaussian beam according to any one of claims 1 to 6, characterized in that: It includes a light intensity distribution formula acquisition module, a light intensity distribution map drawing module, an interval division module, an interval median calculation module, a light intensity measurement module, a model creation module, a light intensity correction model, and a light intensity compensation module. The light intensity distribution formula acquisition module is connected to the light intensity distribution map drawing module, the light intensity distribution map drawing module is connected to the interval division module, the interval division module is connected to the interval median calculation module, the interval median calculation module and the light intensity measurement module are connected to the light intensity correction model, the model creation module is connected to the light intensity correction model, and the light intensity correction model is connected to the light intensity compensation module; The light intensity distribution formula acquisition module is used to obtain the light intensity distribution formula on the axis of a fundamental mode Gaussian beam with a wavelength of λ after passing through a bifocal optical system composed of a Fresnel zone plate and a thin lens; The light intensity distribution diagram drawing module is used to draw the light intensity distribution diagram on the axis of the fundamental mode Gaussian light beam with a wavelength of λ after passing through the bifocal optical system composed of the Fresnel zone plate and the thin lens based on the light intensity distribution formula on the axis; The interval division module is used to divide the light intensity distribution diagram on the axis into a number of intervals in the direction of the axis, and the division standard of the several intervals is: the difference between the light intensity value corresponding to the left endpoint and the light intensity value corresponding to the right endpoint of each interval is n% of the light intensity corresponding to the left endpoint; The interval median calculation module is used to calculate the median of the light intensity values ​​of the divided intervals; The light intensity measurement module is used to measure the light intensity values ​​of several designated points in real time; The model creation module is used to create a light intensity correction model; The light intensity correction model is used to input the light intensity values ​​of several designated points measured in real time and the corresponding theoretical light intensity values ​​into the light intensity correction model for training, and then input the median value of each interval into the light intensity correction model to output the correction value of the median value of each interval; The light intensity compensation module is used to compensate the light intensity of each interval by outputting a correction value of the median of each interval based on the light intensity correction model.

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