Method for generating complex-amplitude domain gradient hologram of spatial light modulator

Abstract

Provided is a method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator, comprising: obtaining an initial pixel plane complex virtual field of the spatial light modulator when WGS iteration converges and an atomic rearrangement path planning result of an atomic array to be rearranged; performing incremental velocity first-order incremental updating based on a pixel plane complex virtual field of a current frame and a light trap position update pair from the atomic rearrangement path planning result of the current frame to obtain an updated pixel plane complex virtual field; and performing calculation of a WGS single-step operator with a predetermined order of a Neumann series as a step number to perform high-order crosstalk correction to obtain a hologram of the spatial light modulator. In this way, by constructing a framework for layer-by-layer approximation of a fixed point according to a Neumann series generated by a hologram, the zeroth-order crosstalk correction can be realized by incremental updating, and the first-order or higher crosstalk correction can be realized by a WGS correction step, thereby significantly improving the time efficiency of high-precision hologram generation.

Description

Technical Field

[0001] This application relates to the field of quantum computing technology, and more specifically, to a method for generating complex amplitude domain gradient flow holograms of spatial light modulators, electronic devices, and computer-readable storage media. Background Technology

[0002] Neutral atoms (such as or Quantum computing is one of the most promising quantum computing routes. Its core advantages are: the same type of atoms have natural uniformity (no manufacturing tolerances and parameter dispersion), the hyperfine ground state coherence time is extremely long (up to 10 seconds, far exceeding the operation time of typical quantum gates), and it allows the realization of high-fidelity fully connected two-qubit gates between two qubits by physically moving atomic qubits.

[0003] This technology captures individual cold atoms with optical tweezers and achieves quantum entanglement gates through Rydberg excitation. Typically, a large-scale programmable optical tweezers array is realized using a spatial light modulator (SLM). The SLM modulates the phase of the incident laser light through individual liquid crystal pixels on a liquid crystal panel. After Fourier transform by a lens, an optical tweezers array is formed on the focal plane, thereby fixing individual cold atoms in individual optical traps by the optical tweezers array.

[0004] During the loading of cold atoms into optical traps constructed from optical tweezers arrays, the probability of each optical trap being occupied by a single atom follows an independent Bernoulli distribution (typical occupancy rate) due to atomic number density fluctuations and photo-induced collision blocking mechanisms. This means that for a quantum array, for example, containing 100 physical bits, the probability of forming a completely defect-free target array after natural random loading is extremely low (approximately). ).

[0005] Therefore, before each quantum computation, an atomic array rearrangement mechanism must be introduced. This involves identifying the current defect state through camera fluorescence imaging, implementing motion planning using low-level control algorithms, and frequently refreshing the hologram (i.e., the holographic phase map) to drive the SLM to change the optical trap positions in real time, physically transforming scattered atoms into a specified defect-free target configuration. Here, the SLM (e.g., comprising 1024×1024 pixels) can simultaneously control the real-time movement of atoms trapped in multiple optical traps by applying a phase delay to each liquid crystal pixel.

[0006] After planning the atomic array rearrangement path, the optical trap must move frame by frame along the planned path. For each frame move, the SLM needs to recalculate a hologram, and the generation of the hologram must ensure that the moved optical trap array remains highly uniform (typically requiring uniform light intensity). Otherwise, atoms will escape the trap due to photothermal heating) and inter-frame phase continuity (typical requirement) Otherwise, quantum coherence would be destroyed, and real-time performance is required. ms / frame (i.e., the SLM refresh rate needs to be 50-200Hz).

[0007] Currently, the latency of a standard WGS (100 times) is typically... The time delay is approximately 1 ms, and phase continuity is not guaranteed; linear phase interpolation (LPI) has a time delay of approximately 1 ms and phase continuity, but intensity uniformity is not guaranteed. The latency of a convolutional neural network (CNN) to generate a hologram in one step is about 0.5ms, but phase continuity is not guaranteed and the generalization effect is poor; the latency of sparse-WPGS (20 times) is about 4ms, and it can partially guarantee phase continuity, but it still does not meet the above requirements for hologram generation.

[0008] Therefore, it is desirable to provide an improved hologram generation scheme. Summary of the Invention

[0009] This application provides a method for generating complex amplitude domain gradient flow holograms for spatial light modulators. By constructing a framework for generating holograms that approximates fixed points in layers according to the Newman series, the zeroth order can be achieved by incremental updates and the first order and above crosstalk correction can be achieved by WGS correction steps, thereby significantly improving the time efficiency of high-precision hologram generation.

[0010] According to one aspect of this application, a method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator is provided, comprising: acquiring the initial pixel plane complex virtual field of the spatial light modulator and the atomic rearrangement path planning result of the atomic array to be rearranged during WGS iteration convergence; performing an incremental velocity first-order incremental update based on the pixel plane complex virtual field of the current frame and the optical trap position update pair of the current frame from the atomic rearrangement path planning result to obtain an updated pixel plane complex virtual field; and performing a high-order crosstalk correction on the updated pixel plane complex virtual field using a WGS single-step operator with a predetermined number of steps of the Newman series to obtain a hologram of the spatial light modulator.

[0011] In the above-mentioned method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator, obtaining the initial pixel plane complex virtual field of the spatial light modulator during WGS iteration convergence includes: determining the steady-state weight and steady-state phase of each optical well during WGS iteration convergence; obtaining the steady-state complex weight of each optical well based on the steady-state weight, steady-state phase, and target amplitude of each optical well; and obtaining the initial pixel plane complex virtual field based on the steady-state complex weight and spatial frequency of each optical well.

[0012] In the above-mentioned method for generating a hologram of the complex amplitude domain gradient flow of a spatial light modulator, determining the steady-state phase of each optical trap during WGS iteration convergence includes: performing pixel-by-pixel phase extraction on the steady-state complex amplitude field of the pixel plane to obtain the outgoing field on the pixel plane of the spatial light modulator; calculating the focal plane complex amplitude field after the outgoing field on the pixel plane of the spatial light modulator is focused by a Fourier lens; sampling the focal plane complex amplitude field at the spatial position coordinates of each optical trap to obtain the complex amplitude value of each optical trap; and extracting the phase from the complex amplitude value of each optical trap to obtain the steady-state phase of each optical trap.

[0013] In the above-mentioned method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator, performing an incremental velocity first-order incremental update based on the pixel plane complex virtual field of the current frame and the optical trap position update pair of the current frame from the atomic rearrangement path planning result to obtain the updated pixel plane complex virtual field includes: determining the spatial frequency coordinates of the current frame and the spatial frequency coordinates of the next frame for each optical trap based on the optical trap position update pair of the current frame from the atomic rearrangement path planning result; and, for each optical trap, subtracting the plane wave carrier of the optical trap based on the frequency of the current frame from the pixel plane complex virtual field of the current frame and adding the plane wave carrier of the optical trap based on the frequency of the next frame to obtain the updated pixel plane complex virtual field.

[0014] In the above-mentioned method for generating a hologram of a gradient flow in the complex amplitude domain of a spatial light modulator, before performing the first-order incremental update of the incremental velocity, it may further include: defining the first-order incremental update of the incremental velocity based on the complex weight of each optical trap and the optical trap position update pair of the current frame from the atomic rearrangement path planning result; and determining that the algebra of the first-order incremental update of the incremental velocity is always equal to the zeroth-order truncation of the Newman series.

[0015] In the above-mentioned method for generating a hologram of a gradient flow in the complex amplitude domain of a spatial optical modulator, determining that the first-order incremental update algebra of the incremental velocity is always equal to the zeroth-order truncation of the Newman series includes: taking the partial derivative of the WGS single-step operator with respect to the position of each optical trap and giving the zeroth-order truncation representation of the Newman series.

[0016] In the above-described method for generating a hologram of a spatial light modulator in the complex amplitude domain gradient flow, the calculation of the updated pixel plane complex virtual field using a WGS single-step operator with a predetermined order of the Newman series as the number of steps to perform high-order crosstalk correction and obtain the hologram of the spatial light modulator includes: determining the predetermined order of crosstalk correction based on the equivalence relationship between the rate of change of the steady-state complex amplitude field of the pixel plane and the term-by-term cumulative structure representation of the Newman series; in the single-step correction based on the predetermined order, performing phase extraction on the updated pixel plane complex virtual field to obtain a phase map before correction, and performing forward diffraction based on Fourier transform on the phase map before correction to obtain a focal plane complex amplitude field; and in the single-step correction, performing amplitude forcing on the focal plane complex amplitude field to obtain an amplitude-forced focal plane complex amplitude field, and performing backward diffraction based on inverse Fourier transform on the amplitude-forced focal plane complex amplitude field to obtain the hologram as the corrected phase map.

[0017] In the above-mentioned method for generating holograms of complex amplitude domain gradient flow in spatial light modulators, determining the order of crosstalk correction based on the equivalence between the rate of change of the steady-state complex amplitude field of the pixel plane and the term-by-term cumulative structure representation of the Newman series includes: representing the fixed-point condition of the WGS single-step operator as an implicit function; calculating the implicit function response of the time derivative of the implicit function by taking the total differential of the implicit function with respect to the optical trap position set to obtain the rate of change of the steady-state complex amplitude field of the pixel plane with respect to the motion of the optical trap; and expanding the rate of change of the steady-state complex amplitude field of the pixel plane with respect to the motion of the optical trap into a Newman series to obtain the equivalence between the rate of change of the steady-state complex amplitude field of the pixel plane and the term-by-term cumulative structure representation of the Newman series.

[0018] In the above-mentioned method for generating a hologram of a complex amplitude domain gradient flow in a spatial light modulator, the rate of change of the steady-state complex amplitude field of the pixel plane with respect to the motion of the optical trap is expressed as the inverse matrix of the difference matrix between the multidimensional diagonal reference identity matrix and the steady-state Jacobian matrix, multiplied by the current frame excitation and then by the velocity field of the optical trap motion. The steady-state Jacobian matrix is ​​the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane, and the current frame excitation is the partial derivative of the WGS single-step operator with respect to the set of optical trap positions.

[0019] In the above-mentioned method for generating complex amplitude domain gradient flow holograms of spatial light modulators, the predetermined order of the crosstalk correction is a fixed order.

[0020] In the above-mentioned method for generating complex amplitude domain gradient flow holograms using spatial light modulators, the fixed order is one or twenty.

[0021] In the above-mentioned method for generating a hologram of a spatial light modulator in the complex amplitude domain gradient flow, after performing high-order crosstalk correction by calculating the WGS single-step operator with a predetermined order of the Newman series as the step number on the updated pixel plane complex virtual field to obtain the hologram of the spatial light modulator, it further includes: giving a stable upper bound of the single-frame error on the order of the inter-frame step size based on the Taylor stretching residual, the Newman truncation error, the WGS residual, and the phase projection error.

[0022] In the above-mentioned method for generating complex amplitude domain gradient flow holograms of spatial light modulators, the predetermined order of the crosstalk correction is an adaptive order.

[0023] In the above-mentioned method for generating a hologram of the complex amplitude domain gradient flow of a spatial light modulator, determining the adaptive order for crosstalk correction includes: establishing a precise bound on the truncation error, and determining an analytical solution for the optimal truncation order based on the precise bound on the truncation error and a preset target accuracy; determining the adaptive shutdown threshold as the difference between the target accuracy and a conservatively estimated lower bound of the spectral radius, based on the truncation error satisfying the residual self-stopping criterion; performing recursive iteration and adaptive accumulation of the series terms in response to the modulus of the predetermined order increment of the Newman series being greater than the adaptive shutdown threshold; and determining the current order as the adaptive order in response to the modulus of the predetermined order increment of the Newman series being less than the adaptive shutdown threshold and / or the number of iterations being greater than the safe maximum order.

[0024] In the above-mentioned method for generating a hologram of the complex amplitude domain gradient flow of a spatial light modulator, after performing high-order crosstalk correction by calculating the WGS single-step operator with a predetermined number of steps of the Newman series on the updated pixel plane complex virtual field to obtain the hologram of the spatial light modulator, the method further includes: determining anomalous optical traps by comparing the focal plane complex amplitude of each optical trap with the target amplitude on a trap-by-trap basis; and performing additional iterative calculations of the WGS single-step operator on the anomalous optical traps to achieve local reconvergence and obtain a hologram after singularity detection and repair.

[0025] In the above-mentioned method for generating a hologram of a spatial light modulator in the complex amplitude domain gradient flow, after performing high-order crosstalk correction by calculating the updated pixel plane complex virtual field using a WGS single-step operator with a predetermined order of the Newman series as the step number to obtain the hologram of the spatial light modulator, the method further includes: obtaining the weight of each optical well in the next frame by multiplying the weight of each optical well in the current frame by its target amplitude and dividing by the magnitude of its complex amplitude; and calculating the phase of each optical well in the next frame based on the hologram and the moved position of each optical well in the current frame, updating the complex weights, and obtaining the pixel plane complex virtual field of the next frame through carrier reconstruction.

[0026] In the above-mentioned method for generating a hologram of a spatial light modulator in the complex amplitude domain gradient flow, after performing high-order crosstalk correction by calculating the updated pixel plane complex virtual field with a predetermined number of steps of the Newman series using the WGS single-step operator to obtain the hologram of the spatial light modulator, the method further includes: after a predetermined frame, re-executing the WGS single-step operator iteration with the position set formed by the moved positions of each optical trap until convergence, so as to obtain the pixel plane complex virtual field reset to the precise fixed point and the weight of each optical trap.

[0027] According to another aspect of this application, an electronic device is provided, including a processor coupled to a memory, the processor being configured to execute a computer program stored in the memory, such that the electronic device performs the complex amplitude domain gradient flow hologram generation method of the spatial light modulator as described above.

[0028] According to another aspect of this application, a computer-readable storage medium is provided, the computer-readable storage medium storing a computer program that, when the computer program is run, implements the method for generating complex amplitude domain gradient flow holograms of spatial light modulators as described above.

[0029] The method for generating complex amplitude domain gradient flow holograms of spatial light modulators provided in this application can significantly improve the time efficiency of high-precision hologram generation by constructing a framework for hologram generation that approximates fixed points in layers according to the Newman series, achieving zeroth-order crosstalk correction through incremental updates and first-order and above through WGS correction steps. Attached Figure Description

[0030] Various other advantages and benefits of this application will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiments below. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. Furthermore, the same reference numerals denote the same parts throughout the drawings.

[0031] Figure 1 The illustration shows a schematic flowchart of a method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to an embodiment of this application.

[0032] Figure 2 The illustration shows a schematic flowchart of the WGS single-step iteration process in the complex amplitude domain gradient flow hologram generation method of the spatial light modulator according to an embodiment of the present application.

[0033] Figure 3The illustration shows a schematic flowchart of the process of obtaining the initial pixel plane complex virtual field in the complex amplitude domain gradient flow hologram generation method of the spatial light modulator according to an embodiment of the present application.

[0034] Figure 4 The illustration shows a schematic flowchart of the incremental velocity first-order incremental update process in the complex amplitude domain gradient flow hologram generation method of a spatial light modulator according to an embodiment of the present application.

[0035] Figure 5 The illustration shows a schematic flowchart of the high-order crosstalk correction process in the complex amplitude domain gradient flow hologram generation method of the spatial light modulator according to an embodiment of the present application.

[0036] Figure 6 The illustration shows a schematic flowchart of the adaptive order determination process in the complex amplitude domain gradient flow hologram generation method of a spatial light modulator according to an embodiment of this application.

[0037] Figure 7 A schematic block diagram of an electronic device according to an embodiment of this application is shown. Detailed Implementation

[0038] Hereinafter, exemplary embodiments according to this application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this application, and not all embodiments of this application. It should be understood that this application is not limited to the exemplary embodiments described herein.

[0039] Figure 1 The illustration shows a schematic flowchart of a method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to an embodiment of this application. Figure 1 As shown, the method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to an embodiment of this application includes the following steps.

[0040] S110, obtain the initial pixel plane complex virtual field and the atomic rearrangement path planning results of the atomic array to be rearranged when the spatial light modulator converges in the WGS iteration.

[0041] As described above, optical tweezers capture individual cold atoms by forming a bright spot with a laser beam highly focused by a lens, thereby locking the cold atom at the focal point through a dipole force generated by the gradient direction towards the focal point due to uneven light intensity. The cold atom can then move with the laser beam. Meanwhile, spatial light modulators utilize their liquid crystal panels (e.g., 1 pixel, of which Each liquid crystal pixel modulates the phase of light passing through it by changing the phase of the hologram. For example, the coordinates of each pixel are represented as... The hologram composed of the applied phase delay is then represented as: , In other words, the hologram is essentially a phase diagram.

[0042] Thus, the input coherent laser beam, after being phase-modulated by the spatial light modulator, passes through a focal length of... Focusing lenses, such as Fourier lenses, are superimposed on the focal plane to form an array of optical tweezers consisting of independent optical tweezers. This array holds atoms within the optical traps of a corresponding optical trap array, allowing the tweezers to move them between the traps. Therefore, for coordinates within the optical trap array on the focal plane... There is a complex amplitude distribution That is, the complex amplitude field of the focal plane, is expressed as:

[0043] in It is the laser wavelength, for example, 399nm. Thus, the first [missing information] in the optical trap target array... The location of the optical trap, for example, denoted as The strength at that point is Therefore, in order to achieve the target amplitude for each optical trap, for example denoted as Holograms are needed. Make In this embodiment, the WGS (Weighted Gerchberg-Saxton) algorithm is used to solve for the hologram. This is a phase recovery problem, and the WGS algorithm is essentially a steady-state (fixed-point) iteration, which will be explained in detail below.

[0044] Specifically, firstly, an initial pixel plane complex amplitude field is constructed on the pixel plane of the spatial light modulator based on the target illumination parameters, and then WGS single-step iteration using the WGS single-step operator is performed on the initial pixel plane complex amplitude field to obtain the pixel plane complex amplitude field of the corresponding iteration round.

[0045] In this embodiment of the application, the target illumination parameters include a set of target amplitudes of each optical trap in a pre-configured target array. (including the first) The target amplitude of each optical trap ), the set of positions of each optical trap (including the first) The position of each optical trap Initial hologram Uniformity convergence accuracy threshold The weights of the initial states of each optical trap (including the first one). (weight of each optical trap), and laser wavelength Focal length of the front Fourier lens .

[0046] Here, the weights of the initial states of each optical trap are denoted as... And the first The weights of the optical traps are denoted as follows: .

[0047] Based on the initial hologram The normalized initial pixel plane complex amplitude field (i.e., the pure phase field with a constant modulus of 1) required for constructing a single-step WGS iteration is expressed as:

[0048] in This represents the complex amplitude field of the SLM pixel plane during the 0th (initial) iteration. ( ,here (This refers to the side length of an SLM LCD panel, expressed in pixels.) Two-dimensional pixel coordinates of an SLM LCD panel ( , The initial phase distribution is the input. The imaginary unit, The natural index. In the following text, the complex amplitude field of the SLM pixel plane is referred to as the pixel plane complex amplitude field.

[0049] Mapping the physical positions of each optical trap in the target array on the focal plane to the spatial frequency coordinates required for diffraction calculations is expressed as:

[0050] in For the first The spatial frequency coordinates (or simply frequencies) corresponding to each optical trap. For the target array on the focal plane, the first The spatial coordinates of each optical trap (or simply, position). For a specific light wave (such as a laser), The focal length of the front Fourier lens. It is a phase period constant.

[0051] In the method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to an embodiment of this application, constructing an initial pixel plane complex amplitude field on the plane of the spatial light modulator based on target illumination parameters includes: obtaining target illumination parameters, wherein the target illumination parameters include: a set of target amplitudes of each optical trap in a pre-configured target array; a set of positions of each optical trap; a set of weights for the initial hologram, uniformity convergence accuracy threshold, and iterative initial states of each optical trap; and the laser wavelength and the focal length of the pre-Fourier lens.

[0052] In the above-mentioned method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator, constructing an initial pixel plane complex amplitude field on the pixel plane of the spatial light modulator based on the target illumination parameters includes: multiplying the initial hologram based on the liquid crystal pixel coordinates of the liquid crystal panel of the spatial light modulator with an imaginary unit and using the result as an exponent term of the natural constant to obtain the initial pixel plane complex amplitude field.

[0053] In the above-mentioned method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator, constructing an initial pixel plane complex amplitude field on the plane of the spatial light modulator based on the target illumination parameters includes: multiplying the position of each optical trap in the target array on the focal plane of the spatial light modulator by a phase period constant and then dividing by the laser wavelength and the focal length of the pre-Fourier lens to obtain the frequency of each optical trap.

[0054] Figure 2 The illustration shows a schematic flowchart of the WGS single-step iterative process in the complex amplitude domain gradient flow hologram generation method of a spatial light modulator according to an embodiment of this application. Figure 2 As shown, the WGS single-step iteration process in the complex amplitude domain gradient flow hologram generation method of the spatial light modulator according to the embodiments of this application includes the following steps.

[0055] Step S111: Divide the pixel plane complex amplitude field of the current round by its magnitude to obtain the phase-processed pixel plane complex amplitude field. That is, after obtaining the initial pixel plane complex amplitude field, perform WGS single-step iterations using the WGS single-step operator on the initial pixel plane complex amplitude field. During the WGS single-step iteration, for example in the... In the nth iteration, first for the current iteration, i.e., the nth iteration... The pixel plane complex amplitude field at the next iteration Performing phase conversion decouples non-physical amplitude fluctuations (corresponding to the hardware properties of pure phase SLM), represented as:

[0056] in For the first The phase-modulated complex amplitude field of the pixel plane in the next iteration (the modulus is always 1). For the first The pixel plane complex amplitude field on the pixel plane of the next iteration of SLM. Let be the modulus of the complex amplitude field in the pixel plane. This essentially expresses the hardware phase modulation property of a pure phase spatial light modulator, since the actual SLM only changes the spatial phase delay of the incident laser. This does not change the amplitude of the laser. Since the calculated result of the complex amplitude field of the pixel plane obtained in each step of the WGS single-step iteration during the forward-inverse Fourier iteration of the wave field is a complex number containing both amplitude and phase, it can be obtained by dividing by its own modulus. This decouples non-physical amplitude oscillations and fluctuations, retaining only pure phase information to achieve holographic phase recovery.

[0057] Step S112: Perform a forward Fourier transform on the phased pixel plane complex amplitude field to obtain the focal plane complex amplitude field on the focal plane. Here, the phased pixel plane complex amplitude field... Performing a forward Fourier transform to simulate lens diffraction projection onto the focal plane is represented as:

[0058] That For the first The complex amplitude field of the focal plane on the focal plane in the next iteration. For the positive Fourier transform operator, The position on the focal plane (represented as spatial coordinates). For the position on the corresponding focal plane The frequency (represented as spatial frequency coordinates), for Summation represents the position of all pixels traversed on the SLM plane. They came to seek peace.

[0059] Step S113: At each optical trap position in the target array, the complex amplitude field of the focal plane on the focal plane is divided by its modulus and multiplied by the target amplitude and the weight of the current round to obtain the amplitude-constrained complex amplitude field of the focal plane. That is, at each optical trap position in the target array... An amplitude constraint is applied at this point, and the actual diffraction phase is recombined with the target weighted amplitude, which is expressed as: For the first The complex amplitude field of the focal plane after amplitude constraint in the next iteration For the first The iteration of the ... Weights of the optical trap For the first The target amplitude of the optical trap For the first Position of the next iteration Complex amplitude (including amplitude and phase) at the focal plane. Its modulus length.

[0060] Step S114: Perform an inverse Fourier transform on the amplitude-constrained focal plane complex amplitude field to obtain the pixel plane complex amplitude field for the next iteration. Here, performing an inverse Fourier transform on the amplitude-constrained focal plane complex amplitude field yields the next iteration, i.e., the [number missing]th iteration. The pixel plane complex amplitude field on the SLM pixel plane in the next iteration is expressed as:

[0061] in It is the total number of optical traps in the target array.

[0062] In summary, the complete WGS single-step operator is represented as:

[0063] Those skilled in the art will understand that the pixel plane complex amplitude field and the focal plane complex amplitude field are actually tensors composed of complex numbers containing amplitude and phase at each position. That is, the pixel plane complex amplitude field is composed of the pixel plane complex amplitude corresponding to each position of the pixel plane, while the focal plane complex amplitude field is composed of the focal plane complex amplitude corresponding to each position of the focal plane, i.e., each optical trap position.

[0064] In the method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to an embodiment of this application, performing WGS single-step iteration using the WGS single-step operator on the initial pixel plane complex amplitude field to obtain the pixel plane complex amplitude field of the corresponding iteration round includes: dividing the pixel plane complex amplitude field of the current round by its magnitude to obtain a phased pixel plane complex amplitude field; performing a forward Fourier transform on the phased pixel plane complex amplitude field to obtain a focal plane complex amplitude field on the focal plane; at each optical trap position in the target array, dividing the focal plane complex amplitude field by its magnitude and multiplying it by the target amplitude and the weight of the current round to obtain an amplitude-constrained focal plane complex amplitude field; and performing an inverse Fourier transform on the amplitude-constrained focal plane complex amplitude field to obtain the pixel plane complex amplitude field of the next round.

[0065] Additionally, it can be done in the current round, i.e., the [number]th round. In the next iteration, the optical trap position is extracted. The actual diffraction amplitude of each optical trap in the complex amplitude of the focal plane at that location And based on the gain negative feedback law, adaptive weight updates are performed (if the actual weight is too weak, compensation is amplified; if the weight is too strong, suppression is performed), as follows:

[0066] in and The first , No. During the first iteration The weights of each optical trap.

[0067] In other words, due to the inherent long-range spatial interference crosstalk of the Fourier diffraction integral, the photon energy at each point in the optical tweezers array is difficult to be uniform (resulting in uneven brightness and causing random photothermal escape of the central atom). This can be addressed by monitoring the ideal value. (i.e., the first) (ideal target amplitude of each optical trap) and current actual value The ratio (which is the first) After the first simulation iteration of forward injection, at the specified position The complex amplitude field of diffracted light intensity generated by actual interference (amplitude value), if the actual light intensity at a certain optical trap is too weak (ratio) If the calculation weight of that point is increased, it will be compensated for and amplified; if it is too strong, it will be suppressed, so that the actual amplitude of each optical trap tends to its target amplitude. This ensures that all neutral atoms on the array are in a deep potential well with highly uniform energy, meaning the light intensity uniformity meets the convergence criterion. .

[0068] In the method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to an embodiment of this application, performing WGS single-step iteration using the WGS single-step operator on the initial pixel plane complex amplitude field to obtain the pixel plane complex amplitude field of the corresponding iteration round further includes: dividing the target amplitude of each optical well by the modulus of the focal plane complex amplitude at the position of each optical well and multiplying it by the weight of each optical well in the current round to obtain the weight of each optical well in the next round.

[0069] Then, the light intensity uniformity index is obtained by dividing the standard deviation of the mode length of the complex amplitude of the focal plane of each optical trap in the target array by the mean, and the steady-state complex amplitude field of the pixel plane is determined in response to the light intensity uniformity index being less than the uniformity convergence accuracy threshold.

[0070] Here, the discrete distribution of the actual light intensity of all optical traps in the target array is statistically analyzed, and a scalar index of light intensity uniformity is calculated. ,in, Let be the standard deviation of the mode length (i.e., amplitude) of the complex amplitude at the focal plane of each optical trap. The average amplitude of each optical trap is expressed as follows:

[0071] The scalar index of light intensity uniformity With the preset uniformity convergence accuracy threshold In comparison, the preset uniformity convergence accuracy threshold is used here. In practice, it is usually taken as 0.1%.

[0072] If the scalar index of light intensity uniformity Greater than the preset uniformity convergence accuracy threshold Then continue to update the pixel plane complex amplitude field of the SLM. and the weights of each optical trap Otherwise, the weight of the optical trap is determined. Full convergence, i.e., the weights at this point It has stabilized and can be considered a parameter rather than a dynamic variable. In practice, approximately 100 iterations are typically sufficient to achieve the desired scalar index of light intensity uniformity. Less than the preset uniformity convergence accuracy threshold .

[0073] In this embodiment of the application, the complete state of WGS consists of two types of variables, represented as follows:

[0074] in A hologram of SLM. The weight set consists of the weights of each optical trap, for example, represented as a weight vector. When treated as parameters rather than dynamic variables, the state simplifies to And converges to the steady-state complex amplitude field of the pixel plane. , can be represented as:

[0075] here, This is a complete WGS single-step operator (including phase transformation, forward transformation, amplitude forcing, and inverse transformation). It is the set of locations of all optical traps in the target array.

[0076] At this point, the complete state of WGS after convergence. That is, the fully convergent state variables of WGS Approximately equal to a stable hologram after convergence The state approximately degenerates to contain only phase, which indicates that after repeated oscillations along the optical path, the entire optical diffraction coherent network reaches an energy-phase equilibrium. In other words, if the hologram at this point... The input is given to the SLM, and after being diffracted by a real lens through a parallel lens, it hits the focal plane and can achieve the preset... The required complex amplitude distribution of the focal plane is accurately generated. Then, the WGS single-step operator is executed again in this state. Since the input and output are identical, no further drift in the complex amplitude field occurs. Therefore, the steady-state complex amplitude field of the pixel plane... That is, WGS single-step operator The fixed point. This is also the basis for subsequent treatment of atomic position shifts ( The premise that the measurement of crosstalk in the optical field caused by changes is valid is based on the following assumptions.

[0077] The steady-state complex amplitude field of the pixel plane is obtained. Then, the steady-state complex amplitude field of the pixel plane can be obtained. The initial pixel plane complex virtual field is obtained.

[0078] Figure 3 The illustration shows a schematic flowchart of the process of obtaining the initial pixel plane complex virtual field in the complex amplitude domain gradient flow hologram generation method of the spatial light modulator according to an embodiment of this application. Figure 3 As shown, the process of obtaining the initial pixel plane complex virtual field in the complex amplitude domain gradient flow hologram generation method of the spatial light modulator according to the embodiments of this application includes the following steps.

[0079] Step S115: Determine the steady-state weights and steady-state phases of each optical trap during WGS iteration convergence. That is, as described above, by iterating the calculation of the WGS single-step operator until convergence to a fixed point, the iteration of the WGS single-step operator is considered complete, i.e., WGS iteration convergence. From this, the steady-state complex amplitude field of the pixel plane converged by the WGS iteration can be obtained. Furthermore, when WGS converges iteratively, the th... The weights of each optical trap are obtained through iteration to obtain steady-state weights. That is, when the complex amplitude field of the pixel plane is in a steady state at the end of the WGS iteration, it is assumed that the weight of each optical trap is also in a steady state and no longer changes significantly.

[0080] Here, for example, in the first The steady-state weights of each optical trap are denoted as... .

[0081] Furthermore, when WGS converges, the first iteration... The phase of each optical trap is represented as Then we have:

[0082] in, It is the first The steady-state phase of each optical trap It is the steady-state complex amplitude field of the pixel plane; It is the first The location of each optical trap.

[0083] Specifically, in the process of obtaining the steady-state phase of each optical trap from the steady-state complex amplitude field of the pixel plane, SLM spatial projection is first performed, that is, the phase is extracted pixel by pixel from the steady-state complex amplitude field of the pixel plane to construct the pure phase emission field on the SLM pixel plane. .

[0084] here, This refers to the steady-state complex amplitude field of the pixel plane in the pixel domain of the spatial light modulator (SLM). High-precision pixel-by-pixel phase (argument) extraction is performed. For the discretized SLM pixel array, the steady-state complex amplitude field of the pixel plane is... In pixel coordinates The number is a complex number, which can be written in Cartesian coordinate form:

[0085] Then extract the argument of the complex number. Operation, on a single pixel The specific calculation at this point is expressed as follows:

[0086] Furthermore, in order to adapt to the physical control of gray levels in pure phase SLM (typically 0 to...), (corresponding to 8-bit or 12-bit values), typically requiring further processing of the output value from... default Mapped to The interval mapping formula is:

[0087] in, It is a complex number The real part, It is a complex number The imaginary part, It is the imaginary unit, and It is a two-parameter arctangent function, defined as: It is the physical phase value finally extracted from the pixel (the hologram in coordinates). (phase quantity at the location).

[0088] Then, through Fast Fourier Transform Calculate the complex amplitude field of the focal plane after the pure phase outgoing field on the SLM pixel plane is focused by a Fourier lens, for example, denoted as...

[0089] Then, on the discretized focal plane grid, the address is located to the first... The position of each optical trap Sample the complex amplitude value at this location. Here, the complex amplitude value It is used to represent the first The complex amplitude and phase scalar of an optical trap in steady state.

[0090] Finally, the same phase extraction operation as described above is performed. From the complex amplitude value The steady-state phase of the optical trap is obtained.

[0091] Step S116: Obtain the steady-state complex weights for each optical well based on its steady-state weights, steady-state phase, and target amplitude. Here, in the... The complex weight of each optical trap is denoted as In this case, the calculation is as follows:

[0092] in It is the first The target amplitude of the optical trap.

[0093] Step S117: The initial pixel plane complex virtual field is obtained based on the steady-state complex weights and spatial frequencies of each optical trap. Here, the initial pixel plane complex virtual field is expressed as:

[0094] in It is the first The frequency of each optical trap. That is, for the above steady-state complex weighted... By using a plane wave carrier, i.e. The initial pixel plane complex virtual field is obtained by linearly superimposing the basis to obtain the complex amplitude domain corresponding to the steady-state complex amplitude field of the pixel plane. The initial pixel plane complex virtual field reconstructs the hologram in the complex amplitude domain.

[0095] In the method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to an embodiment of this application, obtaining the initial pixel plane complex virtual field of the spatial light modulator during WGS iteration convergence includes: determining the steady-state weight and steady-state phase of each optical well during WGS iteration convergence; obtaining the steady-state complex weight of each optical well based on the steady-state weight, steady-state phase, and target amplitude of each optical well; and obtaining the initial pixel plane complex virtual field based on the steady-state complex weight and spatial frequency of each optical well.

[0096] In the above-described method for generating a gradient flow hologram in the complex amplitude domain, determining the steady-state phase of each optical trap during WGS iteration convergence includes: performing pixel-by-pixel phase extraction on the steady-state complex amplitude field of the pixel plane to obtain the outgoing field on the pixel plane of the spatial light modulator; calculating the focal plane complex amplitude field after the outgoing field on the pixel plane of the spatial light modulator is focused by a Fourier lens; sampling the focal plane complex amplitude field at the position of each optical trap to obtain the complex amplitude value of each optical trap; and extracting the phase from the complex amplitude value of each optical trap to obtain the steady-state phase of each optical trap.

[0097] Furthermore, it is also necessary to obtain the atomic rearrangement path planning results, which include atom-target pairing and frame allocation schemes. Here, in the embodiments of this application, the atomic rearrangement path planning results can be obtained in various ways, for example, the atom-target configuration of each atom can be obtained using the Hungarian algorithm. The frame allocation scheme is obtained through greedy graph coloring. That is, the optical trap set is moved using atom-target pairing and a frame allocation scheme. ,in Indicates the first The optical trap in the first The position of the frame.

[0098] Step S120: Based on the pixel plane complex virtual field of the current frame and the optical trap position update of the current frame from the atomic rearrangement path planning result, perform incremental velocity first-order incremental update to obtain the updated pixel plane complex virtual field.

[0099] Figure 4 The illustration shows a schematic flowchart of the first-order incremental velocity update process in the complex amplitude domain gradient flow hologram generation method of a spatial light modulator according to an embodiment of this application. Figure 4 As shown, the incremental velocity first-order incremental update process in the spatial light modulator complex amplitude domain gradient flow hologram generation method according to the embodiments of this application includes the following steps.

[0100] Step S121: Define the first-order incremental update of the incremental velocity based on the complex weights of each optical trap and the optical trap position update of the current frame from the atomic rearrangement path planning result. That is, in this embodiment, the first-order incremental update of the incremental velocity (IV) is defined as:

[0101] in, For SLM pixel coordinates, It is the first The complex weights of the current frame of each optical trap. and They are the first The spatial frequency coordinates of each optical trap before and after movement are updated based on the optical trap position of the current frame from the atomic rearrangement path planning results. To obtain. That is, for the first... The optical trap in the first Spatial location of a frame and in the Spatial location of a frame ,but ,and .

[0102] Here, as mentioned above For the first For each plane wave carrier corresponding to an optical trap, the first-order incremental update of IV directly represents the field change introduced by the moving optical trap in the complex amplitude domain by removing the old carrier and superimposing the new carrier. That is, performing a first-order incremental update on the moving optical trap in the complex virtual field can avoid recalculating the entire hologram.

[0103] Step S122: Determine that the first-order incremental update algebra of the incremental velocity is always equal to the zeroth-order truncation of the Newman series.

[0104] Specifically, the applicant of this application proves that the first-order incremental update algebra of the IV is always equal to the zeroth-order truncation (i.e., the Neumann series) of the Neumann series (e.g., also known as the Neumann power series). (Truncation)

[0105] Among them, by The explicit form of the position Find the partial derivative (fixed) That is, fixed ):

[0106] but The truncation is given as follows:

[0107] This replaces the first-order Taylor expansion with an exact plane-wave difference, which holds exactly for any step size. Clearly, this is identical to the first-order incremental IV update described above. This represents the optical trap displacement in the current frame. In other words, the incremental virtual field update is a zeroth-order exact implementation of the Newman hierarchical approximation, which ensures that subsequent higher-order corrections are based on no truncation bias. The IV increment is a reliable carrier contribution from the moving optical trap. In absolute terms, the relative error of the zeroth-order truncation of the Newman series... However, for the machine precision of IEEE 754 double-precision floating-point numbers, it is approximately... In other words, any lower bound of the relative error obtained based on double-precision floating-point arithmetic should be on the order of magnitude of the precision of the double-precision floating-point machine (e.g., approximately). (on the order of magnitude).

[0108] Step S123: Perform the incremental velocity first-order incremental update on the pixel plane complex virtual field of the current frame to obtain the updated pixel plane complex virtual field of the current frame. For example, the pixel plane complex virtual field of the current frame is denoted as... Then, for each moving optical trap, the operation of performing the first-order incremental update of the IV is expressed as:

[0109] Then we have:

[0110] In other words, by superimposing the carrier differential in the defined IV first-order incremental update on a per-light-well basis, it is equivalent to adding the IV first-order incremental update all at once, thus completing the Newman series with minimal computing power. Update the fixed point.

[0111] It is understood that, in the embodiments of this application, performing an incremental velocity first-order incremental update on the pixel plane complex virtual field based on the current frame's pixel plane complex virtual field and the current frame's optical trap position update from the atomic rearrangement path planning result to obtain the updated pixel plane complex virtual field may only include the step of performing the incremental velocity first-order incremental update on the pixel plane complex virtual field of the current frame to obtain the updated pixel plane complex virtual field of the current frame.

[0112] As described above, in the embodiments of this application, the first-order incremental update of the incremental velocity explicitly corresponds to the zeroth-order term of the Newman series, i.e. The term "order" is not an approximation of the first-order Taylor expansion but an exact algebraic identity. Here, in this embodiment, it is named "Incremental Velocity First-Order Incremental Update" because it is a linearization incremental correction operation, not the order number of the Newman series. That is, since it has been proven above that the algebraic value of the "Incremental Velocity First-Order Incremental Update" is identical to the zeroth-order truncation of the Newman series, the "first order" in "Incremental Velocity First-Order Incremental Update" is not in the same numbering system as the Newman series. Those skilled in the art will understand that, to distinguish it from the order numbering system of the Newman series, this "Incremental Velocity First-Order Incremental Update" can also be simply referred to as "Incremental Velocity Update."

[0113] That is, in the method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to the embodiments of this application, performing an incremental velocity first-order incremental update based on the pixel plane complex virtual field of the current frame and the optical trap position update pair of the current frame from the atomic rearrangement path planning result to obtain the updated pixel plane complex virtual field includes: determining the frequency of the current frame and the frequency of the next frame for each optical trap based on the optical trap position update pair of the current frame from the atomic rearrangement path planning result; and, for each optical trap, subtracting the plane wave carrier of the optical trap based on the frequency of the current frame from the pixel plane complex virtual field of the current frame and adding the plane wave carrier of the optical trap based on the frequency of the next frame to obtain the updated pixel plane complex virtual field.

[0114] In the above-mentioned method for generating a hologram of a gradient flow in the complex amplitude domain of a spatial light modulator, before performing the first-order incremental update of the incremental velocity, it may further include: defining the first-order incremental update of the incremental velocity based on the complex weight of each optical trap and the optical trap position update pair of the current frame from the atomic rearrangement path planning result; and determining that the algebra of the first-order incremental update of the incremental velocity is always equal to the zeroth-order truncation of the Newman series.

[0115] In the above-mentioned method for generating a hologram of a gradient flow in the complex amplitude domain of a spatial optical modulator, determining that the first-order incremental update algebra of the incremental velocity is always equal to the zeroth-order truncation of the Newman series includes: taking the partial derivative of the WGS single-step operator with respect to the position of each optical trap and giving the zeroth-order truncation representation of the Newman series.

[0116] Step S130: Perform high-order crosstalk correction on the updated pixel plane complex virtual field using a WGS single-step operator with a predetermined number of steps of the Newman series to obtain the hologram of the spatial light modulator.

[0117] Figure 5 The illustration shows a schematic flowchart of the high-order crosstalk correction process in the complex amplitude domain gradient flow hologram generation method of a spatial light modulator according to an embodiment of this application. Figure 5 As shown, the high-order crosstalk correction process in the complex amplitude domain gradient flow hologram generation method of the spatial light modulator according to the embodiments of this application includes the following steps.

[0118] Step S131: Determine the predetermined order of crosstalk correction based on the equivalence relationship between the rate of change of the steady-state complex amplitude field of the pixel plane and the term-by-term cumulative structural representation of the Newman series.

[0119] Here, the applicant of this application has discovered that the rate of change of the steady-state complex amplitude field of the pixel plane is equivalent to the term-by-term summable structure representation of the Newman series. Specifically, the fixed-point condition of the WGS single-step operator is written as an implicit function to obtain:

[0120] Calculate its implicit functional response with respect to the time derivative of the optical trap location set. Taking the total differential, we get:

[0121] The steady-state Jacobian matrix corresponding to the steady-state complex amplitude field of the pixel plane is, in other words, the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane. The rate of change of the steady-state complex amplitude field of the pixel plane with respect to the motion of the optical trap is then... Represented as:

[0122] in It is a multidimensional diagonal reference identity matrix. Essentially, it's a WGS crosstalk amplifier, representing the total response after the disturbance has fully converged through an infinite number of WGS iterations. It is used as the WGS single-step operator for the optical trap position set. The positional partial derivative matrix of the partial derivatives can be called the current frame excitation, and It is the velocity field of the optical trap's motion. That is, it is determined by the implicit function at the fixed point. right The total differential, calculated using the implicit function theorem, can represent how the movement of the optical trap causes changes in the hologram. This characterizes the cumulative crosstalk that leaks from any moving optical trap to all other optical traps via the superposition of diffraction fields. The positional derivative is... This only describes the direct effect of the moving optical trap on the hologram. However, since WGS iterates to a fixed point, this initial perturbation will be repeatedly propagated and superimposed through the WGS single-step operator, forming an infinite series. The geometric series converges when the spectral radius is less than 1. This is called a crosstalk amplifier. The essence of optical crosstalk is to amplify the single direct effect into a converged total effect. Moving one optical trap will cause leakage through the diffraction field to affect all optical traps.

[0123] Furthermore, the above equation holds true if WGS converges, and the necessary and sufficient condition for WGS convergence is that the WGS single-step operator... At steady state (i.e., at a fixed point), the Jacobian satisfies the spectral radius. .

[0124] Then, the rate of change of the steady-state complex amplitude field of the pixel plane with respect to the motion of the optical trap is... Expanding into a Newman series, where the inverse operator form and convergence condition are as described above. The inverse can be transformed into a power series that can be summed term by term:

[0125] in The steady-state Jacobian matrix represents Power of 1 yes spectral radius, and It is the sequence number of the series term.

[0126] As mentioned above, based on the Newman expansion, we have:

[0127] The first of which The disturbance caused by the movement of the corresponding optical trap is propagated through WGS iteration. The contributions after the step, among which The term refers to the IV increment in step S120, and The term represents a successive higher-order correction to the crosstalk. In other words, it is proven that the rate of change of the steady-state complex amplitude field in the pixel plane is equivalent to the term-by-term summable structural representation of the Newman series.

[0128] Then, based on the term-by-term summable structure representation of the Newman series, by performing stage-by-stage summation with a predetermined order, we obtain:

[0129] in It is the predetermined order. It is the first The steady-state complex amplitude field of the pixel plane of the frame The Newman truncation solution, It is the steady-state Jacobian matrix. power, and , is the excitation of the current frame.

[0130] In the embodiments of this application, if This involves performing a crosstalk higher-order correction calculation based on the WGS single-step operator, which takes approximately 0.1 ms and is based on the spectral radius. (For example, when atoms are at rest) ), can bring A 100-fold increase in accuracy.

[0131] That is, approximating the true fixed-point solution using a finite number of power series. , This is known as IV update (algebraic identity), and Superimposing a higher-order crosstalk correction is equivalent to adding the crosstalk contribution from the perturbation propagation step to the first-order IV result, making the hologram closer to the true optimal solution. In other words, if the predetermined order... Then first from Starting with the incremental update, perform another calculation of the WGS single-step operator to obtain the result containing... The first-order correction. The predetermined order is... Then it is directly added to the above. .

[0132] As described above, in the embodiments of this application, the predetermined order It can be a fixed order, such as one, and is calibrated all at once during the offline phase. Furthermore, in the embodiments of this application, the predetermined order... It can also be an adaptive order, which will be explained in detail below.

[0133] That is, at the predetermined order In this case, an additional calculation based on the WGS single-step operator is performed to perform a higher-order crosstalk correction.

[0134] Step S132: In the single-step correction based on the predetermined order, phase extraction is performed on the updated pixel plane complex virtual field to obtain the phase map before correction, and forward diffraction based on Fourier transform is performed on the phase map before correction to obtain the focal plane complex amplitude field.

[0135] For the updated pixel plane complex virtual field The phase diagram before correction is obtained by taking its argument:

[0136] Wherein, the phase diagram before correction Phase in ,and It is the complex argument operator as described above. This can preserve only the phase and discard the amplitude of the complex virtual field in the pixel plane, corresponding to the phase conversion step of the WGS single-step operator above.

[0137] Then, a Fast Fourier Transform is performed on the uncorrected phase map to simulate the imaging of a Fourier lens on the focal plane:

[0138] in It is the complex amplitude field of the focal plane. It is the output complex light field of the spatial light modulator, and This represents the Fast Fourier Transform. This enables the diffraction mapping from the pixel plane to the focal plane in the spatial light modulator. This allows us to calculate the actual light field distribution generated by the current phase map on the focal plane, corresponding to the forward Fourier transform step of the WGS single-step operator above.

[0139] In step S133, during the single-step correction, the focal plane complex amplitude field is amplitude-forced to obtain an amplitude-forced focal plane complex amplitude field, and the amplitude-forced focal plane complex amplitude field is subjected to inverse diffraction based on inverse Fourier transform to obtain the hologram as the corrected phase map.

[0140] That is, for the complex amplitude field of the focal plane The weight of each optical trap and target amplitude For each optical trap location, the target amplitude is forced to preserve the phase: It is the first The complex amplitude of the focal plane at each optical trap location, and This indicates phase extraction, and This represents the total number of optical traps. This corresponds to the amplitude forcing of the WGS single-step operator, i.e., applying it on the focal plane. The amplitude is constrained while the phase is preserved, thereby pulling the focal plane optical field back into the target feasible region of the equal intensity optical trap and suppressing intensity non-uniformity.

[0141] Then, it is diffracted back to the pixel plane of the spatial light modulator through inverse Fourier transform, i.e., the complex amplitude field of the focal plane forced by amplitude. Using the input as input, perform an inverse Fourier transform (IFFT) and take the argument to obtain the corrected phase map. , represented as:

[0142] That is, the complex amplitude field corrected by the focal plane is inversely mapped back to the pixel plane of the SLM and re-phased, completing a full high-order crosstalk correction loop based on the WGS single-step operator (corresponding to...). By truncating the phase diagram, a hologram of the spatial light modulator is obtained, which serves as the corrected phase diagram.

[0143] In the method for generating a hologram of a spatial light modulator in the complex amplitude domain gradient flow according to an embodiment of this application, performing high-order crosstalk correction on the updated pixel plane complex virtual field using a WGS single-step operator with a predetermined order of the Newman series as the number of steps to obtain the hologram of the spatial light modulator includes: determining a predetermined order of crosstalk correction based on the equivalence relationship between the rate of change of the steady-state complex amplitude field of the pixel plane and the term-by-term cumulative structure representation of the Newman series; in a single correction based on the predetermined order of the crosstalk correction, performing phase extraction on the updated pixel plane complex virtual field to obtain a phase map before correction, and performing forward diffraction based on Fourier transform on the phase map before correction to obtain a focal plane complex amplitude field; and in the single correction, performing amplitude forcing on the focal plane complex amplitude field to obtain an amplitude-forced focal plane complex amplitude field, and performing backward diffraction based on inverse Fourier transform on the amplitude-forced focal plane complex amplitude field to obtain the hologram as the corrected phase map.

[0144] In the method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to an embodiment of this application, determining the order of crosstalk correction based on the equivalence between the rate of change of the steady-state complex amplitude field of the pixel plane and the term-by-term cumulative structure representation of the Newman series includes: representing the fixed-point condition of the WGS single-step operator as an implicit function; calculating the implicit function response of the time derivative of the implicit function by taking the total differential of the implicit function with respect to the optical trap position set to obtain the rate of change of the steady-state complex amplitude field of the pixel plane with respect to the motion of the optical trap; and expanding the rate of change of the steady-state complex amplitude field of the pixel plane with respect to the motion of the optical trap into a Newman series to obtain the equivalence between the rate of change of the steady-state complex amplitude field of the pixel plane and the term-by-term cumulative structure representation of the Newman series.

[0145] In the method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to an embodiment of this application, the rate of change of the steady-state complex amplitude field of the pixel plane with respect to the motion of the optical trap is expressed as the inverse matrix of the difference matrix between the multidimensional diagonal reference identity matrix and the steady-state Jacobian matrix, multiplied by the current frame excitation and then multiplied by the optical trap motion velocity field, wherein the steady-state Jacobian matrix is ​​the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane, and the current frame excitation is the partial derivative of the WGS single-step operator with respect to the optical trap position set.

[0146] In the method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to an embodiment of this application, the predetermined order of the crosstalk correction is a fixed order.

[0147] Furthermore, in the above-mentioned method for generating complex amplitude domain gradient flow holograms of spatial light modulators, the fixed order is one when efficiency is prioritized, and twenty when accuracy is prioritized.

[0148] In this embodiment, single-frame error stability can be defined based on higher-order crosstalk correction. Specifically, based on the truncation solution and correction process, single-frame errors can be orthogonally decomposed into four categories (assuming...). The inter-frame step size is ): Taylor stretching residuals (finite displacements): That is, each frame ; Newman truncation error: It is independent of the optical trap displacement and is purely a series truncation; WGS Residual: Fixed-Point Iterated Residual ,here It is the WGS iteration residual tolerance; Phase projection error: phase constraint The feasible region projection optimized by holograms introduces additional errors.

[0149] Here, the above errors correspond to four sources: finite displacement, crosstalk truncation, incomplete convergence of fixed points, and phase constraint projection.

[0150] Based on these four types of errors, a stable upper bound for single-frame error can be given, expressed as:

[0151] The Taylor stretch residual is a single frame at the fixed-point change level. (rather than) , This holds only if the first-order term is symmetrically eliminated.

[0152] Furthermore, the Newman truncation error includes:

[0153] exist Under normalizable conditions Otherwise, operator norms are required.

[0154] here It is the Newman truncation order ( ), It is the optical trap displacement per frame. It is the excitation term for the current frame.

[0155] That is, in the embodiments of this application, the upper bound of single-frame error stability is The magnitude of the error, where the Newman truncation error explicitly depends on the truncation order. This ensures that the frame-by-frame hologram error is bounded and does not diverge with the dominant frame, thus satisfying the inter-frame phase continuity requirement. and uniformity of light intensity .

[0156] In the method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to an embodiment of this application, after performing high-order crosstalk correction by calculating the WGS single-step operator with a predetermined order of the Newman series as the step number on the updated pixel plane complex virtual field to obtain the hologram of the spatial light modulator, it further includes: giving a stable upper bound of single-frame error on the order of the inter-frame step size based on Taylor stretching residual, Newman truncation error, WGS residual and phase projection error.

[0157] As mentioned above, in a fixed order (Offline parameter tuning) When running iterative correction based on the Newman series, considering the spectral radius The position of the optical trap changes with each frame, for example, when the atom is stationary. During rapid, large displacement, the first frame can reach Fixed order, for example Up to 80% of matrix-vector multiplication is wasted in slow frames.

[0158] Therefore, in this embodiment of the application, the predetermined order of the crosstalk correction is an adaptive order. Figure 6 The illustration shows a schematic flowchart of the adaptive order determination process in the complex amplitude domain gradient flow hologram generation method of a spatial light modulator according to an embodiment of this application. Figure 6 As shown, the adaptive order determination process in the complex amplitude domain gradient flow hologram generation method of the spatial light modulator according to the embodiments of this application includes the following steps.

[0159] Step S1311: Establish the truncation error precision bound, and determine the analytical solution of the optimal truncation order based on the truncation error precision bound and the preset target precision.

[0160] Here, based on the steady-state Jacobian matrix... and current frame excitation Establish a precise bound for the truncation error. Among these, The truncation solution is expressed as:

[0161] The true solution is:

[0162] Then we have:

[0163] Take the upper bound of the norm:

[0164] Given a pre-set target accuracy Then the analytical expression for the optimal truncation order is:

[0165] in yes Truncation solution, It is a real, stationary solution. yes First-order truncation error, It is the current frame spectral radius It rounds up. It is the optimal truncation order.

[0166] That is, due to the truncation error Geometric attenuation, by providing an analytical correspondence between order and accuracy, shows that the accuracy target is fixed while... Each frame is different, so the optimal truncation order is... The core degree of freedom lies in real-time tracking .

[0167] Step S1312: Based on the truncation error satisfying the residual self-stopping criterion, determine the adaptive shutdown threshold as the difference between the target accuracy multiplied by a conservative estimate of the lower bound of the spectral radius.

[0168] In other words, a residual self-stopping criterion can be implemented to achieve zero-overhead adaptation. This is achieved through the steady-state Jacobian matrix. Current frame excitation The target accuracy spectral radius (For example, having a conservative lower bound) 0.05), which allows for the construction of structures that do not require explicit estimation. The residual self-stopping iteration, that is, if the Newman series' th... Increment Satisfy recursion And the truncation error satisfies:

[0169] That is, based on the target accuracy and the conservative lower bound of the spectral radius. ,set up And the stopping condition of the loop is:

[0170] Therefore, the adaptive shutdown threshold Calculated as Among them, the conservative lower bound for the spectral radius. satisfy For example, it could be a conservative lower bound estimated online, which can be obtained through power iteration, the Gershgorin bound, or an empirical safe upper bound. Here, the diffraction crosstalk propagation caused by the optical trap movement occurs in the th... Even after a step, residual potential energy remains unreleased. By scaling the precision target, it is ensured that when the crosstalk energy released in a single step is below a threshold, the sum of the energies of all subsequent uncalculated higher-order crosstalk will also necessarily be below the preset precision, thus allowing safe shutdown of iterative calculations. The initial increment of the series recursion... Excitement for the current frame And the initial accumulated solution Also serves as the excitation for the current frame. .

[0171] Step S1313: In response to the fact that the modulus of the predetermined order increment of the Newman series is greater than the adaptive turn-off threshold, recursive iteration and adaptive accumulation of the series terms are performed.

[0172] That is, the series terms recursively iterate to obtain the steady-state Jacobian matrix. Increment with the current order Multiply to generate the next-order perturbation increment. This quantifies the contribution of a new round of crosstalk between optical traps caused by the local diffraction disturbance caused by the previous displacement after another round of diffraction and phase projection constraint propagation by the SLM-focal plane.

[0173] Furthermore, adaptive accumulation will generate the next-order perturbation increment. Accumulate the accumulated solution of the current order. The updated cumulative solution is obtained. This allows for the coherent and constructive superposition of all levels of crosstalk light field components leaked from different propagation orders (i.e., repeated propagation between the SLM and the focal plane a different number of times), so that the reconstructed holographic wavefront gradually approaches the ideal wavefront state after completely suppressing crosstalk.

[0174] Step S1314: In response to the fact that the modulus of the predetermined order increment of the Newman series is less than the adaptive shutdown threshold and / or the number of iterations is greater than the safe maximum order, the current order is determined to be the adaptive order.

[0175] The applicant of this application further demonstrates that the above-mentioned stopping conditions can sufficiently guarantee the target accuracy, that is, as stated above, assuming And the loop stopping condition is:

[0176] Then we have:

[0177] Among them, by

[0178] get:

[0179] because Taking a conservative lower bound (e.g., 0.05), the following equation holds:

[0180] With actual order sequence To quantify the benefits of the project using input, let the fixed order be... Then each frame saves Matrix-vector product, total savings ratio for:

[0181] in It is the total number of frames. It is the first The actual order of the frame.

[0182] Table 1 below shows the savings estimates for typical motion scenarios (where...) , )

[0183] Table 1

[0184] As can be seen, when Approaching 1 o'clock On the contrary, it exceeded This will trigger The system safely truncates and returns with slightly lower precision; this is the signal to switch to cold reconstruction.

[0185] It is important to note that, firstly The computation time in cuBLAS nrm2 is approximately 0.01 ms, far less than a single csrmv (≈0.05 ms), and the overhead is negligible; secondly Preferably, the value is 50, and the cold reconstruction flag is automatically triggered when the trigger rate is >0.1%; in addition, each frame can be recorded. Timing, runtime automatic callback optimization Or the maximum speed for rearrangement.

[0186] In the method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to an embodiment of this application, the predetermined order of the crosstalk correction is an adaptive order.

[0187] In the above-mentioned method for generating a hologram of the complex amplitude domain gradient flow of a spatial light modulator, determining the order of crosstalk correction includes: establishing a precise bound on the truncation error, and determining an analytical solution for the optimal truncation order based on the precise bound on the truncation error and a preset target accuracy; determining an adaptive shutdown threshold based on the residual self-stopping criterion that the truncation error satisfies the target accuracy multiplied by a conservatively estimated lower bound of the spectral radius; performing recursive iteration and adaptive accumulation of the series terms in response to the modulus of the predetermined order increment of the Newman series being greater than the adaptive shutdown threshold; and determining the current order as the adaptive order in response to the modulus of the predetermined order increment of the Newman series being less than the adaptive shutdown threshold and / or the number of iterations being greater than the safe maximum order.

[0188] In this embodiment, after obtaining the hologram of the spatial light modulator, singularity detection and repair can be further performed. This is based on the complex amplitude field of the focal plane. With target amplitude The measured amplitude and the target amplitude are compared one by one in each optical trap to detect abnormal optical traps and perform local repairs, as shown in the following:

[0189] in It is the first The measured focal plane amplitude of each optical trap It is its target amplitude. It is the standard deviation of focal plane intensity, for example, usually three times its standard deviation. This serves as a statistical anomaly threshold. In other words, it defines, in a statistical sense, the optical trap that deviates excessively from the target, i.e., the aforementioned WGS residual. The local out-of-bounds points can be identified, which can help identify individual bad points that the above-mentioned incremental IV update + single-step WGS correction failed to correct. For example, in the embodiments of this application, the singularity detection is implemented with cuBLAS ZDOTC, with a latency of <0.005ms.

[0190] Then, taking the anomalous optical trap set as input, additional WGS single-step operator iterations are performed on it to achieve local reconvergence; for example, it can be performed as follows: WGS single-step operator iteration reduces the error to Local fixed points within the tolerance are re-converged to prevent individual intensity deviations from the optical trap from causing photo-induced detachment of atoms, while maintaining low overall computational cost.

[0191] In the method for generating a hologram of a spatial light modulator with a complex amplitude domain gradient flow according to an embodiment of this application, after performing a high-order crosstalk correction by calculating the updated pixel plane complex virtual field with a predetermined number of steps of the Newman series using a WGS single-step operator to obtain the hologram of the spatial light modulator, the method further includes: determining anomalous optical traps by comparing the focal plane complex amplitude field of each optical trap with the target amplitude on a trap-by-trap basis; and performing additional WGS single-step operator iterative calculations on the anomalous optical traps to achieve local reconvergence and obtain a hologram after singularity detection and repair.

[0192] Furthermore, in this embodiment of the application, after obtaining the hologram of the spatial light modulator, weight and phase updates can be further performed. The weight and phase updates are based on the current frame. Weight of each optical trap The weight set and target amplitude The set of target amplitudes Based on measured amplitude To adjust the weights for the next frame, it is represented as:

[0193] Therefore, by using WGS weight adaptive recursion, inter-frame intensity drift is suppressed to ensure that subsequent frames remain in the same position. The convergence neighborhood.

[0194] Furthermore, based on current holograms After the current frame is moved The position of each optical trap The set of optical trap locations To calculate the phase required for the complex weights of the next frame. , represented as:

[0195] At the same time, the updated complex weights are obtained:

[0196] And obtain the pixel plane complex virtual field of the next frame through carrier reconstruction. This maintains inter-frame consistency in the complex amplitude domain and ensures phase continuity. .

[0197] In the method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to an embodiment of this application, after performing high-order crosstalk correction by calculating the updated pixel plane complex virtual field using a WGS single-step operator with a predetermined order of the Newman series as the number of steps to obtain the hologram of the spatial light modulator, the method further includes: obtaining the weight of each optical well in the next frame by multiplying the weight of each optical well in the current frame by its target amplitude and dividing by the magnitude of its complex amplitude; and calculating the phase of each optical well in the next frame based on the hologram and the moved position of each optical well in the current frame, updating the complex weights, and obtaining the pixel plane complex virtual field of the next frame through carrier reconstruction.

[0198] In addition, in this embodiment, cold reconstruction can be performed according to a preset period, that is, in response to a predetermined number of frames, such as 20 frames. The set of positions formed by the moved positions of each optical trap Re-execute the WGS single-step operator iteration until convergence, in order to transform the complex virtual field. and weight Reset to the precise fixed point.

[0199] Here, because the IV incremental update plus the higher-order crosstalk correction based on Neumann truncation is a first-order / finite-order approximation, the frame-by-frame accumulated error is calculated as follows: The growth (the specific number of frames required for stabilization can be determined experimentally or through simulation based on the spectral radius distribution) and periodic precise reset can truncate drift accumulation, ensuring that the intensity / phase degradation does not occur in the long-term rearranged sequence.

[0200] In the method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to an embodiment of this application, after performing high-order crosstalk correction by calculating the updated pixel plane complex virtual field with a predetermined number of steps of the Newman series using the WGS single-step operator to obtain the hologram of the spatial light modulator, the method further includes: after a predetermined frame, re-executing the WGS single-step operator iteration until convergence using the position set formed by the moved positions of each optical trap, to obtain the pixel plane complex virtual field reset to a precise fixed point and the weight of each optical trap.

[0201] After obtaining the hologram of the spatial light modulator, the spatial light modulator can be used to drive the atoms to move frame by frame along the planned trajectory, thereby realizing the rearrangement of the atomic array and forming a defect-free target array.

[0202] In this embodiment, the steady-state Jacobian matrix is ​​the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane. Furthermore, the WGS single-step operator... Including pixel plane complex amplitude field Length of the module Since the computation involves both complex conjugate and non-holomorphic mappings, its derivative can be processed using Wirtinger calculus to calculate the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane. Of course, those skilled in the art will understand that other methods can also be used to calculate the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane, such as converting the complex function into a method of differentiating the mapping over two-dimensional real space.

[0203] Furthermore, those skilled in the art will understand that weights Sufficient convergence can be viewed as an assumption of parameter simplification, if the weights... If convergence is not achieved, a complete block Jacobian matrix is ​​required. That is, the derivation of the steady-state Jacobian matrix described below assumes that the weights have fully converged, as illustrated above. Otherwise, it is necessary to compute the complete block Jacobian matrix corresponding to the non-converged weights as an optional extension that can be derived from this application.

[0204] Specifically, obtaining the steady-state Jacobian matrix using Wirtinger calculus can include the following steps.

[0205] The phased pixel-plane steady-state complex amplitude field is constructed based on the phased operation in the WGS single-step operator, and the Jacobian coefficients of each optical trap corresponding to the phased pixel-plane steady-state complex amplitude field are obtained. Here, for the pixel-plane steady-state complex amplitude field... Phase conversion is performed to decouple the amplitude, and only the phase is retained to obtain the phase-converted pixel plane steady-state complex amplitude field. :

[0206] Then, the phased pixel plane steady-state complex amplitude field is... Perform Fourier transform and then apply it to the spatial frequency coordinates of each optical trap. Take the modulus at point 1 to obtain the first... Focal plane amplitude of each optical trap :

[0207] Based on the Weight of each optical trap Target amplitude Amplitude of focal plane The first rank required to obtain the subsequent rank-k expansion Jacobian coefficient of each optical trap (Eliminating the (Explicit dependence of amplitude)

[0208] A focal plane tangent space projection operator is constructed based on the complex perturbation vector acting on the phased pixel plane steady-state complex amplitude field to project the complex perturbation vector onto the imaginary part direction of the focal plane. Here, for the pixel plane steady-state complex amplitude field... Wirtinger calculus respectively for and Find the partial derivative, expressed as:

[0209] in Represents phase mapping Here, the phase mapping pairs and It is simultaneously dependent and not holomorphic, therefore the standard complex derivative does not exist. The two Wirtinger partial derivatives can give its complete first-order linear response, avoiding the omission of the antiholomorphic term.

[0210] Then, the two partial derivatives are applied to the first-order complex perturbation vector. The combined effects of these operators can be simplified to a projection operator that retains only the tangential (imaginary) phase component while filtering out the radial amplitude component, expressed as:

[0211] in This represents the operation of taking the imaginary part of a complex number. Represents the pixel coordinates applied to the SLM. The complex perturbation vector at that point. Here, for the complex perturbation vector... Its function is to have That is, only the imaginary components perpendicular to the local phase of a small perturbation on the SLM will change the pure phase field, while the radial amplitude component is filtered out by the pure phase constraint. Thus, the focal plane tangent space projection operator is obtained. , it put along Projecting the direction using the imaginary part, where It is the first The phase of each optical trap.

[0212] That is, in the steady-state complex amplitude field of the pixel plane fixed point (Right now ) at, to Applying a perturbation, denoted as the first-order complex perturbation vector. ,Depend on Phased pixel plane steady-state complex amplitude field exist The disturbance at that point is:

[0213] in This indicates the operation of extracting the real part of a complex number.

[0214] Define the pixel plane tangent space projection operator (It projects the complex perturbation vector onto a pure virtual direction orthogonal to the existing phase on the pixel plane), resulting in:

[0215] in It is a normalized perturbation field that retains only the pure phase variation component after projection is applied. Position on the SLM pixel plane The applied complex perturbation vector, It is the steady-state complex amplitude field of the pixel plane (as a reference field). It is the operator for extracting the imaginary part of a complex number, and It is the imaginary unit.

[0216] Then perform a forward Fourier transform, that is:

[0217] Amplitude-forced linearization is used for steady-state complex amplitude fields at the focal plane. At this point, the phase-normalized perturbation is calculated as follows:

[0218] in This indicates that the perturbation at the focal plane is also projected onto a phase perpendicular to its convergence. The imaginary (tangential) direction.

[0219] Therefore, the above pixel plane tangent space projection operator With the projection of the imaginary part of the focal plane here Combined, and due to the setting of the perturbation by the position of the SLM pixel plane The injection and projection operators are defined according to the phase distribution at the starting point, thus obtaining the focal plane tangent space projection operator. This indicates that the complex perturbation vector can only propagate backward in the component along the phase tangent direction, thus filtering out the radial component.

[0220] The steady-state Jacobian matrix is ​​obtained by multiplying the Jacobian coefficients of each optical trap, the tangent space projection operator, and the plane wave factor used for plane wave modulation. That is, based on the forward Fourier transform. perturbation When propagated to the focal plane, it will appear at the target frequency point in the Fourier integral. Introduce a base factor at [location]. The updated complex amplitude field of the focal plane is reflected back to the pixel plane of the SLM through an inverse Fourier transform, i.e. This allows the inverse transform to be calculated from the focal plane. Each optical trap returns to the pixel of the SLM. At this point, the inverse phase factor is introduced. This forms the plane wave factor used for plane wave modulation. In other words, plane wave modulation configures each optical trap with its frequency. Determined plane wave factor , used to indicate the first Coordinates of each optical trap in the SLM plane and Phase transfer between them.

[0221] Then, the Jacobian coefficient of each optical trap is... The tangent space projection operator and the plane wave factor Multiplying them together yields the matrix elements of the steady-state Jacobian matrix:

[0222] in, These are the matrix elements of the steady-state Jacobian matrix, representing coordinates. When a disturbance occurs at a location, it causes the coordinates to... The differential rate of change of the complex amplitude, It is the total number of optical traps in the target array. Indicates the first Each optical trap in spatial frequency coordinates The interference plane wave factor under the coordinate difference is used to... Spatial phase transfer is performed on top. Used to locate the source point Disturbance at the location Projected towards the The characteristic imaginary part direction of each optical trap It is a one-dimensional composite dimension reduction projection operator.

[0223] This is equivalent to applying the linearity of the forward and inverse Fourier transforms, along with the linearization of amplitude constraints, to each optical trap position. The local perturbation at a single point is represented by the Jacobian-Vector Product (JVP) backpropagation, and the interference plane wave factor terms of all optical traps are combined to obtain the explicit elements of the expansion of the Jacobian matrix describing the crosstalk differential rate of the perturbation at any pixel on the SLM plane to other coordinate nodes on the entire SLM plane, i.e., the above. .

[0224] Therefore, the obtained steady-state Jacobian matrix accurately represents WGS at the microscopic level, where the steady-state Jacobian matrix is ​​essentially a matrix with a rank of maximum value. The coupling response of the optical system is not only modulated by the ratio of weight to amplitude, but its energy is also dependent on the plane wave substrate across the entire plane, as part of the operator superposition of (i.e., the total number of optical traps in the target array). The divergent interference accurately presents the complex superposition and leakage entanglement of each optical trap field at the holographic spatial frequency.

[0225] Therefore, those skilled in the art will understand that calculating the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane by applying a small perturbation to the steady-state complex amplitude field of the pixel plane using Wirtinger calculus is essentially based on the WGS single-step operator, through the steady-state complex amplitude field of the pixel plane... fixed point (Right now ) at, to Apply micro-perturbation The matrix elements of the steady-state Jacobian matrix are obtained through the phase transformation, forward Fourier transform, amplitude forcing, and inverse Fourier transform process of the WGS single-step operator.

[0226] That is, by Phased pixel plane steady-state complex amplitude field exist The disturbance at that point is:

[0227] Based on linear forward Fourier transform:

[0228] Based on linear amplitude forcing, in At this point, the phase-normalized perturbation is:

[0229] Finally, based on the linear inverse Fourier transform and by combining the results of the four steps, we obtain:

[0230] That is, the focal plane tangent space projection operator corresponds to the inverse part of the phase transformation and amplitude forcing steps, while the Jacobian coefficient and plane wave factor correspond to the forward Fourier transform, the amplitude part of the amplitude forcing step, and the inverse Fourier transform.

[0231] In the method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to an embodiment of this application, calculating the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane to obtain the steady-state Jacobian matrix includes: calculating the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane by applying a micro-perturbation to the steady-state complex amplitude field of the pixel plane using Wirtinger calculus to obtain the steady-state Jacobian matrix.

[0232] Furthermore, in the aforementioned method for generating a hologram of a complex amplitude domain gradient flow in a spatial light modulator, the calculation of the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane by applying a micro-perturbation to the steady-state complex amplitude field of the pixel plane using Wirtinger calculus to obtain the steady-state Jacobian matrix includes: constructing a phased steady-state complex amplitude field of the pixel plane based on the phased phase in the WGS single-step operator and obtaining the Jacobian coefficients of each optical trap corresponding to the phased steady-state complex amplitude field of the pixel plane; constructing a focal plane tangent space projection operator for projecting the complex perturbation vector onto the imaginary part direction of the focal plane based on the complex perturbation vector acting on the phased steady-state complex amplitude field of the pixel plane; and multiplying the Jacobian coefficients of each optical trap, the focal plane tangent space projection operator, and the plane wave factor for plane wave modulation to obtain the steady-state Jacobian matrix.

[0233] In this embodiment of the application, since the total pixel size of the SLM is extremely large (e.g. The storage of the steady-state Jacobian matrix may require a large amount of storage space, therefore sparsification is desired. Here, the physical oscillation characteristics of the steady-state Jacobian matrix are considered because of the plane wave factor. Interference with distance exhibits antiphase cancellation (i.e., when...) Time oscillations superimpose and cancel each other out. The crosstalk characteristic width (characterized by the aperture diffraction limit of the SLM) is an optical property. When a physical lattice point extends beyond a specific nearest-neighbor diffraction range boundary, the crosstalk value rapidly decays and degrades. Therefore, it is possible to construct a probe vector that is non-zero only within the neighborhood of the optical trap. Thus, utilizing the rank... Structure, only needs to be detected sparse elements, of which It is half the side length of the neighborhood, meaning the neighborhood is the target optical trap. Grid points. Among them, the crosstalk feature width. Represented as:

[0234] in It is the laser wavelength. It is the focal length of the Fourier lens, and This is the effective illumination aperture size of the spatial light modulator (e.g., the product of the number of pixels and the pixel pitch, on the order of millimeters), which determines the angular resolution limit of SLM diffraction. It is important to note that here... This is not the minimum center-to-center distance (minimum optical trap spacing) between adjacent optical traps in the target optical trap array; the order of magnitude of the minimum optical trap spacing is approximately... For example, in With a crosstalk characteristic width of approximately 8.19 mm, the crosstalk characteristic width is calculated. Approximately 9.74 .

[0235] Specifically, nearest neighbor detection can be performed per light trap using torch.autograd.functional.jvp ( Grid-based sparse elements are stored in cuSPARSE CSR format (approximately 24MB) to avoid explicit storage. A dense matrix, in which Here, torch.autograd.functional.jvp computes the Jacobian-vector product to probe the vector. (in the neighborhood) Grid processing 1) Column-by-column detection The non-zero element is represented as:

[0236] in It is the amplitude of an infinitesimal perturbation (take the limit after differentiation). It is obtained directly using the directional derivative. With probe vector The product does not require explicit construction. For dense matrices, by probing each local basis vector, the nearest non-zero columns of the Jacobian can be extracted, reducing the computational cost from... It drops to a level proportional to bandwidth.

[0237] In the method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to an embodiment of this application, after obtaining the steady-state Jacobian matrix, the method further includes: probing the non-zero elements of the steady-state Jacobian matrix column by column with probe vectors that are non-zero only in the neighborhood of the optical trap to extract the non-zero elements of the steady-state Jacobian matrix and obtain a sparsified steady-state Jacobian matrix.

[0238] In addition, in this embodiment of the application, the current frame excitation is the partial derivative of the WGS single-step operator with respect to the positions of all optical traps in the current frame, and its calculation process includes the following steps.

[0239] The phased steady-state complex amplitude field of the pixel plane is modulated pixel by pixel using the horizontal and vertical coordinates of the pixel plane of the SLM to obtain the horizontal coordinate modulation field and the vertical coordinate modulation field.

[0240] That is, for the phased pixel plane steady-state complex amplitude field The positional partial derivative originates from the plane wave factor. For the position of the optical trap Factors lost during differentiation ,in Since the SLM's pixel coordinates are constants, the pixel coordinates need to be used as the multiplicative operator. and It acts on the phased field. Therefore, using the horizontal coordinate... with vertical coordinate Pixel-by-pixel modulation of phase-shifted pixel plane steady-state complex amplitude field The transverse coordinate modulation field is obtained. and longitudinal coordinate modulation field :

[0241] In other words, the differential theorem of the Fourier transform states that differentiating the frequency domain with respect to frequency is equivalent to multiplying the spatial domain by the coordinates. (Optical trap position) By frequency Entering the phase of a plane wave, taking its derivative yields the coordinate factor, therefore using coordinates... and Modulated pixel plane steady-state complex amplitude field This transforms position sensitivity into an object that can be directly calculated using Fourier transform.

[0242] Fourier transform is performed on the transverse and longitudinal modulation fields, and samples are taken at the frequency of each optical trap to obtain the transverse and longitudinal modulation spectrum sample values ​​of each optical trap.

[0243] That is, the frequency of each optical trap on the focal plane. It is achieved by using the phased pixel plane steady-state complex amplitude field The frequency of each optical trap, obtained by Fourier transform after performing Fourier transforms on the transverse and longitudinal coordinate modulation fields respectively. The above transformation results are sampled to obtain the transverse and longitudinal component modulation spectrum sample values ​​for each optical trap:

[0244] in It is a two-dimensional continuous (or discrete) forward Fourier transform integral operator, which can transform the coordinate modulation field to the focal plane and sample it at the target optical trap frequency, at each sampling point. This forms a column vector. Furthermore, the resulting complex value is proportional to the direction and amplitude of the first-order change in the complex amplitude field of the focal plane when the optical trap is moved, and serves as the frequency domain carrier of position sensitivity.

[0245] The transverse and longitudinal component modulation spectrum samples of each optical trap are multiplied by a frequency-coordinate mapping constant to combine the positional derivative components of each optical trap along the transverse and longitudinal directions.

[0246] That is, the sampled values ​​of the transverse component modulation spectrum of each optical trap. and longitudinal component modulation spectrum sampling value Multiply by the frequency-coordinate mapping constant (This is a physical conversion of coordinate modulation equivalent to frequency domain differentiation), and the position partial derivatives of each optical trap along the transverse and longitudinal directions are obtained by combining them:

[0247] The position of each optical trap Represented as This is to deconstruct the local spatial degrees of freedom in the horizontal and vertical directions. Here, in order to correct for the dependency simplification assumption (the ordinary multiplication factor)... Algorithm errors, such as those caused by replacing the integral weighting term, lead to a systematic overestimation of crosstalk strength. Expanding along the Fourier kernel phase angle of the true wavefront, when the... When an optical trap attempts to physically offset itself, a chained partial derivative operation is performed within the originally smooth integral transform network. Furthermore, the spatial matrix scale dimension coordinates (i.e., the horizontal coordinates) of the SLM plane of the liquid crystal panel are... with vertical coordinate The direct weighted operator is injected into the integral kernel to calculate the flux distortion partial derivatives of each optical trap caused by the shift drive, which is expressed as follows:

[0248] here, It is the WGS single-step operator with respect to the first step in the focal plane. The horizontal coordinates of each optical trap The lateral partial derivative component represents the rate of change of the entire projection field induced by a very small lateral physical movement of the optical trap. As described above, the global optical coupling constant multiplier derived from the derivative of the exponentially transferred phase factor of the far-field Fourier diffraction integral can be represented.

[0249] In other words, when performing partial derivative calculations on the target optical trap, if the frequency domain spatial constant components (such as spatial frequency coordinates) are simply used... While directly extracting the common multiplier simplifies computation, it neglects the practical realities of large-aperture planar light emission in SLMs. The calculation of the partial derivative of the WGS single-step operator with respect to the light trap position considers the core factors causing changes in the reconstruction domain due to focus movement, which depends on the solid plane coordinate distribution of the liquid crystal pixels in the source-end holographic liquid crystal panel. and For steady-state phase field After non-uniform aperture-scale weighted modulation, the spatial spectrum abrupt change that occurs at a specific wave vector accurately reproduces the spatial differential law followed by the light path when the optical trap undergoes forced motion.

[0250] The position partial derivative components of each optical trap along the lateral and longitudinal directions are flattened into column vectors of complex amplitude fields and spliced ​​according to the lateral and longitudinal coordinates of the optical trap to obtain the position partial derivative matrix.

[0251] In other words, after traversing all the optical traps, the partial derivatives of the positions along the lateral and longitudinal axes corresponding to each individual optical trap are summarized to generate a set of components for the discrete sites. Here, since the motion of each optical trap includes lateral and longitudinal axes (usually denoted as second-order degrees of freedom, i.e., each optical trap has...), the partial derivatives of the positions along the lateral and longitudinal axes are summarized to generate a set of components for the discrete sites. shaft and The vector behavior of the axis translation state space is thus normalized and configured into a high-dimensional coherent tensor. For example, setting the shape mapping boundary of the macroscopic array (e.g., the total number of optical traps is...) The total number of degrees of freedom for overall displacement is The positional partial derivative components of each optical trap along the lateral and longitudinal directions are flattened into column vectors of the complex amplitude field of the pixel plane, and then... By sequentially concatenating the horizontal and vertical coordinates, we obtain the position partial derivative matrix representing how the minute movements of all optical trap positions are linearly mapped to the changes in the complex amplitude field of the pixel plane on the SLM plane.

[0252] In the method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator according to an embodiment of this application, the current frame excitation is the partial derivative of the WGS single-step operator with respect to the positions of all optical traps, and the calculation process includes: modulating the phased pixel plane steady-state complex amplitude field pixel by pixel with the horizontal and vertical coordinates of the pixel plane of the SLM to obtain a horizontal coordinate modulation field and a vertical coordinate modulation field; performing Fourier transform on the horizontal coordinate modulation field and the vertical coordinate modulation field and sampling at the frequency of each optical trap to obtain the horizontal component modulation spectrum sampling value and the vertical component modulation spectrum sampling value of each optical trap; multiplying the horizontal component modulation spectrum sampling value and the vertical component modulation spectrum sampling value of each optical trap by a frequency-coordinate mapping constant to combine the positional partial derivative components of each optical trap along the horizontal and vertical directions; and flattening the positional partial derivative components of each optical trap along the horizontal and vertical directions into column vectors of the pixel plane complex amplitude field and splicing them according to the horizontal and vertical coordinate order of the optical traps to obtain the current frame excitation.

[0253] In summary, the method for generating holograms of the complex amplitude domain gradient flow of a spatial light modulator according to the embodiments of this application expands the response of the fixed point to the optical trap movement into a Newman series. It proves that the incremental update of the complex amplitude domain (removing the old carrier and superimposing the new carrier) and the zeroth-order term of the Newman series are algebraic identities rather than numerical approximations, establishing a precise mathematical foundation for the incremental update. Furthermore, it constructs a framework for hologram generation that approximates the fixed point hierarchically according to the Newman series. Specifically, the zeroth-order term is precisely achieved by the incremental update, while higher orders above the first order are supplemented with crosstalk higher-order terms by the WGS correction step. In particular, the method for generating holograms of the complex amplitude domain gradient flow of a spatial light modulator according to the embodiments of this application, by taking the first-order truncation of the Newman series (incremental update + one WGS correction step), can exchange approximately 0.1ms of additional computation for approximately... times (in) In the convergence neighborhood or slow frames, for the first frame with fast large displacement... The improved accuracy (which can be addressed through adaptive truncation or cold reconstruction if the value increases) significantly enhances the time efficiency of high-precision hologram generation.

[0254] Specifically, the method for generating complex amplitude domain gradient flow holograms of spatial light modulators according to embodiments of this application uses an A100 graphics card and has a total number of optical traps. Under these conditions, incremental updates take approximately 0.030ms, a single WGS correction takes approximately 0.100ms, singularity detection takes <0.005ms, and buffer updates take approximately 0.001ms, totaling approximately 0.14ms / frame, which fully meets the real-time requirement of <1ms / frame. Furthermore, under the background requirement of uniform light intensity as described above... Inter-frame phase continuity Furthermore, based on a real-time performance of <1ms / frame, the complex amplitude domain gradient flow hologram generation method for spatial light modulators according to the embodiments of this application can substantially achieve uniform light intensity. Inter-frame phase continuity And the real-time performance is approximately 0.14ms / frame.

[0255] Furthermore, the complex amplitude domain gradient flow hologram generation method for spatial light modulators according to embodiments of this application introduces adaptive Newman truncation. The truncation order for each frame is determined online through the residual self-stopping principle, making the order adaptive with the frame spectrum radius (fewer iterations for slow frames, more iterations for fast frames). The incremental norm check reuses intermediate iteration results, resulting in almost zero additional overhead. Moreover, by orthogonally decomposing single-frame errors into four sources (Taylor stretching residual, Newman truncation error, WGS residual, and phase projection error), a quantifiable error stability boundary is provided.

[0256] According to an embodiment of this application, an electronic device is further provided, the electronic device including a processor and a memory, the processor being coupled to the memory, the processor being configured to execute a computer program stored in the memory, such that the electronic device performs the complex amplitude domain gradient flow hologram generation method of a spatial light modulator according to an embodiment of this application as described above.

[0257] Figure 7 A schematic block diagram of an electronic device according to an embodiment of this application is shown. Figure 7 As shown, an electronic device 200 according to an embodiment of this application includes a coupled processor 210 and a memory 220.

[0258] According to an embodiment of this application, a computer program product is further provided, the computer program product comprising: computer program code, which, when the computer program code is run on a computer, causes the computer to execute the complex amplitude domain gradient flow hologram generation method of the spatial light modulator according to an embodiment of this application as described above.

[0259] According to an embodiment of this application, a computer-readable storage medium is further provided, the computer-readable medium storing program code, which, when run on a computer, causes the computer to execute the complex amplitude domain gradient flow hologram generation method of the spatial light modulator according to an embodiment of this application as described above.

[0260] The terms “component,” “module,” “system,” etc., used in this specification are used to refer to computer-related entities, hardware, firmware, combinations of hardware and software, software, or software in execution. For example, a component can be, but is not limited to, a process running on a processor, a processor, an object, an executable file, an execution thread, a program, and / or a computer. As illustrated, applications running on computing devices and computing devices can both be components. One or more components may reside in a process and / or an execution thread, and components may be located on a single computer and / or distributed among two or more computers. Furthermore, these components can be executed from various computer-readable media on which various data structures are stored. Components can communicate, for example, via local and / or remote processes based on signals having one or more data packets (e.g., data from two components interacting with another component between a local system, a distributed system, and / or a network, such as the Internet interacting with other systems via signals).

[0261] Those skilled in the art will recognize that the various illustrative logical blocks and steps described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this application.

[0262] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0263] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0264] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0265] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0266] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0267] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for generating complex amplitude domain gradient flow holograms of a spatial light modulator, characterized in that, include: Obtain the initial pixel plane complex virtual field and the atomic rearrangement path planning results of the atomic array to be rearranged when the spatial light modulator converges in the WGS iteration; Based on the pixel plane complex virtual field of the current frame and the optical trap position update of the current frame from the atomic rearrangement path planning result, an incremental velocity first-order incremental update is performed to obtain the updated pixel plane complex virtual field; and, The updated pixel plane complex virtual field is subjected to high-order crosstalk correction by performing a WGS single-step operator with a predetermined number of steps of the Newman series to obtain the hologram of the spatial light modulator.

2. The method for generating complex amplitude domain gradient flow holograms of spatial light modulators as described in claim 1, characterized in that, Obtaining the initial pixel-plane complex virtual field of the spatial light modulator during WGS iteration convergence includes: Determine the steady-state weights and steady-state phases of each optical trap during WGS iteration convergence; The steady-state complex weights of each optical well are obtained based on its steady-state weights, steady-state phase, and target amplitude; and, The initial pixel plane complex virtual field is obtained based on the steady-state complex weight and spatial frequency of each optical trap.

3. The method for generating complex amplitude domain gradient flow holograms of spatial light modulators as described in claim 2, characterized in that, Determining the steady-state phase of each optical trap during WGS iterative convergence includes: Pixel-by-pixel phase extraction is performed on the steady-state complex amplitude field of the pixel plane to obtain the output field on the pixel plane of the spatial light modulator; Calculate the complex amplitude field of the focal plane after the outgoing field on the pixel plane of the spatial light modulator is focused by a Fourier lens; The complex amplitude field of the focal plane is sampled at the spatial location coordinates of each optical trap to obtain the complex amplitude value of each optical trap; and, The phase is extracted from the complex amplitude value of each optical trap to obtain the steady-state phase of each optical trap.

4. The method for generating complex amplitude domain gradient flow holograms of spatial light modulators as described in claim 1, characterized in that, The pixel plane complex virtual field based on the current frame and the optical trap position update of the current frame from the atomic rearrangement path planning result are used to perform an incremental velocity first-order incremental update to obtain the updated pixel plane complex virtual field, including: Based on the optical trap position update pair of the current frame from the atomic rearrangement path planning results, the spatial frequency coordinates of each optical trap in the current frame and the spatial frequency coordinates in the next frame are determined; and, For each optical trap, the pixel plane complex virtual field of the current frame is subtracted from the plane wave carrier of the optical trap based on the frequency of the current frame, and then the plane wave carrier of the optical trap based on the frequency of the next frame is added to obtain the updated pixel plane complex virtual field.

5. The method for generating complex amplitude domain gradient flow holograms of a spatial light modulator as described in claim 4, characterized in that, Before performing the first-order incremental update of the incremental velocity, the following is further included: The incremental velocity first-order incremental update is defined based on the complex weights of each optical trap and the optical trap position update of the current frame from the atomic rearrangement path planning results; and, The first-order incremental update algebra of the incremental velocity is determined to be always equal to the zeroth-order truncation of the Newman series.

6. The method for generating complex amplitude domain gradient flow holograms of a spatial light modulator as described in claim 5, characterized in that, Determining that the first-order incremental update algebra of the incremental velocity is always equal to the zeroth-order truncation of the Newman series includes: The partial derivative of the WGS single-step operator with respect to the position of each optical trap is obtained, and the zeroth-order truncated representation of the Newman series is given.

7. The method for generating complex amplitude domain gradient flow holograms of spatial light modulators as described in claim 1, characterized in that, To obtain the hologram of the spatial light modulator, high-order crosstalk correction is performed by calculating the updated pixel plane complex virtual field using a WGS single-step operator with a predetermined number of steps in the Newman series. This includes: The predetermined order of crosstalk correction is determined based on the equivalence between the rate of change of the steady-state complex amplitude field of the pixel plane and the term-by-term cumulative structural representation of the Newman series. In the single-step correction based on the predetermined order, phase extraction is performed on the updated pixel plane complex virtual field to obtain the phase map before correction, and forward diffraction based on Fourier transform is performed on the phase map before correction to obtain the focal plane complex amplitude field; and, In the single-step correction, the focal plane complex amplitude field is amplitude-forced to obtain an amplitude-forced focal plane complex amplitude field, and the amplitude-forced focal plane complex amplitude field is subjected to inverse diffraction based on inverse Fourier transform to obtain the hologram as the corrected phase map.

8. The method for generating complex amplitude domain gradient flow holograms of a spatial light modulator as described in claim 7, characterized in that, The order of crosstalk correction is determined based on the equivalence between the rate of change of the steady-state complex amplitude field in the pixel plane and the term-by-term cumulative structural representation of the Newman series. The fixed-point condition of the WGS single-step operator is expressed as an implicit function; The implicit function response, which is the time derivative of the implicit function, is obtained by calculating the total differential of the implicit function with respect to the set of optical trap positions, to obtain the rate of change of the steady-state complex amplitude field of the pixel plane with respect to the motion of the optical trap; and, The rate of change of the steady-state complex amplitude field of the pixel plane with respect to the motion of the optical trap is expanded into a Newman series to obtain the equivalence between the rate of change of the steady-state complex amplitude field of the pixel plane and the term-by-term cumulative structure representation of the Newman series.

9. The method for generating complex amplitude domain gradient flow holograms of a spatial light modulator as described in claim 8, characterized in that, The rate of change of the steady-state complex amplitude field of the pixel plane with respect to the motion of the optical trap is expressed as the inverse matrix of the difference matrix between the multidimensional diagonal reference identity matrix and the steady-state Jacobian matrix, multiplied by the current frame excitation and then by the motion velocity field of the optical trap. The steady-state Jacobian matrix is ​​the partial derivative of the WGS single-step operator with respect to the steady-state complex amplitude field of the pixel plane, and the current frame excitation is the partial derivative of the WGS single-step operator with respect to the set of optical trap positions.

10. The method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator as described in claim 1, characterized in that, The predetermined order of the crosstalk correction is a fixed order.

11. The method for generating complex amplitude domain gradient flow holograms of a spatial light modulator as described in claim 10, characterized in that, The fixed order is one or twenty.

12. The method for generating complex amplitude domain gradient flow holograms of a spatial light modulator as described in claim 1, characterized in that, After performing high-order crosstalk correction on the updated pixel plane complex virtual field using a WGS single-step operator with a predetermined number of steps (Neuman series) to obtain the hologram of the spatial light modulator, the process further includes: Based on Taylor stretching residuals, Newman truncation error, WGS residuals, and phase projection error, we present a stable upper bound for single-frame error on the order of the inter-frame step size.

13. The method for generating complex amplitude domain gradient flow holograms of a spatial light modulator as described in claim 1, characterized in that, The predetermined order of the crosstalk correction is an adaptive order.

14. The method for generating complex amplitude domain gradient flow holograms of a spatial light modulator as described in claim 13, characterized in that, Determining the adaptive order of crosstalk correction includes: Establish a precise bound on the truncation error, and determine an analytical solution for the optimal truncation order based on the precise bound on the truncation error and a preset target accuracy; The adaptive shutdown threshold is determined based on the residual self-stopping criterion that the truncation error satisfies the target accuracy multiplied by the difference between the target accuracy and the conservative estimate of the lower bound of the spectral radius. In response to the modulus of the predetermined order increment of the Newman series being greater than the adaptive turn-off threshold, recursive iteration and adaptive accumulation of the series terms are performed; and, In response to the fact that the modulus of the predetermined order increment of the Newman series is less than the adaptive shutdown threshold and / or the number of iterations is greater than the safe maximum order, the current order is determined to be the adaptive order.

15. The method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator as described in claim 1, characterized in that, After performing high-order crosstalk correction on the updated pixel plane complex virtual field using a WGS single-step operator with a predetermined number of steps (Neuman series) to obtain the hologram of the spatial light modulator, the process further includes: Abnormal optical traps are identified by comparing the complex amplitude of the focal plane of each optical trap with the target amplitude, trap by trap; and, Additional WGS single-step operator iterative calculations are performed on the anomalous optical trap to achieve local reconvergence and obtain a hologram that has undergone singularity detection and repair.

16. The method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator as described in claim 1, characterized in that, After performing high-order crosstalk correction on the updated pixel plane complex virtual field using a WGS single-step operator with a predetermined number of steps (Neuman series) to obtain the hologram of the spatial light modulator, the process further includes: The weight of each optical well in the next frame is obtained by multiplying the weight of each optical well in the current frame by its target amplitude and then dividing by the magnitude of its complex amplitude; and, Based on the hologram and the position of each optical trap in the current frame after movement, the phase of each optical trap in the next frame is calculated, the complex weights are updated, and the pixel plane complex virtual field of the next frame is obtained through carrier reconstruction.

17. The method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator as described in claim 1, characterized in that, After performing high-order crosstalk correction on the updated pixel plane complex virtual field using a WGS single-step operator with a predetermined number of steps (Neuman series) to obtain the hologram of the spatial light modulator, the process further includes: After a predetermined frame, the WGS single-step operator iteration is re-executed using the set of positions formed by the moved positions of each optical trap until convergence, in order to obtain the pixel plane complex virtual field reset to the precise fixed point and the weight of each optical trap.

18. An electronic device, characterized in that, The device includes a processor coupled to a memory, the processor being configured to execute a computer program stored in the memory to cause the electronic device to perform a method for generating a complex amplitude domain gradient flow hologram of a spatial light modulator as described in any one of claims 1 to 17.

19. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed, implements the method for generating complex amplitude domain gradient flow holograms of a spatial light modulator as described in any one of claims 1 to 17.

Images