Phase generation method of bessel beam phase plate and wavefront coding system

Abstract

The embodiment of the application provides a phase generation method of a Bessel beam phase plate and a wavefront coding system. The wavefront coding system comprises a first lens group, a second lens group and a Bessel beam phase plate. The back focal plane of the first lens group is coplanar with the front focal plane of the second lens group. The Bessel beam phase plate is located at the front focal plane of the second lens group and is used for modulating the phase of light to form a Bessel beam at the back focal plane of the second lens group. The Bessel beam can be obtained by modulating the Bessel beam phase plate, so that the extended focal depth is obtained in the wavefront coding system, the point spread function intensity distribution in the range of the extended focal depth is nearly unchanged and there is no lateral translation, and a high-quality recovered image can be obtained through subsequent digital processing.

Description

Technical Field

[0001] This application relates to the field of computational optical imaging technology, and in particular to a phase generation method and wavefront coding system for a Bessel beam phase plate. Background Technology

[0002] Wavefront coding is a computational imaging technique that integrates optical design and digital processing. Its core idea is to introduce a special phase mask at the aperture stop of the optical system to actively modulate the wavefront distribution of the system, thereby obtaining an intermediate image that is insensitive to defocus aberrations. A key feature is that the system's point spread function remains stable within a certain range. Although the intermediate image becomes blurred, a clear image can be recovered by decoding the acquired blurred image using digital image processing algorithms. The main advantages of this technique are that it significantly extends the system's depth of field, enabling mechanical focusing-free imaging, while reducing the requirements for the precision of optical component manufacturing and assembly tolerances, thus contributing to system miniaturization and cost reduction.

[0003] The phase mask is the core of wavefront coding. Existing phase masks are often cubic phase plates, and their phase expression is as follows: (x, y) = α(x 3 + y 3 ), where x and y are the coordinates in the height and width directions, respectively. (x, y) represents the phase at (x, y) on the phase mask, and α is a preset coefficient. This expression shows that the phase distribution is not rotationally symmetric. The system point spread function obtained using a cubic phase plate is as follows: Figure 1 As shown, it is also not rotationally symmetric. Figure 1 In the middle, the z-direction is the optical axis direction, and the y-direction is the width direction.

[0004] Depend on Figure 1 As can be seen, the point spread function at different optical axis positions is shifted. However, the same point spread function is usually used in the decoding process. Therefore, this shift will cause the point spread function used to be different from the actual point spread function, which in turn leads to a reduction in the quality of the recovered image. Summary of the Invention

[0005] The purpose of this application is to provide a phase generation method and wavefront coding system for a Bessel beam phase plate, so as to obtain an extended depth of focus in the wavefront coding system, in which the point spread function intensity distribution within the range is almost unchanged and there is no lateral translation, which is beneficial for obtaining a high-quality restored image through subsequent digital processing. The specific technical solution is as follows:

[0006] In a first aspect of this application, a wavefront coding system is provided, the wavefront coding system comprising a first lens group, a second lens group, and a Bessel beam phase plate;

[0007] The rear focal plane of the first lens group is coplanar with the front focal plane of the second lens group;

[0008] The Bessel beam phase plate is located at the front focal plane of the second lens group and is used to form a Bessel beam at the rear focal plane of the second lens group by modulating the phase of the light rays.

[0009] In a second aspect of this application, a phase generation method for a Bessel beam phase plate is provided, the method comprising:

[0010] Obtain the initial phase;

[0011] Based on the initial phase and preset amplitude, the complex amplitude at the front focal plane of the second lens group in the wavefront coding system described in the first aspect above is constructed as the first complex amplitude;

[0012] The first complex amplitude is adjusted in a direction that makes the complex amplitude formed at the back focal plane of the second lens group and the plurality of target field planes in the form of a Bessel beam to obtain the second complex amplitude; wherein each of the target field planes is parallel to the back focal plane and the distance between the target field plane and the back focal plane is not greater than a preset depth of focus;

[0013] The phase of the second complex amplitude is used as the phase of the phase plate of the Bessel beam.

[0014] In one possible embodiment, adjusting the first complex amplitude in a direction that causes the complex amplitude formed at the back focal plane and multiple target field planes to resemble a Bessel beam, to obtain the second complex amplitude, includes:

[0015] Until the preset iteration conditions are met, repeat the following steps:

[0016] The first complex amplitude is calculated as the complex amplitude formed by the first complex amplitude propagating from the front focal plane sequentially through multiple target field planes and back to the front focal plane, and is taken as the third complex amplitude; wherein, each time it propagates to a target field plane, the amplitude of the complex amplitude is modified to the amplitude of the Bessel beam at the target field plane;

[0017] The phase of the third complex amplitude is rotated symmetrically to obtain the fourth complex amplitude;

[0018] The amplitude of the third complex amplitude is modified to the preset amplitude, and the phase is modified to the phase of the fourth complex amplitude to obtain a new first complex amplitude. Then, the calculation is returned to obtain the complex amplitude formed by the first complex amplitude propagating from the front focal plane through multiple target field planes and the rear focal plane and back to the front focal plane, which is the third complex amplitude step, until the preset iteration condition is met.

[0019] If the iteration conditions are met, the latest obtained fourth complex amplitude is taken as the second complex amplitude;

[0020] In one possible embodiment, the iteration conditions include:

[0021] The loop executes for a preset number of times; or,

[0022] At each of the target field planes and the back focal plane, the difference between the amplitude formed by the first complex amplitude and the amplitude expected to be formed by the Bessel beam is less than a preset difference threshold.

[0023] In one possible embodiment, the calculation of the first complex amplitude as the third complex amplitude, formed by the first complex amplitude propagating sequentially from the front focal plane through multiple target field planes and then back to the front focal plane, includes:

[0024] The first complex amplitude is calculated by Fourier transform to obtain the complex amplitude formed by the propagation of the first complex amplitude from the front focal plane to the rear focal plane, which is then used as the fifth complex amplitude.

[0025] The fifth complex amplitude is calculated using the angular spectrum propagation function to obtain the complex amplitude formed by the beam propagating from the back focal plane back to the back focal plane sequentially through multiple target field planes, and is taken as the sixth complex amplitude; wherein, each time the beam propagates to a target field plane, the amplitude of the complex amplitude is modified to the amplitude of the Bessel beam at the target field plane;

[0026] The sixth complex amplitude is calculated by inverse Fourier transform and is used as the complex amplitude formed by the reverse propagation from the rear focal plane to the front focal plane.

[0027] In one possible embodiment, the phase modification of the third complex amplitude to obtain a fourth complex amplitude by rotational symmetry includes:

[0028] The third complex amplitude is averaged in the circumferential direction to obtain the fourth complex amplitude.

[0029] In one possible embodiment, obtaining the initial phase includes:

[0030] The phase of the conical mirror is obtained as the initial phase, and the phase of the conical mirror changes linearly with the radial distance.

[0031] In a third aspect of this application, a phase generation apparatus for a Bessel beam phase plate is provided, the apparatus comprising:

[0032] The acquisition module is used to acquire the initial phase;

[0033] An initialization module is used to construct, based on the initial phase and preset amplitude, a complex amplitude at the front focal plane of the second lens group in the wavefront coding system described in the first aspect above, as the first complex amplitude;

[0034] The calculation module is used to adjust the first complex amplitude in a direction that makes the complex amplitude formed at the back focal plane of the second lens group and the multiple target field planes in the form of a Bessel beam, to obtain a second complex amplitude; wherein each of the target field planes is parallel to the back focal plane and the distance between the target field plane and the back focal plane is not greater than a preset focal depth; and the phase of the second complex amplitude is used as the phase of the Bessel beam phase plate.

[0035] In one possible embodiment, the calculation module adjusts the first complex amplitude in a direction that causes the complex amplitude formed at the back focal plane and multiple target field planes to be in the form of a Bessel beam, to obtain a second complex amplitude, including:

[0036] Until the preset iteration conditions are met, repeat the following steps:

[0037] The first complex amplitude is calculated as the complex amplitude formed by the first complex amplitude propagating from the front focal plane sequentially through multiple target field planes and back to the front focal plane, and is taken as the third complex amplitude; wherein, each time it propagates to a target field plane, the amplitude of the complex amplitude is modified to the amplitude of the Bessel beam at the target field plane;

[0038] The phase of the third complex amplitude is rotated symmetrically to obtain the fourth complex amplitude;

[0039] The amplitude of the third complex amplitude is modified to the preset amplitude, and the phase is modified to the phase of the fourth complex amplitude to obtain a new first complex amplitude. Then, the calculation is returned to obtain the complex amplitude formed by the first complex amplitude propagating from the front focal plane through multiple target field planes and the rear focal plane and back to the front focal plane, which is the third complex amplitude step, until the preset iteration condition is met.

[0040] If the iteration conditions are met, the latest obtained fourth complex amplitude is taken as the second complex amplitude;

[0041] In one possible embodiment, the iteration conditions include:

[0042] The loop executes for a preset number of times; or,

[0043] At each of the target field planes and the back focal plane, the difference between the amplitude formed by the first complex amplitude and the amplitude expected to be formed by the Bessel beam is less than a preset difference threshold.

[0044] In one possible embodiment, the calculation of the first complex amplitude as the third complex amplitude, formed by the first complex amplitude propagating sequentially from the front focal plane through multiple target field planes and then back to the front focal plane, includes:

[0045] The first complex amplitude is calculated by Fourier transform to obtain the complex amplitude formed by the propagation of the first complex amplitude from the front focal plane to the rear focal plane, which is then used as the fifth complex amplitude.

[0046] The fifth complex amplitude is calculated using the angular spectrum propagation function to obtain the complex amplitude formed by the beam propagating from the back focal plane back to the back focal plane sequentially through multiple target field planes, and is taken as the sixth complex amplitude; wherein, each time the beam propagates to a target field plane, the amplitude of the complex amplitude is modified to the amplitude of the Bessel beam at the target field plane;

[0047] The sixth complex amplitude is calculated by inverse Fourier transform and is used as the complex amplitude formed by the reverse propagation from the rear focal plane to the front focal plane.

[0048] In one possible embodiment, the phase modification of the third complex amplitude to obtain a fourth complex amplitude by rotational symmetry includes:

[0049] The third complex amplitude is averaged in the circumferential direction to obtain the fourth complex amplitude.

[0050] In one possible embodiment, obtaining the initial phase includes:

[0051] The phase of the conical mirror is obtained as the initial phase, and the phase of the conical mirror changes linearly with the radial distance.

[0052] In a fourth aspect of this application, a wavefront-coded optical system is also provided, comprising:

[0053] A first lens group, a phase plate, and a second lens group are arranged sequentially along the optical path;

[0054] The phase plate is positioned at the overlap of the rear focal plane of the first lens group and the front focal plane of the second lens group, and serves as the aperture stop of the optical system.

[0055] The phase plate is configured to have a target phase distribution such that the point spread function of the optical system is approximately in the form of a zero-order Bessel function.

[0056] The method for generating the target phase distribution includes:

[0057] The initial light field is set using the phase of the conical mirror as the initial phase;

[0058] Multiple iterative loops of Fourier transform and inverse Fourier transform are performed between the plane where the phase plate is located and the back focal plane of the second lens group.

[0059] In each iteration, the light field is propagated to multiple target field planes set along the optical axis, and the amplitude of each target field plane is replaced with the target amplitude while retaining its phase.

[0060] The light field is backpropagated back to the plane where the phase plate is located, and a rotational symmetry constraint is applied to the obtained phase to update the phase distribution on the phase plate;

[0061] Repeat the above iterations until the preset conditions are met to obtain the target phase distribution.

[0062] In one possible embodiment, the focal length of the first lens group is f1, the focal length of the second lens group is f2, the optical path distance between the first lens group and the phase plate is f1, the optical path distance between the phase plate and the second lens group is f2, and the optical path distance between the second lens group and the image plane is f2, forming a 2f1+2f2 system.

[0063] In one possible embodiment, the method for generating the target phase distribution further includes:

[0064] Step 1: Using the cone mirror phase φ axicon As the initial phase, the initial optical field U0 = exp(iφ) is set to a constant amplitude. axicon );

[0065] Step 2: Calculate the complex amplitude U at the back focal plane of the second lens group using Fourier transform. B = F{U0};

[0066] Step 3: Put U B Propagated to the first target field plane z1, the complex amplitude U is obtained. z1 ;

[0067] Step 4: Keep U z1 With the phase unchanged, its amplitude is replaced by the target field amplitude A. T The updated complex amplitude U is obtained. z1new ;

[0068] Step 5: Put U z1new Propagate to the next target field plane and repeat the amplitude replacement operation until all target field planes have been traversed;

[0069] Step 6: Propagate the updated complex amplitude of the last target field plane back to the back focal plane to obtain U. Bnew ;

[0070] Step 7: Calculate the complex amplitude U of the plane containing the phase plate using the inverse Fourier transform. F = F -1 {U Bnew};

[0071] Step 8: For U F By applying rotational symmetry constraints to the phase, the updated phase distribution is obtained;

[0072] Step 9: Put U F The amplitude is replaced with a constant, the updated phase is retained, a new light field is formed, and the process returns to step 2 for iteration until the convergence condition is met.

[0073] Step 10: Use the final phase distribution as the target phase distribution.

[0074] In a fifth aspect of this application, an electronic device is also provided, comprising:

[0075] Memory, used to store computer programs;

[0076] When a processor executes a program stored in memory, it implements any of the methods described in the second aspect above.

[0077] In a sixth aspect of this application, a computer program product comprising instructions is also provided, which, when run on a computer, causes the computer to perform any of the methods described in the second aspect above.

[0078] Beneficial effects of the embodiments in this application:

[0079] The phase generation method and wavefront coding system of the Bessel beam phase plate provided in this application embodiment can form a Bessel beam by modulation of the Bessel beam phase plate, so as to obtain an extended depth of focus in the wavefront coding system. The intensity distribution of the point spread function within its range is almost unchanged and there is no lateral translation, which is beneficial to obtain a high-quality restored image through subsequent digital processing.

[0080] Of course, implementing any product or method of this application does not necessarily require achieving all of the advantages described above at the same time. Attached Figure Description

[0081] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other embodiments can be obtained based on these drawings.

[0082] Figure 1 The distribution of the point spread function along the optical axis when using a cubic phase plate;

[0083] Figure 2 The distribution of the point spread function along the optical axis when a Bessel beam is generated in the image plane;

[0084] Figure 3 A schematic diagram of the optical path for generating a Bessel beam using an annular slit;

[0085] Figure 4 A schematic diagram of the optical path for generating a Bessel beam using a conical lens;

[0086] Figure 5 A schematic diagram of the structure of a wavefront coding system provided in this application;

[0087] Figure 6 A schematic flowchart illustrating a phase generation method for a Bessel beam phase plate provided in this application;

[0088] Figure 7 A flowchart illustrating the first complex amplitude adjustment method provided in this application;

[0089] Figure 8 A schematic flowchart of another phase generation method for a Bessel beam phase plate provided in this application;

[0090] Figure 9 A schematic flowchart of another phase generation method for a Bessel beam phase plate provided in this application;

[0091] Figure 10 The generated phase and the distribution of the diffusion function at each treatment point are shown in the diagram.

[0092] Figure 11 This is a schematic diagram of the structure of an electronic device provided in this application. Detailed Implementation

[0093] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art based on this application are within the scope of protection of this application.

[0094] Before explaining the phase generation method of the Bessel beam phase plate and the wavefront encoding system provided in this application, the optical concepts involved in this paper will be briefly explained below:

[0095] Complex amplitude: In complex form, it is used to represent the amplitude and phase of a light wave, and its expression is: Where x, y, and z are the coordinates in the height, width, and optical axis directions, respectively; U(x, y, z) is the complex amplitude at (x, y, z); and A(x, y, z) is the amplitude at (x, y, z). (x, y, z) represents the phase at (x, y, z). In this paper, the height direction and width direction refer to any two mutually perpendicular directions on the cross-section of the beam.

[0096] Point spread function (PSF): A function describing the system's response to imaging from an ideal point source. It represents the intensity distribution formed on the image plane after the point source passes through the system. The PSF is a key parameter for evaluating system resolution, aberrations, and imaging quality, and it is also a crucial parameter in wavefront coding techniques.

[0097] Aperture stop: This is a key component in the system that actually controls the cross-section of the light beam, determining the maximum aperture through which light can pass.

[0098] Bessel beams: An n-order Bessel beam is a diffraction-free beam with a concentric ring cross-section. Its spatial spectrum is characterized by a sharp ring with uniform intensity distribution and an n-order vortex phase. When a Bessel beam is generated at the image plane of the system, the system's point spread function can be described by a zero-order Bessel function, as shown below. Figure 2 As shown, by Figure 2 It can be seen that the point spread function does not shift (or only shifts slightly) at different positions on the optical axis.

[0099] Since generating a Bessel beam at the image plane of the system can reduce or even eliminate the translation of the point spread function at different positions on the optical axis, thereby avoiding the degradation of the restored image quality caused by translation, it is necessary to generate a Bessel beam at the image plane of the system. Existing methods for generating Bessel beams are through annular slits or through conical lenses.

[0100] The optical path for generating a Bessel beam through the annular slit is as follows: Figure 3 As shown, although this method can generate a Bessel beam, the light is affected by the annular slit, resulting in only a portion of the light passing through the slit. This leads to a low intensity of the generated Bessel beam, which in turn results in a low signal-to-noise ratio of the optical signal acquired by the wavefront coding system, making it difficult to accurately recover the image.

[0101] The optical path for generating a Bessel beam through a conical lens is as follows: Figure 4 As shown, the Bessel beam transmission region is located immediately behind the conical lens, making it difficult to form a Bessel beam at the image plane of the system.

[0102] It is evident that neither annular slits nor conical lenses can generate high-brightness Bessel beams at the system's image plane. While phase masks do not affect the beam brightness at the system's image plane, existing phase masks cannot modulate Bessel beams.

[0103] Based on this, this application provides a phase generation method for a Bessel beam phase plate and a wavefront encoding system to modulate a Bessel beam on the image plane of the system using a phase plate (i.e., a phase mask).

[0104] The wavefront coding system provided in this application is as follows: Figure 5 As shown, it includes:

[0105] A first lens group 100, a second lens group 200, and a Bessel beam phase plate 300 are included. The rear focal plane of the first lens group 100 is coplanar with the front focal plane of the second lens group 200. The Bessel beam phase plate 300 is located at the front focal plane of the second lens group and is used to form a Bessel beam at the rear focal plane of the second lens group 200 by modulating the phase of the light rays. In this embodiment, the Bessel beam is formed by the Bessel beam phase plate to obtain an extended depth of focus in the wavefront coding system. The point spread function intensity distribution within this range is nearly constant and there is no lateral shift, which is beneficial for obtaining a high-quality restored image through subsequent digital processing.

[0106] Figure 5 In the example shown, f1 and f2 are the focal lengths of the first lens group 100 and the second lens group 200, respectively. It is understandable that... Figure 5 This is merely a schematic diagram. This application does not limit the first lens group 100 and the second lens group 200 to include only one lens. In other possible embodiments, the first lens group 100 and the second lens group 200 may each include multiple lenses. Furthermore, the wavefront coding system may also include an image acquisition device, such as a CCD (Charge Coupled Device) camera. The CCD camera is positioned on the image plane of the second lens group 200 to acquire images for subsequent image inpainting based on the acquired images, thereby recovering an image with extended depth of field.

[0107] Corresponding to the aforementioned wavefront coding system, this application also provides a phase generation method for a Bessel beam phase plate, used to determine... Figure 5 The phase of the Bessel beam phase plate in the wavefront coding system shown is determined by the method as follows: Figure 6 As shown, it includes:

[0108] Step S101: Obtain the initial phase; Step S102: Based on the initial phase and the preset amplitude, construct the complex amplitude at the front focal plane in the wavefront coding system as the first complex amplitude; Step S103: Adjust the first complex amplitude in a direction that makes the complex amplitude formed at the back focal plane of the second lens group and multiple target field planes resemble a Bessel beam, to obtain the second complex amplitude, wherein each target field plane is parallel to the back focal plane, and the distance between each target field plane and the back focal plane is not greater than a preset focal depth; Step S104: Use the phase of the second complex amplitude as the phase of the Bessel beam phase plate. Using this embodiment, the first complex amplitude can be adjusted with the amplitude at the back focal plane and multiple target field planes as the target, thereby obtaining a complex amplitude at the back focal plane and multiple target field planes that resembles a Bessel beam. By loading this phase onto the Bessel beam phase plate, the Bessel beam phase plate can be modulated to form a Bessel beam, and the point spread function of the Bessel beam at different optical axis positions has no (or only a small) translation.

[0109] The following will explain steps S101 to S104 respectively:

[0110] In step S101, the initial phase can be any phase. For example, it can be a user-preset phase or a phase randomly generated by a random algorithm. Since the initial phase is the phase of the first complex amplitude, and the second complex amplitude is obtained by adjusting the first complex amplitude, theoretically, the closer the initial phase is to the phase of the second complex amplitude, the faster the first complex amplitude can be adjusted to the second complex amplitude, thereby improving the phase generation efficiency. Therefore, when the initial phase is user-preset, the user can estimate a phase that is close to the phase of the second complex amplitude as the initial phase based on their own experience and prior knowledge.

[0111] In step S102, the amplitude of the constructed first complex amplitude is a preset amplitude, and the phase is the initial phase. It can be understood that, as can be seen from the previous description of Bessel beams, Bessel beams are beams with a specific phase distribution, which is independent of amplitude. Therefore, the preset amplitude can be any non-zero amplitude (an amplitude of 0 is equivalent to a system with no incident beam, in which case it is obviously impossible to form a Bessel beam). For example, in one possible embodiment, the preset amplitude can be set to 1 to simplify subsequent calculations.

[0112] In steps S103 and S104, it is understood that if a beam exhibits a Bessel beam form at any cross-section along the optical axis, then the beam can be considered a Bessel beam. This application sets multiple target field planes near the back focal plane. Since the target field planes are parallel to the back focal plane, and the back focal plane is perpendicular to the optical axis, the target field planes and the back focal plane can be considered as multiple cross-sections of the optical axis. Thus, as long as the number of target field planes is sufficient, and the complex amplitude of the modulated beam at the target field plane and the back focal plane exhibits a Bessel beam form, a Bessel beam can be considered modulated. "Sufficient" here means greater than a preset threshold number. This threshold number can be set by the user according to their needs. It is understood that the more target field planes there are, the closer the generated beam is to a Bessel beam, and the higher the image restoration quality. Therefore, the threshold number is larger for scenarios with higher image restoration quality and smaller for scenarios with lower image restoration quality.

[0113] Therefore, in this application, the first complex amplitude is adjusted in a direction such that the complex amplitudes formed by the beam at the back focal plane and these multiple target field planes are in the form of a Bessel beam. It can be considered that the second complex amplitude obtained in this way satisfies the following condition: if the phase of the incident beam at the front focal plane is equal to the phase of the second complex amplitude, a Bessel beam will be generated at the image plane of the system. In other words, as long as the Bessel beam phase plate can adjust the phase of the beam incident on the front focal plane to the phase of the second complex amplitude, a Bessel beam can be generated at the image plane of the system. Therefore, the phase of the second complex amplitude can be used as the phase of the Bessel phase plate.

[0114] The position of the target field planes can be set according to user needs. However, in order to make the beam generated at the image plane as close as possible to the Bessel beam, the target field planes should be set as evenly as possible in front of and behind the back focal plane. Here, "in front of and behind" refers to the front and back along the optical axis, and "evenly set" means that multiple field planes are set at equal intervals with the back focal plane along the optical axis. For example, assuming there are a total of 4 target field planes, and assuming the coordinate of the back focal plane in the optical axis is z0, then the coordinates of these four target field planes in the optical axis are z0-2Δz, z0-Δz, z0+Δz, and z0+2Δz, respectively, where Δz is a preset interval.

[0115] The adjustment of the first complex amplitude can be iterative, that is, gradually adjusting the first complex amplitude to the second complex amplitude through multiple adjustments. Alternatively, the first complex amplitude can be adjusted to the second complex amplitude in a single step. For example, an objective function can be constructed based on optical theory, with the first complex amplitude as the independent variable and the rotational symmetry of the complex amplitudes at each target field plane and the back focal plane as the dependent variable. The solution is then used to find the first complex amplitude that maximizes the rotational symmetry output by the objective function, which is then taken as the second complex amplitude.

[0116] It is understandable that the purpose of forming a Bessel beam at the image plane is to improve the image restoration quality. However, the depth of field in a normally captured image is finite. If objects beyond the depth of field are outside the image, they should appear as blurred images. Therefore, the beams emitted by these objects do not require high-quality restoration. In other words, although a Bessel beam needs to be formed at the image plane, it is only necessary to form the Bessel beam within a certain depth of field of the back focal plane. Beams outside this certain depth of field can be considered as emitted by objects outside the depth of field. Even if these beams are not Bessel beams, they will not affect the image restoration quality. Therefore, in the process of adjusting to obtain the second complex amplitude, it is not necessary to consider whether the beams outside the certain depth of field are Bessel beams. Therefore, in this application, the target field plane is set within the preset depth of field of the back focal plane.

[0117] The following will provide an exemplary description of how to adjust the first complex amplitude; see [link to documentation]. Figure 7 , Figure 7 In the example shown, the front focal plane and the rear focal plane both refer to the front focal plane and the rear focal plane of the second lens group in the aforementioned wavefront coding system, including:

[0118] Until the preset iteration conditions are met, the following steps S201 to S203 are executed repeatedly: Step S201: Calculate the complex amplitude formed by the first complex amplitude propagating from the front focal plane sequentially through multiple target field planes and back to the front focal plane, and use it as the third complex amplitude; wherein, each time it propagates to a target scene plane, the amplitude of the complex amplitude is modified to the amplitude of the Bessel beam at that target field plane; Step S202: Perform rotational symmetry processing on the phase of the third complex amplitude to obtain the fourth complex amplitude; Step S203: Modify the amplitude of the third complex amplitude to the preset amplitude and modify the phase to the phase of the fourth complex amplitude to obtain a new first complex amplitude, and return to execute step S201. If the preset iteration conditions are met, execute step S204; Step S204: Use the newly obtained fourth complex amplitude as the second complex amplitude. By using this embodiment, the adjustment of the first complex amplitude is decomposed into an iterative process. In each iteration, only the complex amplitude formed after the propagation of the complex amplitude needs to be calculated, thus effectively reducing the implementation difficulty of the phase generation method.

[0119] The following will explain steps S201 to S204 respectively:

[0120] In step S201, "propagating from the front focal plane sequentially through multiple target field planes and back to the front focal plane" means: propagating from the front focal plane and ultimately back to the front focal plane, passing through the rear focal plane and all target field planes during the propagation process. Furthermore, the propagation can repeatedly pass through the rear focal plane and any target field plane, and the order of passing is not limited. For example, suppose there are four target field planes, denoted as target field planes A to D, with coordinates z0-2Δz, z0-Δz, z0+Δz, and z0+2Δz along the optical axis, respectively, and the coordinate of the rear focal plane along the optical axis is z0. The propagation process can be in the order of coordinates from front to back along the optical axis, that is: front focal plane → target field plane A → target field plane B → rear focal plane → target field plane C → target field plane D → front focal plane. The propagation process can also be to propagate to the rear focal plane first and then to each target field plane in sequence, that is: front focal plane → rear focal plane → target field plane A → target field plane B → target field plane C → target field plane D → front focal plane. It can also be front focal plane → rear focal plane → target field plane A → target field plane B → target field plane C → target field plane D → rear focal plane → front focal plane.

[0121] The amplitude of a Bessel beam at the target field plane refers to the expected amplitude of a Bessel beam at the target field plane, assuming it is generated at the image plane. It is understood that, since Bessel beams are uniform along the optical axis, the expected amplitude of each Bessel beam at each target field plane is equal, denoted as A in this paper. T Furthermore, the phase of the complex amplitude will remain unchanged during the process of modifying the amplitude.

[0122] By modifying the amplitude of the complex amplitude to A when propagating to the target field plane. T It can simulate the situation where a beam with uniform amplitude along the optical axis is generated in the image plane, and the phase of the third complex amplitude formed by the beam that propagates back to the front focal plane can be regarded as: the phase mask required to generate a beam with more uniform amplitude along the optical axis at the image plane.

[0123] In step S202, rotational symmetry processing refers to a process that makes the phase exhibit rotational symmetry. This processing can be considered as applying a rotational symmetry constraint to the third complex amplitude, thereby enabling the resulting fourth complex amplitude to form a beam with a more rotationally symmetric phase at the image plane. As explained above, the phase of the third complex amplitude can generate a beam with a more uniform amplitude along the optical axis at the image plane. Therefore, the fourth complex amplitude, adjusted based on the third complex amplitude, can not only form a beam with a more rotationally symmetric phase at the image plane, but also a beam with a more uniform amplitude along the optical axis. A beam with a uniform amplitude and rotational symmetry along the optical axis can be considered a Bessel beam. Therefore, the phase of the fourth complex amplitude can generate a beam at the image plane that is closer to a Bessel beam.

[0124] In steps S203 and S204, the phase of the fourth complex amplitude is continuously updated iteratively, which enables the phase of the fourth complex amplitude to generate a beam that is increasingly close to the Bessel beam at the image plane. When the iteration condition is met, it can be considered that the phase of the fourth complex amplitude can generate a beam that is sufficiently close to the Bessel beam at the image plane. In other words, it can be approximately considered that the phase of the fourth complex amplitude can generate a Bessel beam at the image plane. Therefore, the phase of the fourth complex amplitude can be used as a phase mask at this time, which means that the fourth complex amplitude can be used as the second complex amplitude.

[0125] The preset iteration condition can be that the number of iterations reaches a preset threshold, or that the convergence of the phase of the fourth complex amplitude reaches a preset convergence threshold. In this paper, the convergence of the phase of the fourth complex amplitude refers to the difference between the phase of the fourth complex amplitude obtained in the latest iteration and the phase of the fourth complex amplitude obtained in the previous iteration. When the difference is less than the preset difference threshold, the convergence of the phase of the fourth complex amplitude can be considered to have reached the preset convergence threshold.

[0126] As explained above, the propagation process can be: front focal plane → back focal plane → target field plane A → target field plane B → target field plane C → target field plane D → back focal plane → front focal plane. Using this propagation process, the method for calculating the third complex amplitude is as follows:

[0127] The first complex amplitude is calculated from the front focal plane to the rear focal plane using Fourier transform, and is taken as the fifth complex amplitude. The fifth complex amplitude is calculated from the rear focal plane through multiple target field planes and back to the rear focal plane using the angular spectrum propagation function, and is taken as the sixth complex amplitude. Each time the beam propagates to a target field plane, the amplitude of the complex amplitude is modified to the amplitude of the Bessel beam at that target field plane. The sixth complex amplitude is calculated from the rear focal plane back to the front focal plane using inverse Fourier transform, and is taken as the third complex amplitude. This embodiment converts the propagation process calculation into (inverse) Fourier transform and angular spectrum propagation, further reducing the difficulty of phase generation.

[0128] In one possible embodiment, the aforementioned rotationally symmetric processing is specifically performed by averaging the third complex amplitude in the circumferential direction to obtain the fourth complex amplitude.

[0129] In one possible embodiment, the aforementioned method of obtaining the initial phase specifically involves obtaining the cone mirror phase as the initial phase, wherein the cone mirror phase is equivalent to a conical lens, and its phase changes linearly with radial distance. By using this embodiment and selecting the cone mirror phase as the initial phase, the number of iterations required to obtain the second complex amplitude can be reduced, thereby improving the phase generation efficiency.

[0130] The phase generation method of the Bessel beam phase plate provided in this application will be explained in detail below with specific calculation formulas. See [link to relevant documentation]. Figure 8 ,include:

[0131] Step S301: Obtain the cone mirror phase as the initial phase, and construct the complex amplitude at the front focal plane with the preset amplitude as the amplitude and the initial phase as the phase, as the first complex amplitude.

[0132] Let the phase of the cone be denoted as axicon Let the first complex amplitude be denoted as U0, and the preset amplitude be 1. Then the first complex amplitude can be expressed as U0 = exp(i axicon ).

[0133] Step S302: Perform a Fourier transform on the first complex amplitude to obtain the complex amplitude formed by the back focal plane, which is used as the fifth complex amplitude;

[0134] The Fourier transform operator is denoted as F{·}, and the fifth complex amplitude is denoted as U. B Then the fifth complex amplitude can be expressed as U B =F{ U0}.

[0135] Step S303: Substitute the fifth complex amplitude into the angular spectrum propagation function to obtain the complex amplitude formed at the first target field plane.

[0136] According to the angular spectrum propagation theory, the angular spectrum propagation function can be expressed as {F{·}}exp(ik) z ·△Z), where k z Let U be the component of the wave vector along the optical axis (i.e., the z-direction), and ΔZ be the distance between the two planes. Let U be the complex amplitude formed by the first target field plane. z1 And the distance between the first target field plane and the back focal plane is denoted as ΔZ. B1 Then the complex amplitude formed by the first target field plane can be expressed as U z1 = F -1 { F {U B} exp(ik z ·△Z B1 )}, where F -1 {·} represents the inverse Fourier transform.

[0137] Step S304, U z1 The amplitude is modified to the amplitude of the Bessel beam at the first target field plane, while keeping the phase unchanged.

[0138] The complex amplitude obtained after modifying the amplitude is denoted as U. z1new , then U z1new It can be represented as U z1new =A T exp(i·angle(U) z1 ), where angle(·) represents phase, angle(U) z1 That is, U z1 The phase.

[0139] Step S305, U z1new Substituting the angular spectrum propagation function, we obtain the complex amplitude U formed at the second target field plane. z2 and U z2 The amplitude was modified to A T And keeping the phase unchanged, we get U z2new And so on, until U is obtained. zNnew .

[0140] Where N is the total number of target field planes, and since the Nth target field plane is the last target field plane, U will be referred to as such in the following text. zNnew Let it be U zendnew .

[0141] Step S306, U zendnew Substituting the angular spectrum propagation function, we obtain the complex amplitude formed at the back focal plane, which is taken as the sixth complex amplitude.

[0142] Let the sixth complex amplitude be denoted as U. BnewThen the sixth complex amplitude can be expressed as U Bnew = F -1 { F {U zNnew} exp(-ik z ·△Z Bend )}, where △Z Bend This is the distance between the back focal plane and the last target field plane.

[0143] Step S307, for U Bnew Perform an inverse Fourier transform to obtain the complex amplitude formed by the repropagation to the front focal plane, which is used as the third complex amplitude.

[0144] Let the third complex amplitude be denoted as U. F Then the third complex amplitude can be expressed as U F = F -1 { U Bnew}

[0145] Step S308: The third complex amplitude is averaged in the circumferential direction to obtain the fourth complex amplitude.

[0146] Let the fourth complex amplitude be denoted as U. F (r), then the fourth complex amplitude in polar coordinates can be expressed as .in, This represents the total number of azimuth angles. Let be the i-th azimuth angle, and r be the radial radius in polar coordinates.

[0147] Step S309: Replace the amplitude of the third complex amplitude with a preset amplitude and modify the phase to the phase of the fourth complex amplitude to obtain a new first complex amplitude.

[0148] Let the new first complex amplitude be denoted as U. Fnew (r), since the preset amplitude is 1, the new first complex amplitude can be expressed as U. Fnew (r) = exp(i·angle(U) F (r)).

[0149] Step S310: Repeat steps S302 to S309 until the preset iteration condition is met, and obtain the phase of the latest obtained first complex amplitude, i.e., angle(U). Fnew (r)), which serves as the phase of the Bessel beam phase plate.

[0150] Understandable, Figure 8 The example shown is only one possible one. Figure 8 In the example shown, the constraint condition is determined after each execution of step S306. In other possible embodiments, it can also be done as follows: Figure 9As shown, after step S309, it is determined whether the constraint conditions are met. Furthermore, in... Figure 8 In the example shown, the constraint can be that the difference is less than a preset difference threshold. Figure 9 In the example shown, the constraint can be that the number of times the aforementioned loop is executed reaches a preset threshold.

[0151] In Figure 8 or Figure 9 The phase is determined by the method such as Figure 10 As shown in (a), after the phase is loaded onto the phase plate of the Bessel beam, the point spread function at each position is obtained through simulation calculation as follows: Figure 10 (b) Figure 10 (c) Figure 10 (d) Figure 10 (e) Figure 10 (f) in Figure 10 (g) in Figure 10 As shown in (h) in the diagram.

[0152] Corresponding to the aforementioned phase generation method for a Bessel beam phase plate, this application also provides a phase generation device for a Bessel beam phase plate, the device comprising: an acquisition module for acquiring an initial phase;

[0153] An initialization module is used to construct, based on the initial phase and preset amplitude, a complex amplitude at the front focal plane of the second lens group in the wavefront coding system described in the first aspect above, as the first complex amplitude;

[0154] The calculation module is used to adjust the first complex amplitude in a direction that makes the complex amplitude formed at the back focal plane of the second lens group and the multiple target field planes in the form of a Bessel beam, to obtain a second complex amplitude; wherein each of the target field planes is parallel to the back focal plane and the distance between the target field plane and the back focal plane is not greater than a preset focal depth; and the phase of the second complex amplitude is used as the phase of the Bessel beam phase plate.

[0155] In one possible embodiment, the calculation module adjusts the first complex amplitude in a direction that causes the complex amplitude formed at the back focal plane and multiple target field planes to be in the form of a Bessel beam, to obtain a second complex amplitude, including:

[0156] Until the preset iteration conditions are met, repeat the following steps:

[0157] The first complex amplitude is calculated as the complex amplitude formed by the first complex amplitude propagating from the front focal plane sequentially through multiple target field planes and back to the front focal plane, and is taken as the third complex amplitude; wherein, each time it propagates to a target field plane, the amplitude of the complex amplitude is modified to the amplitude of the Bessel beam at the target field plane;

[0158] The phase of the third complex amplitude is rotated symmetrically to obtain the fourth complex amplitude;

[0159] The amplitude of the third complex amplitude is modified to the preset amplitude, and the phase is modified to the phase of the fourth complex amplitude to obtain a new first complex amplitude. Then, the calculation is returned to obtain the complex amplitude formed by the first complex amplitude propagating from the front focal plane through multiple target field planes and the rear focal plane and back to the front focal plane, which is the third complex amplitude step, until the preset iteration condition is met.

[0160] If the iteration conditions are met, the latest obtained fourth complex amplitude is taken as the second complex amplitude;

[0161] In one possible embodiment, the iteration conditions include:

[0162] The loop executes for a preset number of times; or,

[0163] At each of the target field planes and the back focal plane, the difference between the amplitude formed by the first complex amplitude and the amplitude expected to be formed by the Bessel beam is less than a preset difference threshold.

[0164] In one possible embodiment, the calculation of the first complex amplitude as the third complex amplitude, formed by the first complex amplitude propagating sequentially from the front focal plane through multiple target field planes and then back to the front focal plane, includes:

[0165] The first complex amplitude is calculated by Fourier transform to obtain the complex amplitude formed by the propagation of the first complex amplitude from the front focal plane to the rear focal plane, which is then used as the fifth complex amplitude.

[0166] The fifth complex amplitude is calculated using the angular spectrum propagation function to obtain the complex amplitude formed by the beam propagating from the back focal plane back to the back focal plane sequentially through multiple target field planes, and is taken as the sixth complex amplitude; wherein, each time the beam propagates to a target field plane, the amplitude of the complex amplitude is modified to the amplitude of the Bessel beam at the target field plane;

[0167] The sixth complex amplitude is calculated by inverse Fourier transform and is used as the complex amplitude formed by the reverse propagation from the rear focal plane to the front focal plane.

[0168] In one possible embodiment, the phase modification of the third complex amplitude to obtain a fourth complex amplitude by rotational symmetry includes:

[0169] The third complex amplitude is averaged in the circumferential direction to obtain the fourth complex amplitude.

[0170] In one possible embodiment, obtaining the initial phase includes:

[0171] The phase of the conical mirror is obtained as the initial phase, and the phase of the conical mirror changes linearly with the radial distance.

[0172] This embodiment provides a wavefront-coded optical system, such as Figure 5 As shown, the optical system includes a first lens group 100, a Bessel beam phase plate 300, and a second lens group 200 arranged sequentially along the optical path. The Bessel beam phase plate 300 is positioned at the intersection of the rear focal plane of the first lens group 100 and the front focal plane of the second lens group 200, serving as the aperture stop of the optical system. The focal length of the first lens group 100 is f1, the focal length of the second lens group 200 is f2, the optical path distance between the first lens group 100 and the Bessel beam phase plate 300 is f1, the optical path distance between the Bessel beam phase plate 300 and the second lens group 200 is f1, and the optical path distance between the second lens group 200 and the image plane is f2, forming a 2f1+2f2 system.

[0173] The Bessel beam phase plate 300 is configured to have a target phase distribution such that the point spread function of the optical system approximates a zero-order Bessel function. This target phase distribution is generated using an iterative phase retrieval method, such as... Figure 8 As shown, the specific steps are as follows:

[0174] Step 1: Using the cone mirror phase φ axicon As the initial phase, the initial optical field U0 = exp(iφ) is set to a constant amplitude. axicon ).

[0175] Step 2: Calculate the complex amplitude U at the 200° back focal plane of the second lens group using Fourier transform. B = F{U0}.

[0176] Step 3: According to the angular spectrum propagation theory, U B Propagated to the first target field plane z1, the complex amplitude U is obtained. z1 = F -1 {F{U B}·exp(-ik z ·Δz B1 )}, where k z Let Δz be the component of the wave vector in the z-direction of propagation. B1 This is the distance between the rear focal plane and the position of the first target field plane.

[0177] Step 4: Keep U z1 With the phase unchanged, its amplitude is replaced by the target field amplitude A. T The updated complex amplitude U is obtained. z1new = A T ·exp(i·angle(U z1 )).

[0178] Step 5: According to the angular spectrum propagation theory, U z1new Propagated to the next target field plane z2, the complex amplitude U is obtained. z2 =F -1 {F{U z1new}·exp(ik z ·Δz 12 )}, where Δz 12 This is the distance between positions z1 and z2.

[0179] Step 6: Replace the amplitude at z2 with the target field amplitude A. T The phase remains unchanged, resulting in U. z2new = A T ·exp(i·angle(U z2 )).

[0180] Step 7: Repeat steps 5 and 6 to propagate the light field from position zi to position zi+1, and repeat the amplitude replacement operation until all target field planes have been traversed.

[0181] Step 8: According to the angular spectrum propagation theory, propagate the updated complex amplitude of the last target field plane back to the rear focal plane to obtain U. Bnew = F -1 {F{U zendnew}·exp(-ik z ·Δz Bend )}, where U zendnew The new complex amplitude, Δz, represents the last target field. Bend This represents the distance between the back focal plane and the location of the last target field.

[0182] Step 9: Calculate the complex amplitude U at the plane (front focal plane) where the phase plate 300 of the Bessel beam is located using inverse Fourier transform. F = F -1 {U Bnew}

[0183] Step 10: For U F Applying rotational symmetry constraints to the phase of U in polar coordinates F (r) = (1 / N φ ) Σ_{i=1}^{N φ} U F (r, φ i ), where r is the radial radius, φ_i is the i-th azimuth angle, and N_φ is the total number of azimuth angles.

[0184] Step 11: Put U F The amplitude is replaced with a constant, while the updated phase is retained, forming a new optical field U.Fnew (r) = exp(i·angle(U F (r))) and return to step 2 for iteration.

[0185] Step 12: Repeat steps 2 through 11 until the convergence condition is met. The final phase obtained is angle(U). F (r)) is used as the target phase distribution.

[0186] In the above method, the target field plane is set along the optical axis, parallel to the back focal plane, and the distance between the target field plane and the back focal plane is no greater than a preset depth of focus. In each iteration, the light field propagates between the plane containing the Bessel beam phase plate 300 and the back focal plane of the second lens group 200 through Fourier transform and inverse Fourier transform. At each target field plane, the amplitude of the light field is replaced with the target amplitude while preserving its phase; after propagating back to the plane containing the Bessel beam phase plate 300, a rotational symmetry constraint is applied to the obtained phase to update the phase distribution. The above iterations are repeated until the preset conditions are met, and the target phase distribution is obtained.

[0187] The Bessel beam phase plate 300 modulates the phase of the light rays, making the point spread function of the optical system approximately the form of a zero-order Bessel function, thereby maintaining the stability of the point spread function within a certain depth of field. Figure 10 Figure (a) shows the phase determined using the above method. After this phase is applied to the Bessel beam phase plate 300, the point spread function at each position is obtained through simulation calculation, as shown below. Figure 10 (b) Figure 10 (c) Figure 10 (d) Figure 10 (e) Figure 10 (f) in Figure 10 (g) in Figure 10 As shown in (h), it can be seen that the point spread function maintains good consistency at different axial positions and there is no lateral translation phenomenon, which is beneficial for obtaining high-quality restored images through subsequent digital processing.

[0188] This application also provides an electronic device, such as... Figure 11 As shown, it includes:

[0189] Memory 501 is used to store computer programs;

[0190] When processor 502 executes the program stored in memory 501, it performs the following steps:

[0191] Obtain an initial phase; based on the initial phase and a preset amplitude, construct a complex amplitude at the front focal plane of the second lens group in the wavefront coding system described in the first aspect above, as a first complex amplitude; adjust the first complex amplitude in a direction that makes the complex amplitudes formed at the rear focal plane of the second lens group and multiple target field planes in the form of a Bessel beam, to obtain a second complex amplitude; wherein each target field plane is parallel to the rear focal plane, and the distance between the target field plane and the rear focal plane is not greater than a preset focal depth; use the phase of the second complex amplitude as the phase of the Bessel beam phase plate.

[0192] Furthermore, the aforementioned electronic device may also include a communication bus and / or a communication interface, with the processor 502, communication interface, and memory 501 communicating with each other via the communication bus.

[0193] The communication bus mentioned in the above electronic devices can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus can be divided into address bus, data bus, control bus, etc. For ease of illustration, only one thick line is used to represent it in the diagram, but this does not mean that there is only one bus or one type of bus.

[0194] The communication interface is used for communication between the aforementioned electronic devices and other devices.

[0195] The memory may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Optionally, the memory may also be at least one storage device located remotely from the aforementioned processor.

[0196] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0197] In another embodiment provided in this application, a computer-readable storage medium is also provided, which stores a computer program that, when executed by a processor, implements the steps of the phase generation method for any of the Bessel beam phase plates described above.

[0198] In another embodiment provided in this application, a computer program product containing instructions is also provided, which, when run on a computer, causes the computer to execute the phase generation method of any of the Bessel beam phase plates in the above embodiments.

[0199] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a solid-state drive (SSD), etc.

[0200] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0201] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system, apparatus, electronic device, and computer program product embodiments are basically similar to the method embodiments, so the descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0202] The above description is merely a preferred embodiment of this application and is not intended to limit the scope of protection of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application are included within the scope of protection of this application.

Claims

1. A wavefront coding system, characterized in that, The wavefront encoding system includes a first lens group, a second lens group, and a Bessel beam phase plate; The rear focal plane of the first lens group is coplanar with the front focal plane of the second lens group; The Bessel beam phase plate is located at the front focal plane of the second lens group and is used to form a Bessel beam at the rear focal plane of the second lens group by modulating the phase of the light rays. The phase of the Bessel beam phase plate is generated as follows: an initial phase is obtained; based on the initial phase and a preset amplitude, a complex amplitude at the front focal plane of the second lens group is constructed as a first complex amplitude; the first complex amplitude is adjusted in a direction that makes the complex amplitudes formed at the rear focal plane of the second lens group and multiple target field planes in the form of a Bessel beam to obtain a second complex amplitude; wherein each target field plane is parallel to the rear focal plane and the distance between the target field plane and the rear focal plane is not greater than a preset depth of focus; the phase of the second complex amplitude is used as the phase of the Bessel beam phase plate.

2. A method for generating the phase of a Bessel beam phase plate, characterized in that, The method includes: Obtain the initial phase; Based on the initial phase and preset amplitude, the complex amplitude at the front focal plane of the second lens group in the wavefront coding system of claim 1 is constructed as the first complex amplitude; The first complex amplitude is adjusted in a direction that makes the complex amplitude formed at the back focal plane of the second lens group and the plurality of target field planes in the form of a Bessel beam to obtain the second complex amplitude; wherein each of the target field planes is parallel to the back focal plane and the distance between the target field plane and the back focal plane is not greater than a preset depth of focus; The phase of the second complex amplitude is used as the phase of the phase plate of the Bessel beam.

3. The method according to claim 2, characterized in that, The step of adjusting the first complex amplitude in a direction that makes the complex amplitude formed at the back focal plane and multiple target field planes resemble a Bessel beam to obtain the second complex amplitude includes: Until the preset iteration conditions are met, repeat the following steps: The first complex amplitude is calculated as the complex amplitude formed by the first complex amplitude propagating from the front focal plane sequentially through multiple target field planes and back to the front focal plane, and is taken as the third complex amplitude; wherein, each time it propagates to a target field plane, the amplitude of the complex amplitude is modified to the amplitude of the Bessel beam at the target field plane; The phase of the third complex amplitude is rotated symmetrically to obtain the fourth complex amplitude; The amplitude of the third complex amplitude is modified to the preset amplitude, and the phase is modified to the phase of the fourth complex amplitude to obtain a new first complex amplitude. Then, the calculation is returned to obtain the complex amplitude formed by the first complex amplitude propagating from the front focal plane through multiple target field planes and the rear focal plane and back to the front focal plane, which is the third complex amplitude step, until the preset iteration condition is met. If the iteration conditions are met, the latest obtained fourth complex amplitude is taken as the second complex amplitude.

4. The method according to claim 2, characterized in that, Iteration conditions include: The loop executes for a preset number of times; or, At each of the target field planes and the back focal plane, the difference between the amplitude formed by the first complex amplitude and the amplitude expected to be formed by the Bessel beam is less than a preset difference threshold.

5. The method according to claim 3, characterized in that, The calculated first complex amplitude, which propagates sequentially from the front focal plane through multiple target field planes and back to the front focal plane, forms the third complex amplitude, including: The first complex amplitude is calculated by Fourier transform to obtain the complex amplitude formed by the propagation of the first complex amplitude from the front focal plane to the rear focal plane, which is then used as the fifth complex amplitude. The fifth complex amplitude is calculated using the angular spectrum propagation function to obtain the complex amplitude formed by the beam propagating from the back focal plane back to the back focal plane sequentially through multiple target field planes, and is taken as the sixth complex amplitude; wherein, each time the beam propagates to a target field plane, the amplitude of the complex amplitude is modified to the amplitude of the Bessel beam at the target field plane; The sixth complex amplitude is calculated by inverse Fourier transform and is used as the complex amplitude formed by the reverse propagation from the rear focal plane to the front focal plane.

6. The method according to claim 3, characterized in that, The phase modification of the third complex amplitude to obtain the fourth complex amplitude by rotational symmetry includes: The third complex amplitude is averaged in the circumferential direction to obtain the fourth complex amplitude.

7. The method according to claim 2, characterized in that, The process of obtaining the initial phase includes: obtaining the cone mirror phase as the initial phase, wherein the cone mirror phase varies linearly with radial distance.

8. A wavefront-coded optical system, characterized in that, include: A first lens group, a phase plate, and a second lens group are arranged sequentially along the optical path; The phase plate is positioned at the overlap of the rear focal plane of the first lens group and the front focal plane of the second lens group, and serves as the aperture stop of the optical system. The phase plate is configured to have a target phase distribution such that the point spread function of the optical system is approximately in the form of a zero-order Bessel function. The method for generating the target phase distribution includes: The initial light field is set using the phase of the conical mirror as the initial phase; Multiple iterative loops of Fourier transform and inverse Fourier transform are performed between the plane where the phase plate is located and the back focal plane of the second lens group; In each iteration, the light field is propagated to multiple target field planes set along the optical axis, and the amplitude of each target field plane is replaced with the target amplitude while retaining its phase. The light field is backpropagated back to the plane where the phase plate is located, and a rotational symmetry constraint is applied to the obtained phase to update the phase distribution on the phase plate; Repeat the above iterations until the preset conditions are met to obtain the target phase distribution.

9. The wavefront coding optical system according to claim 8, characterized in that, The focal length of the first lens group is f1, the focal length of the second lens group is f2, the optical path distance between the first lens group and the phase plate is f1, the optical path distance between the phase plate and the second lens group is f2, and the optical path distance between the second lens group and the image plane is f2, forming a 2f1+2f2 system.

10. The wavefront coding optical system according to claim 9, characterized in that, The method for generating the target phase distribution further includes: Step 1: Using the cone mirror phase φ axicon As the initial phase, the initial optical field U0 = exp(iφ) is set to a constant amplitude. axicon ); Step 2: Calculate the complex amplitude U at the back focal plane of the second lens group using Fourier transform. B = F{U0}; Step 3: Put U B Propagated to the first target field plane z1, the complex amplitude U is obtained. z1 ; Step 4: Keep U z1 With the phase unchanged, its amplitude is replaced by the target field amplitude A. T The updated complex amplitude U is obtained. z1new ; Step 5: Put U z1new Propagate to the next target field plane and repeat the amplitude replacement operation until all target field planes have been traversed; Step 6: Propagate the updated complex amplitude of the last target field plane back to the back focal plane to obtain U. Bnew ; Step 7: Calculate the complex amplitude U of the plane containing the phase plate using the inverse Fourier transform. F = F -1 {U Bnew }; Step 8: For U F By applying rotational symmetry constraints to the phase, the updated phase distribution is obtained; Step 9: Put U F The amplitude is replaced with a constant, the updated phase is retained, a new light field is formed, and the process returns to step 2 for iteration until the convergence condition is met. Step 10: Use the final phase distribution as the target phase distribution.

Images